High efficiency multiplexing

Abstract

In one method for measuring radiation, the radiation is temporally and / or spatially separated by a modulator to direct at least N different combinations of radiation incident on each region into at least two and fewer than N discontinuous directions. The total intensity of the radiation in each direction is measured using a detector configured for each modulator, and the detector outputs are statistically analyzed to obtain information relating to the spectral properties of the radiation. In this manner, substantially all energy received at the inlet aperture of the measuring device is encoded into multiple outputs, and these multiplexed outputs are received by a small number of detectors.

Description

[Technical Field] This invention relates to the measurement of wave fields or particle flux using spatial and / or temporal modulation. The wave field may include spatial variations of at least one characteristic or strain number. This invention is applicable to electromagnetic waves, matter waves, and pressure (acoustic) waves. Waves may be transverse or longitudinal. The spatial variation or strain number of the electromagnetic wave may be amplitude, density, frequency, wavelength, phase, polarization direction of propagation, or origin position. Electromagnetic waves can also be described as photon flux. Matter waves can also be described as particle flux, consisting of electrons, neutrons, atoms, ions, molecules, or aggregates of these. Spatial variations in particle flux can be related to any property of matter, including origin position, velocity, acceleration, charge, mass, spin, quantum state, magnetic or electric dipole. Spatial variations in sound waves can be amplitude, density, velocity, phase, or origin position. The measurement methods can be used in many different fields, including but not limited to crystallography, spectroscopy, interferometry, spectroscopic imaging, imaging, positron emission tomography, microscopy, electron microscopy, mass spectrometry, ion mobility spectroscopy, and capillary electrophoresis. The configurations described herein can also be used in communication systems, radar systems, or other applications as specifically described above. One example is disclosed in US 8345254 (Prystupa), issued on 1 January 2013, for the optical analysis of thin heterogeneous samples. Further information may be obtained by investigation of that disclosure, or the disclosure of that disclosure may be incorporated herein by reference. Another example is PCT Publication Application 2016 / 0011548 (Prystupa), published on January 28, 2016, for the analysis of light and ultrasound reflected from a moving sample. The disclosures in that application may be studied to obtain other information, or the disclosures in that application are incorporated herein by reference. Another example is disclosed in PCT Publication Application 2018 / 018155, published on February 1, 2018, for the separation of particles. The disclosures in that application may be studied to obtain further information, or the disclosures in that application are incorporated herein by reference. The key features of this disclosure are also included below for completeness. [Previous Technology] This invention is an extension of a concept primarily developed in the field of multi-mode spectroscopy. The field of spectroscopy has a vast body of literature. This specification is intended only as an overview, providing further details only to highlight the points of the invention. Readers are advised to refer to Wolfgang Demtroder's *Laser Spectroscopy: Basic Concepts and Instrumentation*, 2nd edition, Springer Publishers, New York (1982) for a practical description of the subject, or Max Born and Emil Wolf's *Principles of Optics*, 7th edition, Cambridge University Press (2002) for a rigorous discussion of the subject. Martin Harwit (1979) provides a good description of the Hadamard spectrometer, which combines the features of a multifunctional dispersive instrument. A typical design of a Hadamard spectrometer includes an entrance slit, collimating elements, diffraction elements, spatial masks, and detectors, as well as focusing optics and folding mirrors at various points along the optical path. In some designs, the order of the diffraction elements and spatial filters is interchanged. Electromagnetic radiation is dispersed into bands by the diffraction elements and focused onto the spatial filter, which directs some, but not all, of the bands to the detector. The detector measures the intensity of electromagnetic radiation from a series of different spatial filters and solves a series of equations to infer the intensity of each band according to a weighting scheme. For a more comprehensive discussion of the topic, see Neil JASloane and Martin Harwit, Masks for Hadamard transform optics and Weighted Design Applied Optics 15(1)107-114 (1976). For example, early hadamard instruments, as illustrated in U.S. Patent 3,578,980 (Decker), issued May 18, 1971, generated a series of hadamard spatial masks by progressively moving a master mask. These systems faced mask alignment problems that led to several technological advancements, none of which were entirely satisfactory. A variation of this design was developed in U.S. Patent 3,586,442 (Tripp), issued June 22, 1971, where a spatially encoded waveband is second-incident on the dispersive element to eliminate dispersion and concentrate the radiation field on the detector. A hadamard system based on rotating masks was developed. U.S. Patent 6,271,917 (Hagler), issued August 7, 2001, mentions that the steps in the transmission of a binary mask produce ringing under Fourier analysis, and the proposed mask uses tiered transmission to form slits. The Haddamard method has been applied to interferometers to generate hybrid Fourier transform spectrometers. In U.S. Patent 4750834, issued June 14, 1988, Fateley et al. described a method of placing an electrically variable shield in the plane of the interference pattern. In U.S. Patent 5488474, issued January 30, 1996, Fateley et al. also provided a method for reducing central clustering of interferograms in FTIR spectrometers. This invention extends these methods to provide an improved signal-to-noise ratio. In U.S. Patent 4856897, issued on August 15, 1989, Fateley et al. described a Raman spectrometer based on a motor-driven electro-optic shield and a single detector. The objective of this invention is to improve the signal-to-noise ratio performance of this design. Recently, mask-based hademad designs have been proposed, which dynamically generate patterns using electro-optic effects (liquid crystals) such as those described in U.S. Patent 5,235,461 (Kirsch), issued August 10, 1993, or electromechanical effects (micromirror arrays) such as those described in U.S. Patent 5,504,575 (micromirror arrays), issued April 2, 1996. These methods have several problems. The duty cycle and therefore the sampling rate are limited by the transition time of the mask from one specified state to another. In liquid crystal-based designs, the contrast between the transmission and absorption mask regions is less than 10 bits, thus limiting the accuracy achievable by the instrument. The duty cycle of micromirror-based designs is limited by thermal load. Furthermore, micromirror designs suffer from diffraction and non-uniformity of resolution. Another recent hademad variant illuminates a fixed array of hademad masks and uses a focal plane array, such as that described in U.S. Patent 5,050,989 (Van Tassel), issued September 24, 1991, to measure the transmission pattern. This design has the advantage of being mechanically stable without moving parts, but it has the disadvantage of requiring a huge focal plane array. In practical projects, given the low cost of silicon-based focal plane arrays, this method is limited to the visible region of the spectrum. Spatial dimensions can be multiplexed in the same way as spectral dimensions. Generally, this is spectral imaging, which produces a data cube with both spatial and spectral dimensions. In US Patent 758972, issued September 15, 2009, Coifman et al. described an apparatus for multispectral imaging using a mosaic array of filters. In US Patent 8345254, multiplexing is further extended to amplify other weak signals. The amount of information in the data cube and the necessary processing requirements led to the development of compressed sampling schemes based on the idea that correlations between points in the cube can be used to reduce the number of parameters required to describe the cube. A more comprehensive description is given by McMackin et al. in US Patent 8717484, issued May 6, 2014. A key drawback shared by all the Hadhamad variants mentioned above is that, even neglecting optical losses, on average only half of the EM radiation from the inlet aperture is received by the detector. This limitation is partially overcome by the configurations shown in U.S. Patents 4,615,619 and 4,799,795 (Fateley), issued October 7, 1986, and January 24, 1989, respectively. These patents propose using an array of electro-optic filters that can transmit and reflect EM radiation to produce a standard Hadhamad mask. Fateley, referring to Figure 5, proposes that both transmitted and reflected radiation can be measured, which in principle improves the effective transmission. However, Fateley's implementation provides only 50% modulation (5% to 55% transmission). Only half of the EM radiation from the inlet aperture is effectively utilized. Fateley does not provide any disclosure regarding how information from the second detector is used. Another limitation of all the Haddamard variants mentioned above is that the optimal spectral resolution achievable is limited by the fixed geometry of the masking element size. The Hadhamed transform time-of-flight mass spectrometer was first described by Brock et al. (1998). The ion system is continuously introduced, skimmed, accelerated, and collimated via an electrojet needle. The collimated ion beam is incident on a Bradbury-Nielsen shutter, which either delivers the ion beam unbiased toward the detector or deflects it above and below the beam axis. The apparatus was later modified by adding detectors above and below the beam axis (Trapp, 2004) to allow measurement of both the direct and deflected beams. Compared to the previous version, the modification increased the duty cycle to nearly 100% and improved the SNR by 29%. Theoretically, a 44% improvement is expected. The difference is attributed to incomplete separation of the ion stream that contributes to the false detector channel. In both versions, the shutter is temporally modulated according to the columns of the Hadhamed matrix to deliver ion packets with pseudo-random time shifts. Each packet unfolds in the field-free zone where the lightest ions travel fastest. The detector receives overlapping time-shifted packets according to the chronological order of each column. An inverse Hadamad transformation is performed to recover the original mass distribution within each packet. In subsequent work, Hudgens et al. modulated the ion source to generate Hadamad patterns. Brock, A.; Rodriguez, N.; Zare, N., Hadamard Transform Time-of-Flight Mass Spectroscopy, Analytical Chemistry, 70, 3735-3741 (1998). Trapp, O.; Kimmel, JR; Yoon, OK; Zuleta, IA; Fernandez, FM; Zare, RN. Continuous Two Channel Time-of-Flight Mass Spectroscopic Detection of Electrosprayed Ions. Agnew. Chem. Int., 43rd ed., 6541-6544 (2004). Hudgens, JW; Bergeron, D. Haddamard transform electron ionization time-of-flight mass spectrometer, Review of Scientific Instruments 79(1): 014102 (2008). The disclosures of each of the above references are incorporated herein by reference or may be studied for other details of the constructions that may be used herein. [Summary of the Invention] This invention relates to a modulation system and method for analyzing wave and particle flux. Those skilled in physics will understand that the physical phenomena measured by this invention can be described by both particles and waves, and the choice of description is a matter of convenience. Modulation can be spatial, temporal, or both. Waves can be electromagnetic waves, matter waves, or pressure waves. According to one definition of the present invention, a method is provided for measuring one or more properties of an incident radiation, the method comprising the steps of: collecting the incident radiation to be measured; dividing the incident radiation into N packets, each packet containing radiation having a different value of a first property; separating the radiation packets temporally or spatially using a time modulator or a spatial modulator and changing the modulator using a modulation sequence to direct N different combinations of the incident radiation packets into at least two disjoint paths, wherein the sum of the radiation intensities of all disjoint paths is at least 60% of the total incident radiation; measuring the total radiation intensity in each path using a detector for each modulator configuration to provide a plurality of detector outputs; and statistically analyzing the detector outputs to obtain information relating to the properties of the radiation to be measured; wherein the modulator configuration sequence includes at least two configurations, for which each packet is introduced into the disjoint paths. In one specific instance, the radiation is spatially separated and guided to N>2 different regions in a measurement surface to be characterized based on source location, energy, frequency, wavelength, phase, or polarization, and the modulator is a spatial modulator placed at the measurement surface. In another specific instance, the radiation system is temporally separated using a gate modulator. According to another definition of the present invention, a method for measuring one or more properties of an incident radiation is provided, the method comprising the step of: collecting the incident radiation to be measured; The incident radiation is directed to a time modulator, a spatial modulator, or a time and spatial modulator; the modulator cyclically undergoes a sequence of M configurations, in which the radiation is divided into N parts according to the location and / or time of the incident radiation on the modulator, and a majority of each part of the incident radiation is directed to one of P disjoint paths, wherein the sum of the radiation intensities of all parts and all paths is at least 60% of the incident radiation intensity; the total radiation intensity in each path is measured using a detector for each modulator configuration to provide a plurality of detector outputs; the detector outputs are statistically analyzed to obtain information related to certain properties of the radiation to be measured; wherein P is greater than or equal to two and less than N; and wherein M is greater than or equal to N, and the modulator configuration sequence includes at least two configurations, for which a majority of each part is directed to a different path. In one specific instance, the radiation is spatially divided into N>2 parts based on source location, energy, frequency, wavelength, phase, or polarization and guided to N different regions in a measurement surface to be characterized, wherein the modulator is a spatial modulator placed at the measurement surface. In another specific instance, the radiation is divided into N>2 parts in time using, for example, a gate modulator, and the gate modulator is modulated according to the sequence. Preferably, the configuration of the modulator sequence is selected such that a matrix representation Z of the sequence configuration has the following properties: ZTZ is nonsingular; where Z has MP columns and N rows, and where each column of Z represents a measurement at a detector and each row of Z represents a range of a particle flux parameter. The elements of Z represent the fraction of particle flux received by the detector for each range specified for a column of a measurement. According to another definition of the present invention, a method is provided for measuring one or more strain values ​​of incident radiation within an interval of an independent variable, the method comprising the steps of: collecting the incident radiation to be measured; directing more than half of the incident radiation in each interval to one of at least two discontinuous paths using a spatial modulator or a temporal modulator, the modulator undergoing a sequence of configurations such that each member of the sequence directs one different combination of the incident radiation in the interval to each path, wherein the sum of the radiation intensities of all discontinuous paths is at least 60% of the total incident radiation; measuring the total radiation intensity in each path using a detector for each modulator configuration to provide a plurality of detector outputs; and statistically analyzing the detector outputs to obtain information relating to the strain values ​​of the radiation to be measured. As used herein, the term "gate" or "gate modulator" refers to a device that performs the function of acquiring a flux or particles and delivering more than half of that flux of particles to at least two different destinations at different times. One example of a gate is a multiplexer. The terms "division" and "range" are used interchangeably. They both refer to intervals that are typically independent spatial or temporal parameters, but refer to parameters that are related to both spatial and temporal parameters. The terms "statistical approach" and "statistical analysis" refer to analytical methods based on multivariate statistics, correlations, and probabilities such as those calculated directly in least squares or in the intermediate layers of neural networks. This is a general description without regard to the number of modulator configurations, the type of modulator, or the type of variable. This definition includes both partially and completely determined equation systems. Dependent means a property of radiation that can be independently of a property of radiation or unrelated to something such as time or space. In a specific instance, radiation is spatially separated and guided to N>2 different regions in a measurement surface to be characterized based on an independent property selected from a set of source location, energy, frequency, wavelength, phase, or polarization, and wherein the modulator is a spatial modulator placed at the measurement surface. In another specific example, the radiation received within a time interval T from the independent property system is temporally separated into N>2 time segments using a gate modulator. These time segments may have equal lengths T / N or unequal lengths. In the case of dependent property system intensities, time segments of equal length can be used to measure the shape of a laser pulse. A gate modulator in a time-of-flight optical spectrometer can divide a pulse of photons traveling through a dispersive medium into unequal time segments to measure the photon flux within equal wavelength intervals. Preferably, the number of different configurations of the modulator is greater than or equal to the number of groups of the independent property. This ensures that all variables can be solved. Preferably, the modulator configuration sequence includes at least two configurations for each group, wherein most of the radiation within the group is directed to different paths. Preferably, each path has a plurality of detectors, each of which measures radiation traveling along the path in a different energy range. In one specific instance, the radiation to be measured comes from a dispersive spectrometer. In one specific instance, the radiation to be measured comes from a Fourier transform spectrometer. In one specific instance, the radiation to be measured comes from an imaging spectrometer. In this specific instance, each path may have a plurality of detectors, each detector measuring radiation emitted from a different set of regions within the object being observed. In one specific instance, the radiation to be measured comes from an interference pattern. In one specific instance, the radiation to be measured comes from a diffractometer. In a specific instance, the Raman scattering of the radiation system to be measured. In one specific instance, the radiation to be measured originates from the nucleus of a particle. In one specific instance, the spatial modulator is refracted. In one specific instance, the spatial modulator is reflective. In one specific instance, the spatial modulator is diffracted. In a specific instance, the detector on each path generates an analog voltage, which is subtracted from a reference voltage level before being converted to digital form. In one specific example, the present invention receives a wave having at least one property that changes with position and time, encodes the property spatially along two or more paths using a spatial modulator, encodes the property temporally along each path using a temporal modulator, measures the wave intensity temporally along each path using a detector, and analyzes information from all detectors to provide information about the wave incident on the analyzer. That is, typically, a spatial modulator is used to perform a sequence of measurements, thereby encoding wave properties that change with the different positions of each measurement in the sequence. This sequence can be repeated to further improve the signal-to-noise ratio. In this specific example, the present invention is conceptually an intermediate between a single-detector multiplexed instrument such as a Fourier or Haddamal spectrometer and a non-multiplexed linear array of detectors. The present invention provides a signal-to-noise ratio superior to conventional multiplexed linear arrays of detectors while using a small number of detectors. That is, in another specific example, the present invention receives a wave having at least one property that changes over time, receives the wave at a detector that generates an analog signal proportional to the wave property, modulates the analog signal in time to two or more integrators, and analyzes information from all integrators to provide information about the wave incident on the analyzer. This specific example provides a method for measuring the dynamics of recurrence, featuring improved time resolution and improved signal-to-noise performance. In another specific instance, the spatial and temporal modulation instances mentioned above can be combined. The radiation may consist of particles selected from a list including, but not limited to, the following: photons, electrons, positrons, subatomic particles, protons, neutrons, ions, atoms, or molecules. Preferably, the sum of the radiation intensities measured for all different directions is at least 90% of the total radiation intensity incident on the measurement surface. Preferably, the modulator directs radiation in at least three directions. Preferably, the modulator produces a cyclic arrangement with a basic mask having at least two dissimilar regions. Preferably, the modulator directs at least half, and preferably more than 90%, of the radiation incident on each region of a basic shield to a different direction. Preferably, at least one region of the basic shield of the modulator directs a portion of the radiation incident on that region to a first direction and directs at least some of the radiation incident on that region to a different, opposite direction. In some specific instances, at least one region of the modulator is translated or rotated during a measurement such that at least a portion of one of the modulator's basic masking regions passes through at least two measurement regions. Preferably, the fraction of the radiation directed to each dissimilar direction in each measurement region is calculated as the time-weighted geometric fraction of the radiation directed to that direction by the shielding region. In some cases, the basic mask is a Hadhamed mask or a pseudo-random mask. In some cases, spatial modulators produce a cyclic arrangement of a basic mask, and at least a portion of the mask characteristics are determined by the movement of the mask during a measurement period. However, non-cyclic arrangements may also be used, for example, where each mask element is individually adjustable, as in a micromirror array. Cyclic arrangements are caused by masks with fixed geometries. Preferably, at least one element of the modulator has at least two different configurations, such as a micromirror array, a micrograting, a liquid crystal, or an electro-optic device. Preferably, the output of each detector is normalized to the sum of the outputs of all detectors. Preferably, these properties of the radiation to be measured are obtained by multivariate least squares analysis. Preferably, the information in the radiation to be measured is obtained by principal component analysis of the original detector output (as described above) or the normalized detector output (as described above). One important feature is the use of statistical analysis to analyze a radiation pattern with N regions to find a small number of m latent variables; m measurements are performed, and the value of each latent variable is inferred using statistical analysis. This feature is useful in some relevant cases within the N regions and in some cases where the N regions contain little to no information of interest. Each latent variable describes a portion of the total variance in the basic N-region dataset. Users can choose to use only as many latent variables as are needed to model the N-region dataset with an acceptable level of accuracy. For example, if the latent variables are found using PCA, the first m latent variables typically describe the majority of the variance in the basic N-region dataset. Empirically, the first three latent variables often describe more than 90% of the variance in infrared spectra with hundreds of spectral regions. Users can choose to use three latent variables as an acceptable approximation of the N-region dataset, or choose to use more latent variables to improve the accuracy of the approximation. Preferably, the total radiation intensity summed over all detectors is modified for at least some of the spatial modulator configurations; and in each modulator configuration, an original intensity value is generated at each detector; wherein the total intensity of the modulator configuration is C=SUM(detector intensity di), where the data vector is loaded with the value di'=di / C, such that this normalization compensates for the variation in intensity. In one instance, the modulator includes a dynamic Tpritz mask and changes the resolution by varying the sampling rate. In one important end-use, the radiation system is provided by a time-of-flight mass spectrometer. In one important end-use, the radiation system is provided by fluorescence decay. In one important end use, radiation is provided by a flow cell used to measure fluid flow rate. In one important end-use, radiation is provided by light reflected from self-analyzed particles. In one important end-use, radiation is provided by ultrasound waves emitted from a solid material to analyze the density of the material. Preferably, a bandpass filter is used to limit the range of wavelengths propagating through the detection system and to determine the boundary conditions for analyzing the system. Preferably, a bandpass filter is used to remove spectral bands with small diagnostic values, so that the dynamic range of the detector is used only to measure spectral bands with larger diagnostic values. Preferably, a bandpass filter is used to optimize the instrument sensitivity for detecting a specific analyte by weighting the contribution of the spectral band in proportion to the importance of the different spectral bands. According to another aspect of the present invention, a method for measuring one or more properties of an incident radiation is provided, the method comprising the steps of: collecting the incident radiation to be measured; dividing the incident radiation into N packets, each packet containing radiation having a different value of a first property; separating the radiation packets temporally or spatially using a temporal or spatial modulator and changing the modulator using a modulation sequence to guide at least N different combinations of the incident radiation packets into at least two disjoint paths; measuring the total radiation intensity in each path using a detector configured for each modulator to provide a plurality of detector outputs; statistically analyzing the detector outputs to obtain information relating to the properties of the radiation to be measured; wherein the radiation pattern having N regions is analyzed by statistical analysis to find a small number of m latent variables in a spectrum; performing m measurements, and using statistical analysis to infer the value of each latent variable. According to another aspect of the present invention, a method for measuring one or more properties of incident radiation is provided, the method comprising the steps of: collecting the incident radiation to be measured; dividing the incident radiation into N packets, each packet containing radiation having a different value of one of the first properties; separating the radiation packets temporally or spatially using a time or space modulator and changing the modulator using a modulation sequence to guide at least N different combinations of the incident radiation packets into at least two disjoint paths; measuring the total radiation intensity in each path using a detector configured for each modulator to provide a plurality of detector outputs; statistically analyzing the detector outputs to obtain information relating to the properties of the radiation to be measured; wherein the intensity of one of the radiations changes for each of the plurality of samples; and in each time sample, an original intensity value is generated at a first detector A and a second detector B; wherein the time step (time The total intensity in step) is C=A+B, where the data vector is loaded with values ​​a'=A / C and b'=B / C, so that this normalization compensates for the change in intensity. According to another aspect of the present invention, a method for measuring one or more properties of an incident radiation is provided, the method comprising the steps of: collecting the incident radiation to be measured; dividing the incident radiation into N packets, each packet containing radiation having a different value of one of the first properties; separating the radiation packets temporally or spatially using a temporal or spatial modulator and changing the modulator using a modulation sequence to guide at least N different combinations of the incident radiation packets into at least two disjoint paths; measuring the total radiation intensity in each path using a detector configured for each modulator to provide a plurality of detector outputs; and statistically analyzing the detector outputs to obtain information relating to the properties of the radiation to be measured; wherein the modulator includes a dynamic Teplitz mask and changes the resolution by varying the sampling rate. According to another aspect of the present invention, a method for measuring one or more properties of an incident radiation is provided, the method comprising the steps of: collecting the incident radiation to be measured; dividing the incident radiation into N packets, each packet containing radiation having a different value of a first property; separating the radiation packets temporally or spatially using a time- or space-based modulator and changing the modulator using a modulation sequence to direct at least N different combinations of the incident radiation packets into at least two disjoint paths; measuring the total radiation intensity in each path using a detector configured for each modulator to provide a plurality of detector outputs; statistically analyzing the detector outputs to obtain information relating to the properties of the radiation to be measured; including the steps of: estimating the time-weighted contribution of each band to the total intensity received by each detector in each measurement and setting the coefficients of the Z matrix to explicitly model the time-weighted contributions. This is functionally equivalent to applying a convolution, and even in the case of a single detector, the resulting H matrix is ​​not binary and singular. As described in more detail below, the configuration disclosed herein provides a multiplexing method for efficiently measuring the properties of particle flux using an optimal number of detectors. In a specific instance, these particles are photons. In the following discussion, the terms photon, electromagnetic radiation, and radiation are used interchangeably. The method can be used for applications including, but not limited to, spectroscopy, crystallography, interferometry, imaging, and spectral imaging. The collecting optics known in this technique are used to focus at least three (and usually more) distinct portions of electromagnetic radiation and project these portions onto a surface to be measured, and a spatial modulator on this surface directs at least two portions to a differential detector. These portions of radiation can be varied according to source, polarization, wavelength, phase, or any combination thereof. In another specific example, these particles are neutrons. This method can be used in applications including neutron scattering and neutron diffraction. In another specific example, these particles are electrons. This method can be used in applications including electron diffraction and electron microscopy. In another specific example, these particles consist of protons and ions. This method can be used in applications including mass spectrometry, ion mobility spectrometry, and capillary electrophoresis. In yet another specific example, these particles move together to form pressure waves from atoms or molecules. This method can be used in applications including acoustic spectroscopy and acoustic imaging. The objective of this invention is to collect and measure greater than 60%, and preferably substantially all, of the incident wave or particle flux energy. For illustrative purposes, reference is made herein to electromagnetic radiation, but the concepts described also apply to other waves, such as, but not limited to, sound waves, neutron waves, electron waves, ion waves, atomic waves, and molecular waves. Referring now to electromagnetic waves, this invention includes a selectable bandpass filter, a spatial or temporal modulator, two or more detector sets or integrators, a control system, and an analysis system. A bandpass filter is used to limit the range of wavelengths propagating through the detection system and to determine the boundary conditions for solving equation (3) (see below) by the analysis system. Secondly, a bandpass filter can be used to remove spectral bands with small diagnostic values, so that the detector's dynamic range is used only to measure spectral bands with larger diagnostic values. Thirdly, a bandpass filter can be used to optimize the instrument sensitivity for detecting an analyte by weighting the contribution of that spectral band in proportion to the importance of different spectral bands determined by chemometric analysis (e.g., eigenvectors associated with a particular analyte). The advantage of this method is that the dynamic range of the detector array or integrator is optimally utilized to achieve the best possible accuracy in analyte measurement. In a specific example, a spatial modulator is controlled by a system that steps through a sequence of configurations. In each configuration, the spatial modulator divides the incident radiation into two or more portions having spectral content specific to the configuration, and each portion is measured using a different set of detectors. In the simplest case, there is a one-to-one correspondence between detectors and portions. In cases where a wider wavelength range is being measured, a set of detectors can be used to measure each portion. For example, a set may include, but is not limited to, UV detectors, visible light detectors, near-infrared detectors, mid-infrared detectors, microwave detectors, and radio wave detectors. It should be understood that additional optics such as prisms, gratings, bandpass filters, dichroic mirrors, mirrors, and lenses are used to direct each spectral region to the appropriate detector. The intensity or amplitude at each detector is integrated (using heterodyne) and the result is transmitted to an analysis unit. A spatial modulator can divide incident radiation by transmitting one portion and reflecting one or more other portions, or by reflecting two or more portions in different directions. Alternatively, a spatial modulator can divide incident radiation by transmitting one portion and refracting one or more portions in different directions, or by refracting two or more portions in different directions. Alternatively, a spatial modulator can divide incident radiation by transmitting one portion and diffracting one or more portions in different directions, or by diffracting two or more portions in different directions. Generally, any combination of transmission, reflection, refraction, and diffraction can be used to achieve the purpose of directing different portions of radiation in different directions. In some specific instances, the spatial modulator and its associated optics and detectors move relative to the source of the radiation to be measured, and this relative motion produces the desired modulation. For example, an image on a spatial modulator of a satellite orbiting the Earth moves relative to the spatial modulator at a near-constant speed and modulates the image information in the same way as if the image were stationary and the modulator were moving. In both cases, relative motion produces modulation. Other methods familiar to those skilled in this technique can be used to manipulate non-electromagnetic waves. In a specific example described below, radiation reflected from a rapidly moving object is collected and transmitted to the entrance slit of the spectrometer. The total radiation received at each time step varies due to variations in the distance and orientation of the object relative to the irradiation source and the collecting optics. At each time step, an initial intensity value is generated at detector A (reflection) and detector B (transmission). The total intensity in the time step is C = A + B. The data vector is loaded with values ​​a' = A / C and b' = B / C. This normalization compensates for variations in the overall signal level. In another specific example, the radiation to be measured is incident on one or more detectors for a total measurement time T. For illustrative purposes, these detectors may be photodiodes, which produce photoelectrons via the photoelectric effect. The total measurement time is divided into N intervals. During each time interval, a time modulator selects one of a plurality of integrators according to a pseudo-random sequence as discussed below and directs substantially all of the photoelectrons generated during that time interval to the selected integrator. In the simplest case of two integrators A and B, A or B receives photoelectrons during each time interval, and the sum of the photoelectrons received by A and B in time interval T is substantially equal to the total number of photoelectrons generated by the photodiode in time interval T. In the case of N unique sequences, the measurement procedure is repeated at least N times, and the number of photoelectrons received by each integrator for each measurement is transmitted to the analysis system. Now, turning to the reference analysis system, attention should be paid to the general elements in all the specific examples of the multiplexing system mentioned above. The difference lies in the details of implementation. The general multiplexing equation system is y=AZb+e (1) Where y is the observation row vector, A is the instrument function, Z is the matrix of multiplication coefficients, b is the row vector of particle flux intensity, and e is the row vector of residuals due to measurement errors or uncertainties. Each column of Z contains the multiplication coefficients for a single measurement at a detector, and the corresponding column of the measurement vector y contains the measured values. Each row of Z corresponds to a series of values ​​for an independent parameter. There is no restriction on the range represented in each row. The range of values ​​represented in each row may be discontinuous, and the range in each row may represent different fractions of the total span of the independent parameters represented by all rows. The range represented in each row is discontinuous for the measurement of the underlying parameters discussed herein. The ranges represented by the rows of Z may overlap. The multiplication coefficients in each row of Z represent the fraction of particle flux or radiation that guides a path to the detector specified by the column within a specified interval. Each measurement cycle includes at least two detectors and two columns of Z. The instrument function in an optical system is, for example, a convolution of the efficiency of each optical component in the system. For simplicity, matrix A is chosen as the ideal system of identity matrix I in the following discussion. The multiplexing coefficients of Z represent the geometry of the spatial modulator or the time segment of the time modulator. The residuals (noise) are chosen to be uncorrelated in the following discussion. For the less common case where the residuals are correlated, the solution is known to those skilled in this technique. There are n spectral intensities and n measurements of different combinations of these n spectral intensities. The size of Z is n×n, and the sizes of both b and y are n×l. This special case of Z has the solution b=Z⁻¹y (2) If the Z column is further Hadamard encoded, the Z matrix is ​​usually referred to as the S matrix in the literature. The S matrix exists only for the specific value n = 2m - 1, where m is an integer greater than or equal to 0. The S matrix has the useful property that the inverse matrix is ​​easy to compute and all its elements can be reduced to binary code, thus greatly simplifying the computation. The S matrix method uses an approximation of half the particle flux (n / 2 + 1) / n. Prior techniques include the S matrix method used in tandem, which provides a theoretical square root (2) improvement in the SNR due to the increased signal transmission. Equation 1 also describes a linear array of detectors. In this case, Z is the identity matrix I. The instrument function matrix A includes terms describing the differences in response between the detectors in the array. There are n spectral intensities and n simultaneous measurements performed by the n detectors. This invention is a concrete example of equation (1) without the simplifying assumptions that generate equation (2). The general case used in this invention is computationally more demanding, but the additional calculations are justified by the further improvement in signal-to-noise ratio relative to the increase in signal-to-noise ratio achievable by the simpler case described by equation (2). As discussed above, this invention includes d detectors or integrators (d>=2) and also allows for the possibility of repeating measurements c times (c>=1). In this invention, the size of Z is ndc×n; the size of y is ndc×l; and the size of b is n×l. It should be noted that the minimum value of nd (c=1) of measurements is required. It should be understood herein that n is the number of parameters measured, which may be latent parameters. Data analysis can still be performed even if data acquisition is interrupted by a non-integer value of c>1. Furthermore, the matrix elements of Z are typically complex numbers, rather than integers as in previous techniques. For the following discussion, it is convenient to consider that Z includes a convolution with respect to the instrument function matrix A, since convolution with respect to A typically introduces non-integer elements. Due to its size, Z cannot be directly inverted in this case. In fact, the spectral intensity b can be estimated with minimum error using multiple least squares (MLS) solutions of equation (1): b = (ZTZ)⁻¹ZTy (3) For further discussion, it is convenient to define H = (ZTZ)⁻¹ZT. The covariance matrix ZTZ is symmetric, which simplifies the calculation of the inverse matrix. In general, calculating the inverse matrix is ​​computationally intensive. It should be noted that if the seed sequence of the Z series is cyclic, then ZTZ is always a cyclic matrix and therefore the inverse matrix can be calculated using the Discrete Fourier Transform. Other solutions to Equation 1 are possible and may be better for larger values ​​of N. An alternative approach is to correlate the measurement vector y with the known input vector b to infer the coefficients of the transformation from y to b. This approach can be performed by direct methods and by unsupervised methods such as neural networks. While the MLS method is a better approach for solving Equation 1 for medium-sized systems (N < 1024), other statistical methods such as supervised and unsupervised correlations will also be effective and are within the scope of this invention. This invention imposes few constraints on the form of Z. For measuring N bands using Equation 3, all that is required is that Z has at least N columns; each band is represented in at least one column; each column is unique; and the ZTZ system is non-singular. That is, measurements can be performed using a convenient form of Z and transformed to another reference for calculation. The elements of Z are not limited to integers as in the prior art, but are generally complex numbers. However, in most applications, the elements of Z are real numbers in the interval [0,1] and represent the fraction of radiation directed to the detector. It should be recognized that multiplying all elements of Z by a common factor will produce equivalent results and may be preferable when calculations are performed using integer operations for performance reasons. Different choices of Z produce different signal-to-noise ratios in the solutions to Equation (3). Z is chosen to balance engineering considerations such that the RMS noise in the results calculated according to Equation (3) is minimized. One important class of solutions is constructed by a cyclical arrangement or a basic pattern of a seed pattern having at least two distinct regions. As mentioned above, the Hadhamed patterns in the prior art are a subset of this category optimized to minimize RMS noise, at least in the case of a single detector. Within the scope of this invention, the Hadhamed pattern is extended to two detectors by including the complement of the Hadhamed pattern for a second detector. For two or more detectors, a pseudo-random seed sequence can be used as the basis for a cyclic permutation. For two or more detectors within the scope of this invention, the basic seed pattern for each detector can be generated by randomly assigning values ​​between 0 and 1 to each detector for each measurement, such that the sum across all detectors equals 1 for each measurement. The value assigned to each row represents the fraction of the particle flux incident on the corresponding range of independent parameters to be directed to the designated detector. RMS noise can be minimized by a genetic algorithm that iteratively mutates the seed sequence and calculates the RMS noise according to Equation 3. Another important category of seed patterns is based on Tpritz patterns, which have a block of 1s and a block of 0s. Entity masks with Tpritz patterns are generally easier to create than masks based on pseudo-random seeds because the entity size of the region can be larger. Alternatively, elements of Z can be selected so that there is no relationship between columns, in order to optimize the signal-to-noise ratio. In applications, y represents the quantity measured. y can be written as y = yb + ys (4) Where yb is a constant fundamental signal and ys represents a variable signal. Substituting into (3), we get b = Hyb + Hys (5) Since yb is a constant vector, Hyb is also a constant vector. Equation 5 indicates that a constant can be added to any input signal y, and the unique effect is a constant shift in the resulting spectrum b. In hardware, the signal y is typically an analog voltage (but can be another measurable), which has been shifted, amplified, and then digitized. The hardware components operate within set limits that define the dynamic range of the detection system. Ideally, the dynamic range of the detection system is set to match the range of the input signal generated by the sample to be measured. The detection system can be calibrated by performing the following steps. 1. Measure y with zero offset and low magnification in a representative set of samples. 2. Determine the mean minimum and maximum signal values ​​and standard deviation of each sample in the representative set. 3. Set the minimum expected signal to the average minimum value minus three times the standard deviation. 4. Set the maximum expected signal to the average maximum signal plus three times the standard deviation. 5. Set the voltage offset to the expected minimum signal. 6. Set the amplification gain g to (detection system dynamic range) / (expected maximum value - expected minimum value). During operation, ys is measured within the dynamic range of the detection system and then digitized. For many applications, the only part of interest is ys. Depending on the situation, the digital value of yb can be added to recover y. For many practical applications of pattern recognition within the scope of this invention, calculating the spectral intensity vector b is not necessary. As can be seen from Equation 3, b is a linear combination of y vector elements. As explained in the normalization procedure above, y vector elements can be a linear combination of measurement results. Any analytical procedure for calculating the combination of spectral intensities b can also be applied to the measurement vector y and will produce equivalent results relative to a different set of representations of the fundamental vectors. To a layperson, different sets or fundamental vectors are simply different coordinate systems. For example, in three-dimensional space, a point can be represented in Cartesian coordinates as {x, y, z} or equivalently in spherical coordinates as {r, θ, Φ}. In most practical applications, the number of dimensions is greater than three. The analytical procedure can be any multivariate statistical analysis method, such as LDA, MLS, PLS, PCA, or propagation methods, such as neural networks. For example, pattern recognition algorithms such as Principal Component Analysis (PCA) habitually calculate a linear combination of b vector elements in the way that best captures the dataset. Since the elements of vector b are linear combinations of the elements of vector y, it can be concluded that the PCA algorithm can use the original data vectors y as input to directly produce equivalent results. The configuration described herein enables the acquisition of spectra with different levels of spatial resolution. In the prior art, resolution was fixed by a spatial encoder. In this invention, spectral resolution can be increased by increasing the sampling rate. The corresponding code is changed to reflect the higher sampling rate by copying the input. For example, the code sequence {1001101} becomes {11 00 00 11 11 00 11} when the resolution is doubled. Although resolution can be increased indefinitely by this method, the practical limit is determined by the resolution of the system that guides the particle flux to the spatial modulator. Sampling time increases proportionally to resolution: doubling the spectral resolution requires doubling the sampling time. Fourier transform spectrometers have the same time dependence, but require shifting the scanning mirror in the interferometer by up to two times. The improved resolution in this invention can be achieved by a single electronic component without changing any mechanical parts. As shown in Figure 14 below, only specific operating parameters provide effective results with enhanced resolution. The resolution of the array detector is fixed. By reducing the slit width, the resolution in conventional dispersive instruments is improved, resulting in a loss of throughput. Therefore, the sampling time increases with the square of the resolution improvement. Multiplexing instruments have clear advantages. Regarding the work cycle, the configuration described in this article can be operated in both static and dynamic modes. In static mode, the spatial modulator remains in a fixed configuration for the duration of each measurement. For a single detector, this corresponds to the conventional Hadhamed spectrometer in the prior art. In this mode, there is a one-to-one correspondence between the physical region of the modulator and the grouping of particle fluxes. In dynamic mode, the spatial modulator moves relative to the spatially variable particle flux to be measured. This relative motion results in a one-to-many relationship between the grouping of particle flux and the physical regions of the modulator. During a measurement cycle, the particle flux from each region is directed to different detectors based on the relative time-weighted geometry of the modulator region used for each detector. A Tullitzer pattern can consist of two or more sets of spatially distinct regions. Each set of regions is designed to direct substantially all incident EM radiation onto a detector or a set of detectors other than that set's region. Components may include one or more optical elements to concentrate EM radiation from spatially separated regions of that set onto the detector. Each set's region may use reflection, transmission, refraction, or diffraction to direct EM radiation toward the detector or a set of detectors. Transmissive regions can be constructed by placing a transmissive material within the region, or more preferably by placing a slit within the region. Reflective regions can be constructed by placing a highly reflective material within the region. The reflective material is preferably a metal, such as Al, Ag, or Au, which have high reflectivity over a broad spectral range. Dielectric mirrors can provide higher reflectivity over a narrower spectral range. Other materials providing high reflectivity in the region of interest can be used. The incident angle can be varied to provide a set of reflective regions directed toward different detectors. In some specific instances, these reflective regions have planar surfaces, and in others, they have curved surfaces to concentrate EM radiation at the detector. Refractive regions can be constructed by placing a material with a refractive index >1 within the region. The refractive material is preferably generally wedge-shaped such that the overall direction of EM radiation exiting the refractive region is not parallel to the overall direction of EM radiation on the refractive region. Refractive regions with different exit directions can be constructed by varying the wedge angle. Specifically, two or more sets of regions can be constructed using two or more distinct wedge angles. The surface of the refractive region can be planar or curved to concentrate EM radiation at the detector. Diffraction regions can be constructed by placing diffraction gratings within the regions. Diffraction gratings can be transmissive or reflective. Since EM radiation of different wavelengths will fall on spatially separated diffraction surfaces in sets with a common grating period, the set of paths leading to the common detector is a line in Theta-Z space. It should be noted that diffraction gratings can act as several logical regions because the incident radiation is guided to several diffraction orders. The relative intensity in each order can be tuned by modifying parameters such as the flare angle, groove depth, or grating material. Diffraction regions with different emission directions can be constructed by changing the grating period. The diffraction surface can be planar or curved to concentrate EM radiation at the detector. The reflective and refractive regions envisioned in this invention create a spatial modulator that is essentially variable in three dimensions compared to previously designed, which were essentially two-dimensional. Two-dimensional spatial modulators are generally easier to manufacture than three-dimensional ones, but three-dimensional spatial modulators can offer superior performance. The diffraction region option has the advantage of allowing multiple output directions to be combined with ease of manufacture at the expense of reduced efficiency. 41…Second Surface / Measuring Surface [Simplified Explanation of the Diagram] A specific example of the invention will now be described with reference to the accompanying drawings, in which: Figure 1 is an isometric view of a particle sorting device, showing an example in which one of the methods according to the invention can be used. Figure 2 is a vertical cross-sectional view through the device in Figure 1. Figure 3 is a schematic diagram of the measurement system 28 of the device in Figures 1 and 2, with two detectors configured according to the present invention. Figure 4 shows a representative cross-section of the spatial modulator with three types of reflective regions shown in Figure 3. Figure 4A shows a graph of curves arranged in a row to guide radiation incident on different parts of the measurement surface to different types of regions in three directions. Figure 5 is similar to Figure 4, except that the fixed mirror system is replaced with a movable mirror that can be switched between three positions. Figure 6 shows a representative cross-section of a spatial modulator with three types of refractive regions. Figure 7 is similar to Figure 6, except that it uses a single type of refractive element and applies an electric field to change the refractive index, thereby directing the incident radiation in three different directions. Figure 8 shows a representative cross-section of a spatial modulator with three types of diffraction regions. Figure 9A is a view of a space encoder disk characterized by being parallel to the axis of rotation. Figure 9B is a view of a space encoder disk that is perpendicular to the axis of rotation. Figure 10 is a graph of RMS noise pairs convolution based on numerical simulations using the configuration shown in Figure 3, with 23 channels and three sampling models. Figure 11 is a graph similar to Figure 10, except that the calculation is performed on 127 channels, which has more practical applications than the 23-channel case. Figure 12 is a graph of RMS noise versus convolution, which shows the dependence of a 127-channel system on RMS noise as the number of detectors changes. Figure 13 shows the RMS noise pair of the space modulator operating cycle with 127 channels moving at a constant speed. Figure 14 is a graph of the RMS noise pair of the system with three detectors and 23 channels with respect to the first 10 harmonics of the reference sampling frequency in the operating cycle. Figure 15 is a schematic diagram of the time-of-flight mass spectrometer with three detectors using the present invention. Figure 16 shows a schematic diagram of the system for measuring fluorescence decay using the present invention. Figure 17 shows a schematic diagram of a system for a flow channel using the present invention. Figure 18A shows a schematic diagram of the weighting function used in the measurement procedure of this invention. Figure 18B shows a schematic diagram of the dependent parameters to be measured. Figure 18C shows a schematic diagram of the integral intensity of the dependency parameter in Figure 18B. Figure 19A illustrates an example weighted function of the present invention. Figure 19B illustrates an example weighted function of the present invention. Figure 19C illustrates an example weighted function of the present invention. Figure 20A illustrates the effect of relative motion on the weighting function of this invention. Figure 20B shows an example of the most general weighting function of the present invention.

Implementation Method

Claims

1. A method for measuring one or more variables of incident radiation within an interval of an independent variable, wherein the one or more variables change according to the independent variable, the method comprising the steps of: collecting the incident radiation to be measured; directing more than half of the incident radiation in each interval to one of at least two disjoint paths using a spatial modulator or a temporal modulator, the modulator undergoing a sequence of configurations such that each member of the sequence directs different combinations of incident radiation within the interval to each path; wherein the sum of the radiation intensities of all disjoint paths is at least 60% of the total incident radiation; measuring the total radiation intensity in each path using a detector configured for each modulator to provide a plurality of detector outputs; and statistically analyzing the detector outputs to obtain information relating to the strain values ​​of the radiation to be measured.

2. The method as described in claim 1, wherein the modulator cyclically undergoes a sequence of M configurations, in each configuration, the incident radiation is divided into N parts according to the location and / or time of the incident radiation incident on the modulator, and a majority of each part of the incident radiation is directed to one of P discontinuous paths; wherein P is greater than or equal to two and less than N, and wherein M is greater than or equal to N, and the modulator configuration sequence includes at least two configurations, for which a majority of each part is directed to a different path.

3. The method as claimed in claim 1, wherein the radiation is spatially separated and directed to N>2 different regions to be characterized in the measurement surface based on the source location, wavelength, phase or polarization, and wherein the modulator is a spatial modulator placed at the measurement surface.

4. The method as described in any one of claims 1-3, wherein the radiation is divided in time into N>2 parts using a gate modulator modulated according to the sequence.

5. The method as described in any one of claims 1-3, wherein the configuration of the sequence of the modulator is selected such that the matrix representation Z of the configuration of the sequence has the following properties: ZTZ is nonsingular; wherein Z has MP columns and N rows, and wherein each column of Z represents a measurement in a detector and each row of Z represents a range of independent parameters, and the elements of Z represent the fraction of particle flux from each range in that column.

6. The method as described in claim 5, wherein at least one element of Z is a non-integer.

7. The method as described in claim 5, wherein when convolution is applied to the matrix, the encoding pattern is neither binary nor orthogonal.

8. The method as described in any one of claims 1-3, wherein the radiation is spatially separated and directed to N>2 different regions to be characterized in the measurement surface based on independent properties selected from a set of source locations, wavelengths, phases or polarizations, and wherein the modulator is a spatial modulator placed at the measurement surface.

9. The method described in any one of claims 1-3, wherein the radiation is spatially separated based on an independent property, wherein the independent property is time, and the radiation is temporally separated using a gate modulator.

10. The method as described in claim 9, wherein the number of different configurations of the modulator is greater than or equal to the number of groups of the independent property.

11. The method as described in any one of claims 1-3, wherein the modulator configuration sequence includes at least two configurations for each group, wherein a majority of the radiation within each group is directed to different paths.

12. The method as described in any one of claims 1-3, wherein each path has a plurality of detectors, and wherein each detector measures radiation traveling along the path in a different energy range.

13. The method as described in any one of claims 1-3, wherein each path has multiple detectors and each detector on the path measures radiation from a different origin region.

14. The method as described in any one of claims 1-3, wherein the radiation to be measured originates from one of the following: a dispersive spectrometer; a Fourier transform spectrometer; an imaging spectrometer; an interference pattern; a diffractometer; from Raman scattering; a particle nucleus; a time-of-flight mass spectrometer; fluorescence decay; a flow meter for measuring fluid flow rate; light reflected from a particle being analyzed; radiation reflected from a vibratingly excited solid material; and an interference pattern generated by radiation reflected from a reference surface.

15. The method as described in any one of claims 1-3, wherein the spatial modulator is one of refractive, reflective, or diffractive properties.

16. The method as described in any one of claims 1-3, wherein the detector on each path generates an analog voltage, and the analog voltage is subtracted from a reference voltage level before being converted to digital form.

17. The method as described in any one of claims 1-3, wherein the modulator generates a cyclic arrangement of basic masks having at least two dissimilar regions.

18. The method as described in claim 17, wherein the fraction of the radiation directed to each dissimilar direction in each measurement region is calculated as the time-weighted geometric fraction by which the shielding region directs the radiation to that direction.

19. The method as described in claim 17, wherein the modulator generates a cyclic arrangement of the basic mask, and at least a portion of the mask characteristics are determined by the movement of the mask during a measurement period.

20. The method as described in claim 17, wherein at least one element of the modulator has at least two different configurations.

21. The method as described in claim 17, wherein the modulator includes a dynamic Teplitz mask and varies the resolution by changing the sampling rate.

22. The method as described in any one of claims 1-3, wherein each detector output is normalized to the sum of the outputs of those detectors.

23. The method as described in any one of claims 1-3, wherein the properties of the radiation to be measured are obtained by multivariate least squares analysis.

24. The method as described in any one of claims 1-3, wherein the information in the radiation to be measured is obtained by multivariate statistical analysis of the output of the original detector or the output of the normalized detector.

25. The method as described in any one of claims 1-3, wherein the information in the radiation to be measured is obtained by correlation analysis of the original detector outputs or the normalized detector outputs.

26. The method as described in any one of claims 1-3, wherein a radiation pattern having N regions is analyzed by statistical analysis to find a small number of m latent variables in the spectrum; m measurements are performed, and the value of each latent variable is inferred using statistical analysis.

27. The method as described in any one of claims 1-3, wherein the total radiation intensity summed for all detectors changes with at least some of the spatial modulator configurations; and in each modulator configuration, an original intensity value is generated for each detector; wherein the total intensity of the modulator configuration is C=SUM(detector intensity di), wherein the data vector is loaded with the value di'=di / C such that this normalization compensates for the variation in intensity.

28. The method as described in any one of claims 1-3, wherein a bandpass filter limits the range of wavelengths propagating through the measurement system to determine boundary conditions for analyzing the system.

29. The method as described in claim 28, wherein the bandpass filter is further used to optimize instrument sensitivity by weighting the transmittance of different spectral bands in the measurement system in proportion to the importance of the spectral bands for the measurement of a particular analyte.

30. The method as described in any one of claims 1-3, wherein the intensity of the radiation changes with each of a plurality of samples, and at each time sample, the original intensity value is generated at a first detector A and a second detector B, wherein the total intensity in the time step is C=A+B, and wherein the data vector is loaded with values ​​a'=A / C and b'=B / C such that this normalization compensates for the change in intensity.

31. The method as described in any one of claims 1-3 above, comprising: The incident radiation is divided into N packets, each packet containing radiation with different values ​​of the first property; The radiation packets are separated in time or space using a temporal or spatial modulator and the modulator is changed using a modulation sequence to direct at least N different combinations of incident radiation onto at least two disjoint paths. include The following steps are taken: in each measurement, estimate the time-weighted contribution of each band pair to the total intensity received by each detector and set the coefficients of the Z matrix in order to explicitly model these time-weighted contributions.

32. The method as described in any one of claims 1-3, wherein the spatial modulator and associated optics and detector move relative to the source of the radiation to be measured, and the relative motion produces the desired modulation.

33. The method of any one of claims 1-3, wherein the modulator cyclically undergoes a sequence of M configurations, in which the incident radiation is divided into N parts according to the position of the radiation incident on the modulator, and a majority of each part of the incident radiation is directed to one of P discontinuous paths; wherein P is greater than or equal to two and less than N, and wherein M is greater than or equal to N, and the modulator configuration sequence includes at least two configurations, for which a majority of each part is directed to a different path.

34. The method of any one of claims 1-3, wherein the modulator cyclically undergoes a sequence of M configurations, in which the incident radiation is divided into N parts according to the time of incident on the modulator, and a majority of each part of the incident radiation is directed to one of P discontinuous paths; wherein P is greater than or equal to two and less than N, and wherein M is greater than or equal to N, and the modulator configuration sequence includes at least two configurations, for which a majority of each part is directed to a different path.

35. The method as described in any one of claims 1-3, wherein the modulators are arranged without gaps between regions to provide a single package fraction.

36. The method as described in any one of claims 1-3, wherein the spatial modulator remains in a fixed configuration for the duration of each measurement.

37. The method as described in any one of claims 1-3, wherein the spatial modulator is relatively movable relative to the spatially variable particle flux to be measured, and during a measurement cycle, the particle flux from each region is directed to different detectors according to the relative time-weighted geometric cross section of the modulator region for each detector.

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