Methods for spectrally resolving fluorophores of sample by generalized least squares, and systems for the same

Abstract

SOLUTION: Aspects of the present disclosure include methods for spectrally resolving light from fluorophores in a sample. The methods according to certain embodiments include detecting, with a light detection system, light from a sample having a plurality of fluorophores having overlapping fluorescence spectra, and spectrally resolving light from each fluorophore in the sample with a generalized least squares algorithm. In some embodiments, the methods include estimating the abundance of one or more of the fluorophores in the sample, such as on a particle. In certain instances, the methods include identifying the particle in the sample based on the abundance of each fluorophore, and sorting the particle. The methods according to some embodiments include spectrally resolving the light from each fluorophore by calculating a spectral unmixing matrix for the fluorescence spectra of each fluorophore. Systems and integrated circuit devices (e.g., a field programmable gate array) for practicing the subject methods are also provided.SELECTED DRAWING: None

Description

[Background technology]

[0001] Flow particle sorting systems, such as sorting flow cytometers, are used to sort particles in a fluid sample based on at least one measured characteristic of the particles. In a flow particle sorting system, particles in fluid suspension, such as molecules, analyte-bound beads, or individual cells, flow through a detection region where a sensor detects particles in the stream of the type to be sorted. Upon detecting particles of the type to be sorted, the sensor activates a sorting mechanism that selectively separates the particles of interest.

[0002] Particle detection is typically performed by passing a fluid stream through a detection region where the particles are exposed to radiation from one or more lasers, and the particles' light scattering and fluorescence properties are measured. Particles or components thereof can be labeled with fluorescent dyes to facilitate detection, and multiple different particles or components may be labeled with spectrally distinct fluorescent dyes to allow simultaneous detection of different particles or components. Detection is performed using one or more optical sensors to facilitate independent measurement of the fluorescence of each distinct fluorescent dye.

[0003] To separate particles in a sample, a droplet charging mechanism charges droplets in the flowstream containing the particle type to be separated by charge at a separation point in the flowstream. The droplets pass through an electrostatic field and may be deflected into one or more collection vessels based on the polarity and magnitude of the droplet's charge. Uncharged droplets are not deflected by the electrostatic field. Summary of the Invention [Means for solving the problem]

[0004] Aspects of the present disclosure include methods for spectrally resolving light from fluorophores in a sample. In certain embodiments, the methods detect light from a sample having multiple fluorophores with overlapping fluorescence spectra using a light detection system and spectrally resolve the light from each fluorophore in the sample using a generalized least squares algorithm. In some embodiments, the methods estimate the abundance of one or more of the fluorophores in the sample, such as on particles. In some cases, the methods identify and sort particles in the sample based on the abundance of each fluorophore. In some embodiments, the methods spectrally resolve the light from each fluorophore by calculating a spectral unmixing matrix for the fluorescence spectrum of each fluorophore. Systems and integrated circuit devices (e.g., field programmable gate arrays) for implementing the subject methods are also provided.

[0005] In some embodiments, the sample of interest comprises multiple fluorophores, and the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample. In some cases, the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample by 10 nm or more, e.g., 25 nm or more, e.g., 50 nm or more. In some cases, the fluorescence spectrum of one or more fluorophores in the sample overlaps with the fluorescence spectra of two different fluorophores in the sample by, e.g., 10 nm or more, e.g., 25 nm or more, e.g., 50 nm or more. In other embodiments, the sample of interest comprises multiple fluorophores whose fluorescence spectra do not overlap. In these embodiments, the fluorescence spectrum of each fluorophore is adjacent to at least one other fluorophore within 10 nm or less, e.g., 9 nm or less, e.g., 8 nm or less, e.g., 7 nm or less, e.g., 6 nm or less, e.g., 5 nm or less, e.g., 4 nm or less, e.g., 3 nm or less, e.g., 2 nm or less, e.g., 1 nm or less.

[0006] In some embodiments, the light detection system detects light from the sample in one or more light detector channels, e.g., multiple light detection channels. Optionally, multiple light detectors are used to detect the light. Optionally, a data signal is generated in each of the light detector channels in response to the detected light. In some embodiments, the light is spectrally resolved by fluorophore in real time. Optionally, the method uses an integrated circuit, e.g., a field programmable gate array (FPGA), to spectrally resolve the light in real time.

[0007] In some embodiments, the covariance of the data signals at each photodetector channel is determined. Optionally, the covariance of the data signals at each photodetector channel includes one or more of an inherent sample variation component and a measurement variation component. Optionally, the covariance of the data signals at each photodetector channel includes electronic noise. Optionally, the covariance of the data signals at each photodetector channel includes shot noise. Optionally, the covariance of the data signals varies linearly with the generated data signals. Optionally, the covariance of the data signals varies quadratically with the generated data signals. Optionally, the covariance of the data signals is correlated across two or more of the multiple photodetector channels. Optionally, the covariance of the data signals is calculated according to:

[0008]

number

[0009] In some cases, the covariance of the data signal is calculated using a covariance matrix. In some cases, the covariance matrix includes non-zero diagonal values. In some cases, the covariance is calculated using a covariance matrix according to:

[0010]

number

[0011] Here, diag(x) indicates generating a diagonal matrix from a column vector x, and cov(a, b) indicates the covariance between a and b.

[0012] In some embodiments, the generalized least squares problem is calculated by multiplying by the inverse of the calculated covariance matrix. In some embodiments, the method estimates the covariance of the data signal based on the fluorescence intensities across two or more photodetectors of the photodetection system. In some embodiments, the method estimates the covariance of the data signal based on the fluorescence intensities across each of the photodetection channels. In some embodiments, the generalized least squares problem is calculated according to:

[0013]

number

[0014] In some cases, the method further generates an estimated covariance matrix a priori. In some cases, a generalized least squares problem is applied in real time (e.g., using an integrated circuit such as a field programmable gate array). In some cases, an a priori noise model is used to estimate the covariance of each event (e.g., calculating the covariance matrix of each event in real time). In some cases, the a priori noise model uses only the data collected for each particular event. In some cases, the covariance matrix includes estimates from the entire collected data set. In some cases, the covariance matrix is generated by an iterative optimization method that empirically adjusts the covariance matrix to minimize the variance of the unmixed data.

[0015] In some embodiments, the covariance of the data signal is determined by estimating it by iterative optimization using a covariance matrix that minimizes the variance of the unmixed data signal. In some embodiments, the generalized least squares problem is characterized by a Cholesky decomposition of the covariance matrix. In some embodiments, the covariance matrix Σ y =CC T Characterize the generalized least squares problem by computing the Cholesky decomposition of to solve the triangular system and generate the transformed input for the ordinary least squares algorithm according to:

[0016]

number

[0017] In some embodiments, a method finds a least-squares solution to a generalized least-squares problem. Optionally, the least-squares solution to the generalized least-squares problem is found by one or more of matrix decomposition, matrix factorization, QR decomposition, Cholesky decomposition, singular value decomposition, LDL decomposition, forward substitution, and backward substitution. Optionally, the method finds the least-squares solution to the generalized least-squares problem by solving the so-called normal equations by Cholesky or LDL decomposition, for example, according to

[0018]

number

[0019] In some cases, the method finds a least-squares solution to a generalized least-squares problem by Cholesky or LDL decomposition according to:

[0020]

number

[0021] In some embodiments, the method finds a least-squares solution to a generalized least-squares problem by matrix decomposition.

[0022]

number

[0023]

number

[0024] Systems for implementing the subject methods are also provided. In certain embodiments, the system includes a light source configured to illuminate a sample having multiple fluorophores with overlapping fluorescence spectra; a light detection system having multiple light detectors; and a processor operably coupled to a memory, the memory storing instructions that, when executed by the processor, cause the processor to spectrally resolve light from each fluorophore in the sample using a generalized least squares problem. In some cases, the system is configured to detect light in one or more light detector channels, e.g., multiple light detection channels, with the light detection system. In some cases, the system includes multiple light detectors. In some cases, the light detector includes one or more photomultiplier tubes. In some cases, the light detection system includes a photodetector array. In some cases, the photodetector array includes a charge-coupled device.

[0025] In some embodiments, the memory stores instructions that, when executed by the processor, cause the processor to determine a covariance of the data signals at each photodetector channel. Optionally, the covariance of the data signals at each photodetector channel includes an inherent sample variation component and a measurement variation component. Optionally, the covariance of the data signals at each photodetector channel includes electronic noise. Optionally, the covariance of the data signals at each photodetector channel includes shot noise. Optionally, the covariance of the data signals varies linearly with the generated data signals. Optionally, the covariance of the data signals varies quadratically with the generated data signals. Optionally, the covariance of the data signals is correlated across two or more of the multiple photodetector channels. Optionally, the memory has instructions for calculating the covariance of the data signals according to:

[0026]

number

[0027] In some cases, the memory has instructions for calculating the covariance of the data signal using a covariance matrix. In some cases, the covariance matrix includes non-zero diagonal values. In some cases, the memory has instructions for calculating the covariance using a covariance matrix according to:

[0028]

number

[0029] Here, diag(x) indicates generating a diagonal matrix from a column vector x, and cov(a, b) indicates the covariance between a and b.

[0030] In some cases, the memory has instructions for calculating a generalized least squares problem by multiplying by the inverse of the calculated covariance matrix. In some cases, the memory has instructions for estimating the covariance of the data signal based on the fluorescence intensities across two or more photodetectors of the photodetection system. In some cases, the memory has instructions for estimating the covariance of the data signal based on the fluorescence intensities across each of the photodetection channels.

[0031] In some embodiments, the memory comprises instructions for computing a generalized least squares problem according to:

[0032]

number

[0033] In some cases, the memory includes instructions for estimating the covariance matrix a priori. In some cases, the memory includes instructions for applying a generalized least squares problem in real time (e.g., using an integrated circuit such as a field programmable gate array). In some cases, an a priori noise model is used to estimate the covariance of each event (e.g., calculating the covariance matrix of each event in real time). In some cases, the a priori noise model uses only the data collected for each particular event. In some cases, the covariance matrix includes estimates from the entire collected data set.

[0034] In some embodiments, the memory comprises instructions for determining the covariance of the data signal by estimating by iterative optimization using a covariance matrix that minimizes the variance of the unmixed data signal. Optionally, the memory comprises instructions for computing a generalized least squares problem by Cholesky decomposition of the covariance matrix. Optionally, the generalized least squares problem is solved by solving the covariance matrix Σ y =CC T to solve the triangular system and generate the transformed input for the ordinary least squares algorithm according to

[0035]

number

[0036] In some embodiments, the memory comprises instructions for finding a least-squares solution to a generalized least-squares problem. Optionally, the memory comprises instructions for finding a least-squares solution to the generalized least-squares problem by one or more of matrix decomposition, matrix factorization, QR decomposition, Cholesky decomposition, singular value decomposition, LDL decomposition, forward substitution, and backward substitution. Optionally, the memory comprises instructions for finding a least-squares solution to the generalized least-squares problem by solving the so-called normal equations by Cholesky or LDL decomposition, for example according to the following Cholesky or LDL decomposition:

[0037]

number

[0038] Optionally, the memory contains instructions for finding a least squares solution to a generalized least squares problem using Cholesky or LDL decomposition according to:

[0039]

number

[0040] In some embodiments, the memory comprises instructions for finding a least-squares solution to a generalized least-squares problem by matrix decomposition.

[0041]

number

[0042]

number

[0043] In some embodiments, the system includes a processor operatively coupled to a memory, the memory storing instructions that, when executed by the processor, cause the processor to estimate the abundance of one or more fluorophores in a sample. Optionally, the memory has instructions for estimating the abundance of one or more fluorophores on particles in the sample. In some embodiments, the memory has instructions for identifying particles in the sample based on the estimated abundance of each fluorophore on the particles. Optionally, the system includes a particle sorter for sorting the identified particles in the sample.

[0044] Further provided is an integrated circuit device programmed to spectrally resolve light from multiple fluorophores in a sample using a generalized least squares problem. In embodiments, the integrated circuit device may be a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), a complex programmable logic device (CPLD), or other integrated circuit device.

[0045] In some embodiments, the integrated circuit device is programmed to determine a covariance of the data signals at each photodetector channel. Optionally, the covariance of the data signals at each photodetector channel includes an inherent sample variation component and a measurement variation component. Optionally, the covariance of the data signals at each photodetector channel includes electronic noise. Optionally, the covariance of the data signals at each photodetector channel includes shot noise. Optionally, the covariance of the data signals varies linearly with the generated data signals. Optionally, the covariance of the data signals varies quadratically with the generated data signals. Optionally, the covariance of the data signals is correlated across two or more of the multiple photodetector channels. Optionally, the integrated circuit device is programmed to calculate the covariance of the data signals according to:

[0046]

number

[0047] In some cases, the integrated circuit device is programmed to calculate the covariance of the data signal using a covariance matrix. In some cases, the covariance matrix includes non-zero diagonal values. In some cases, the integrated circuit device is programmed to calculate the covariance using the covariance matrix according to:

[0048]

number

[0049] Here, diag(x) indicates generating a diagonal matrix from a column vector x, and cov(a, b) indicates the covariance between a and b.

[0050] In some embodiments, the integrated circuit device is programmed to calculate the generalized least squares problem by multiplying by the inverse of the calculated covariance matrix. In some embodiments, the integrated circuit device is programmed to estimate the covariance of the data signal based on the fluorescence intensities across two or more photodetectors of the optical detection system. In some embodiments, the integrated circuit device is programmed to estimate the covariance of the data signal based on the fluorescence intensities across each of the optical detection channels. In some embodiments, the integrated circuit device is programmed to calculate the generalized least squares problem according to:

[0051]

number

[0052] In some cases, the integrated circuit device is programmed to estimate the covariance matrix a priori. In some cases, the integrated circuit device is programmed to apply a generalized least squares problem in real time (e.g., using an integrated circuit such as a field programmable gate array). In some cases, an a priori noise model is used to estimate the covariance of each event (e.g., calculating the covariance matrix of each event in real time). In some cases, the a priori noise model uses only the data collected for each particular event. In some cases, the covariance matrix includes estimates from the entire collected data set. In some cases, the covariance matrix is generated by an iterative optimization method that empirically adjusts the covariance matrix to minimize the variance of the unmixed data.

[0053] In some embodiments, the integrated circuit device is programmed to determine the covariance of the data signal by estimating it by iterative optimization using a covariance matrix that minimizes the variance of the unmixed data signal. Optionally, the integrated circuit device is programmed to compute a generalized least squares problem by Cholesky decomposition of the covariance matrix. Optionally, the generalized least squares problem is solved by solving the covariance matrix Σ y =CC T to solve the triangular system and generate the transformed input for the ordinary least squares algorithm according to

[0054]

number

[0055] In some embodiments, the integrated circuit device is programmed to find a least-squares solution to a generalized least-squares problem. Optionally, the integrated circuit device is programmed to find a least-squares solution to the generalized least-squares problem by one or more of matrix decomposition, matrix factorization, QR decomposition, Cholesky decomposition, singular value decomposition, LDL decomposition, forward substitution, and backward substitution. Optionally, the integrated circuit device is programmed to find a least-squares solution to the generalized least-squares problem by solving the so-called normal equations by Cholesky or LDL decomposition, for example according to

[0056]

number

[0057] In some cases, the integrated circuit device is programmed to find a least squares solution to a generalized least squares problem using Cholesky or LDL decomposition according to:

[0058]

number

[0059] In some embodiments, the integrated circuit device is programmed to find a least-squares solution to a generalized least-squares problem by matrix decomposition.

[0060]

number

[0061]

number

[0062] In some embodiments, the integrated circuit device is programmed to estimate the abundance of one or more fluorophores in the sample based on the calculated spectral unmixing matrix. Optionally, the integrated circuit device is programmed to estimate the abundance of one or more fluorophores on particles in the sample. In some embodiments, the integrated circuit device is programmed to identify particles in the sample based on the estimated abundance of each fluorophore on the particle. Optionally, the integrated circuit device is programmed to sort the identified particles in the sample. [Brief explanation of the drawings]

[0063] The invention can be best understood from the following detailed description when read in conjunction with the accompanying drawings, in which:

[0064] [Figure 1A] 1 is a flowchart illustrating a method for spectrally decomposing light using a generalized least squares problem according to one embodiment. [Figure 1B] 1 is a chart showing the measured raw dispersion from particles in a sample illuminated with light according to an embodiment. [Figure 1C] 10 is a chart illustrating the determination of second-order noise coefficients in measurement covariance according to an embodiment. [Figure 1D-1]1 is a diagram showing the estimation of the unmixing spread when there is no covariance (i.e., it is zero). [Figure 1D-2] 1 is a diagram showing the estimation of the unmixing spread when there is no covariance (i.e., it is zero). [Figure 2A] FIG. 10 illustrates a comparison of correlation and anti-correlation of second-order noise according to an embodiment. [Figure 2B] 1 is a chart showing a comparison of unmixing using ordinary least squares and weighted least squares with spectral unmixing using a generalized least squares problem according to an embodiment. [Figure 3A] FIG. 1 illustrates an image-enabled particle sorter according to an embodiment. [Figure 3B] FIG. 1 illustrates image-based particle sorting data processing according to an embodiment. [Figure 4A] FIG. 1 is a functional block diagram illustrating a particle analysis system according to an embodiment. [Figure 4B] FIG. 1 illustrates a flow cytometer according to an embodiment. [Figure 5] FIG. 1 is a functional block diagram illustrating an example of a particle analysis control system according to an embodiment. [Figure 6A] FIG. 1 is a schematic diagram illustrating a particle sorting system according to an embodiment. [Figure 6B] FIG. 1 is a schematic diagram illustrating a particle sorting system according to an embodiment. [Figure 7] FIG. 1 is a block diagram illustrating a computing system according to an embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0065] Aspects of the present disclosure include methods for spectrally resolving light from fluorophores in a sample. In certain embodiments, the methods detect light from a sample having multiple fluorophores with overlapping fluorescence spectra using a light detection system and spectrally resolve the light from each fluorophore in the sample using a generalized least squares problem. In some embodiments, the methods estimate the abundance of one or more of the fluorophores in the sample, such as on particles. In some cases, the methods identify and sort particles in the sample based on the abundance of each fluorophore. In some embodiments, the methods spectrally resolve the light from each fluorophore by calculating a spectral unmixing matrix for the fluorescence spectrum of each fluorophore. Systems and integrated circuit devices (e.g., field programmable gate arrays) for implementing the subject methods are also provided.

[0066] Before the present invention is described in more detail, it is to be understood that the invention is not limited to the particular embodiments described, as such may, of course, vary. The scope of the present invention will be limited only by the appended claims, and it is to be further understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting.

[0067] When a range of values is given, it is understood that each intervening value, to the tenth of the unit of the lower limit unless the context clearly indicates otherwise, between the upper and lower limits of that range, and any other stated or intervening value in that stated range, is encompassed within the invention. The upper and lower limits of these smaller ranges may independently be included in the smaller ranges and are also encompassed within the invention, subject to any specifically excluded limit in the stated range. Where the stated range includes one or both of the limits, ranges excluding either or both of those included limits are also encompassed within the invention.

[0068] In this specification, a range is presented with the term "about" before the numerical values. The term "about" is used herein to literally support the exact number that it precedes, as well as a number that is close to or approximately the number that it precedes. When determining whether a number is close to or approximately a specifically stated number, the unstated number that is close or approximately the number may be a number that, in the context in which the specifically stated number is presented, provides a substantial equivalent to the specifically stated number.

[0069] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Although any methods and materials similar or equivalent to those described herein can also be used in the practice or testing of the present invention, representative illustrative methods and materials are described.

[0070] All publications and patents cited herein are incorporated by reference to the same extent as if each individual publication or patent was specifically and individually indicated to be incorporated by reference, and are incorporated by reference to disclose and describe the methods and / or materials in connection with which the publications are cited. The citation of any publication is for its disclosure prior to the filing date and should not be construed as an admission that the present invention is not entitled to antedate such publication by virtue of prior invention. Further, the dates of publication provided may be different from the actual publication dates, which may need to be independently confirmed.

[0071] It should be noted that, as used in this specification and the appended claims, the singular forms "a," "an," and "the" include plural referents unless the context clearly dictates otherwise. It should be further noted that the claims may be drafted to exclude any optional element. Accordingly, this statement is intended to serve as a predicate for use of exclusive terminology, such as "solely," "only," or the use of a "negative" limitation in connection with the recitation of claim elements.

[0072] As will be apparent to those skilled in the art upon reading this disclosure, each of the individual embodiments described and illustrated herein comprises separate components and features which may be readily separated from or combined with any of the features of the other multiple embodiments without departing from the scope or spirit of the invention. Any recited method may be carried out in the order of events recited or in any other order which is logically possible.

[0073] Although the apparatus and methods have been or will be described for grammatical fluidity with functional descriptions, it should be clearly understood that the claims, unless expressly recited under 35 U.S.C. 112, should not be construed as necessarily limited in any way by limitations of "means" or "step" construction, but should be accorded the full scope of the meaning and equivalents of the definition given by the claims under the judicial theory of equivalents, and that if a claim is expressly recited under 35 U.S.C. 112, it should be accorded the full statutory equivalents under 35 U.S.C. 112.

[0074] As summarized above, the present disclosure provides a method for spectrally resolving fluorophores in a sample using a generalized least squares algorithm. In further describing embodiments of the present disclosure, we first describe in more detail a method for spectrally resolving fluorophores in a sample, including estimating the abundance of each fluorophore in the sample (e.g., on particles in the sample) and identifying and sorting particles based on the estimated abundance of each fluorophore. We then describe systems and integrated circuit devices that are programmed to implement the subject method using a generalized least squares algorithm.

[0075] A method for spectrally resolving light from fluorophores with overlapping fluorescence spectra in a sample using a generalized least squares algorithm Aspects of the present disclosure include methods for spectrally resolving light from fluorophores, including light with overlapping fluorescence spectra in a sample. In embodiments, light from each fluorophore is resolved (e.g., unmixed) using a generalized least squares algorithm. In some cases, spectral unmixing of light from fluorophores using a generalized least squares algorithm models covariances arising from measurement variations in a particle analyzer, such as a flow cytometer. In certain embodiments, the generalized least squares algorithm provides lower variance in the unmixed data than spectrally resolving light from fluorophores using an ordinary least squares algorithm or a weighted least squares algorithm. In some cases, spectral unmixing is more accurate compared to a weighted least squares algorithm when measurement noise is correlated between photodetectors in a light detection system. In some embodiments, the methods described herein provide measurement data from a sample that accounts for heteroscedasticity and non-zero covariance in the measurement data. In some cases, the generalized least squares algorithm described herein uses the inverse of the estimated covariance matrix for each event as a weighting matrix to whiten and decorrelate the data and ensure optimality (minimum variance) of the least squares solution. In some cases, the subject method estimates the covariance resulting from measurement variability alone, without the effects of inherent sample variability. FIG. 1A is a flowchart illustrating a method for spectrally resolving light using a generalized least squares algorithm according to one embodiment. As described in more detail below, data signals are generated from detected light from particles illuminated in a flowstream (101), and covariances between photodetectors are determined for each event (102) (i.e., the measurement variance is calculated for each particle). A generalized least squares algorithm applies the calculated measurement covariance to spectrally resolving the data signal (103).

[0076] The term "spectrally resolve" is used herein in its conventional sense to refer to spectrally distinguishing each fluorophore in a sample by assigning or attributing overlapping wavelengths of light to each contributing fluorophore. In embodiments, overlapping spectral components of fluorescence due to each fluorophore are determined by finding a solution to a generalized least squares problem. In some cases, a generalized least squares algorithm (as described in more detail below) calculates a spectral unmixing matrix. In some embodiments, the sample of interest has multiple fluorophores, and the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample. In some cases, the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample by 5 nm or more, e.g., 10 nm or more, e.g., 25 nm or more, e.g., 50 nm or more. In some cases, the fluorescence spectrum of one or more fluorophores in the sample overlaps with the fluorescence spectra of two or more different fluorophores in the sample, e.g., the fluorescence spectral overlap is 5 nm or more, e.g., 10 nm or more, e.g., 25 nm or more, e.g., 50 nm or more. In other embodiments, the sample of interest contains multiple fluorophores whose fluorescence spectra do not overlap. In these embodiments, the fluorescence spectrum of each fluorophore is adjacent to at least one other fluorophore within 10 nm or less, e.g., 9 nm or less, e.g., 8 nm or less, e.g., 7 nm or less, e.g., 6 nm or less, e.g., 5 nm or less, e.g., 4 nm or less, e.g., 3 nm or less, e.g., 2 nm or less, e.g., 1 nm or less.

[0077] In practicing the subject methods, a light source is used to illuminate a sample, and light from the sample is detected using a light detection system having one or more light detectors. In some cases, the light detection system has multiple light detectors. In some embodiments, the sample is a biological sample. The term "biological sample" is used in its conventional sense to refer to a whole organism, a plant, a fungus, or a subset of animal tissues, cells, or components, as may be found in blood, mucus, lymph, synovial fluid, cerebrospinal fluid, saliva, bronchoalveolar lavage fluid, amniotic fluid, amniotic cord blood, urine, vaginal fluid, or semen, as the case may be. Thus, "biological sample" refers to both a naturally occurring organism or a subset of its tissues, and homogenates, lysates, or extracts prepared from an organism or a subset of its tissues, including, but not limited to, plasma, serum, spinal fluid, lymph, skin sections, respiratory tract, gastrointestinal tract, cardiovascular, genitourinary tract, tears, saliva, milk, blood cells, tumors, and organs. The biological sample may be tissue from any type of organism, including both healthy and diseased tissue (e.g., cancerous, malignant, necrotic, etc.). In certain embodiments, the biological sample is a liquid sample, such as blood or a derivative thereof, e.g., plasma, tears, urine, semen, etc.; in some cases, the sample is a blood sample, including whole blood, such as blood obtained from venipuncture or finger stick (which may or may not be combined with any reagents, such as preservatives, anticoagulants, etc., prior to assay).

[0078] In some embodiments, the sample source is a "mammal" or "mammalian," which terms are used broadly to describe organisms belonging to the class Mammalia, including the orders Carnivora (e.g., dogs and cats), Rodentia (e.g., mice, guinea pigs, and rats), and Primates (e.g., humans, chimpanzees, and monkeys). In some cases, the subject is a human. The methods may be applied to samples obtained from human subjects of both genders and at any stage of development (i.e., newborn, infant, juvenile, adolescent, adult), and in some embodiments, the human subject is a juvenile, adolescent, or adult. While the present invention may be applied to samples from human subjects, it should be understood that the methods may also be performed on samples from other animal subjects (i.e., "non-human subjects"), including, but not limited to, birds, mice, rats, dogs, cats, livestock, and horses.

[0079] In practicing the subject methods, a sample (e.g., in a flow stream of a flow cytometer) is illuminated with light from a light source. In some embodiments, the light source is a broadband light source, emitting light having a wide range of wavelengths, e.g., 50 nm or greater, e.g., 100 nm or greater, e.g., 150 nm or greater, e.g., 200 nm or greater, e.g., 250 nm or greater, e.g., 300 nm or greater, e.g., 350 nm or greater, e.g., 400 nm or greater, e.g., 500 nm or greater. For example, one suitable broadband light source emits light having a wavelength between 200 nm and 1500 nm. Another example of a suitable broadband light source includes a light source that emits light having a wavelength between 400 nm and 1000 nm. When the method involves illumination with a broadband light source, broadband light source protocols of interest may include, but are not limited to, halogen lamps, deuterium arc lamps, xenon arc lamps, stabilized fiber-coupled broadband light sources, broadband LEDs with continuous spectra, superluminescent light emitting diodes, semiconductor light emitting diodes, broad spectrum LED white light sources, multi-LED integrated white light sources, or any combination thereof, among other broadband light sources.

[0080] In other embodiments, the methods involve irradiating using a narrowband light source that emits at a specific wavelength or narrow range of wavelengths, e.g., irradiating using a light source that emits light over a narrow range of wavelengths, such as 50 nm or less, for example 40 nm or less, for example 30 nm or less, for example 25 nm or less, for example 20 nm or less, for example 15 nm or less, for example 10 nm or less, for example 5 nm or less, for example 2 nm or less, e.g., irradiating using a light source that emits light of a specific wavelength (i.e., monochromatic light). When the methods involve irradiating using a narrowband light source, narrowband light source protocols of interest include, but are not limited to, narrow wavelength LEDs, laser diodes, or broadband light sources coupled to one or more optical bandpass filters, diffraction gratings, monochromators, or any combination thereof.

[0081] In some embodiments, the method uses one or more lasers to irradiate the sample. As discussed above, the type and number of lasers will vary depending on the sample and the desired light to be collected, and may be a gas laser, such as a helium-neon laser, an argon laser, a krypton laser, a xenon laser, a nitrogen laser, a CO laser, a CO laser, an argon-fluorine (ArF) excimer laser, a krypton-fluorine (KrF) excimer laser, a xenon-chlorine (XeCl) excimer laser, or a xenon-fluorine (XeF) excimer laser, or a combination thereof. In other cases, the method uses a dye laser, such as a stilbene laser, a coumarin laser, or a rhodamine laser, to irradiate the flowstream. In still other cases, the method irradiates the flowstream using a metal vapor laser, such as a helium-cadmium (HeCd) laser, a helium-mercury (HeHg) laser, a helium-selenium (HeSe) laser, a helium-silver (HeAg) laser, a strontium laser, a neon-copper (NeCu) laser, a copper laser, or a gold laser, and combinations thereof. In still other cases, the method irradiates the flowstream using a solid-state laser, such as a ruby laser, a Nd:YAG laser, a NdCrYAG laser, an Er:YAG laser, a Nd:YLF laser, a Nd:YVO4 laser, a Nd:YCa4O(BO3)3 laser, a Nd:YCOB laser, a titanium sapphire laser, a thulium YAG laser, a ytterbium YAG laser, a Yb2O3 laser, or a cerium-doped laser, and combinations thereof.

[0082] The sample may be illuminated using one or more of the light sources described above, e.g., two or more light sources, e.g., three or more light sources, e.g., four or more light sources, e.g., five or more light sources, e.g., ten or more light sources. The light sources may include any combination of light source types. For example, in some embodiments, the method uses an array of lasers to illuminate the sample in the flowstream, e.g., an array having one or more gas lasers, one or more dye lasers, and one or more solid state lasers.

[0083] The sample may be irradiated using a wavelength in the range of 200 nm to 1500 nm, e.g., 250 nm to 1250 nm, e.g., 300 nm to 1000 nm, e.g., 350 nm to 900 nm, e.g., 400 nm to 800 nm. For example, if the light source is a broadband light source, the sample may be irradiated using a wavelength of 200 nm to 900 nm. In other cases, if the light source includes multiple narrowband light sources, the sample may be irradiated using a specific wavelength in the range of 200 nm to 900 nm. For example, the light source may be multiple narrowband LEDs (1 nm to 25 nm), each independently emitting light having a wavelength in the range of 200 nm to 900 nm. In other embodiments, the narrowband light source includes one or more lasers (e.g., a laser array), and the sample is irradiated with a specific wavelength in the range of 200 nm to 700 nm using a laser array including, for example, gas lasers, excimer lasers, dye lasers, metal vapor lasers, and solid-state lasers as described above.

[0084] When two or more light sources are used, the light sources may be used to illuminate the sample simultaneously, sequentially, or a combination thereof. For example, each of the light sources may be used to illuminate the sample simultaneously. In other embodiments, each of the light sources is used to illuminate the flow stream sequentially. When two or more light sources are used to sequentially illuminate the sample, the time for which each light source illuminates the sample may independently be 0.001 microseconds or more, such as 0.01 microseconds or more, such as 0.1 microseconds or more, such as 1 microsecond or more, such as 5 microseconds or more, such as 10 microseconds or more, such as 30 microseconds or more, such as 60 microseconds or more. For example, the method may involve irradiating the sample using a light source (e.g., a laser) for a duration in the range of 0.001 microseconds to 100 microseconds, such as 0.01 microseconds to 75 microseconds, such as 0.1 microseconds to 50 microseconds, such as 1 microsecond to 25 microseconds, such as 5 microseconds to 10 microseconds. In embodiments in which two or more light sources are used to sequentially illuminate the sample, the duration for which the sample is illuminated by each light source may be the same or different.

[0085] The time between illumination by each light source may further vary as desired, and may be independently separated by a delay of 0.001 microseconds or more, e.g., 0.01 microseconds or more, e.g., 0.1 microseconds or more, e.g., 1 microsecond or more, e.g., 5 microseconds or more, e.g., 10 microseconds or more, e.g., 15 microseconds or more, e.g., 30 microseconds or more, e.g., 60 microseconds or more. For example, the time between illumination by each light source may be in the range of 0.001 microseconds to 60 microseconds, e.g., 0.01 microseconds to 50 microseconds, e.g., 0.1 microseconds to 35 microseconds, e.g., 1 microsecond to 25 microseconds, e.g., 5 microseconds to 10 microseconds. In some embodiments, the time between illumination by each light source is 10 microseconds. In embodiments in which the sample is illuminated sequentially by more than two (i.e., three or more) light sources, the delay between illumination by each light source may be the same or different.

[0086] The sample may be illuminated continuously or at discrete intervals. In some cases, the method involves illuminating the sample continuously with the light source. In other cases, the method involves illuminating the sample at discrete intervals with the light source, such as every 0.001 milliseconds, 0.01 milliseconds, 0.1 milliseconds, 1 millisecond, 10 milliseconds, 100 milliseconds, 1000 milliseconds, or other intervals.

[0087] Depending on the light source, the sample may be illuminated from a variety of distances, such as 0.01 mm or more, for example 0.05 mm or more, for example 0.1 mm or more, such as 0.5 mm or more, for example 1 mm or more, such as 2.5 mm or more, for example 5 mm or more, such as 10 mm or more, for example 15 mm or more, such as 25 mm or more, for example 50 mm or more. Furthermore, the angle or illumination may vary within the range of 10° to 90°, such as 15° to 85°, for example 20° to 80°, such as 25° to 75°, for example 30° to 60°, for example an angle of 90°.

[0088] In certain embodiments, the method irradiates the sample with two or more beams of frequency-shifted light. As described above, a light beam generator having a laser and an acousto-optical device for frequency shifting the laser light may be used. In these embodiments, the method irradiates the acousto-optical device using a laser. Depending on the desired wavelength of light generated in the output laser beam (e.g., for use in irradiating a sample in a flow stream), the laser may have a variety of specific wavelengths within the range of 200 nm to 1500 nm, e.g., 250 nm to 1250 nm, e.g., 300 nm to 1000 nm, e.g., 350 nm to 900 nm, e.g., 400 nm to 800 nm. The acousto-optical device may be irradiated using one or more lasers, e.g., two or more lasers, e.g., three or more lasers, e.g., four or more lasers, e.g., five or more lasers, e.g., ten or more lasers. The lasers may include any combination of laser types. For example, in some embodiments, the method irradiates the acousto-optical device using an array of lasers, e.g., an array having one or more gas lasers, one or more dye lasers, and one or more solid-state lasers.

[0089] When two or more lasers are used, the lasers may be used to illuminate the acousto-optic device simultaneously, sequentially, or a combination thereof. For example, each of the lasers may be used to illuminate the acousto-optic device simultaneously. In other embodiments, each of the lasers may be used to illuminate the acousto-optic device sequentially. When two or more lasers are used to illuminate the acousto-optic device sequentially, the time for which each laser illuminates the acousto-optic device may independently be 0.001 microseconds or more, e.g., 0.01 microseconds or more, e.g., 0.1 microseconds or more, e.g., 1 microsecond or more, e.g., 5 microseconds or more, e.g., 10 microseconds or more, e.g., 30 microseconds or more, e.g., 60 microseconds or more. For example, the method may illuminate the acousto-optic device with a laser for a duration in the range of 0.001 microseconds to 100 microseconds, e.g., 0.01 microseconds to 75 microseconds, e.g., 0.1 microseconds to 50 microseconds, e.g., 1 microsecond to 25 microseconds, e.g., 5 microseconds to 10 microseconds. In embodiments in which the acousto-optic device is illuminated sequentially with two or more lasers, the duration for which the acousto-optic device is illuminated by each laser may be the same or different.

[0090] The time between illumination by each laser may further vary as desired, and may be independently separated by a delay of 0.001 microseconds or more, e.g., 0.01 microseconds or more, e.g., 0.1 microseconds or more, e.g., 1 microsecond or more, e.g., 5 microseconds or more, e.g., 10 microseconds or more, e.g., 15 microseconds or more, e.g., 30 microseconds or more, e.g., 60 microseconds or more. For example, the time between illumination by each light source may be in the range of 0.001 microseconds to 60 microseconds, e.g., 0.01 microseconds to 50 microseconds, e.g., 0.1 microseconds to 35 microseconds, e.g., 1 microsecond to 25 microseconds, e.g., 5 microseconds to 10 microseconds. In some embodiments, the time between illumination by each laser is 10 microseconds. In embodiments in which the acousto-optic device is illuminated sequentially by more than two (i.e., three or more) lasers, the delay between illumination by each laser may be the same or different.

[0091] The acousto-optic device may be illuminated continuously or at discrete intervals. In some cases, the method uses a laser to illuminate the acousto-optic device continuously. In other cases, the laser illuminates the acousto-optic device at discrete intervals, such as every 0.001 milliseconds, 0.01 milliseconds, 0.1 milliseconds, 1 millisecond, 10 milliseconds, 100 milliseconds, e.g., 1000 milliseconds, or other intervals.

[0092] Depending on the laser, the acousto-optic device may be illuminated from a variety of distances, such as 0.01 mm or more, for example 0.05 mm or more, for example 0.1 mm or more, for example 0.5 mm or more, for example 1 mm or more, for example 2.5 mm or more, for example 5 mm or more, for example 10 mm or more, for example 15 mm or more, for example 25 mm or more, for example 50 mm or more. Furthermore, the angle or illumination may vary within a range of 10° to 90°, such as 15° to 85°, for example 20° to 80°, for example 25° to 75°, for example 30° to 60°, for example an angle of 90°.

[0093] In an embodiment, a method applies high frequency drive signals to an acousto-optic device to generate angularly deflected laser beams. Two or more high frequency drive signals, such as three or more high frequency drive signals, for example four or more high frequency drive signals, for example five or more high frequency drive signals, for example six or more high frequency drive signals, for example seven or more high frequency drive signals, for example eight or more high frequency drive signals, for example nine or more high frequency drive signals, for example ten or more high frequency drive signals, for example fifteen or more high frequency drive signals, for example twenty-five or more high frequency drive signals, for example fifty or more high frequency drive signals, for example one hundred or more high frequency drive signals may be applied to the acousto-optic device to generate an output laser beam comprising a desired number of angularly deflected laser beams.

[0094] The angularly deflected laser beams generated by the high frequency drive signals each have an intensity based on the amplitude of the applied high frequency drive signal. In some embodiments, the methods apply high frequency drive signals having amplitudes sufficient to generate angularly deflected laser beams of a desired intensity. In some cases, the applied high frequency drive signals independently each have an amplitude within a range of about 0.001 V to about 500 V, e.g., about 0.005 V to about 400 V, e.g., about 0.01 V to about 300 V, e.g., about 0.05 V to about 200 V, e.g., about 0.1 V to about 100 V, e.g., about 0.5 V to about 75 V, e.g., about 1 V to about 50 V, e.g., about 2 V to about 40 V, e.g., about 3 V to about 30 V, or e.g., about 5 V to about 25 V. The applied high frequency drive signal in some embodiments has a frequency within the range of about 0.001 MHz to about 500 MHz, for example, about 0.005 MHz to about 400 MHz, for example, about 0.01 MHz to about 300 MHz, for example, about 0.05 MHz to about 200 MHz, for example, about 0.1 MHz to about 100 MHz, for example, about 0.5 MHz to about 90 MHz, for example, about 1 MHz to about 75 MHz, for example, about 2 MHz to about 70 MHz, for example, about 3 MHz to about 65 MHz, for example, about 4 MHz to about 60 MHz, for example, about 5 MHz to about 50 MHz.

[0095] In these embodiments, the angularly deflected laser beams of the output laser beam are spatially separated. Depending on the applied high frequency drive signal and the desired illumination profile of the output laser beam, the angularly deflected laser beams may be separated by 0.001 μm or more, such as 0.005 μm or more, such as 0.01 μm or more, such as 0.05 μm or more, such as 0.1 μm or more, such as 0.5 μm or more, such as 1 μm or more, such as 5 μm or more, such as 10 μm or more, such as 100 μm or more, such as 500 μm or more, such as 1000 μm or more, such as 5000 μm or more. In some embodiments, the angularly deflected laser beams overlap, for example, with adjacent angularly deflected laser beams along the horizontal axis of the output laser beam. The overlap of adjacent angularly deflected laser beams (e.g., overlap of beam spots) may be 0.001 μm or more, for example, 0.005 μm or more, for example, 0.01 μm or more, for example, 0.05 μm or more, for example, 0.1 μm or more, for example, 0.5 μm or more, for example, 1 μm or more, for example, 5 μm or more, for example, 10 μm or more, for example, 100 μm or more.

[0096] In some cases, multiple beams of frequency-shifted light are irradiated onto the flow stream, as described in Diebold, et al. Nature Photonics Vol. 7(10); 806-810 (2013) and U.S. Patent Nos. 9,423,353, 9,784,661, 9,983,132, 10,006,852, 10,078,045, 10,036,699, 10,222,316, 10,288,546, 10,324,019, 10,408,758, 10,451,538, 10,620,111, and U.S. Patent Application Publication No. Cells in a flow stream are imaged by fluorescence imaging using radio frequency tag emission (FIRE) to generate a frequency-encoded image, as described in U.S. Patent Application Publication Nos. 2017 / 0133857, 2017 / 0328826, 2017 / 0350803, 2018 / 0275042, 2019 / 0376895, and 2019 / 0376894, the disclosures of which are incorporated herein by reference.

[0097] As noted above, in embodiments, light from the illuminated sample is transmitted to a light detection system, as described in more detail below, and measured by a plurality of photodetectors. In some embodiments, the methods measure light collected over a range of wavelengths (e.g., 200 nm to 1000 nm). For example, the methods may collect a spectrum of light over one or more wavelength ranges from 200 nm to 1000 nm. In still other embodiments, the methods measure light collected at one or more specific wavelengths. For example, light collected at one or more of 450 nm, 518 nm, 519 nm, 561 nm, 578 nm, 605 nm, 607 nm, 625 nm, 650 nm, 660 nm, 667 nm, 670 nm, 668 nm, 695 nm, 710 nm, 723 nm, 780 nm, 785 nm, 647 nm, 617 nm, and any combination thereof. In some embodiments, the methods measure the wavelength of light corresponding to the fluorescence peak wavelength of the fluorophore. In some embodiments, the method measures the collected light across the fluorescence spectrum of each fluorophore in the sample.

[0098] The collected light may be measured continuously or at discrete intervals. In some cases, the method measures the light continuously. In other cases, the method measures the light at discrete intervals, such as every 0.001 milliseconds, every 0.01 milliseconds, every 0.1 milliseconds, every 1 millisecond, every 10 milliseconds, every 100 milliseconds, e.g., every 1000 milliseconds, or other intervals.

[0099] Measurements of collected light may be made one or more times during the subject methods, such as two or more times, such as three or more times, such as five or more times, such as ten or more times, In some embodiments, light propagation is measured two or more times, and the data is optionally averaged.

[0100] Light from the sample may be measured at one or more wavelengths, for example 5 or more different wavelengths, such as 10 or more different wavelengths, for example 25 or more different wavelengths, such as 50 or more different wavelengths, for example 100 or more different wavelengths, such as 200 or more different wavelengths, for example 300 or more different wavelengths, for example light collected at 400 or more different wavelengths may be measured.

[0101] In embodiments, the method uses a generalized least squares algorithm to spectrally resolve light from each fluorophore in the sample. In some embodiments, the overlap between each different fluorophore is determined and the contribution of each fluorophore to the overlapping fluorescence is calculated. In some embodiments, when spectrally resolving light using a generalized least squares algorithm, a spectral unmixing matrix of the fluorescence spectrum is calculated for each of multiple fluorophores in the sample that have overlapping fluorescence detected by the light detection system. For example, spectrally resolving light according to the methods described herein may include the Moore-Penrose inverse or pseudoinverse of the spectral matrix. As described in more detail below, the process of spectrally resolving light from each fluorophore using a generalized least squares algorithm (e.g., calculating a spectral unmixing matrix for each fluorophore) may be used to estimate the abundance of each fluorophore in the sample. In some embodiments, the abundance of each fluorophore associated with a targeted particle may be determined. The abundance of each fluorophore associated with a targeted particle may be used to identify and classify particles. In some cases, the identified or classified particles may be used to sort targeted particles (e.g., cells) in a sample. In some embodiments, sorting is fast enough to spectrally resolve fluorophores in a sample, e.g., by calculating spectral unmixing, allowing particles to be sorted in real time after detection by an optical detection system.

[0102] In some embodiments, a method determines the covariance of data signals in one or more photodetector channels. In some cases, the covariance of data signals in each photodetector channel is determined. The term "covariance of data signals" is used herein in its conventional sense to refer to differential measurements by each photodetector channel. For example, different measurements (per particle and per detector) in embodiments have different noise levels due to both signal-independent constant noise sources (e.g., baseline electronic noise from amplifiers and analog-to-digital converters, and baseline shot noise from constant light sources such as ambient illumination or scattered laser light) and signal-dependent noise sources that vary linearly with the signal (e.g., shot noise resulting from photon measurements following Poisson statistics) or quadratically with the signal (e.g., multiplicative noise resulting from random fluctuations in fluid and illumination intensity as particles flow through the system). FIG. 1B shows raw measurement variance from particles in a sample illuminated with light according to one embodiment. The variance is a function of baseline noise, Poisson noise, and quadratic covariance (CV) noise. FIG. 1C shows the determination of the quadratic noise factor in the measurement covariance. In some cases, quadratic noise coefficients are estimated by fitting curves of variance versus median intensity of light detected by each photodetector channel. In other cases, quadratic covariance coefficients per detector are estimated from raw measurement data using baseline noise per detector and a linear Poisson coefficient. Figure 1D shows the estimation of the unmixing spread when the covariance is absent (i.e., zero). As shown in Figure 1D, including a quadratic term with zero covariance results in an overestimation of the unmixing spread. A comparison of the measured spread with a simulation based on a model without covariance demonstrates this overestimation of the spread. On the other hand, including a quadratic term with a non-zero covariance in the noise model allows for accurate prediction of the unmixing spread.

[0103] In some embodiments, the subject method considers non-zero covariance in measurements from various photodetector channels. Optionally, spectrally resolving the light using a generalized least squares algorithm involves weighting by the inverse of the variance between the photodetector channels. Optionally, measurements from various photodetector channels are decorrelated by multiplying by the inverse of the measurement covariance matrix (as described below). Optionally, the covariance of the data signals in each photodetector channel includes one or more inherent sample and measurement variance components. Optionally, the covariance of the data signals in each photodetector channel includes electronic noise. Optionally, the covariance of the data signals in each photodetector channel includes shot noise. Optionally, the covariance of the data signals varies linearly with the generated data signals. Optionally, the covariance of the data signals varies quadratically with the generated data signals. Optionally, the covariance of the data signals is correlated across two or more of the multiple photodetector channels. Optionally, the covariance of the data signals is calculated according to:

[0104]

number

[0105] In some cases, the covariance of the data signal is calculated using a covariance matrix. In some cases, the covariance matrix includes non-zero diagonal values. In some cases, the covariance is calculated using a covariance matrix according to:

[0106]

number

[0107] Here, diag(x) indicates generating a diagonal matrix from a column vector x, and cov(a, b) indicates the covariance between a and b.

[0108] In some embodiments, the solution to the generalized least squares problem is calculated by multiplying by the inverse of the calculated covariance matrix. In some embodiments, the method estimates the covariance of the data signal based on the fluorescence intensities across two or more photodetectors of the photodetection system. In some embodiments, the method estimates the covariance of the data signal based on the fluorescence intensities across each of the photodetection channels. In some embodiments, the generalized least squares problem is calculated according to:

[0109]

number

[0110] In some cases, the method further generates an estimated covariance matrix a priori. In some cases, a generalized least squares algorithm is applied in real time (e.g., using an integrated circuit such as a field programmable gate array). In some cases, an a priori noise model is used to estimate the covariance of each event (e.g., calculating the covariance matrix of each event in real time). In some cases, the a priori noise model uses only the data collected for each particular event. In some cases, the covariance matrix includes estimates from the entire collected data set. In some cases, the covariance matrix is generated by an iterative optimization method that empirically adjusts the covariance matrix to minimize the variance of the unmixed data.

[0111] In some embodiments, the covariance of the data signal is determined by estimating iterative optimization using a covariance matrix that minimizes the variance of the unmixed data signal. In some embodiments, solving the generalized least squares problem is characterized by a Cholesky decomposition of the covariance matrix. In some embodiments, solving the generalized least squares problem is characterized by a covariance matrix Σ y =CC T to solve the triangular system and generate the transformed input for the ordinary least squares algorithm according to

[0112]

number

[0113] FIG. 2A shows a comparison of correlation and anti-correlation of second-order noise according to one embodiment. In some cases, random fluctuations in measurement signals resulting from system perturbations may be correlated across multiple detectors. A flow stream within a flow cell of a flow cytometer is shown in FIG. 2A, with an illuminating laser beam having a Gaussian beam intensity profile aligned so that it is brightest in the center of the core stream and dimmer toward the edges. Individual particles typically follow linear trajectories within the core stream (i.e., along the axis of the cylindrical core stream), but once they enter the core stream, their radial positions become essentially random. In a properly aligned flow cytometer, a particle passing through the center of the core stream will receive higher illumination by all lasers than an identical particle passing through the core stream closer to the outer edge, and the particle passing through the core stream closer to the outer edge will pass through a region of lower intensity in each beam. This results in a darker signal recorded across all detectors for the second particle compared to the first particle. In other words, while the fluctuations themselves are random, the fluctuations proceed in the same direction in all measurement channels. Imperfect alignment and differences in collection efficiency at different wavelengths mean that such variations are not perfectly correlated between detectors. In some cases, these variations are anticorrelated (i.e., one detector receives a brighter signal while the other receives a fainter signal). In other cases, the structure of the second-order noise is correlated (i.e., has a covariance matrix with non-zero diagonal elements).

[0114] 2B shows a comparison of unmixing using ordinary least squares and weighted least squares with spectral unmixing using a generalized least squares algorithm according to an embodiment. As shown in the example of FIG. 2B, simulation results indicate that in the presence of correlated and unevenly distributed measurement noise, the generalized least squares method can provide significant improvements (lower variance of unmixed data) over both ordinary least squares and weighted least squares methods in spectral measurements using a photodetection system with multiple photodetectors.

[0115] In some embodiments, a method finds a least-squares solution to a generalized least-squares problem. Optionally, the least-squares solution to the generalized least-squares problem is found by one or more of matrix decomposition, matrix factorization, QR decomposition, Cholesky decomposition, singular value decomposition, LDL decomposition, forward substitution, and backward substitution. Optionally, the method finds the least-squares solution to the generalized least-squares problem by solving the so-called normal equations by Cholesky or LDL decomposition, for example, according to

[0116]

number

[0117] In some cases, the method finds a least-squares solution to a generalized least-squares problem by Cholesky or LDL decomposition according to:

[0118]

number

[0119] In some embodiments, the method finds a least-squares solution to a generalized least-squares problem by matrix decomposition.

[0120]

number

[0121]

number

[0122] In some embodiments, the method estimates the covariance resulting from measurement variability alone, without the influence of sample-specific variability. In some embodiments, an analytical covariance model is used to predict the measurement covariance of one or more particles (e.g., each particle in a sample) as a function of that particle's intensity profile across all photodetectors. In some cases, the measurement covariance includes one or more parameters, such as: (1) baseline noise per photodetector; (2) linear Poisson coefficient (photoelectron scaling coefficient) per photodetector; (3) quadratic CV coefficient per photodetector (which may be estimated directly from the raw data); and (4) a quadratic CV correlation coefficient, which describes how correlated the quadratic noise is between each pair of photodetectors. In some cases, the baseline noise and linear Poisson coefficient per photodetector are determined during instrument calibration. In some cases, the quadratic CV coefficient per photodetector can be estimated for each detector from the measured raw data. In some cases, second-order CV correlations are determined by a model-fitting process using measured calibration data of specific classes, such as cells or particles stained with individual fluorochromes and then spectrally unmixed.

[0123] In some embodiments, the inherent variation of one spectral signal source (e.g., a single fluorophore) in a homogeneous particle population is correlated across all photodetectors receiving signals from that fluorophore. In some cases, this can result in high covariance in raw data space. In some cases, when spectrally unmixing a sample, all inherent variation in fluorophore expression is included in the variance of the unmixed signal per fluorophore. In some cases, every other dimension (fluorophore) present in the unmixing matrix has zero variance arising from a single fluorophore source.

[0124] In some cases, when the measurement noise has a non-zero covariance and is at least partially uncorrelated, covariant noise sources contribute to variance in unmixing dimensions that do not correspond to expressed fluorophores. In some cases, the method measures the unmixing variance of unexpressed fluorophore channels in the measurement data to determine ground truth unmixing variance. In some cases, the method applies a noise model including a constant coefficient, a linear coefficient, and a quadratic coefficient, along with a predetermined estimate of the quadratic noise correlation coefficient, and adjusts the correlation coefficient (e.g., through a range of values) until the unmixing variance estimated by the model for the median intensity level of the ground truth sample matches the measured unmixing variance. In some cases, the noise model is then defined and used in the event-by-event calculation of the generalized least squares problem.

[0125] In some embodiments, the method calculates the abundance of one or more fluorophores in the sample from the spectrally resolved light from each fluorophore. In some cases, the abundance of a fluorophore associated with a targeted particle (e.g., chemically bound (i.e., covalently, ionically) or physically bound) is calculated from the spectrally resolved light from each fluorophore associated with the particle. For example, in one example, the relative abundance of each fluorophore associated with a targeted particle is calculated from the spectrally resolved light from each fluorophore. In another example, the absolute abundance of each fluorophore associated with a targeted particle is calculated from the spectrally resolved light from each fluorophore. In certain embodiments, particles may be identified or classified based on the relative abundance of each fluorophore determined to be associated with the particle. In these embodiments, particles may be identified or classified by any convenient protocol, such as by comparing the relative or absolute abundance of each fluorophore associated with the particle to a control sample with known particles, or by performing spectroscopic or other assay analysis of a population of particles (e.g., cells) having calculated relative or absolute abundances of associated fluorophores.

[0126] In certain embodiments, the method sorts one or more particles (e.g., cells) of a sample that are identified based on the estimated abundance of a fluorophore associated with the particle. The term "sorting" is used herein in its conventional sense to refer to separating components of a sample (e.g., droplets containing cells, droplets containing non-cellular particles such as biopolymers) and, optionally, directing the separated components to one or more sample collection vessels. For example, the method sorts two or more components of a sample, e.g., three or more components, e.g., four or more components, e.g., five or more components, e.g., ten or more components, e.g., fifteen or more components, e.g., sorting twenty-five or more components of a sample.

[0127] When sorting identified particles based on the abundance of fluorophores associated with the particles, the method may involve acquiring, analyzing, and recording data using a computer or the like, where multiple data channels record data from each detector used in obtaining the overlapping spectra of the multiple fluorophores associated with the particles. In these embodiments, the analysis involves spectrally resolving (e.g., calculating a spectral unmixing matrix) the light from the multiple fluorophores associated with the particles, whose spectra overlap, and identifying the particles based on the estimated abundance of each fluorophore associated with the particle. The results of this analysis may be communicated to a sorting system configured to generate a set of digitized parameters based on the particle classification.

[0128] In some embodiments, a method for sorting components of a sample involves sorting particles (e.g., cells in a biological sample) using a particle sorting module having deflection plates, as described in U.S. Patent Application Publication No. 2017 / 0299493, filed March 28, 2017, the disclosure of which is incorporated herein by reference. In certain embodiments, cells of a sample are sorted using a sorting determination module having multiple sorting determination units, as described in U.S. Provisional Patent Application No. 62 / 803264, filed February 8, 2019, the disclosure of which is incorporated herein by reference.

[0129] A system for spectrally resolving light from fluorophores with overlapping fluorescence spectra in a sample using a generalized least squares algorithm. As summarized above, aspects of the present disclosure include a system for spectrally resolving light from fluorophores with overlapping fluorescence spectra in a sample. As noted above, the term "spectrally resolving" is used herein in its conventional sense to refer to spectrally distinguishing each fluorophore in a sample by assigning or attributing overlapping wavelengths of light to respective contributing fluorophores. In embodiments, a spectral unmixing matrix is calculated to determine overlapping spectral components of the fluorescence attributable to each fluorophore. In embodiments, the subject system is used to characterize a sample having multiple fluorophores, wherein the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample. In some cases, the fluorescence spectrum of each fluorophore overlaps with the fluorescence spectrum of at least one other fluorophore in the sample by 5 nm or more, e.g., 10 nm or more, e.g., 25 nm or more, e.g., 50 nm or more. In some cases, the fluorescence spectrum of one or more fluorophores in the sample overlaps with the fluorescence spectra of two or more different fluorophores in the sample, for example, the fluorescence spectral overlap is 5 nm or more, such as 10 nm or more, for example 25 nm or more, for example 50 nm or more.

[0130] In embodiments, the system includes a light source configured to illuminate a sample having multiple fluorophores, wherein the fluorescence spectrum of each fluorophore in the sample overlaps with the fluorescence spectrum of at least one other fluorophore. In embodiments, the light source may be any suitable broadband or narrowband light source. Depending on the components in the sample (e.g., cells, beads, non-cellular particles, etc.), the light source may be configured to emit light at various wavelengths within a range of 200 nm to 1500 nm, e.g., 250 nm to 1250 nm, e.g., 300 nm to 1000 nm, e.g., 350 nm to 900 nm, or e.g., 400 nm to 800 nm. For example, the light source may include a broadband light source that emits light having a wavelength within a range of 200 nm to 900 nm. In other cases, the light source may include a narrowband light source that emits at a wavelength within a range of 200 nm to 900 nm. For example, the light source may be a narrowband LED (1 nm to 25 nm) that emits light having a wavelength within a range of 200 nm to 900 nm.

[0131] In some embodiments, the light source is a laser. In some cases, the subject systems include a gas laser, such as a helium-neon laser, an argon laser, a krypton laser, a xenon laser, a nitrogen laser, a CO laser, a CO laser, an argon fluorine (ArF) excimer laser, a krypton fluorine (KrF) excimer laser, a xenon chlorine (XeCl) excimer laser, or a xenon fluorine (XeF) excimer laser, or a combination thereof. In other cases, the subject systems include a dye laser, such as a stilbene laser, a coumarin laser, or a rhodamine laser. In still other cases, lasers of interest include metal vapor lasers, such as a helium cadmium (HeCd) laser, a helium mercury (HeHg) laser, a helium selenium (HeSe) laser, a helium silver (HeAg) laser, a strontium laser, a neon copper (NeCu) laser, a copper laser, or a gold laser, and combinations thereof. In still other cases, the subject systems include solid-state lasers, such as ruby lasers, Nd:YAG lasers, NdCrYAG lasers, Er:YAG lasers, Nd:YLF lasers, Nd:YVO4 lasers, Nd:YCa4O(BO3)3 lasers, Nd:YCOB lasers, titanium sapphire lasers, thulium YAG lasers, ytterbium YAG lasers, Yb2O3 lasers, or cerium-doped lasers, and combinations thereof.

[0132] In other embodiments, the light source is a non-laser light source, such as, but not limited to, a halogen lamp, a deuterium arc lamp, a xenon arc lamp, a light emitting diode, such as a broadband LED with a continuous spectrum, a superluminescent diode, a semiconductor light emitting diode, a broadband LED white light source, a multi-LED integrated, etc. In some cases, the non-laser light source is a stabilized fiber coupled broadband light source, a white light source, or any combination thereof, among other light sources.

[0133] The light source may be positioned at any suitable distance from the sample (e.g., a flow stream in a flow cytometer), for example, at a distance of 0.001 mm or more from the flow stream, for example, 0.005 mm or more, for example, 0.01 mm or more, for example, 0.05 mm or more, for example, 0.1 mm or more, for example, 0.5 mm or more, for example, 1 mm or more, for example, 5 mm or more, for example, 10 mm or more, for example, 25 mm or more, for example, 100 mm or more. In addition, the light source may illuminate the sample at any suitable angle (e.g., relative to the vertical axis of the flow stream), for example, at an angle in the range of 10° to 90°, for example, 15° to 85°, for example, 20° to 80°, for example, 25° to 75°, for example, 30° to 60°, for example, at an angle of 90°.

[0134] The light source may be configured to illuminate the sample continuously or at discrete intervals. In some cases, the system includes a light source configured to continuously illuminate the sample, e.g., having a continuous wave laser that continuously illuminates the flow stream at the interrogation point of the flow cytometer. In other cases, systems of interest include a light source configured to illuminate the sample at discrete intervals, e.g., every 0.001 millisecond, 0.01 millisecond, 0.1 millisecond, 1 millisecond, 10 milliseconds, 100 milliseconds, 1000 milliseconds, or other intervals. When the light source is configured to illuminate the sample at discrete intervals, the system may include one or more additional components for intermittently illuminating the sample with the light source. For example, the subject systems in these embodiments may include one or more laser beam choppers, manual or computer-controlled beam stops, for blocking and exposing the sample to the light source.

[0135] In some embodiments, the light source is a laser. Lasers of interest may include pulsed lasers or continuous wave lasers. For example, the laser may be a gas laser, such as a helium-neon laser, an argon laser, a krypton laser, a xenon laser, a nitrogen laser, a CO laser, a CO laser, an argon fluorine (ArF) excimer laser, a krypton fluorine (KrF) excimer laser, a xenon chlorine (XeCl) excimer laser, or a xenon fluorine (XeF) excimer laser, or a combination thereof; a dye laser, such as a stilbene laser, a coumarin laser, or a rhodamine laser; a metal vapor laser, such as a helium cadmium (HeCd) laser, a helium mercury (HeHg) laser, a helium selenium (HeSe) laser, a helium silver (HeAg) laser, a strontium laser, a neon copper (NeCu) laser, a copper laser, or a gold laser, or a combination thereof; a solid-state laser, such as a ruby laser, a Nd:YAG laser, a NdCrYAG laser, Er:YAG laser, Nd:YLF laser, Nd:YVO4 laser, Nd:YCa4O(BO3)3 laser, Nd:YCOB laser, Ti:sapphire laser, Thulium YAG laser, Ytterbium YAG laser, Yb2O3 laser or Cerium doped laser and combinations thereof; semiconductor diode laser, optically pumped semiconductor laser (OPSL), or frequency doubled or tripled of any of the above lasers.

[0136] In some embodiments, the light source is an optical beam generator configured to generate two or more beams of frequency-shifted light. In some cases, the optical beam generator comprises a laser, a radio frequency generator configured to apply a radio frequency drive signal to an acousto-optic device to generate two or more angularly deflected laser beams. In these embodiments, the laser may be a pulsed laser or a continuous wave laser. For example, the laser of the light beam generator of interest may be a gas laser, such as a helium-neon laser, an argon laser, a krypton laser, a xenon laser, a nitrogen laser, a CO laser, a CO laser, an argon fluorine (ArF) excimer laser, a krypton fluorine (KrF) excimer laser, a xenon chlorine (XeCl) excimer laser, or a xenon fluorine (XeF) excimer laser, or a combination thereof; a dye laser, such as a stilbene laser, a coumarin laser, or a rhodamine laser; a metal vapor laser, such as a helium cadmium (HeCd) laser, a helium mercury (HeHg) laser, a helium selenium (HeSe) laser, a helium silver (HeAg) laser, a strontium laser, a neon copper (NeCu) laser, a copper laser, or a gold laser, or a combination thereof; a solid-state laser, such as a ruby laser, a Nd:YAG laser, a NdCrYAG The laser may be an Er:YAG laser, an Nd:YLF laser, an Nd:YVO4 laser, an Nd:YCa4O(BO3)3 laser, an Nd:YCOB laser, a titanium sapphire laser, a thulium YAG laser, an ytterbium YAG laser, an Yb2O3 laser or a cerium doped laser and combinations thereof.

[0137] The acousto-optic device may be any convenient acousto-optic protocol configured to frequency-shift laser light using applied acoustic waves. In certain embodiments, the acousto-optic device is an acousto-optic deflector. The acousto-optic device of the subject system is configured to generate an angularly deflected laser beam from light from a laser and an applied high-frequency drive signal. The high-frequency drive signal may be applied to the acousto-optic device using any suitable high-frequency drive signal source, such as a direct digital synthesizer (DDS), an arbitrary waveform generator (AWG), or an electrical pulse generator.

[0138] In an embodiment, the controller is configured to apply high frequency drive signals to the acousto-optic device to generate a desired number of angularly deflected laser beams of the output laser beam, for example configured to apply 3 or more high frequency drive signals, for example 4 or more high frequency drive signals, for example 5 or more high frequency drive signals, for example 6 or more high frequency drive signals, for example 7 or more high frequency drive signals, for example 8 or more high frequency drive signals, for example 9 or more high frequency drive signals, for example 10 or more high frequency drive signals, for example 15 or more high frequency drive signals, for example 25 or more high frequency drive signals, for example 50 or more high frequency drive signals, for example configured to apply 100 or more high frequency drive signals.

[0139] In some cases, to generate an intensity profile of the angularly deflected laser beam of the output laser beam, the controller is configured to apply a high frequency drive signal having a varying amplitude within a range, for example, from about 0.001 V to about 500 V, for example, from about 0.005 V to about 400 V, for example, from about 0.01 V to about 300 V, for example, from about 0.05 V to about 200 V, for example, from about 0.1 V to about 100 V, for example, from about 0.5 V to about 75 V, for example, from about 1 V to about 50 V, for example, from about 2 V to about 40 V, for example, from about 3 V to about 30 V, or for example, from about 5 V to about 25 V. The applied high frequency drive signal in some embodiments has a frequency within the range of about 0.001 MHz to about 500 MHz, for example, about 0.005 MHz to about 400 MHz, for example, about 0.01 MHz to about 300 MHz, for example, about 0.05 MHz to about 200 MHz, for example, about 0.1 MHz to about 100 MHz, for example, about 0.5 MHz to about 90 MHz, for example, about 1 MHz to about 75 MHz, for example, about 2 MHz to about 70 MHz, for example, about 3 MHz to about 65 MHz, for example, about 4 MHz to about 60 MHz, for example, about 5 MHz to about 50 MHz.

[0140] In some embodiments, the controller includes a processor to which a memory is operatively coupled, the memory storing instructions that, when executed by the processor, cause the processor to generate an output laser beam including an angularly deflected laser beam having a desired intensity profile. For example, the memory may include instructions for generating two or more, e.g., three or more, e.g., four or more, e.g., five or more, e.g., ten or more, e.g., twenty-five or more, e.g., fifty or more angularly deflected laser beams of the same intensity, e.g., the memory may include instructions for generating one hundred or more angularly deflected laser beams of the same intensity. In other embodiments, the memory may include instructions for generating two or more, e.g., three or more, e.g., four or more, e.g., five or more, e.g., ten or more, e.g., twenty-five or more, e.g., fifty or more angularly deflected laser beams of different intensities, e.g., the memory may include instructions for generating one hundred or more angularly deflected laser beams of different intensities.

[0141] In some embodiments, the controller has a processor to which the memory is operatively coupled, such that the memory stores instructions that, when executed by the processor, cause the processor to generate an output laser beam that increases in intensity from the edge of the output laser beam to the center along a horizontal axis. In these cases, the intensity of the angularly deflected laser beam at the center of the output beam may be in a range of 0.1% to about 99%, for example, 0.5% to about 95%, for example, 1% to about 90%, for example, about 2% to about 85%, for example, about 3% to about 80%, for example, about 4% to about 75%, for example, about 5% to about 70%, for example, about 6% to about 65%, for example, about 7% to about 60%, for example, about 8% to about 55%, or may be in a range of about 10% to about 50% of the intensity of the angularly deflected laser beam at the edge of the output laser beam along the horizontal axis. In other embodiments, the controller has a processor to which the memory is operatively coupled, such that the memory stores instructions that, when executed by the processor, cause the processor to generate an output laser beam that increases in intensity from the edge to the center of the output laser beam along a horizontal axis. In these cases, the intensity of the angularly deflected laser beam at the edge of the output beam may be in a range of 0.1% to about 99%, for example, 0.5% to about 95%, for example, 1% to about 90%, for example, about 2% to about 85%, for example, about 3% to about 80%, for example, about 4% to about 75%, for example, about 5% to about 70%, for example, about 6% to about 65%, for example, about 7% to about 60%, for example, about 8% to about 55%, or may be in a range of about 10% to about 50% of the intensity of the angularly deflected laser beam at the center of the output laser beam along the horizontal axis. In yet another embodiment, the controller has a processor to which a memory is operatively coupled, such that the memory stores instructions that, when executed by the processor, cause the processor to generate an output laser beam having a Gaussian intensity profile along a horizontal axis.In yet another embodiment, the controller has a processor to which the memory is operatively coupled, such that the memory stores instructions that, when executed by the processor, cause the processor to generate an output laser beam having a top-hat intensity profile along a horizontal axis.

[0142] In embodiments, the optical beam generator of interest may be configured to generate spatially separated angularly deflected laser beams of the output laser beam. Depending on the applied high frequency drive signal and the desired irradiance profile of the output laser beam, the angularly deflected laser beams may be separated by 0.001 μm or more, such as 0.005 μm or more, such as 0.01 μm or more, such as 0.05 μm or more, such as 0.1 μm or more, such as 0.5 μm or more, such as 1 μm or more, such as 5 μm or more, such as 10 μm or more, such as 100 μm or more, such as 500 μm or more, such as 1000 μm or more, such as 5000 μm or more. In some embodiments, the system is configured to generate angularly deflected laser beams of the output laser beam that overlap, for example, adjacent angularly deflected laser beams along a horizontal axis of the output laser beam. The overlap of adjacent angularly deflected laser beams (e.g., overlap of beam spots) may be 0.001 μm or more, for example, 0.005 μm or more, for example, 0.01 μm or more, for example, 0.05 μm or more, for example, 0.1 μm or more, for example, 0.5 μm or more, for example, 1 μm or more, for example, 5 μm or more, for example, 10 μm or more, for example, 100 μm or more.

[0143] In some cases, the light beam generator configured to generate two or more beams of frequency-shifted light is disclosed in U.S. Pat. Nos. 9,423,353, 9,784,661, 9,983,132, 10,006,852, 10,078,045, 10,036,699, 10,222,316, 10,288,546, 10,324,019, 10,408,758, 104,515, 105,110, 115,120, 116,130, 117,140, 118,150, 119,160, 120,162, 122,164, 124,166, 126,130, 128,140, 1268, 1282, 1286, 128 ... 38, U.S. Pat. No. 10,620,111, U.S. Patent Application Publication No. 2017 / 0133857, U.S. Patent Application Publication No. 2017 / 0328826, U.S. Patent Application Publication No. 2017 / 0350803, U.S. Patent Application Publication No. 2018 / 0275042, U.S. Patent Application Publication No. 2019 / 0376895, and U.S. Patent Application Publication No. 2019 / 0376894, the disclosures of which are incorporated herein by reference.

[0144] In embodiments, the system includes a light detection system having a plurality of light detectors. Light detectors of interest may include, but are not limited to, optical sensors, such as active pixel sensors (APS), avalanche photodiodes, image sensors, charge-coupled devices (CCDs), intensified charge-coupled devices (ICCDs), light-emitting diodes, photon counters, bolometers, pyroelectric detectors, photoresistors, photocells, photodiodes, photomultiplier tubes, phototransistors, quantum dot photoconductors or photodiodes, and combinations thereof, among other light detectors. In certain embodiments, light from the sample is measured with a charge-coupled device (CCD), a semiconductor charge-coupled device (CCD), an active pixel sensor (APS), a complementary metal-oxide semiconductor (CMOS) image sensor, or an N-type metal-oxide semiconductor (NMOS) image sensor.

[0145] In some embodiments, the light detection system of interest comprises a plurality of light detectors. In some cases, the light detection system comprises a plurality of solid-state detectors, e.g., photodiodes. In some cases, the light detection system comprises a light detector array, e.g., an array of photodiodes. In these embodiments, the light detector array may comprise 4 or more light detectors, e.g., 10 or more light detectors, e.g., 25 or more light detectors, e.g., 50 or more light detectors, e.g., 100 or more light detectors, e.g., 250 or more light detectors, e.g., 500 or more light detectors, e.g., 750 or more light detectors, e.g., 1000 or more light detectors. For example, the detector may be a photodiode array having 4 or more photodiodes, e.g., 10 or more photodiodes, e.g., 25 or more photodiodes, e.g., 50 or more photodiodes, e.g., 100 or more photodiodes, e.g., 250 or more photodiodes, e.g., 500 or more photodiodes, e.g., 750 or more photodiodes, e.g., 1000 or more photodiodes.

[0146] The photodetectors may be arranged in any geometric configuration as desired, including, but not limited to, square, rectangular, trapezoidal, triangular, hexagonal, heptagonal, octagonal, nonagonal, decagonal, dodecagonal, circular, elliptical, and irregular pattern configurations. The photodetectors of the photodetector array may be oriented at angles (relative to the XZ plane) relative to the other photodetectors within a range of 10° to 180°, e.g., 15° to 170°, e.g., 20° to 160°, e.g., 25° to 150°, e.g., 30° to 120°, e.g., 45° to 90°. The photodetector array may have any suitable shape, including rectilinear shapes such as square, rectangular, trapezoidal, triangular, and hexagonal; curvilinear shapes such as circular and elliptical; and irregular shapes such as a parabolic base joined to a planar top. In some embodiments, the photodetector array has a rectangular active surface.

[0147] Each photodetector (e.g., photodiode) in the array may have an active surface with a width in the range of 5 μm to 250 μm, for example 10 μm to 225 μm, for example 15 μm to 200 μm, such as 20 μm to 175 μm, for example 25 μm to 150 μm, for example 30 μm to 125 μm, for example 50 μm to 100 μm, and a length in the range of 5 μm to 250 μm, for example 10 μm to 225 μm, for example 15 μm to 200 μm, for example 20 μm to 175 μm, for example 25 μm to 150 μm, for example 30 μm to 125 μm, for example 50 μm to 100 μm, and the surface area of each photodetector (e.g., photodiode) in the array may be in the range of 25 μm to 250 μm. 2 ~10000 μm 2 , e.g., 50 μm 2 ~9000μm 2 , e.g., 75 μm 2 ~8000μm 2 , e.g., 100 μm 2 ~7000μm 2 , e.g., 150 μm 2 ~6000μm 2 , e.g., 200 μm 2 ~5000μm 2 is within the range.

[0148] The size of the photodetector array may vary depending on the amount and intensity of light, the number of photodetectors, and the desired sensitivity, and may have a length in the range of 0.01 mm to 100 mm, such as 0.05 mm to 90 mm, for example 0.1 mm to 80 mm, for example 0.5 mm to 70 mm, for example 1 mm to 60 mm, for example 2 mm to 50 mm, for example 3 mm to 40 mm, for example 4 mm to 30 mm, for example 5 mm to 25 mm. The width of the photodetector array may further vary in the range of 0.01 mm to 100 mm, for example 0.05 mm to 90 mm, for example 0.1 mm to 80 mm, for example 0.5 mm to 70 mm, for example 1 mm to 60 mm, for example 2 mm to 50 mm, for example 3 mm to 40 mm, for example 4 mm to 30 mm, for example 5 mm to 25 mm. Thus, the active surface of the photodetector array may be 0.1 mm to 100 mm, for example 0.05 mm to 90 mm, for example 0.1 mm to 80 mm, for example 0.5 mm to 70 mm, for example 1 mm to 60 mm, for example 2 mm to 50 mm, for example 3 mm to 40 mm, for example 4 mm to 30 mm, for example 5 mm to 25 mm. 2 ~10000 mm 2 , e.g., 0.5 mm 2 ~5000mm2 , e.g. 1 mm 2 ~1000mm 2 , e.g. 5mm 2 ~500 mm 2 , e.g. 10mm 2 ~100 mm 2 may be in the range of

[0149] The photodetector of interest is configured to measure light collected at one or more wavelengths, for example, two or more wavelengths, for example, five or more different wavelengths, for example, ten or more different wavelengths, for example, twenty-five or more different wavelengths, for example, fifty or more different wavelengths, for example, one hundred or more different wavelengths, for example, two hundred or more different wavelengths, for example, three hundred or more different wavelengths, for example, configured to measure light emitted from a sample in the flow stream at four hundred or more different wavelengths.

[0150] In some embodiments, the photodetector is configured to measure collected light over a range of wavelengths (e.g., 200 nm to 1000 nm). In certain embodiments, the photodetector of interest is configured to collect a spectrum of light over a range of wavelengths. For example, a system may include one or more detectors configured to collect a spectrum of light over one or more wavelength ranges from 200 nm to 1000 nm. In still other embodiments, the detector of interest is configured to measure light from a sample in the flowstream at one or more specific wavelengths. For example, a system may include one or more detectors configured to measure light at one or more of the following wavelengths: 450 nm, 518 nm, 519 nm, 561 nm, 578 nm, 605 nm, 607 nm, 625 nm, 650 nm, 660 nm, 667 nm, 670 nm, 668 nm, 695 nm, 710 nm, 723 nm, 780 nm, 785 nm, 647 nm, 617 nm, and any combination thereof. In certain embodiments, the photodetector may be configured to be paired with a particular fluorophore, such as a fluorophore used with the sample in a fluorescence assay, hi some embodiments, the photodetector is configured to measure the collected light across the fluorescence spectrum of each fluorophore in the sample.

[0151] The light detection system may be configured to measure light continuously or at discrete intervals. In some cases, the light detector of interest is configured to measure collected light continuously. In other cases, the light detection system is configured to measure at discrete intervals, such as every 0.001 milliseconds, 0.01 milliseconds, 0.1 milliseconds, 1 millisecond, 10 milliseconds, 100 milliseconds, e.g., every 1000 milliseconds, or other intervals.

[0152] In embodiments, the system is configured to analyze light from the illuminated sample and spectrally resolve light from each fluorophore in the sample using a generalized least squares algorithm. In some embodiments, the system includes a memory having stored thereon instructions for determining the overlap between each different fluorophore in the sample and calculating the contribution of each fluorophore to the overlapping fluorescence. In certain embodiments, the system is configured to calculate a spectral unmixing matrix for the fluorescence spectra of multiple fluorophores with overlapping fluorescence in the sample detected by the light detection system. As described in more detail below, the system may be further configured to estimate the abundance of each fluorophore in the sample. In certain embodiments, the abundance of each fluorophore associated with a targeted particle may be determined. The system may be configured to identify and classify targeted particles based on the abundance of each fluorophore associated with the targeted particle. In some cases, the system is configured to sort the identified or classified particles. In these embodiments, the system may include a computer control system, and the system may further include one or more computers for fully or partially automating the system to perform the methods described herein.

[0153] In some embodiments, the system includes a computer having a computer-readable storage medium having a computer program stored thereon, the computer program having instructions, when loaded into the computer, to illuminate a flow cell having a sample in a flow stream with a light source, detect light from the flow cell with a light detection system having a plurality of light detectors, spectrally resolve the light from each fluorophore in the sample using a generalized least squares algorithm, estimate the abundance of each fluorophore, and sort particles in the sample based on the estimated fluorophore abundances.

[0154] In some embodiments, the memory stores instructions that, when executed by the processor, cause the processor to determine a covariance of the data signals at each photodetector channel. Optionally, the covariance of the data signals at each photodetector channel includes an inherent sample variation component and a measurement variation component. Optionally, the covariance of the data signals at each photodetector channel includes electronic noise. Optionally, the covariance of the data signals at each photodetector channel includes shot noise. Optionally, the covariance of the data signals varies linearly with the generated data signals. Optionally, the covariance of the data signals varies quadratically with the generated data signals. Optionally, the covariance of the data signals is correlated across two or more of the multiple photodetector channels. Optionally, the memory has instructions for calculating the covariance of the data signals according to:

[0155]

number

[0156] In some cases, the memory has instructions for calculating the covariance of the data signal using a covariance matrix. In some cases, the covariance matrix includes non-zero diagonal values. In some cases, the memory has instructions for calculating the covariance using a covariance matrix according to:

[0157]

number

[0158] Here, diag(x) indicates generating a diagonal matrix from a column vector x, and cov(a, b) indicates the covariance between a and b.

[0159] In some embodiments, the memory has instructions for calculating a generalized least squares problem by multiplying by the inverse of the calculated covariance matrix. In some embodiments, the memory has instructions for estimating the covariance of the data signal based on the fluorescence intensities across two or more photodetectors of the optical detection system. In some embodiments, the memory has instructions for estimating the covariance of the data signal based on the fluorescence intensities across each of the optical detection channels. In some embodiments, the memory has instructions for calculating a generalized least squares problem according to:

[0160]

number

[0161] In some cases, the memory includes instructions for estimating the covariance matrix a priori. In some cases, the memory includes instructions for applying a generalized least squares problem in real time (e.g., using an integrated circuit such as a field programmable gate array). In some cases, an a priori noise model is used to estimate the covariance of each event (e.g., calculating the covariance matrix of each event in real time). In some cases, the a priori noise model uses only the data collected for each particular event. In some cases, the covariance matrix includes estimates from the entire collected data set.

[0162] In some embodiments, the memory comprises instructions for determining the covariance of the data signal by estimating by iterative optimization using a covariance matrix that minimizes the variance of the unmixed data signal. Optionally, the memory comprises instructions for computing a generalized least squares problem by Cholesky decomposition of the covariance matrix. Optionally, the generalized least squares problem is solved by solving the covariance matrix Σ y =CC T to solve the triangular system and generate the transformed input for the ordinary least squares algorithm according to

[0163]

number

[0164] In some embodiments, the memory comprises instructions for finding a least-squares solution to a generalized least-squares problem. Optionally, the memory comprises instructions for finding a least-squares solution to a generalized least-squares problem by one or more of matrix decomposition, matrix factorization, QR decomposition, Cholesky decomposition, singular value decomposition, LDL decomposition, forward substitution, and backward substitution. Optionally, the memory comprises instructions for finding a least-squares solution to a generalized least-squares problem by solving the so-called normal equations by Cholesky or LDL decomposition, for example according to

[0165]

number

[0166] Optionally, the memory contains instructions for finding a least squares solution to a generalized least squares problem using Cholesky or LDL decomposition according to:

[0167]

number

[0168] In some embodiments, the memory comprises instructions for finding a least-squares solution to a generalized least-squares problem by matrix decomposition.

[0169]

number

[0170]

number

[0171] In some embodiments, the memory comprises instructions for finding a least-squares solution to a generalized least-squares problem by LDL decomposition. In certain embodiments, the memory comprises instructions for finding a least-squares solution to a generalized least-squares problem by forward substitution and backward substitution.

[0172] In certain embodiments, the subject system comprises a field programmable gate array, and the spectral unmixing algorithm is calculated in real time on a cell-by-cell basis in the field programmable gate array.

[0173] In some embodiments, the system includes a computer having a computer-readable storage medium having a computer program stored thereon, the computer program further comprising instructions, when loaded into the computer, for calculating the abundance of one or more fluorophores in the sample from the spectrally resolved light from each fluorophore. In some cases, the abundance of fluorophores associated with a targeted particle (e.g., chemically bound (i.e., covalently, ionically) or physically bound) is calculated from the spectrally resolved light from each fluorophore associated with the particle. For example, in one example, the relative abundance of each fluorophore associated with the targeted particle is calculated from the spectrally resolved light from each fluorophore. In another example, the absolute abundance of each fluorophore associated with the targeted particle is calculated from the spectrally resolved light from each fluorophore.

[0174] In certain embodiments, the system is configured to identify or classify particles based on the relative abundance of each fluorophore determined to be associated with the particle. In these embodiments, the subject systems may be configured to identify or classify particles by any convenient protocol, such as by comparing the relative or absolute abundance of each fluorophore associated with the particle to a control sample having known particles, or by performing spectroscopic or other assay analysis of a population of particles (e.g., cells) having calculated relative or absolute abundances of associated fluorophores.

[0175] The system of some embodiments may include a display and an operator input device. The operator input device may be, for example, a keyboard, a mouse, etc. The processing module includes a processor that can access a memory in which instructions for executing the steps of the subject method are stored. The processing module may include an operating system, a graphical user interface (GUI) controller, a system memory, a memory storage device, an input / output controller, a cache memory, a data backup unit, and many other devices. The processor may be a commercially available processor or one of other processors that are or become available. The processor executes an operating system that interfaces with firmware and hardware in a well-known manner to facilitate the processor's coordination and execution of the functions of various computer programs, which may be written in various programming languages, such as Java, Perl, C++, other high-level or low-level languages, and combinations thereof, as is known in the art. The operating system typically cooperates with the processor to coordinate and execute the functions of the other elements of the computer. The operating system also provides scheduling, input / output control, file and data management, memory management, and communication control and related services, all in accordance with known techniques. The processor may be any suitable analog or digital system. In some embodiments, the processor includes analog electronics that provide feedback control, such as negative feedback control.

[0176] The system memory may be any of a variety of known or future memory storage devices. Examples include any commonly available random access memory (RAM), magnetic media such as a resident hard disk or tape, optical media such as a read-write compact disk, flash memory devices, or other memory storage devices. The memory storage device may be any of a variety of known or future devices, including a compact disk drive, tape drive, removable hard disk drive, or diskette drive. These types of memory storage devices typically read from and / or write to a program storage medium (not shown), such as a compact disk, magnetic tape, removable hard disk, or magnetic disk. Any of these program storage media, or other program storage media now in use or that may be developed in the future, may be considered a computer program product. As will be appreciated, these program storage media typically store computer software programs and / or data. Computer software programs, also referred to as computer control logic, are typically stored in the system memory and / or on program storage devices used in conjunction with the memory storage devices.

[0177] In some embodiments, a computer program product is described that includes a computer-usable medium having stored thereon control logic (a computer software program including program code). The control logic, when executed by a processor, a computer, causes the processor to perform the functions described herein. In other embodiments, some functions are implemented primarily in hardware, for example, using hardware state machines. Implementation of hardware state machines to perform the functions described herein will be apparent to one skilled in the relevant art.

[0178] The memory may be any suitable device from which the processor can store and retrieve data, such as a magnetic, optical, or solid-state storage device (including a magnetic or optical disk, tape, RAM, or any other suitable device, fixed or portable). The processor may include a general-purpose digital microprocessor appropriately programmed from a computer-readable medium storing the necessary program code. The program may be provided to the processor remotely via a communications channel or pre-recorded on a computer program product, such as a memory, or on other portable or fixed computer-readable storage media using one of these devices connected to the memory. For example, a magnetic or optical disk may store the program and be read by a disk writer / reader. The system of the present invention further comprises a program, e.g., in the form of a computer program product, an algorithm for use in implementing the method as described above. The program of the present invention may be recorded on a computer-readable medium, e.g., any medium that can be directly read and accessed by a computer. Such media include, but are not limited to, magnetic storage media, such as magnetic disks, hard disk storage media, and magnetic tape; optical storage media, such as CD-ROMs; electrical storage media, such as RAM and ROM; portable flash drives; and hybrids of these categories, such as magnetic / optical storage media.

[0179] The processor may also access a communication channel to communicate with a user at a remote location, meaning that the user does not have direct contact with the system but instead relays input information to the input manager from an external device, such as a computer connected to a wide area network ("WAN"), telephone network, satellite network, or any other suitable communication channel, including a mobile phone (i.e., a smartphone).

[0180] In some embodiments, a system according to the present disclosure may be configured to include a communications interface. In some embodiments, the communications interface includes a receiver and / or a transmitter for communicating with a network and / or another device. The communications interface may be configured for wired or wireless communications, including, but not limited to, radio frequency (RF) communications such as radio frequency identification (RFID), ZigBee communications protocol, WiFi, infrared, wireless universal serial bus (USB), ultra-wideband (UWB), Bluetooth® communications protocol, and cellular communications such as code division multiple access (CDMA) or global system for mobile communications (GSM).

[0181] In one embodiment, the communication interface is configured to include one or more communication ports, e.g., physical ports or interfaces, such as a USB port, an RS-232 port, or any other suitable electrical connection port, to enable data communication between the subject system and other external devices, such as computer terminals (e.g., in a clinic or hospital environment) configured for similar complementary data communication.

[0182] In one embodiment, the communication interface is configured for infrared communication, Bluetooth® communication, or any other suitable wireless communication protocol, allowing the subject system to communicate with other devices, such as computer terminals and / or networks, communication-enabled mobile phones, personal digital assistants, or any other communication devices that a user may use in conjunction with the device.

[0183] In one embodiment, the communication interface is configured to provide a connection for data transfer utilizing the Internet Protocol (IP) via a cellular network, short message service (SMS), a wireless connection to a personal computer (PC) on a local area network (LAN) connected to the Internet, or a WiFi connection to the Internet at a WiFi hotspot.

[0184] In one embodiment, the subject system is configured to communicate wirelessly with a server device via a communications interface using common standards such as 802.11 or Bluetooth® RF protocols or the IrDA infrared protocol. The server device may be another portable device, such as a smartphone, personal digital assistant (PDA), or notebook computer; or a larger device, such as a desktop computer, appliance, etc. In some embodiments, the server device has a display, such as a liquid crystal display (LCD), and input devices, such as buttons, a keyboard, a mouse, or a touchscreen.

[0185] In some embodiments, the communications interface is configured to automatically or semi-automatically communicate data stored in the subject system, e.g., any data storage unit, with a network or server device using one or more of the communications protocols and / or mechanisms described above.

[0186] The output controller may include a controller for any of a variety of known display devices for presenting information to a user, whether human or machine, local or remote. When one of the display devices provides visual information, this information may typically be logically and / or physically organized as an array of pixels. The graphical user interface (GUI) controller may include any of a variety of known or future software programs for providing a graphical input / output interface between the system and the user and for processing user input. The functional elements of the computer may communicate with each other via a system bus. Some of these communications may be achieved using a network or other type of remote communication in alternative embodiments. The output manager may also provide information generated by the processing module to a user at a remote location, for example, via the Internet, telephone, or satellite network, according to known techniques. Presentation of data by the output manager may be performed according to various known techniques. In some examples, the data may include SQL, HTML, or XML documents, emails or other files, or other forms of data. The data may include Internet URL addresses so that the user can obtain additional SQL, HTML, XML, or other documents or data from remote sources. The platform or platforms present in the subject system are typically a class of computers commonly referred to as servers, but may be any type of computer platform now known or later developed. However, the platforms may also be mainframe computers, workstations, or other computer types. The platforms may be networked or not, and may be connected via any type of cabling, now known or later, or other communication systems, including wireless systems. The platforms may be co-located or physically separated.Various operating systems may be used on any of the computer platforms, depending in some cases on the type and / or configuration of the computer platform selected. Suitable operating systems include Windows 10, Windows NT, Windows XP, Windows 7, Windows 8, iOS, Sun Solaris, Linux, OS / 400, Compaq Tru64 Unix, SGI IRIX, Siemens Reliant Unix, Ubuntu, Zorin OS, and the like.

[0187] In certain embodiments, the subject systems include one or more optical conditioning components for conditioning light, e.g., light irradiated onto a sample (e.g., from a laser) or light collected from a sample (e.g., scattered light, fluorescent light). For example, the optical conditioning may expand the size of the light, focus the light, or collimate the light. In some cases, the optical conditioning is a magnification protocol that expands the size of the light (e.g., beam spot), e.g., by 5% or more, e.g., by 10% or more, e.g., by 25% or more, e.g., by 50% or more, e.g., by 75% or more. In other embodiments, the optical conditioning involves focusing the light to reduce the size of the light by 5% or more, e.g., by 10% or more, e.g., by 25% or more, e.g., by 50% or more, e.g., by reducing the size of the beam spot by 75% or more. In certain embodiments, the optical conditioning involves collimating the light. The term "collimate" is used in its conventional sense to refer to optically adjusting the collinearity of light propagation or reducing divergence of light from a common axis of propagation. In some cases, collimation involves narrowing the spatial cross section of the light beam (eg, reducing the beam profile of a laser).

[0188] In some embodiments, the optical adjustment element is a focusing lens having a magnification of 0.1 to 0.95, e.g., a magnification of 0.2 to 0.9, e.g., a magnification of 0.3 to 0.85, e.g., a magnification of 0.35 to 0.8, e.g., a magnification of 0.5 to 0.75, e.g., a magnification of 0.55 to 0.7, e.g., a magnification of 0.6. For example, the focusing lens may be a dichromatic reducing lens with a magnification of about 0.6. The focal length of the focusing lens may vary within a range of 5 mm to 20 mm, e.g., 6 mm to 19 mm, e.g., 7 mm to 18 mm, e.g., 8 mm to 17 mm, e.g., 9 mm to 16 mm, e.g., 10 mm to 15 mm. In one embodiment, the focusing lens has a focal length of about 13 mm.

[0189] In another embodiment, the optical adjustment component is a collimator. The collimator may be any convenient collimation protocol, such as one or more mirrors, curved lenses, or a combination thereof. For example, the collimator may be a single collimating lens in some cases. In other cases, the collimator is a collimating mirror. In still other cases, the collimator has two lenses. In still other cases, the collimator has a mirror and a lens. When the collimator has one or more lenses, the focal length of the collimating lens may vary within a range of 5 mm to 40 mm, such as 6 mm to 37.5 mm, for example 7 mm to 35 mm, for example 8 mm to 32.5 mm, for example 9 mm to 30 mm, for example 10 mm to 27.5 mm, for example 12.5 mm to 25 mm, for example 15 mm to 20 mm.

[0190] In some embodiments, the subject systems include a flow cell nozzle having a nozzle orifice configured to direct a flow stream through the flow cell nozzle. The subject flow cell nozzles have an orifice that delivers a fluid sample to a sample interrogation region, and in some embodiments, the flow cell nozzle has a proximal cylindrical portion defining a longitudinal axis and a distal frusto-conical portion terminating in a flat surface having a nozzle orifice transverse to the longitudinal axis. The length of the proximal cylindrical portion (measured along the longitudinal axis) can vary between 1 mm and 15 mm, e.g., between 1.5 mm and 12.5 mm, e.g., between 2 mm and 10 mm, e.g., between 3 mm and 9 mm, e.g., between 4 mm and 8 mm. The length of the distal frusto-conical portion (measured along the longitudinal axis) can also vary between 1 mm and 10 mm, e.g., between 2 mm and 9 mm, e.g., between 3 mm and 8 mm, e.g., between 4 mm and 7 mm. The diameter of the flow cell nozzle chamber may in some embodiments vary within the range of 1 mm to 10 mm, such as 2 mm to 9 mm, such as 3 mm to 8 mm, such as 4 mm to 7 mm.

[0191] In some cases, the nozzle chamber does not have a cylindrical portion, and the entire flow cell nozzle chamber is frusto-conical in shape. In these embodiments, the length of the frusto-conical nozzle chamber (measured along a longitudinal axis transverse to the nozzle orifice) may be in the range of 1 mm to 15 mm, such as 1.5 mm to 12.5 mm, for example 2 mm to 10 mm, for example 3 mm to 9 mm, for example 4 mm to 8 mm. The diameter of the proximal portion of the frusto-conical nozzle chamber may be in the range of 1 mm to 10 mm, for example 2 mm to 9 mm, for example 3 mm to 8 mm, for example 4 mm to 7 mm.

[0192] In embodiments, the sample flow stream is emitted from an orifice at the distal end of the flow cell nozzle. Depending on the desired characteristics of the flow stream, the orifice of the flow cell nozzle may have any suitable shape, with cross-sectional shapes of interest including, but not limited to, rectilinear cross-sectional shapes, e.g., square, rectangular, trapezoidal, triangular, hexagonal, etc.; curved cross-sectional shapes, e.g., circular, oval, etc.; and irregular shapes, e.g., a parabolic base joined to a planar top. In certain embodiments, flow cell nozzles of interest have circular orifices. The size of the nozzle orifice may vary in some embodiments from 1 μm to 20,000 μm, such as from 2 μm to 17,500 μm, for example, from 5 μm to 15,000 μm, for example, from 10 μm to 12,500 μm, for example, from 15 μm to 10,000 μm, for example, from 25 μm to 7,500 μm, for example, from 50 μm to 5,000 μm, for example, from 75 μm to 1,000 μm, for example, from 100 μm to 750 μm, for example, from 150 μm to 500 μm. In one embodiment, the nozzle orifice is 100 μm.

[0193] In some embodiments, the flow cell nozzle has a sample injection port configured to deliver a sample to the flow cell nozzle. In embodiments, the sample injection system is configured to deliver a suitable flow of sample to the flow cell nozzle chamber. Depending on the desired characteristics of the flow stream, the flow rate of the sample delivered by the sample injection port to the flow cell nozzle chamber may be 1 μL / sec or more, such as 2 μL / sec or more, for example 3 μL / sec or more, for example 5 μL / sec or more, for example 10 μL / sec or more, for example 15 μL / sec or more, for example 25 μL / sec or more, for example 50 μL / sec or more, for example 100 μL / sec or more, for example 150 μL / sec or more, for example 200 μL / sec or more, for example 250 μL / sec or more, for example 300 μL / sec or more, for example 350 μL / sec or more, for example 400 μL / sec or more, for example 450 μL / sec or more, for example 500 μL / sec or more. For example, the flow rate of the sample may be within the range of 1 μL / sec to about 500 μL / sec, for example, 2 μL / sec to about 450 μL / sec, for example, 3 μL / sec to about 400 μL / sec, for example, 4 μL / sec to about 350 μL / sec, for example, 5 μL / sec to about 300 μL / sec, for example, 6 μL / sec to about 250 μL / sec, for example, 7 μL / sec to about 200 μL / sec, for example, 8 μL / sec to about 150 μL / sec, for example, 9 μL / sec to about 125 μL / sec, for example, 10 μL / sec to about 100 μL / sec.

[0194] The sample injection port may be an orifice in the wall of the nozzle chamber, or may be a tube located at the proximal end of the nozzle chamber. When the sample injection port is an orifice in the wall of the nozzle chamber, the orifice may have any suitable shape. Cross-sectional shapes of interest include, but are not limited to, rectilinear cross-sectional shapes such as square, rectangular, trapezoidal, triangular, and hexagonal; curved cross-sectional shapes such as circular and oval; and irregular shapes such as a parabolic bottom joined to a flat top. In one embodiment, the sample injection port has a circular orifice. The size of the orifice of the sample injection port may vary depending on the shape, and in some cases may have an opening in the range of 0.1 mm to 5.0 mm, for example, 0.2 to 3.0 mm, for example, 0.5 mm to 2.5 mm, for example, 0.75 mm to 2.25 mm, for example, 1 mm to 2 mm, for example, 1.25 mm to 1.75 mm, for example, a 1.5 mm opening.

[0195] In some cases, the sample injection port is a tube located at the proximal end of the flow cell nozzle chamber. For example, the sample injection port may be a tube positioned so that the orifice of the sample injection port is aligned with the orifice of the flow cell nozzle. When the sample injection port is a tube positioned so that the orifice of the sample injection port is aligned with the orifice of the flow cell nozzle, the cross-sectional shape of the sample injection tube may have any suitable shape. Cross-sectional shapes of interest include, but are not limited to, rectilinear cross-sectional shapes, such as square, rectangular, trapezoidal, triangular, and hexagonal; curved cross-sectional shapes, such as circular and oval; and irregular shapes, such as a parabolic bottom joined to a flat top. The orifice of the tube may vary depending on the shape and may in some cases have an opening in the range of 0.1 mm to 5.0 mm, e.g., 0.2 to 3.0 mm, e.g., 0.5 mm to 2.5 mm, e.g., 0.75 mm to 2.25 mm, e.g., 1 mm to 2 mm, e.g., 1.25 mm to 1.75 mm, e.g., 1.5 mm. The shape of the tip of the sample injection port may be the same as or different from the cross-sectional shape of the sample injection tube. For example, the orifice of the sample injection port may have a beveled tip with a bevel angle within a range of 1° to 10°, for example, 2° to 9°, for example, 3° to 8°, for example, 4° to 7°, for example, a bevel angle of 5°.

[0196] In some embodiments, the flow cell nozzle further includes a sheath fluid injection port configured to supply sheath fluid to the flow cell nozzle. In embodiments, the sheath fluid injection system is configured to supply a flow of sheath fluid, e.g., along with the sample, to the flow cell nozzle chamber to generate a laminated flow stream of sheath fluid surrounding the sample flow stream. Depending on the desired characteristics of the flow stream, the flow rate of the sheath fluid delivered to the flow cell nozzle chamber may be 25 μL / sec or more, e.g., 50 μL / sec or more, e.g., 75 μL / sec or more, e.g., 100 μL / sec or more, e.g., 250 μL / sec or more, e.g., 500 μL / sec or more, e.g., 750 μL / sec or more, e.g., 1000 μL / sec or more, e.g., 2500 μL / sec or more. For example, the flow rate of the sheath fluid may be within a range of 1 μL / sec to about 500 μL / sec, for example, 2 μL / sec to about 450 μL / sec, for example, 3 μL / sec to about 400 μL / sec, for example, 4 μL / sec to about 350 μL / sec, for example, 5 μL / sec to about 300 μL / sec, for example, 6 μL / sec to about 250 μL / sec, for example, 7 μL / sec to about 200 μL / sec, for example, 8 μL / sec to about 150 μL / sec, for example, 9 μL / sec to about 125 μL / sec, or for example, 10 μL / sec to about 100 μL / sec.

[0197] In some embodiments, the sheath fluid injection port is an orifice in the wall of the nozzle chamber. The orifice of the sheath fluid injection port may have any suitable shape, and cross-sectional shapes of interest include, but are not limited to, rectilinear cross-sectional shapes, such as square, rectangular, trapezoidal, triangular, and hexagonal, curved cross-sectional shapes, such as circular and oval, and irregular shapes, such as a parabolic bottom joined to a flat top. The size of the orifice of the sample injection port may vary depending on the shape, and in some cases may have an opening in the range of 0.1 mm to 5.0 mm, e.g., 0.2 to 3.0 mm, e.g., 0.5 mm to 2.5 mm, e.g., 0.75 mm to 2.25 mm, e.g., 1 mm to 2 mm, e.g., 1.25 mm to 1.75 mm, e.g., a 1.5 mm opening.

[0198] The subject systems may optionally include a sample interrogation region in fluid communication with the orifice of the flow cell nozzle. In these cases, a sample flow stream may be emitted from an orifice at the distal end of the flow cell nozzle, and particles in the flow stream may be illuminated by a light source in the sample interrogation region. The size of the sample interrogation region may vary depending on characteristics of the flow cell nozzle, such as the size of the nozzle orifice and the size of the sample injection port. In embodiments, the sample interrogation region may have a width of 0.01 mm or more, e.g., 0.05 mm or more, e.g., 0.1 mm or more, e.g., 0.5 mm or more, e.g., 1 mm or more, e.g., 2 mm or more, e.g., 3 mm or more, e.g., 5 mm or more, e.g., 10 mm or more. The length of the sample interrogation area may also vary in some cases within the range of 0.01 mm or more, such as 0.1 mm or more, for example 0.5 mm or more, such as 1 mm or more, for example 1.5 mm or more, such as 2 mm or more, for example 3 mm or more, such as 5 mm or more, for example 10 mm or more, such as 15 mm or more, for example 20 mm or more, such as 25 mm or more, for example 50 mm or more.

[0199] The sample interrogation region may be configured to facilitate illumination of a planar cross-section of the emitting flowstream, or may be configured to facilitate illumination of a diffuse field of a predetermined length (e.g., using a diffuse laser or lamp). In some embodiments, the sample interrogation region has a transparent window that facilitates illumination of a predetermined length of the emitting flowstream, e.g., 1 mm or more, e.g., 2 mm or more, e.g., 3 mm or more, e.g., 4 mm or more, e.g., 5 mm or more, e.g., 10 mm or more. Depending on the light source used to illuminate the emitting flowstream (as described below), the sample interrogation region may be configured to pass light in the range of 100 nm to 1500 nm, e.g., 150 nm to 1400 nm, e.g., 200 nm to 1300 nm, e.g., 250 nm to 1200 nm, e.g., 300 nm to 1100 nm, e.g., 350 nm to 1000 nm, e.g., 400 nm to 900 nm, e.g., 500 nm to 800 nm. As such, the sample interrogation region may be formed of any transparent material that passes the desired wavelength range, including but not limited to optical glass, borosilicate glass, Pyrex glass, ultraviolet quartz, infrared quartz, sapphire, and plastics, particularly polymeric plastic materials such as polycarbonate, polyvinyl chloride (PVC), polyurethane, polyether, polyamide, polyimide, or copolymers of these thermoplastics, e.g., PETG (glycol-modified polyethylene terephthalate), polyester. Polyesters of interest include poly(alkylene terephthalates), such as poly(ethylene terephthalate) (PET), bottle-grade PET (a copolymer made based on monoethylene glycol, terephthalic acid, and other comonomers, such as isophthalic acid, cyclohexene dimethanol, etc.), poly(butylene terephthalate) (PBT), poly(hexamethylene terephthalate); poly(alkylene adipates), such as poly(ethylene adipate), poly(1,4-butylene adipate), and poly(hexamethylene adipate); poly(alkylene suberates), such as poly(ethylene suberate); poly(alkylene sebacates), such as poly(ethylene sebacate);Poly(ε-caprolactone) and poly(β-propiolactone); poly(alkylene isophthalates), such as poly(ethylene isophthalate); poly(alkylene 2,6-naphthalene-dicarboxylates), such as poly(ethylene 2,6-naphthalene-dicarboxylate); poly(alkylenesulfonyl-4,4'-dibenzoates), such as poly(ethylenesulfonyl-4,4'-dibenzoate); poly(p-phenylene alkylene dicarboxylates), such as poly(p-phenylene ethylene dicarboxylate); poly(trans-1,4-cyclohexanediyl alkylene dicarboxylates), such as poly(trans-1,4-cyclohexanediyl ethylene dicarboxylate); poly(1,4-cyclohexane-dimethylene alkylene dicarboxylates), such as poly(1,4-cyclohexane-dimethylene ethylene dicarboxylate); poly([2.2.2]-bicyclooctane-1,4- dimethylene alkylene dicarboxylates), such as poly([2.2.2]-bicyclooctane-1,4-dimethyleneethylene dicarboxylate); lactic acid polymers and copolymers, such as (S)-polylactide, (R,S)-polylactide, poly(tetramethylglycolide), and poly(lactide-co-glycolide); and polycarbonates of bisphenol A, 3,3'-dimethylbisphenol A, 3,3',5,5'-tetrachlorobisphenol A, and 3,3',5,5'-tetramethylbisphenol A; polyamides, such as poly(p-phenylene terephthalamide); polyesters, such as polyethylene terephthalate, e.g., Mylar™ polyethylene terephthalate; and the like. In some embodiments, the subject systems include a cuvette disposed in the sample interrogation region. In an embodiment, the cuvette may transmit light in the range of 100 nm to 1500 nm, such as 150 nm to 1400 nm, for example 200 nm to 1300 nm, for example 250 nm to 1200 nm, for example 300 nm to 1100 nm, for example 350 nm to 1000 nm, for example 400 nm to 900 nm, for example 500 nm to 800 nm;

[0200] In certain embodiments, a light detection system having a plurality of light detectors as described above is part of or located in a particle analyzer, such as a particle sorter, hi certain embodiments, the subject system is a flow cytometry system that includes a photodiode and amplifier components as part of the light detection system for detecting light emitted by a sample in a flow stream. Suitable flow cytometry systems include those described in Ormerod (ed.), Flow Cytometry: A Practical Approach, Oxford Univ. Press (1997); Jaroszeski et al. (eds.), Flow Cytometry Protocols, Methods in Molecular Biology No. 91, Humana Press (1997); Practical Flow Cytometry, 3rd ed., Wiley-Liss (1995); Virgo, et al. (2012) Ann Clin Biochem. Jan;49(pt 1):17-28; Linden, et. al., Semin Thromb Hemost. 2004 Oct;30(5):502-11; Alison, et al. J Pathol, 2010 Dec;222(4):335-344; and Herbig, et al. (2007) Crit Rev Ther Drug Carrier Syst., the disclosures of which are incorporated herein by reference. 24(3):203-255.In some cases, flow cytometry systems of interest include the BD Biosciences FACSCanto™ flow cytometer, BD Biosciences FACSCanto™ II flow cytometer, BD Accuri™ flow cytometer, BD Accuri™ C6 Plus flow cytometer, BD Biosciences FACSCelesta™ flow cytometer, BD Biosciences FACSLyric™ flow cytometer, BD Biosciences FACSVerse™ flow cytometer, BD Biosciences FACSymphony™ flow cytometer, BD Biosciences LSRFortessa™ flow cytometer, BD Biosciences LSRFortessa™ X-20 flow cytometer, BD Biosciences FACSPresto™ flow cytometer, BD Biosciences FACSVia™ flow cytometer, and BD Biosciences FACSCalibur™ cell sorter, BD Biosciences FACSCount™ cell sorter, BD Biosciences FACSLyric™ cell sorter ...Verse™ flow cytometer, BD Biosciences FACSSymphony™ flow cytometer, BD Biosciences LSRFortessa™ flow cytometer, BD Biosciences LSRFor These include the BD Biosciences Via™ cell sorter, BD Biosciences Influx™ cell sorter, BD Biosciences Jazz™ cell sorter, BD Biosciences Aria™ cell sorter, BD Biosciences FACSAria™ II cell sorter, BD Biosciences FACSAria™ III cell sorter, BD Biosciences FACSAria™ Fusion cell sorter, BD Biosciences FACSMelody™ cell sorter, and BD Biosciences FACSymphony™ S6 cell sorter.

[0201] In some embodiments, the subject system may be configured with a fusion technology similar to that disclosed in U.S. Pat. Nos. 10,663,476, 10,620,111, 10,613,017, 10,605,713, 10,585,031, 10,578,542, 10,578,469, 10,481,074, 10,302,545, 10,145,793, 10,113,967, 10,006,852, 9,952,076, 9,933,341, 9,726,527, 9,453,789, 9,200,334, 9,097,640, 9,099,909, 9,100,100,110,120,130,140,150,160,170,172,180,190,192,194,195,196,197,198,19 ... Nos. 5494, 9092034, 8975595, 8753573, 8233146, 8140300, 7544326, 7201875, 7129505, 6821740, 6813017, 6809804, 6372506, 5700692, 5643796, 5627040, 5620842, 5602039, 4987086, and 4498766.

[0202] In some embodiments, the subject system is a particle sorting system configured to sort particles using an enclosed particle sorting module, such as described in U.S. Patent Application Publication No. 2017 / 0299493, the disclosure of which is incorporated herein by reference. In certain embodiments, particles (e.g., cells) of a sample are sorted using a sorting determination module having multiple sorting determination units, such as described in U.S. Patent Application Publication No. 2020 / 0256781, the disclosure of which is incorporated herein by reference. In some embodiments, the subject system includes a particle sorting module with deflection plates, such as described in U.S. Patent Application Publication No. 2017 / 0299493, filed March 28, 2017, the disclosure of which is incorporated herein by reference.

[0203] In some cases, the flow cytometry system of the present invention may be implemented using the techniques described in Diebold, et al. Nature Photonics Vol. 7(10); 806-810 (2013) and U.S. Patent Nos. 9,423,353, 9,784,661, 9,983,132, 10,006,852, 10,078,045, 10,036,699, 10,222,316, 10,288,546, 10,324,019, 10,408,758, 10,451,538, 10,620,111, U.S. Patent Application Publication No. 200900222, and the like. and US Patent Publication Nos. 2017 / 0133857, 2017 / 0328826, 2017 / 0350803, 2018 / 0275042, 2019 / 0376895, and 2019 / 0376894, the disclosures of which are incorporated herein by reference, for imaging particles in a flowstream by Fluorescence Imaging Using Radio Frequency Tag Emission (FIRE).

[0204] In certain embodiments, the subject systems are configured to sort one or more particles (e.g., cells) of a sample that are identified based on the estimated abundance of fluorophores associated with the particles, as described above. The term "sorting" is used herein in its conventional sense to refer to separating components of a sample (e.g., cells, non-cellular particles, such as biopolymers, etc.) and, optionally, delivering the separated components to one or more sample collection vessels. For example, the subject systems may be configured to sort a sample having two or more components, e.g., three or more components, e.g., four or more components, e.g., five or more components, e.g., ten or more components, e.g., fifteen or more components, e.g., twenty-five or more components. One or more of the components of the sample, e.g., two or more sample components, e.g., three or more sample components, e.g., four or more sample components, e.g., five or more sample components, e.g., ten or more sample components, may be separated from the sample and delivered to a sample collection vessel, e.g., fifteen or more sample components may be separated from the sample and delivered to a sample collection vessel.

[0205] In some embodiments, particle sorting systems of interest are configured to sort particles using an enclosed particle sorting module, such as described in U.S. Patent Application Publication No. 2017 / 0299493, filed March 28, 2017, the disclosure of which is incorporated herein by reference. In certain embodiments, particles (e.g., cells) of a sample are sorted using a sorting determination module having multiple sorting determination units, such as described in U.S. Patent Application Publication No. 2020 / 0256781, the disclosure of which is incorporated herein by reference. In some embodiments, the subject systems include a particle sorting module with deflection plates, such as described in U.S. Patent Application Publication No. 2017 / 0299493, filed March 28, 2017, the disclosure of which is incorporated herein by reference.

[0206] In one embodiment, the system is a fluorescence imaging system using a radio frequency tag emission imaging particle sorter, as shown in FIG. 3A. The particle sorter 300 includes a light illumination unit 300a including a light source 301 (e.g., a 488 nm laser) that generates an output beam of light 301a, which is split into beams 302a and 302b by a beam splitter 302. The light beam 302a propagates through an acousto-optic device (e.g., an acousto-optic deflector (AOD)) 303 to generate an output beam 303a having one or more angularly deflected beams of light. In some cases, the output beam 303a from the acousto-optic device 303 includes a local oscillator beam and multiple radio frequency comb beams. The light beam 302b propagates through an acousto-optic device (e.g., an acousto-optic deflector (AOD)) 304 to generate an output beam 304a having one or more angularly deflected beams of light. In some cases, output beam 304a generated from acousto-optic device 304 includes a local oscillator beam and multiple high-frequency comb beams. Output beams 303a and 304a generated by acousto-optic device 303 and acousto-optic device 304, respectively, are combined in beam combiner 305 to generate output beam 305a, which is transmitted through optics 306 (e.g., an objective lens) to illuminate particles in flow cell 307. In some embodiments, acousto-optic device 303 (AOD) splits a single laser beam into an array of beamlets, each with a different optical frequency and angle. A second AOD 304 adjusts the optical frequency of a reference beam, which is then superimposed with the array of beamlets in beam combiner 305. In some embodiments, the illumination system having the light source and the acousto-optical device may further include an illumination system described in Schraivogel, et al. (“High-speed fluorescence image-enabled cell sorting” Science (2022), 375 (6578): 315-320) and U.S. Patent Application Publication No. 2021 / 0404943, the disclosures of which are incorporated herein by reference.

[0207] Output beam 305a illuminates sample particles 308 propagating through flow cell 307 (e.g., with sheath fluid 309) at illumination region 310. As shown in illumination region 310, multiple beams (e.g., angularly polarized, high-frequency shifted beams of light shown as dots across illumination region 310) overlap with a reference local oscillator beam (shown as a cross-hatched line across illumination region 310). The overlapping beams exhibit beat behavior due to their different optical frequencies, with each beamlet emitting at a different frequency f 1-n transmits sinusoidal modulation.

[0208] Light from the illuminated sample is transmitted to a light detection system 300b having multiple photodetectors. The light detection system 300b includes a forward scattered light photodetector 311 for generating a forward scattered light image 311a and a side scattered light photodetector 312 for generating a side scattered light image 312a. The light detection system 300b further includes a bright field photodetector 313 for generating a light loss image 313a. In some embodiments, the forward scattered light photodetector 311 and the side scattered light photodetector 312 are photodiodes (e.g., avalanche photodiodes (APDs)). In some cases, the bright field photodetector 313 is a photomultiplier tube (PMT). Fluorescence from the illuminated sample is further detected by fluorescence photodetectors 314-317. In some cases, the photodetectors 314-317 are photomultiplier tubes. Light from the illuminated sample is directed via beam splitter 320 to side-scattered light detection channel 312 and fluorescence detection channels 314-317. Light detection system 300b includes bandpass optics 321-324 (e.g., dichroic mirrors) for transmitting light of predetermined wavelengths to photodetectors 314-317, respectively. In some cases, optic 321 is a 534 nm / 40 nm bandpass. In some cases, optic 322 is a 586 nm / 42 nm bandpass. In some cases, optic 323 is a 700 nm / 54 nm bandpass. In some cases, optic 324 is a 783 nm / 56 nm bandpass. The first number indicates the center of the spectral band. The second number indicates the range of the spectral band. Thus, a 510 / 20 filter extends 10 nm on either side of the center of the spectral band, from 500 nm to 520 nm.

[0209] Data signals generated in response to light detected in forward-scattered light detection channel 311, side-scattered light detection channel 312, bright-field light detection channel 313, and fluorescence detection channels 314-317 are processed by real-time digital processing by processors 350 and 351. Images 311a-317a can be generated in each light detection channel based on the data signals generated by processors 350 and 351. Image-based sorting is performed in response to a sorting signal generated by sorting trigger 352. Sorting unit 300c includes deflection plates 331 for deflecting particles into a sample container 332 or a waste stream 333. In some cases, sorting unit 300c is configured to sort particles using a sealed particle sorting module, such as that described in U.S. Patent Application Publication No. 2017 / 0299493, filed March 28, 2017, the disclosure of which is incorporated herein by reference. In one embodiment, the sorting section 300c includes a sorting determination module having multiple sorting determination units, such as those described in U.S. Patent Application Publication No. 2020 / 0256781, the disclosure of which is incorporated herein by reference.

[0210] FIG. 3B illustrates image-enabled particle sorting data processing according to one embodiment. In some cases, the image-enabled particle sorting data processing is a low-latency data processing pipeline. Each photodetector generates high-frequency modulated pulses that encode an image (waveform). Fourier analysis is performed to reconstruct the image from the modulated pulses. The image processing pipeline generates a set of image features (image analysis) and combines the set of image features with features obtained from the pulse processing pipeline (event packets). Real-time sorting electronics then classify particles based on the image features and make sorting decisions that are used to selectively charge droplets.

[0211] In some embodiments, the system is a particle analyzer, and particle analysis system 401 (FIG. 4A) can be used to analyze and characterize particles with or without physical sorting of the particles into a collection vessel. FIG. 4A is a functional block diagram of a particle analysis system for computation-based sample analysis and particle characterization. In some embodiments, particle analysis system 401 is a flow system. The particle analysis system 401 shown in FIG. 4A can be configured to perform, for example, the methods described herein in whole or in part. Particle analysis system 401 includes a fluidic system 402. Fluidic system 402 can include or be coupled to a sample tube 405 and a moving fluid column within the sample tube through which particles 403 (e.g., cells) of the sample move along a common sample path 409.

[0212] The particle analysis system 401 includes a detection system 404 configured to collect a signal from each particle as it passes through one or more detection stations along a common sample path. A detection station 408 generally refers to a monitoring region 407 of the common sample path. Detection, in some embodiments, may involve detecting light or one or more other properties of the particle 403 as it passes through the monitoring region 407. In FIG. 4A , one detection station 408 is shown with one monitoring region 407. In some embodiments of the particle analysis system 401, multiple detection stations may be provided. Additionally, some detection stations may monitor more than one region.

[0213] Each signal is assigned a signal value, generating a data point for each particle. As described above, this data may be referred to as event data. The data points may be multidimensional data points that include values for each property measured for the particle. The detection system 404 is configured to collect a series of such data points over a first time interval.

[0214] The particle analysis system 401 may further include a control system 406. The control system 406 may include one or more processors, amplitude control circuitry, and / or frequency control circuitry. The illustrated control system may be operatively associated with the fluid system 402. The control system may be configured to generate a calculated signal frequency for at least a portion of the first time interval based on the Poisson distribution and the number of data points collected by the detection system 404 during the first time interval. The control system 406 may further be configured to generate an experimental signal frequency based on the number of data points in the portion of the first time interval. The control system 406 may further compare the experimental signal frequency to the calculated signal frequency or a predetermined signal frequency.

[0215] 4B shows a system 400 for flow cytometry according to an exemplary embodiment of the invention. System 400 includes a flow cytometer 410, a controller / processor 490, and a memory 495. Flow cytometer 410 includes one or more excitation lasers 415a-415c, a focusing lens 420, a flow chamber 425, a forward scatter detector 430, a side scatter detector 435, a fluorescence collection lens 440, one or more beam splitters 445a-445g, one or more bandpass filters 450a-450e, one or more longpass (LP) filters 455a-455b, and one or more fluorescence detectors 460a-460f.

[0216] Pump lasers 415a-415c emit light in the form of laser beams. The wavelengths of the laser beams emitted from pump lasers 415a-415c are 488 nm, 633 nm, and 325 nm, respectively, in the exemplary system of FIG. 4B. The laser beams are first directed through one or more of beam splitters 445a and 445b. Beam splitter 445a transmits 488 nm light and reflects 633 nm light. Beam splitter 445b transmits UV light (light having a wavelength in the range of 10-400 nm) and reflects 488 nm and 633 nm light.

[0217] The laser beam is then directed to a focusing lens 420, which focuses the laser beam onto the portion of the fluid stream where the sample particles reside in a flow chamber 425. The flow chamber is the part of the fluid system that directs particles in the stream, typically one at a time, into the focused laser beam for investigation. The flow chamber can comprise a flow cell in a benchtop cytometer or a nozzle tip in a stream-in air cytometer.

[0218] Light from one or more laser beams interacts with particles in the sample by diffraction, refraction, reflection, scattering, and absorption, and is re-emitted at a variety of different wavelengths depending on the particle's characteristics, such as its size, internal structure, and the presence of one or more fluorescent molecules attached to or naturally present on or within the particle. The fluorescent radiation, as well as the diffracted, refracted, reflected, and scattered light, may be sent through one or more of beam splitters 445a-445g, bandpass filters 450a-450e, longpass filters 455a-455b, and fluorescence collection lens 440 to one or more of forward scatter detector 430, side scatter detector 435, and one or more fluorescence detectors 460a-460f.

[0219] The fluorescence collection lens 440 collects light emitted from particle-laser beam interactions and directs it toward one or more beam splitters and filters. Bandpass filters, such as bandpass filters 450a-450e, allow a narrow range of wavelengths to pass through the bandpass filter. For example, bandpass filter 450a is a 510 / 20 filter. The first number represents the center of the spectral band. The second number represents the extent of the spectral band. Thus, a 510 / 20 filter extends 10 nm on either side of the center of the spectral band, from 500 nm to 520 nm. Shortpass filters transmit light with wavelengths below a specified wavelength. Longpass filters, such as longpass filters 455a-455b, transmit light with wavelengths above a specified wavelength. For example, longpass filter 455a, a 670 nm longpass filter, transmits light above 670 nm. Filters are often selected to optimize the specificity of the detector for a particular fluorochrome. The filter may be configured so that the spectral band of light transmitted to the detector approximates the emission peak of the fluorescent dye.

[0220] Beam splitters direct light of different wavelengths in different directions. Beam splitters can be characterized by filter properties such as short-pass and long-pass. For example, beam splitter 445g is a 620SP beam splitter, meaning that beam splitter 445g transmits light with wavelengths of 620 nm or less and reflects light with wavelengths longer than 620 nm in different directions. In one embodiment, beam splitters 445a-445g can include optical mirrors such as dichroic mirrors.

[0221] The forward scatter detector 430 is positioned slightly off-axis from the direct beam passing through the flow cell and is configured to detect diffracted light, or excitation light traveling mostly forward through or around the particle. The intensity of light detected by the forward scatter detector depends on the overall size of the particle. The forward scatter detector may include a photodiode. The side scatter detector 435 is configured to detect refracted and reflected light from the particle's surface and internal structure, which tends to increase as the particle's structure becomes more complex. Fluorescent emission from fluorescent molecules bound to the particle may be detected by one or more fluorescence detectors 460a-460f. The side scatter detector 435 and the fluorescence detector may include photomultiplier tubes. The signals detected by the forward scatter detector 430, side scatter detector 435, and fluorescence detector may be converted to electronic signals (voltage) by the detectors. This data may provide information about the sample.

[0222] Those skilled in the art will recognize that flow cytometers according to embodiments of the present invention are not limited to the flow cytometer shown in Figure 4B, but may include any flow cytometer known in the art. For example, a flow cytometer may have any number of lasers, beam splitters, filters, and detectors at various wavelengths and in a variety of different configurations.

[0223] During operation, the operation of the flow cytometer is controlled by the controller / processor 490, and measurement data from the detectors may be stored in memory 495 and processed by the controller / processor 490. Although not explicitly shown, the controller / processor 490 is coupled to the detectors to receive output signals from the detectors, and may further be coupled to the electrical and electromechanical components of the flow cytometer 410 to control lasers, fluid flow parameters, etc. An input / output (I / O) functionality 497 may also be provided in the system. The memory 495, controller / processor 490, and I / O functionality 497 may be provided entirely as an integral part of the flow cytometer 410. In such an embodiment, a display may also form part of the I / O functionality 497 to present experimental data to a user of the flow cytometer 410. Alternatively, some or all of the memory 495 and the controller / processor 490 and I / O functionality may be part of one or more external devices, such as a general-purpose computer. In some embodiments, some or all of memory 495 and controller / processor 490 may be in wireless or wired communication with flow cytometer 410. Controller / processor 490 in conjunction with memory 495 and I / O functionality 497 may be configured to perform a variety of functions related to the preparation and analysis of flow cytometer experiments.

[0224] The system illustrated in FIG. 4B includes six different detectors that detect fluorescence within six different wavelength bands (which may be referred to herein as "filter windows" for a given detector) as determined by the configuration of filters and / or splitters in the beam path from the flow cell 425 to each detector. Different fluorescent molecules used in a flow cytometer experiment emit light in their own characteristic wavelength bands. The particular fluorescent labels used in the experiment and their associated fluorescence emission bands may be selected to roughly match the filter windows of the detectors. However, as more detectors are provided and more labels are utilized, perfect correspondence between filter windows and fluorescence emission spectra is not possible. While the peak of the emission spectrum of a particular fluorescent molecule may lie within the filter window of one particular detector, it is generally true that a portion of that label's emission spectrum also overlaps with the filter window of one or more other detectors. This may be referred to as spillover. I / O functionality 497 may be configured to receive data for a flow cytometer experiment with a panel of fluorescent labels and multiple cell populations with multiple markers (each cell population having a subset of multiple markers). I / O functionality 497 may be further configured to receive biological data assigning one or more markers to one or more cell populations, marker concentration data, emission spectrum data, data assigning labels to one or more markers, and cytometer configuration data. Flow cytometer experimental data, such as label spectral characteristics and flow cytometer configuration data, may be further stored in memory 495. Controller / processor 490 may be configured to evaluate one or more assignments of labels to markers.

[0225] 5 is a functional block diagram of an example particle analysis control system for analyzing and displaying biological events, such as an analysis controller 500. The analysis controller 500 can be configured to perform various processes for controlling the graphical display of biological events.

[0226] A particle analyzer or particle sorting system 502 may be configured to acquire the biological event data. For example, a flow cytometer may generate flow cytometry event data. The particle analyzer 502 may be configured to provide the biological event data to the analysis controller 500. A data communication channel may be included between the particle analyzer or particle sorting system 502 and the analysis controller 500. The biological event data may be provided to the analysis controller 500 via the data communication channel.

[0227] The analysis controller 500 may be configured to receive biological event data from the particle analyzer or particle sorting system 502. The biological event data received from the particle analyzer or particle sorting system 502 may include flow cytometry event data. The analysis controller 500 may be configured to provide a graphical display including a first plot of the biological event data on the display device 506. The analysis controller 500 may be further configured to render a region of interest as a gate around a population of the biological event data displayed by the display device 506, e.g., overlaid on the first plot. In some embodiments, the gate may be a logical combination of one or more illustrated regions of interest plotted on a histogram or bivariate plot of a parameter. In some embodiments, the display may be used to display particle parameters or saturation detector data.

[0228] Analysis controller 500 may further be configured to display the in-gate biological event data on display device 506 differently from other events in the outside-gate biological event data. For example, analysis controller 500 may be configured to render the color of the biological event data included within the gate differently from the color of the outside-gate biological event data. Display device 506 may be implemented as a monitor, tablet computer, smartphone, or other electronic device configured to present a graphical interface.

[0229] The analysis controller 500 may be configured to receive a gate selection signal identifying a gate from a first input device. For example, the first input device may be implemented as a mouse 510. The mouse 510 may initiate a gate selection signal to the analysis controller 500 identifying a gate to be displayed or manipulated via the display device 506 (e.g., by clicking on or within the desired gate when the cursor is over the desired gate). In some embodiments, the first device may be implemented as a keyboard 508 or other means for providing input signals to the analysis controller 500, such as a touchscreen, a pen, a photodetector, or a voice recognition system. Some input devices may include multiple input functions. In such embodiments, each input function may be considered an input device. For example, as shown in FIG. 5, the mouse 510 may include a right mouse button and a left mouse button, and the right mouse button and the left mouse button may each generate a trigger event.

[0230] A trigger event can cause the analysis controller 500 to change how the data is displayed, which portions of the data are actually displayed on the display device 506, and / or provide input to further processing, such as selecting a population of interest for particle sorting.

[0231] In some embodiments, the analysis controller 500 may be configured to detect when a gate selection is initiated by the mouse 510. The analysis controller 500 may further be configured to automatically modify the visualization of the plot to facilitate gating. This modification may be made based on a particular distribution of the biological event data received by the analysis controller 500.

[0232] The analysis controller 500 may be connected to a storage device 504. The storage device 504 may be configured to receive and store biological event data from the analysis controller 500. The storage device 504 may be further configured to receive and store flow cytometry event data from the analysis controller 500. The storage device 504 may be further configured to enable retrieval of biological event data, such as flow cytometry event data, by the analysis controller 500.

[0233] A display device 506 may be configured to receive display data from the analysis controller 500. The display data may include plots of the biological event data and gates outlining sections of the plots. The display device 506 may be further configured to modify the information displayed in response to input received from the analysis controller 500 in conjunction with input from the particle analyzer 502, the storage device 504, the keyboard 508, and / or the mouse 510.

[0234] In some embodiments, the analysis controller 500 can generate a user interface for receiving example events for filtering. For example, the user interface can include controls for receiving example events or example images. The example events or images, or example gates, can be provided prior to collection of event data for a sample, or can be provided based on an initial set of events for a portion of the sample.

[0235] FIG. 6A is a schematic diagram illustrating a particle sorting system 600 (e.g., particle analyzer or particle sorting system 502) according to one embodiment presented herein. In some embodiments, the particle sorting system 600 is a cell sorting system. As shown in FIG. 6A, a droplet-forming transducer 602 (e.g., a piezoelectric oscillator) is coupled to a fluid conduit 601, which may be coupled to, include, or be a nozzle 603. Within the fluid conduit 601, a sheath fluid 604 hydrodynamically focuses a sample fluid 606 containing particles 609 into a moving fluid column 608 (e.g., a stream). Within the moving fluid column 608, the particles 609 (e.g., cells) are aligned in a single file and traverse a monitoring region 611 (e.g., where the laser and the stream intersect) that is illuminated by an illumination source 612 (e.g., a laser). Vibration of droplet-forming transducer 602 causes moving fluid column 608 to break up into multiple droplets 610 , some of which contain particles 609 .

[0236] During operation, a detection station 614 (e.g., an event detector) identifies when a particle (or cell) of interest crosses the monitoring region 611. The detection station 614 feeds a timing circuit 628, which in turn feeds a flash charge circuit 630. At a droplet break-off point, signaled by a timed droplet delay (Δt), a flash charge can be applied to the moving fluid column 608 so that the droplet of interest carries a charge. The droplet of interest may contain one or more particles or cells to be sorted. The charged droplets can then be sorted by activating a deflection plate (not shown) to deflect the charged droplets into a receptacle, such as a collection tube or a multi-well or microwell sample plate, where a well or microwell can be specifically associated with the droplet of interest. As shown in FIG. 6A, the droplets can be collected in a drain receptacle 638.

[0237] A detection system 616 (e.g., a droplet boundary detector) serves to automatically determine the phase of the droplet drive signal as a particle of interest passes through the monitoring region 611. An exemplary droplet boundary detector is described in U.S. Pat. No. 7,679,039, the entire contents of which are incorporated herein by reference. The detection system 616 enables the instrument to accurately calculate the position of each detected particle within the droplet. The detection system 616 may provide an amplitude signal 620 and / or a phase signal 618, which are then provided (via an amplifier 622) to an amplitude control circuit 626 and / or a frequency control circuit 624. The amplitude control circuit 626 and / or the frequency control circuit 624 then control the droplet forming transducer 602. The amplitude control circuit 626 and / or the frequency control circuit 624 may be provided within the control system.

[0238] In some embodiments, the sorting electronics (e.g., detection system 616, detection station 614, and processor 640) can be coupled to a memory configured to store detected events and sorting decisions based on the detected events. The sorting decisions can be included in the event data for the particles. In some embodiments, detection system 616 and detection station 614 can be implemented as a single detection unit or can be communicatively coupled such that event measurements can be collected by either detection system 616 or detection station 614 and provided to a non-collection element.

[0239] FIG. 6B is a schematic diagram illustrating a particle sorting system according to one embodiment presented herein. The particle sorting system 600 shown in FIG. 6B includes deflection plates 652 and 654. An electric charge can be applied via a stream of charging wires within the barbs, generating a stream of droplets 610 containing particles 609 for analysis. The particles can be illuminated using one or more light sources (e.g., lasers) to generate light scattering and fluorescence information. The information about the particles is analyzed by sorting electronics or other detection systems (not shown in FIG. 6B). Deflection plates 652 and 654 can be independently controlled to attract or repel the charged droplets and direct them toward a desired collection vessel (e.g., one of 672, 674, 676, or 678). 6B, deflector plates 652 and 654 can be controlled to direct particles along a first path 662 toward a container 674 or along a second path 668 toward a container 678. If the particle is not of interest (e.g., does not exhibit scattering or illumination information within a specified sorting range), the deflector plates may allow the particle to continue along path 664. Such uncharged droplets may be directed into a waste container, such as via an aspirator 670.

[0240] Sorting electronics can be included to initiate measurement collection, receive fluorescent signals for the particles, and determine how to adjust the deflection plates to sort the particles. Exemplary implementations of the embodiment shown in Figure 6B include the BD FACSAria™ system of flow cytometers, commercially available from Becton, Dickinson and Company (Franklin Lakes, NJ).

[0241] Integrated Circuit Devices Aspects of the present disclosure further include an integrated circuit device programmed to spectrally resolve light from each fluorophore in a sample using a generalized least-squares problem, as described in the methods detailed above. In some embodiments, the integrated circuit device of interest comprises a field-programmable gate array (FPGA). In other embodiments, the integrated circuit device comprises an application-specific integrated circuit (ASIC). In still other embodiments, the integrated circuit device comprises a complex programmable logic device (CPLD). In some embodiments, the subject integrated circuit device is programmed to determine overlap between each different fluorophore in the sample and calculate the contribution of each fluorophore to the overlapping fluorescence. In certain embodiments, the integrated circuit is programmed to calculate a spectral unmixing matrix for fluorescence spectra of multiple fluorophores with overlapping fluorescence in the sample detected by a light detection system having multiple photodetectors. In certain embodiments, an integrated circuit device according to certain embodiments is programmed to calculate a spectral unmixing matrix for fluorescence spectra of multiple fluorophores for each cell in the sample. As described in more detail below, the integrated circuit device may also be programmed to estimate the abundance of each fluorophore in the sample. In some embodiments, the abundance of each fluorophore associated with the targeted particle may be determined. The integrated circuit may be programmed to identify and classify the targeted particle based on the abundance of each fluorophore associated with the targeted particle. In some cases, the integrated circuit is configured to sort the identified or classified particle.

[0242] In some embodiments, the integrated circuit device is programmed to determine a covariance of the data signals at each photodetector channel. Optionally, the covariance of the data signals at each photodetector channel includes an inherent sample variation component and a measurement variation component. Optionally, the covariance of the data signals at each photodetector channel includes electronic noise. Optionally, the covariance of the data signals at each photodetector channel includes shot noise. Optionally, the covariance of the data signals varies linearly with the generated data signals. Optionally, the covariance of the data signals varies quadratically with the generated data signals. Optionally, the covariance of the data signals is correlated across two or more of the multiple photodetector channels. Optionally, the integrated circuit device is programmed to calculate the covariance of the data signals according to:

[0243]

number

[0244] In some cases, the integrated circuit device is programmed to calculate the covariance of the data signal using a covariance matrix. In some cases, the covariance matrix includes non-zero diagonal values. In some cases, the integrated circuit device is programmed to calculate the covariance using the covariance matrix according to:

[0245]

number

[0246] Here, diag(x) indicates generating a diagonal matrix from a column vector x, and cov(a, b) indicates the covariance between a and b.

[0247] In some embodiments, the integrated circuit device is programmed to calculate the generalized least squares problem by multiplying by the inverse of the calculated covariance matrix. In some embodiments, the integrated circuit device is programmed to estimate the covariance of the data signal based on the fluorescence intensities across two or more photodetectors of the optical detection system. In some embodiments, the integrated circuit device is programmed to estimate the covariance of the data signal based on the fluorescence intensities across each of the optical detection channels. In some embodiments, the integrated circuit device is programmed to calculate the generalized least squares problem according to:

[0248]

number

[0249] In some cases, the integrated circuit device is programmed to estimate the covariance matrix a priori. In some cases, the integrated circuit device is programmed to apply a generalized least squares problem in real time (e.g., using an integrated circuit such as a field programmable gate array). In some cases, an a priori noise model is used to estimate the covariance of each event (e.g., calculating the covariance matrix of each event in real time). In some cases, the a priori noise model uses only the data collected for each particular event. In some cases, the covariance matrix includes estimates from the entire collected data set. In some cases, the covariance matrix is generated by an iterative optimization method that empirically adjusts the covariance matrix to minimize the variance of the unmixed data.

[0250] In some embodiments, the integrated circuit device is programmed to determine the covariance of the data signal by estimating it by iterative optimization using a covariance matrix that minimizes the variance of the unmixed data signal. Optionally, the integrated circuit device is programmed to compute a generalized least squares problem by Cholesky decomposition of the covariance matrix. Optionally, the generalized least squares problem is solved by solving the covariance matrix Σ y =CCT to solve the triangular system and generate the transformed input for the ordinary least squares algorithm according to

[0251]

number

[0252] In some embodiments, the integrated circuit device is programmed to find a least-squares solution to a generalized least-squares problem. Optionally, the integrated circuit device is programmed to find a least-squares solution to the generalized least-squares problem by one or more of matrix decomposition, matrix factorization, QR decomposition, Cholesky decomposition, singular value decomposition, LDL decomposition, forward substitution, and backward substitution. Optionally, the integrated circuit device is programmed to find a least-squares solution to the generalized least-squares problem by solving the so-called normal equations by Cholesky or LDL decomposition, for example according to

[0253]

number

[0254] In some cases, the integrated circuit device is programmed to find a least squares solution to a generalized least squares problem using Cholesky or LDL decomposition according to:

[0255]

number

[0256]

number

[0257]

number

[0258] In some embodiments, the integrated circuit device is programmed to estimate the abundance of one or more fluorophores in the sample based on the calculated spectral unmixing matrix. Optionally, the integrated circuit device is programmed to estimate the abundance of one or more fluorophores on particles in the sample. In some embodiments, the integrated circuit device is programmed to identify particles in the sample based on the estimated abundance of each fluorophore on the particle. Optionally, the integrated circuit device is programmed to sort the identified particles in the sample.

[0259] In some embodiments, the integrated circuit of interest is programmed to calculate the abundance of one or more fluorophores in the sample from the spectrally resolved light from each fluorophore. In some cases, the abundance of a fluorophore bound (e.g., chemically bound (i.e., covalently, ionically) or physically bound) to a target particle is calculated from the spectrally resolved light from each fluorophore bound to the particle. For example, in one example, the integrated circuit is programmed to calculate the relative abundance of each fluorophore bound to the target particle from the spectrally resolved light from each fluorophore. In another example, the integrated circuit is programmed to calculate the absolute abundance of each fluorophore bound to the target particle from the spectrally resolved light from each fluorophore.

[0260] In some embodiments, the integrated circuit is programmed to identify or classify particles based on the relative abundance of each fluorophore determined to be associated with the particle. In these embodiments, the integrated circuit may be programmed to identify or classify particles by any convenient protocol, such as by comparing the relative or absolute abundance of each fluorophore associated with the particle to a control sample having known particles, or by performing spectroscopic or other assay analysis of a population of particles (e.g., cells) having calculated relative or absolute abundances of associated fluorophores.

[0261] kit Aspects of the present disclosure further include kits, which include one or more of the integrated circuits described herein. In some embodiments, the kits may further include a program for the subject systems, such as in the form of a computer-readable medium (e.g., a flash drive, USB storage, compact disc, DVD, Blu-ray disc, etc.) or instructions for downloading the program from an Internet web protocol or cloud server. The kits may further include instructions for practicing the subject methods. These instructions may be present in the subject kits in a variety of forms, one or more of which may be present in the kit. One form in which these instructions may be provided is information printed on a suitable medium or substrate, such as one or more pieces of paper on which the information is printed, kit packaging, a package insert, etc. Another form in which these instructions may be provided is a computer-readable medium on which the information is recorded, such as a diskette, compact disc (CD), portable flash drive, etc. Another form in which these instructions may be present is a website address that may be used via the Internet to access the information at a remote location.

[0262] usefulness The subject systems, methods, and computer systems find use in a variety of applications where it is desirable to analyze and separate particle components in a sample in a fluid medium, such as a biological sample. In some embodiments, the systems and methods described herein are used for flow cytometric characterization of biological samples labeled with fluorescent tags. In other embodiments, the systems and methods are used for spectroscopy of emitted light. Additionally, the subject systems and methods find use in enhancing signals obtained from light collected from a sample (e.g., in a flow stream). In some cases, the present disclosure finds use in enhancing measurements of light collected from a sample illuminated in a flow stream within a flow cytometer. Embodiments of the present disclosure find use where it is desirable to provide a flow cytometer with increased cell sorting accuracy, improved particle collection, particle charging efficiency, more accurate particle charging, and improved particle deflection during cell sorting.

[0263] Embodiments of the present disclosure further find use in applications where cells prepared from biological samples may be desirable for use in research, clinical trials, or therapy. In some embodiments, the subject methods and devices may facilitate obtaining individual cells prepared from a targeted fluid or tissue biological sample. For example, the subject methods and systems may facilitate obtaining cells from fluid or tissue samples used as research or diagnostic specimens for diseases such as cancer. Similarly, the subject methods and systems may facilitate obtaining cells from fluid or tissue samples used for therapy. The disclosed methods and devices enable the separation and collection of cells from biological samples (e.g., organs, tissues, tissue slices, fluids) with high efficiency and low cost compared to conventional flow cytometry systems.

[0264] experiment Spectral unmixing and covariance modeling according to certain embodiments of the present disclosure are described below, and the scope of the present disclosure is not intended to be limited to the exemplary embodiments shown and described below.

[0265] 1. Definitions and Terminology 1.1 Variables

[0266]

number

[0267] GLS A linear mixed model is used to describe the measured signals in the flow cytometer.

[0268]

number

[0269]

number

[0270] There are many mathematically equivalent solutions to this problem, but with various trade-offs in terms of computational complexity and numerical stability. A common approach is to solve the so-called "normal equations"

[0271]

number

[0272]

number

[0273] In the case of fluorescence measurements using a flow cytometer, the measured data meet the first requirement (mainly due to the use of baseline restoration in signal processing), but do not necessarily meet the second and third requirements. Weighted least squares (WLS) allows optimal unmixing even in the presence of heteroscedasticity, and generalized least squares (GLS) allows optimal unmixing in the presence of both heteroscedasticity and correlated noise (non-zero detector covariance). Both WLS and GLS can be considered as transformations that modify the data to satisfy the three assumptions of the Gauss-Markov theorem, similar to how Orthogonal Least Squares (OLS) can be applied to transformation problems.

[0274] The generalized least squares method takes a similar form to the WLS problem, but instead of using a diagonal weight matrix, we fit the raw detector signal Σ y The inverse of the full covariance matrix of is used, so that it is possible to account for non-zero detector covariances arising from correlated noise sources.

[0275]

number

[0276] Here, G=(Σ y ) -1 This solution follows the same general approach as WLS, but uses a more complex off-diagonal weight matrix G:

[0277]

number

[0278] This problem may be solved using the following matrix decomposition technique: Cholesky decomposition (technically LDL decomposition, which is a special case of Cholesky) gives X T GX to LDL T where L is unit lower triangular (meaning it has ones on the diagonal) and D is the diagonal.

[0279]

number

[0280] The final equation gives us the GLS solution, using two intermediate vectors z and u along the way to reduce the problem to a fully triangular and diagonal solution.

[0281] Furthermore, this technology has (Σ y ) -1 To avoid this, it is possible to do the following instead:

[0282]

number

[0283] Noise Model definition

[0284]

number

[0285] Single detector noise model The variance of a flow cytometry intensity signal is described using the following noise model (shown here for a single detector i):

[0286]

number

[0287] Although baseline and Poisson errors between detectors are uncorrelated, the same assumption cannot be made for CV0. Because detectors are grouped by laser line, all detectors for a given laser line sample the same point in time, meaning that time-dependent errors will be correlated to some extent between detectors on the same laser line. Furthermore, other random fluctuations in the fluid or laser intensity / position (which affect particle position) may correlate or anti-correlate between laser lines, while chromatic aberration effects in the collection optics may cause different detectors on the same laser line to be less than perfectly correlated.

[0288] Thus (where the operator diag(z) transforms a column vector z into a diagonal matrix):

[0289]

number

[0290] Detector covariance in the absence of biological spread Overall raw variance-covariance matrix Σ in the absence of biological spread y0 is given by the following formula:

[0291]

number

[0292] Regardless of the scope of the appended claims, the present disclosure is further defined by the following notes.

[0293] Appendix 1. Detecting light from a sample having multiple fluorophores with overlapping fluorescence spectra using a light detection system; A method in which a generalized least squares algorithm is used to spectrally resolve the light from each fluorophore in a sample.

[0294] Clause 2. The method of clause 1, wherein the light detection system detects light in multiple light detector channels.

[0295] Clause 3. The method of clause 1 or clause 2, wherein the optical detection system comprises a plurality of optical detectors.

[0296] Clause 4. The method of clause 2 or clause 3, generating a data signal in each of the photodetector channels in response to the detected light.

[0297] Clause 5. The method of clause 4, wherein the covariance of the data signals in each photodetector channel is determined.

[0298] Appendix 6. The covariance of the data signal in each photodetector channel is the inherent sample variability component, and Measurement fluctuation components 6. The method of claim 5, comprising:

[0299] Clause 7. The method of clause 5 or 6, wherein the covariance of the data signals in each photodetector channel includes electronic noise.

[0300] Clause 8. The method of clause 5 or 6, wherein the covariance of the data signals in each photodetector channel includes shot noise.

[0301] Appendix 9. The method of any one of appendices 5 to 8, wherein the covariance of the data signals varies linearly with the generated data signals.

[0302] Appendix 10. The method of any one of appendices 5 to 8, wherein the covariance of the data signals varies quadratically with the generated data signals.

[0303] Clause 11. The method of any one of clauses 5 to 10, wherein the covariance of the data signals is correlated across two or more of the multiple photodetector channels.

[0304] Clause 12. The method of any one of clauses 5 to 11, wherein the covariance of the data signal is calculated according to:

number

[0305] Appendix 13. The method of any one of appendices 5 to 12, wherein the covariance matrix is used to calculate the covariance of the data signals.

[0306] Clause 14. The method of clause 13, wherein the covariance matrix includes non-zero diagonal values.

[0307] Clause 15. The method of clause 12 or 13, wherein the covariance is calculated using a covariance matrix according to:

number

[0308] Appendix 16. The method of any one of appendices 13 to 15, wherein the generalized least squares algorithm solves the generalized least squares problem by multiplying the calculated covariance matrix by the inverse.

[0309] Appendix 17. The method of any one of appendices 5 to 16, wherein the covariance of the data signals is estimated based on the fluorescence intensity across two or more photodetectors of the optical detection system.

[0310] Clause 18. The method of clause 17, wherein the covariance of the data signal is estimated based on the fluorescence intensity across each of the light detection channels.

[0311] Appendix 19. The method of any one of appendices 1 to 18, wherein when solving a generalized least squares problem, the method calculates according to:

number

[0312] Appendix 20. The method of any one of appendices 1 to 19, wherein the estimated covariance matrix is generated a priori.

[0313] Clause 21. The method of any one of clauses 13 to 20, wherein the covariance of the data signal is determined by estimating it by iterative optimization using a covariance matrix that minimizes the variance of the unmixed data signal.

[0314] Appendix 22. The method of any one of appendices 13 to 20, wherein a Cholesky decomposition of the covariance matrix is used when solving the generalized least squares problem.

[0315] Appendix 23. The method of any one of appendices 1 to 22 for finding a least-squares solution to a generalized least-squares problem.

[0316] Clause 24. The method of any one of clauses 1 to 23, wherein the least-squares solution to the generalized least-squares problem is minimized by one or more of matrix decomposition, matrix factorization, QR decomposition, Cholesky decomposition, singular value decomposition, LDL decomposition, forward substitution, and backward substitution.

[0317] Appendix 25. The method of Appendix 24, wherein a least-squares solution to a generalized least-squares problem is obtained by Cholesky decomposition or LDL decomposition.

[0318] Appendix 26. The method of Appendix 25, wherein a least-squares solution to a generalized least-squares problem is minimized by Cholesky decomposition according to:

number

[0319] Appendix 27. The method of appendix 25 or 26, wherein a least-squares solution to a generalized least-squares problem is obtained by Cholesky decomposition or LDL decomposition according to the following:

number

[0320] Appendix 28. The method of appendix 23 for finding a least-squares solution to a generalized least-squares problem by matrix decomposition.

[0321] Appendix 29. The method of appendix 23 for finding a least-squares solution to a generalized least-squares problem by matrix factorization.

[0322] Appendix 30. The method of appendix 23 for finding a least-squares solution to a generalized least-squares problem by QR decomposition.

[0323]

number

[0324] Appendix 32. The method of appendix 23 for finding a least-squares solution to a generalized least-squares problem by singular value decomposition.

[0325] Clause 33. The method of clause 32, wherein the generalized least squares problem is computed using singular value decomposition according to:

number

[0326] Appendix 34. The method of appendix 23 for finding a least-squares solution to a generalized least-squares problem by LDL decomposition.

[0327] Appendix 35. The method of Appendix 23 for finding a least-squares solution to a generalized least-squares problem by forward and backward substitution.

[0328] Item 36. The method of any one of items 1-35, wherein light from each fluorophore is spectrally resolved in real time.

[0329] Clause 37. The method of clause 36, wherein integrated circuits are used to spectrally resolve light from each fluorophore in real time.

[0330] Clause 38. The method of clause 37, wherein the integrated circuit comprises a field programmable gate array (FPGA).

[0331] Clause 39. The method of any one of clauses 1-38, wherein the fluorescence spectrum of each fluorophore in the sample overlaps with the fluorescence spectrum of at least one other fluorophore.

[0332] Clause 40. The method of clause 39, wherein the fluorescence spectrum of each fluorophore in the sample overlaps with the fluorescence spectrum of at least one other fluorophore by 10 nm or more.

[0333] Clause 41. The method of clause 39, wherein the fluorescence spectrum of each fluorophore in the sample overlaps with the fluorescence spectrum of at least one other fluorophore by 25 nm or more.

[0334] Clause 42. The method of clause 39, wherein the fluorescence spectrum of at least one fluorophore in the sample overlaps with the fluorescence spectra of two different fluorophores in the sample.

[0335] Clause 43. The method of clause 42, wherein the fluorescence spectrum of at least one fluorophore in the sample overlaps with the fluorescence spectra of two different fluorophores in the sample by 10 nm or more.

[0336] Clause 44. The method of clause 42, wherein the fluorescence spectrum of at least one fluorophore in the sample overlaps with the fluorescence spectra of two different fluorophores in the sample by 25 nm or more.

[0337] Appendix 45. The method of any one of appendices 1 to 44, wherein the sample is irradiated with a light source.

[0338] Clause 46. The method of clause 45, wherein the light source comprises a laser.

[0339] Clause 47. The method of clause 46, wherein the light source comprises multiple lasers.

[0340] Clause 48. A light source configured to illuminate a sample having a plurality of fluorophores with overlapping fluorescence spectra; a light detection system having a plurality of light detectors; a processor to which the memory is operatively coupled; It is equipped with The memory stores instructions that, when executed by the processor, cause the processor to spectrally resolve light from each fluorophore in the sample using a generalized least squares algorithm.

[0341] Clause 49. The system of clause 48, configured to detect light in a plurality of photodetector channels by a light detection system.

[0342] Clause 50. The system of clause 48 or 49, wherein the optical detection system comprises a plurality of optical detectors.

[0343] Clause 51. The system of clause 50, wherein the photodetector comprises one or more photomultiplier tubes.

[0344] Addendum 52. The system of any one of Addendums 48 to 51, wherein the optical detection system comprises a photodetector array.

[0345] Clause 53. The system of clause 52, wherein the photodetector array comprises a photodiode.

[0346] Clause 54. The system of clause 53, wherein the photodetector array comprises a charge-coupled device.

[0347] Addendum 55. The system of any one of Addendums 48 to 54, wherein the memory stores instructions that, when executed by the processor, cause the processor to determine the covariance of the data signals in each photodetector channel.

[0348] Appendix 56. The covariance of the data signal in each photodetector channel is the inherent sample variability component, and Measurement fluctuation components 56. The system of claim 55, comprising:

[0349] Clause 57. The system of clause 55 or 56, wherein the covariance of the data signals in each photodetector channel includes electronic noise.

[0350] Clause 58. The system of clause 55 or 56, wherein the covariance of the data signals in each photodetector channel includes shot noise.

[0351] Addendum 59. The system of any one of Addendums 55 to 58, wherein the covariance of the data signal varies linearly with the generated data signal.

[0352] Addendum 60. The system of any one of Addendums 55-58, wherein the covariance of the data signal varies quadratically with the generated data signal.

[0353] Addendum 61. The system of any one of Addendums 55-60, wherein the covariance of the data signals is correlated across two or more of the multiple photodetector channels.

[0354] Addendum 62. The system of any one of Addendums 48-61, wherein the memory stores instructions that, when executed by the processor, cause the processor to calculate the covariance according to:

number

[0355] Addendum 63. The system of any one of Addendums 48-62, wherein the memory stores instructions that, when executed by the processor, cause the processor to calculate the covariance of the data signal using the covariance matrix.

[0356] Clause 64. The system of clause 63, wherein the covariance matrix includes non-zero diagonal values.

[0357] Clause 65. The system of clause 63 or 64, wherein the memory stores instructions that, when executed by the processor, cause the processor to calculate the covariance using a covariance matrix according to:

number

[0358] Addendum 66. The system of any one of Addendums 63-65, wherein the memory stores instructions that, when executed by the processor, cause the processor to calculate a generalized least squares problem by multiplying the data signal by the inverse of the calculated covariance matrix.

[0359] Addendum 67. A system described in any one of Addendums 55 to 66, wherein the memory stores instructions that, when executed by the processor, cause the processor to estimate the covariance of the data signal based on the fluorescence intensity across two or more photodetectors of the photodetection system.

[0360] Addendum 68. A system described in any one of Addendums 55 to 66, wherein the memory stores instructions that, when executed by the processor, cause the processor to estimate the covariance of the data signal based on the fluorescence intensity across each of the light detection channels.

[0361] Addendum 69. The system of any one of Addendums 48-68, wherein the memory stores instructions that, when executed by the processor, cause the processor to calculate a generalized least squares problem according to:

number

[0362] Addendum 70. The system of any one of Addendums 48-69, wherein the memory stores instructions that, when executed by the processor, cause the processor to a priori generate an estimated covariance matrix.

[0363] Addendum 71. The system of any one of Addendums 48-70, wherein the memory stores instructions that, when executed by the processor, cause the processor to determine the covariance of the data signal by estimating iterative optimization using a covariance matrix that minimizes the variance of the unmixed data signal.

[0364] Addendum 72. The system of any one of Addendums 48-71, wherein the generalized least squares problem includes a Cholesky decomposition of the covariance matrix.

[0365] Addendum 73. The system of any one of Addendums 48-72, wherein the memory stores instructions that, when executed by the processor, cause the processor to determine a least-squares solution to a generalized least-squares problem.

[0366] Addendum 74. The system of any one of Addendums 48-73, wherein the memory stores instructions that, when executed by the processor, cause the processor to find a least-squares solution to a generalized least-squares problem by one or more of matrix decomposition, matrix factorization, QR decomposition, Cholesky decomposition, singular value decomposition, LDL decomposition, forward substitution, and backward substitution.

[0367] Clause 75. The system of Clause 74, wherein the memory stores instructions that, when executed by the processor, cause the processor to find a least-squares solution to a generalized least-squares problem using Cholesky decomposition.

[0368] Clause 76. The system of Clause 75, wherein the memory stores instructions that, when executed by the processor, cause the processor to find a least-squares solution to a generalized least-squares problem using Cholesky decomposition according to:

number

[0369] Clause 77. The system of Clause 75 or 76, wherein the memory stores instructions that, when executed by the processor, cause the processor to find a least-squares solution to a generalized least-squares problem using Cholesky or LDL decomposition according to:

number

[0370] Clause 78. The system of Clause 74, wherein the memory stores instructions that, when executed by the processor, cause the processor to find a least-squares solution to a generalized least-squares problem by matrix decomposition.

[0371] Clause 79. The system of Clause 74, wherein the memory stores instructions that, when executed by the processor, cause the processor to find a least-squares solution to a generalized least-squares problem by matrix factorization.

[0372] Clause 80. The system of Clause 74, wherein the memory stores instructions that, when executed by the processor, cause the processor to find a least-squares solution to a generalized least-squares problem using QR decomposition.

[0373]

number

[0374] Clause 82. The system of Clause 74, wherein the memory stores instructions that, when executed by the processor, cause the processor to find a least-squares solution to a generalized least-squares problem using singular value decomposition.

[0375] Clause 83. The system of Clause 82, wherein the memory stores instructions that, when executed by the processor, cause the processor to compute a generalized least squares problem using singular value decomposition according to:

number

[0376] Clause 84. The system of Clause 74, wherein the memory stores instructions that, when executed by the processor, cause the processor to find a least-squares solution to a generalized least-squares problem using LDL decomposition.

[0377] Clause 85. The system of Clause 74, wherein the memory stores instructions that, when executed by the processor, cause the processor to find a least-squares solution to a generalized least-squares problem by forward and backward substitution.

[0378] Addendum 86. The system of any one of Addendums 48-85, configured to spectrally resolve light from each fluorophore in real time.

[0379] Addendum 87. The system of any one of Addendums 48 to 86, further comprising an integrated circuit.

[0380] Clause 88. The system of clause 87, wherein the integrated circuit comprises a field programmable gate array (FPGA).

[0381] Addendum 89. The system of any one of Addendums 48 to 88, wherein the light source comprises a laser.

[0382] Addendum 90. The system of Addendum 89, wherein the light source comprises multiple lasers.

[0383] Appendix 91. An integrated circuit programmed to spectrally resolve light from each fluorophore in a sample having multiple fluorophores with overlapping fluorescence spectra using a generalized least squares problem.

[0384] Clause 92. The integrated circuit of Clause 91, wherein the integrated circuit is a field programmable gate array (FPGA).

[0385] 93. The integrated circuit of claim 91, wherein the integrated circuit is an application specific integrated circuit (ASIC).

[0386] 94. The integrated circuit of claim 91, wherein the integrated circuit is a complex programmable logic device (CPLD).

[0387] Addendum 95. The integrated circuit of any one of Addendums 91-94, programmed to determine the covariance of the data signals in each photodetector channel of the photodetection system.

[0388] Appendix 96. The covariance of the data signal in each photodetector channel is the inherent sample variability component, and Measurement fluctuation components 96. The integrated circuit of claim 95, comprising:

[0389] Addendum 97. The integrated circuit of any one of Addendums 95 to 96, wherein the covariance of the data signals in each photodetector channel includes electronic noise.

[0390] Addendum 98. The integrated circuit of any one of Addendums 95 to 96, wherein the covariance of the data signals in each photodetector channel includes shot noise.

[0391] Addendum 99. The integrated circuit of any one of Addendums 95-98, wherein the covariance of the data signals varies linearly with the generated data signal.

[0392] Appendix 100. The integrated circuit of any one of Appendixes 95-98, wherein the covariance of the data signals varies quadratically with the generated data signal.

[0393] Clause 101. The integrated circuit of any one of Clauses 95-98, wherein the covariance of the data signals is correlated across two or more of the plurality of photodetector channels.

[0394] Clause 102. The integrated circuit of any one of Clauses 95-101, programmed to calculate covariance according to:

number

[0395] Clause 103. The integrated circuit of any one of Clauses 95-102, programmed to calculate the covariance of the data signal using a covariance matrix.

[0396] Clause 104. The integrated circuit of Clause 103, wherein the covariance matrix includes non-zero diagonal values.

[0397] Clause 105. The integrated circuit of any one of clauses 103 and 104, programmed to calculate covariance using a covariance matrix according to:

number

[0398] Clause 106. The integrated circuit of any one of Clauses 103-105, programmed to calculate a generalized least squares problem by multiplying the data signal by the inverse of the calculated covariance matrix.

[0399] Addendum 107. The integrated circuit of any one of Addendums 91-106, programmed to estimate a covariance of a data signal based on fluorescence intensity across two or more photodetectors of the photodetection system.

[0400] Addendum 108. The integrated circuit of any one of Addendums 91-106, programmed to estimate a covariance of the data signal based on the fluorescence intensity across each optical detection channel of the optical detection system.

[0401] Clause 109. The integrated circuit of any one of Clauses 91-108, programmed to calculate a generalized least squares problem according to:

number

[0402] Addendum 110. The integrated circuit of any one of Addendums 91-109, programmed to a priori generate an estimated covariance matrix.

[0403] Addendum 111. The integrated circuit of any one of Addendums 91-110, programmed to determine the covariance of the data signal by estimating it through iterative optimization using a covariance matrix that minimizes the variance of the unmixed data signal.

[0404] Addendum 112. The integrated circuit of any one of Addendums 91-111, wherein the generalized least squares problem includes a Cholesky decomposition of a covariance matrix.

[0405] Addendum 113. The integrated circuit of any one of Addendums 91-112, programmed to find a least-squares solution to a generalized least-squares problem.

[0406] Appendix 114. The integrated circuit of any one of Appendixes 91-113, programmed to find a least-squares solution to a generalized least-squares problem by one or more of matrix decomposition, matrix factorization, QR decomposition, Cholesky decomposition, singular value decomposition, LDL decomposition, forward substitution, and backward substitution.

[0407] Clause 115. The integrated circuit of Clause 114, programmed to find a least-squares solution to a generalized least-squares problem via Cholesky decomposition or LDL decomposition.

[0408] Clause 116. The integrated circuit of Clause 115, programmed to find a least-squares solution to a generalized least-squares problem using Cholesky decomposition according to:

number

[0409] Clause 117. The integrated circuit of clause 115 or 116, programmed to find a least-squares solution to a generalized least-squares problem using Cholesky decomposition or LDL decomposition.

number

[0410] Clause 118. The integrated circuit of Clause 114, programmed to find a least-squares solution to a generalized least-squares problem by matrix decomposition.

[0411] Clause 119. The integrated circuit of Clause 114, programmed to find a least-squares solution to a generalized least-squares problem by matrix factorization.

[0412] Clause 120. The integrated circuit of Clause 114, programmed to find a least-squares solution to a generalized least-squares problem using QR decomposition.

[0413]

number

[0414] Clause 122. The integrated circuit of Clause 114, programmed to find a least-squares solution to a generalized least-squares problem by singular value decomposition.

[0415] Clause 123. The integrated circuit of Clause 122, programmed to compute a generalized least squares problem using singular value decomposition according to:

number

[0416] Clause 124. The integrated circuit of Clause 114, programmed to find a least-squares solution to a generalized least-squares problem using LDL decomposition.

[0417] Clause 125. The integrated circuit of Clause 114, programmed to find a least-squares solution to a generalized least-squares problem by forward substitution and backward substitution.

[0418] Item 126. The integrated circuit of any one of Items 91-125, programmed to spectrally resolve light from each fluorophore in real time.

[0419] Although the foregoing invention has been described in some detail by way of illustration and example, for purposes of clarity of understanding, it will be readily apparent to those skilled in the art that, in light of the teachings of the invention, certain changes and modifications may be made thereto without departing from the spirit or scope of the appended claims.

[0420] Accordingly, the foregoing merely illustrates the essence of the present invention. It is clear that those skilled in the art will be able to devise various configurations that embody the essence of the present invention and are within the spirit and scope of the present invention, although not explicitly described or shown herein. Furthermore, all examples and conditional language set forth herein are intended essentially to aid the reader in understanding the essence of the present invention and the concepts provided by the inventors to advance the art, and should not be construed as limiting the scope of the present invention to the specifically set forth examples and conditions. Furthermore, all statements herein that describe the essence, aspects, and embodiments of the present invention, as well as specific examples of the present invention, are intended to encompass both structural and functional equivalents of the present invention. Additionally, such equivalents are intended to include both currently known equivalents and future-developed equivalents, i.e., all elements developed that perform the same function, regardless of structure. Furthermore, the descriptions disclosed herein are not intended to be publicly disclosed, regardless of whether such disclosure is explicitly recited in the claims.

[0421] Accordingly, it is not intended that the scope of the present invention be limited to the exemplary embodiments shown and described herein. Rather, the scope and spirit of the present invention are embodied by the appended claims. With respect to claims, 35 U.S.C. 112(f) or 35 U.S.C. 112(6) are expressly provided to be invoked with respect to a limitation in a claim only when the precise phrase "means for" or "step for" appears at the beginning of such limitation in the claim; if such precise phrase is not used in a claim limitation, 35 U.S.C. 112(f) or 35 U.S.C. 112(6) is not invoked.

[0422] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority under 35 U.S.C. §119(e) of the filing date of U.S. Provisional Patent Application No. 63 / 622,370, filed January 18, 2024, the entire disclosure of which is incorporated herein by reference.

Claims

1. detecting light from a sample having multiple fluorophores with overlapping fluorescence spectra using a light detection system; A method in which a generalized least squares algorithm is used to spectrally resolve light from each fluorophore in the sample.

2. The method of claim 1 , wherein the light detection system detects light in multiple light detector channels.

3. The method of claim 1 or 2, wherein the light detection system comprises a plurality of light detectors.

4. 4. The method of claim 2, further comprising generating a data signal in each of the photodetector channels in response to the detected light.

5. The method of claim 4 , further comprising determining a covariance of the data signals in each photodetector channel.

6. The covariance of the data signal in each photodetector channel is the inherent sample variability component, and Measurement fluctuation components The method of claim 5 , comprising:

7. 7. The method of claim 5 or 6, wherein the covariance of the data signals is correlated across two or more of the plurality of photodetector channels.

8. The method according to any one of claims 5 to 7, wherein a covariance matrix is used to calculate the covariance of the data signals.

9. The method of claim 8 , wherein the covariance matrix includes non-zero diagonal values.

10. The method of any one of claims 5 to 9, further comprising estimating the covariance of the data signals based on the fluorescence intensities across two or more photodetectors of the photodetection system.

11. A method according to any one of claims 1 to 10 for finding a least-squares solution to a generalised least-squares problem.

12. 12. The method of any one of claims 1 to 11, wherein the least squares solution to the generalized least squares problem is minimized by one or more of matrix decomposition, matrix factorization, QR decomposition, Cholesky decomposition, singular value decomposition, LDL decomposition, forward substitution, and backward substitution.

13. 13. The method of any one of claims 1 to 12, wherein the light from each fluorophore is spectrally resolved in real time.

14. a light source configured to illuminate a sample having a plurality of fluorophores with overlapping fluorescence spectra; a light detection system having a plurality of light detectors; a processor to which the memory is operatively coupled; It is equipped with The memory stores instructions that, when executed by the processor, cause the processor to spectrally resolve light from each fluorophore in the sample using a generalized least squares algorithm.

15. An integrated circuit that is programmed to use a generalized least squares problem to spectrally resolve light from each fluorophore in a sample having multiple fluorophores with overlapping fluorescence spectra.

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