Optical Department

Abstract

The present invention relates to an optical system including a microscope having an optical axis, an illumination source for the microscope, and a self-referencing phase imaging system. The illumination source is configured to illuminate an object space. The microscope is configured to couple an object plane and an image plane in the object space, and the self-referencing phase imaging system is located in or near the image plane. The self-referencing phase imaging system is configured to generate real intensity and phase images of the object space. The temporal coherence (TC) of the illumination source is between 0.4% and 6%, and the spatial coherence (SC) of the illumination source at the level of the self-referencing phase imaging system is between 0.4% and 10%. The optical system further includes a processing unit configured to numerically propagate the real image along the optical axis.

Description

[Technical Field]

[0001] The present application relates to an optical system. Such an optical system makes it possible to measure the concentration of nanoparticles, in particular without prior knowledge of the nanoparticles and without requiring modification of the nanoparticles or their medium. [Background Art]

[0002] In the prior art, optical measurement of nanoparticle concentration encounters the problem of providing a tool that determines the measurement volume in which nanoparticles are imaged. In fact, the volume in which nanoparticles can be detected depends on the size and properties of the nanoparticles as well as the optical system. Therefore, it is difficult to optically measure the concentration of nanoparticles without prior knowledge of the physical properties of the nanoparticles, so there is a need for an optical system that can facilitate this measurement.

[0003] For the purposes of the present application, the following definitions apply. -"Temporal coherence TC" of an illumination light source: the ratio of the wavelength range of the illumination light source divided by its center wavelength. -"Spatial coherence SC" of an illumination light source in an optical system: the ratio of the illumination numerical aperture of the optical system to the collection numerical aperture. -"Self-referencing phase imaging system": a self-referencing detection system or detector that provides the phase of an incident wave in addition to light intensity. This system is self-referencing because it does not use a separate optical arm as a reference. "Real image": an image of the intensity and phase of a wave field at an object plane, captured by the self-referencing phase imaging system used. "Numerically propagated image": an image of the intensity and phase of a wave field in a plane parallel to the object plane. It is numerically calculated using conventional propagation methods based on a real image, and the wave equation is solved. "Image volume": the volume imaged by numerical propagation of a real image. "Image nanoparticles" or "image particles": Nanoparticles that form a clear image or an image with maximum spatial energy density within a real image (this is especially true when the nanoparticles are within the object plane) or within a numerically propagated image (this is especially true when the nanoparticles are outside the object plane). "Numerical depth of field": The thickness in the direction of the optical axis of a volume imaged by numerical propagation, particularly a volume centered on a real image capable of faithfully imaging nanoparticles. This is the effective thickness for reconstructing a volume imaged by numerical propagation based on a real image. In other words, the numerically propagated image reflects the reality of object space. A numerically propagated image is created on a numerically propagated image that is considered faithful to the physical objects that exist within object space, and only these objects. "White laser" or "supercontinuum laser": An illumination source with high spatial coherence and near-zero temporal coherence.

[0004] The numerical depth of field defined above depends on the signal-to-noise ratio for detecting the imaged object. Furthermore, the numerical depth of field is less than or equal to the depth of field of the optical system used (hereinafter referred to as "optical" depth of field for clarity). On the other hand, the optical depth of field depends on the spatial and temporal coherence of the light used for imaging.

[0005] Therefore, in an optical system where the spatial and temporal coherence (SC, TC) approaches (0,0), the limit of the optical depth of field imposed by these two parameters approaches infinity, but the noise level increases, making it difficult or even impossible to achieve any numerical propagation of the real image, and thus the numerical depth of field is limited. On the other hand, in an optical system where at least one of SC and TC approaches infinity, the noise decreases, but the optical depth of field approaches 0. The real image contains only objects that are perfectly in focus. This also makes it difficult or even impossible to achieve any numerical propagation of the real image, and thus the numerical depth of field is limited.

[0006] Furthermore, in a fixed optical system, the signal-to-noise ratio of imaging nanoparticles depends on their size and properties. Therefore, the numerical depth of field also depends on the size and properties of the nanoparticles.

[0007] Therefore, ideally, an optical system is needed that can be used to generate a real image of nanoparticles without requiring prior knowledge of at least one of the dimensions and properties of the nanoparticles, and that provides a satisfactory numerical depth of field for this real image. [Overview of the project] [Means for solving the problem]

[0008] In this context, the present application relates to an optical system comprising a microscope having an optical axis, an illumination source for the microscope, and a self-referencing phase imaging system. The illumination source is configured to illuminate object space. The microscope is configured to couple the object plane and the image plane in object space. The self-referencing phase imaging system is positioned in or near the image plane and is configured to generate a real image of the intensity and phase of the object plane. The temporal coherence of the illumination source is between 0.4% and 6%, and the spatial coherence of the illumination source at the level of the self-referencing phase imaging system is between 0.4% and 10%. The optical system further includes a processing unit configured to numerically propagate the real image along the optical axis.

[0009] In some embodiments, the temporal coherence of the illumination source is around 2.2%, and the spatial coherence of the illumination source at the level of a self-referencing phase imaging system is around 2.5%.

[0010] In some embodiments, the illumination source is a white laser that irradiates the bandpass filter. In variations, the illumination source may also be a white plasma source or a laser diode that irradiates the bandpass filter.

[0011] In some embodiments, the illumination light source is configured to irradiate an object space in a nanoparticle solution, and the processing unit is configured to count the number of imaging nanoparticles in a real image, to numerically propagate the real image along the optical axis within an image volume of a predetermined thickness, to count the number of imaging nanoparticles in the numerically propagated image, to calculate the dimensions of the object volume corresponding to the image volume, and to calculate the nanoparticle concentration based on the counted number of imaging nanoparticles (N) and the dimensions of the object volume.

[0012] In some embodiments, the predetermined thickness is less than or equal to the numerical depth of field.

[0013] In some embodiments, a processing unit determines the numerical depth of field. It is configured to count the number of imaged nanoparticles in a real image obtained using a self-reference phase imaging system for a nanoparticle solution. The real image is configured to propagate numerically within an image volume of variable thickness that increases, It is configured to count the number of imaging nanoparticles in the image that have been numerically propagated. The system is configured to analyze the variation in the number of imaging nanoparticles counted as a function of the variable thickness of the image volume, and to identify the limiting thickness of the image volume at which the number of imaging nanoparticles no longer increases in accordance with the variable thickness of the image volume and reaches a flat area. It is configured to determine the numerical depth of field based on the identified limiting thickness.

[0014] In some embodiments, the optical system further includes a computer memory for storing a chart, which shows the correspondence between the amplitude (hereinafter referred to as "amplitude R") of a field formed from information about at least one of the real and imaginary parts of the wave field generated by imaging nanoparticles for various types of nanoparticles, and the numerical depth of field. Amplitude R can, in particular, correspond to the amplitude of the Lithoff field.

[0015] In some embodiments, the processing unit refers to a chart and determines a numerical depth of field based on the amplitude R of the imaged nanoparticles in the actual image.

[0016] In some embodiments, for a solution containing a mixture of nanoparticles, an illumination light source is configured to illuminate an object space in the solution, and the processing unit is configured to: count imaged nanoparticles in an actual image, measure the amplitude R of these imaged nanoparticles, refer to the chart as described above, and determine a numerical depth of field associated with each of these imaged nanoparticles, be configured to numerically propagate an actual image along an optical axis within an image volume of a predetermined thickness denoted as D, check using the chart whether, for each imaged nanoparticle in the numerically propagated image on each plane of the image volume, the amplitude R of the nanoparticle corresponds to a numerical depth of field denoted as H that is at least twice the distance between the numerically propagated image in which the nanoparticle is imaged and the actual image, hold the nanoparticle for counting if it corresponds, and not hold the nanoparticle for counting if it does not correspond, be configured to calculate, for each counted nanoparticle, an associated object volume that corresponds to an image volume of thickness D when H≧D, and corresponds to an image volume of a thickness equal to the numerical depth of field H associated with the nanoparticle when H<D, be configured to calculate, for all counted nanoparticles, a nanoparticle concentration equal to the sum of the reciprocals of the associated object volumes.

[0017] The above-mentioned features and advantages, as well as other features and advantages, will become apparent upon reading the following detailed description for carrying out the invention, which refers to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] [Figure 1] This figure is a graph showing the number N of nanoparticles imaged in an image volume of variable thickness Dv, in units of micrometers (μm). [Figure 2] This figure is a graph showing the numerical depth of field H in micrometers (μm) as a function of the amplitude R in arbitrary units (a.u.) of the peak of the retroreflection of imaging nanoparticles. [Figure 3] This figure shows an example of spatial coherence (SC) and temporal coherence (TC) regions. DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[0019] An example of the optical system according to the present invention comprises a microscope having an optical axis, an illumination light source, a self-referencing phase imaging system more simply referred to as a "detector", and a processing unit configured to numerically propagate real images. The illumination light source illuminates the microscope that couples an object plane and an image plane including the detector. The detector generates phase and intensity images.

[0020] To determine the position of nanoparticles within an object volume, the spatial coherence SC and temporal coherence TC regions of the illumination light source are selected based on real images so as to enable faithful numerical propagation of a nanoparticle solution. Numerical propagation refers to the numerical propagation of a real image along the optical axis within an image volume of a predetermined thickness that does not exceed the numerical depth of field.

[0021] Numerical propagation is only faithful for a specific thickness of the image volume symmetrically distributed on both sides of the real image. Beyond this limiting thickness, the numerically propagated image exhibits artifacts and no longer represents the substance of the solution sample. This limiting thickness corresponds to the numerical depth of field.

[0022] In particular, illuminators are used in which their spatial coherence SC and temporal coherence TC are selected or modified so that the illuminator operates within a desired coherence region. Figure 3 shows the coherence regions (SC and TC) selected for an illuminator. This region is limited to 0.4% to 6% within the temporal coherence (TC) region and 0.4% to 10% within the spatial coherence (SC) region, as follows. This region includes the optimal operating modes TC=2.2% and SC=2.5%.

[0023] Those skilled in the art may, in particular, consider the following illumination sources in order to carry out the present invention. - Laser diode (Thorlabs L405P150: wavelength 405nm and output 150mW), estimated temporal coherence TC = 0.25% (spectral width 1nm over a central wavelength of 405nm). By applying wavelength modulation during the integration interval of the detector used (e.g., 1ms), the optimal temporal coherence TC = 2.2% can be approached. - Also known as a "supercontinuum laser," this is a white laser filtered by a bandpass filter (a supercontinuum laser as referenced in the Leukos Electro VIS430). - A white plasma source filtered by a bandpass filter, where the nanoparticle signal is strong enough to outweigh the noise. - An illumination source (e.g., a laser diode) whose temporal coherence TC approaches 0 when combined with a temporal coherence adjustment method (electronic trigger) based on high-frequency wavelength fluctuations. - A lighting source (e.g., a lighting source equipped with a collimation system) in which spatial coherence SC approaches 0, in combination with a spatial coherence adjustment method, such as one based on a system for focusing or dispersing a beam, one based on coupling with a multimode optical fiber, or one based on the high-frequency motion (rotation / vibration / scanning) of an optical element. - Superluminescent diode.

[0024] It should be noted that, using known microscopes, it has been proven that the present invention is perfectly feasible if the spatial coherence is around 2% (and therefore the optimal value is around SC = 2.5%). The teachings in this application do not establish an equivalence relationship between these two concepts, which have different properties, when presenting the spatial and temporal coherence domains. Therefore, constraints belonging to the temporal and spatial coherence intervals are understood to be cumulative conditions that must be satisfied simultaneously.

[0025] Furthermore, it should be understood that points where spatial coherence is zero (SC=0) or points where temporal coherence is zero (TC=0) have no physical meaning. Therefore, in this application, the spatial or temporal coherence intervals extending between 0 and the upper limit are open intervals that do not contain the value 0.

[0026] The spatial and temporal coherence region shown in Figure 3 will hereinafter be referred to as the "main region." As shown above, the operating modes within the main region that are considered optimal for the present invention are obtained at TC = 0.022 (2.2%) and SC = 0.025 (2.5%).

[0027] Bringing TC or SC close to 0 is not a preferred embodiment. This is because the presence of optical noise (speckle or laser granularity) due to spatial and temporal coherence increases the background noise level, degrading nanoparticle detection and thereby reducing the number of detected nanoparticles and the possible propagation volume. Therefore, the region suitable for implementing the present invention is the region excluding TC=0 or SC=0.

[0028] In this application, if the two parameters TC and SC are within the interval containing the value TC = 2.2% and the interval containing the value SC = 2.5%, respectively, and if these two intervals are strictly within the intervals of the main region shown in Figure 3, that is, between 0.4% and 6% for TC and between 0.4% and 10% for SC, then the temporal coherence TC of the illumination source is considered to be around 2.2%, and the spatial coherence SC of the illumination source at the level of a self-referencing phase imaging system is considered to be around 2.5%. In other words, the combination of TC = 2.2% and SC = 2.5% is considered to be the "optimal operating point" of this optical system, and in the intent of this application, "close to the optimal point" refers to any sub-region of the main region that contains the optimal point. For example, sub-regions with a range of 1.7% to 2.7% for TC and a range of 2% to 3% for SC can be cited.

[0029] In the prior art, a low but relatively common value of spatial coherence is typically SC = 0.1%. Therefore, prior art literature that teaches minimizing or approaching zero spatial coherence should be interpreted as teaching the selection of an SC value less than 0.1%. Consequently, this is not assumed to correspond to the conditions for implementing the present invention, which are within the spatial coherence SC interval [0.4%; 10%].

[0030] In the prior art, a relatively low but common value for temporal coherence is typically TC = 0.02% (this value is unrelated to the general low spatial coherence value SC mentioned above). Therefore, prior art documents that teach minimizing temporal coherence TC should be interpreted as teaching the selection of a TC value less than 0.02%. Consequently, this teaching is not considered to correspond to the conditions for implementing the present invention, which involve a temporal coherence TC interval of [0.4%; 6%].

[0031] To generate such an optical system, it would suffice to confirm one of the following regarding a given illumination source: that the illumination source corresponds to the spatial and temporal coherence region mentioned above, or that the signal-to-noise ratio provided by the illumination source on the detector allows for the detection of nanoparticles and the numerical propagation of real images.

[0032] In this application, a detector that generates phase and intensity images is understood to be a detector that not only generates actual phase measurements, but also, equally, generates quantities that allow for the reconstruction of phase information, either as quantities proportional to the phase, as optical path differences, or as one or more phase gradients that can be reconstructed by integration.

[0033] For example, the following devices can be used as detectors. - For example, a multidirectional shift interferometer device that uses a modified Hartmann mask obtained by superimposing an amplitude grating with a given period p and a phase grating with a period 2.p, such as the detector referred to as "SID4" and commercially available from "Phasics," - A wavefront analyzer used to establish a wavefront phase map, combined with an intensity detector for simultaneously analyzing wave phase and intensity using a common spatial reference. - Wavefront analyzers or imagers known from prior art, such as curvature analyzers, Shack-Hartmann sensors, quantitative phase microscope assemblies such as self-referencing numerical holography devices, etc.

[0034] Determining the numerical depth of field for calculating the concentration of nanoparticles relies on the numerical propagation of real images for calculating the wave field within the object volume. To solve the wave equation in a heterogeneous medium (as in the case where the medium contains a collection of nanoparticles) and perform numerical propagation, it is possible to apply a number of techniques or methods known from the prior art, including, in particular, the ray method (or geometrical optics), the Born weak scattering method, the Litoff approximation, the parabolic approximation method, and the intensity transport equation.

[0035] In some embodiments, a microscope is used that rotates to the center of an optical axis coinciding with the z-axis of an orthogonal reference frame (O,x,y,z) in image space, and a surface detector S is positioned on the image plane z=0 to provide measurements of the intensity and phase of a complex field incident on the detector. This creates a real image on the detector of the intensity and phase around an object surface that is optically conjugate to the detector surface, also known as a holographic image of nanoparticles placed within an object volume.

[0036] First, the number of imaging nanoparticles n(z=0) in the real image is counted. Then, using numerical propagation of thickness d symmetrically with respect to the image plane (i.e., the plane of the real image), it is possible to obtain an image of a plane d / 2 away from the detector and an image of a plane d away from each other. Subsequently, the number of imaging nanoparticles n(-d / 2) and n(d / 2) in these two planes can be counted. An addition is performed to obtain a certain number N(d) = n(0) + n(-d / 2) + n(d / 2) in the image volume of thickness d. In other words, this addition is performed by summing the imaging nanoparticles in the plane within the image volume (in this case, the plane of the detector) with the imaging nanoparticles on the surface of the image volume of thickness d.

[0037] It is easy to demonstrate that by gradually propagating the -d / 2 image into the -d plane and the +d / 2 image into the +d plane, that is, by increasing the image volume symmetrically with respect to the image by a thickness of d, the number of nanoparticles imaged in two new planes located outside the image volume, where the number of nanoparticles is known beforehand, can be counted by two numerical propagations. The known number of imaged nanoparticles in the internal volume are added to the new planes and are added stepwise to the number of imaged nanoparticles in these new planes. Therefore, for a variable image volume thickness Dv = k * d (where k is a positive integer), the following holds: N((k+1)*d)=N(k*d)+n(k*d / 2)+n(-k*d / 2).

[0038] Thereafter, it is possible to plot a graph or curve N(Dv) representing the number of imaged nanoparticles N as a function of the variable thickness Dv for a given experiment, or an average curve for a plurality of experiments (a plurality of actual images of the same nanoparticle solution).

[0039] For a given population of nanoparticles (of constant size and properties), with an illumination light source having controlled spatial and temporal coherence, the number of imaged nanoparticles N present in an increasingly large imaging volume (which may be an average when a plurality of experiments are performed) does not increase linearly, but it is observed that over the thickness range k1*d ≦ Dv ≦ k2*d (k1<k2), the curve protrudes along the thickness axis Dv, and reaches a peak at a constant value exceeding the flat portion or flat portion zone P that extends to maintain a substantially constant value within the range of measurement error along the N axis. Then, the value H = k1*d can be determined as the numerical depth of field of the experimental apparatus used and of the population of imaged nanoparticles.

[0040] The above explanation is illustrated with the example in Figure 1. In this example, the nanoparticles used are polystyrene particles with a diameter of 100 nm. Figure 1 is a graph showing the number of imaging nanoparticles N in an image volume V with a variable thickness Dv in micrometers (μm) after numerical propagation of a real image within the image volume V. This image volume V is centered on the plane of the real image, and its thickness Dv increases symmetrically on both sides of the real image. The imaging nanoparticles are counted in the numerically propagated image, spaced apart from each other, to reconstruct the image volume V. This process was performed for multiple real images (thin lines) of the same sample. Subsequently, these relationships are averaged to obtain a thick curve N(Dv). This curve N(Dv) exhibits monotonic growth up to the upper limit beyond the flat zone P (enclosed by the dotted line in Figure 1). Within the range of the flat zone, the number of imaging nanoparticles N is approximately stable with respect to Dv. Therefore, within zone P, there is a critical thickness at which the number of imaged nanoparticles N starts and peaks at a specific value denoted by N(H). In the example in the figure, N(H) is around 16. The numerical depth of field H corresponds to the aforementioned critical thickness. In the example in the figure, the numerical depth of field H is estimated to be equal to 25 μm.

[0041] When the thickness Dv is greater than H, the reconstruction of the volume by numerical propagation is considered no longer faithful to the actual substance of the object volume. In fact, the fact that N peaks and then increases with Dv (when Dv > H) does not correspond to the physical substance of a homogeneous sample of nanoparticles (in the case of nanoparticles, N must always increase with Dv). When Dv > H, numerical propagation no longer makes it possible to reconstruct an image of objects that are physically present within the object volume, and instead creates an image of objects that are not present within the object volume.

[0042] To avoid or limit the counting of artifacts as much as possible, numerical propagation over a distance selected so as to be less than or equal to the numerical depth of field H determined by a reference nanoparticle (i.e., a given image volume thickness D) would be one preferred mode of implementation for determining the concentration of a nanoparticle population without prior knowledge.

[0043] Step d is selected so that it is less than the axial resolution of the microscope and so that faithful sampling of the volume is possible.

[0044] The numerical depth of field value of a nanoparticle depends on the volume of the nanoparticle and on the absolute difference in the complex refractive index between the nanoparticle and the surrounding medium in a given wavelength, given SC and TC, and a given imaging system (illuminance and focusing numerical aperture).

[0045] The inventors have discovered that the Litoff approximation is particularly applicable to the calculation of nanoparticle concentrations. In fact, by calculating the complex Litoff field, and especially its intensity, it becomes easier to detect imaging nanoparticles in real images and numerically propagated images.

[0046] The Litoff approximation described here is valid for the spatial coherence SC region and the temporal coherence TC region of the illumination source, as mentioned earlier.

[0047] The intensity l(x,y,zi) and phase phi(x,y,zi) in the detector plane (real image) (zi=0), or in the plane of the numerically propagated image (non-zero zi), are used in other application fields as the basis for forming the complex Lithov field r(x,y,zi) using equations known from prior art.

[0048] Subsequently, the intensity Lithov image R(x,y,zi) at zi in the plane is formed according to the formula R(x,y,zi)=|r(x,y,zi)|2, using the square of the absolute value of the complex Lithov amplitude in this plane. Alternatively, for the same purpose, the Lithov amplitude image can be obtained by forming the square root of R as a function of x,y in the plane zi.

[0049] Using Lithoff intensity is particularly effective for detecting imaging nanoparticles, whether in real or propagating images. In fact, nanoparticles that are sharp in the plane under consideration can be given a positive signal on zero background using Lithoff intensity or amplitude, regardless of the properties of the nanoparticles (this signal will be visible in the intensity or amplitude of the Lithoff field, whether it is included in the real or imaginary part of the real or propagating image).

[0050] Therefore, as described above, using Lithoff intensity is a preferred method for identifying and counting imaging nanoparticles in an image volume after numerical propagation (by calculating the Lithoff field for each numerically propagated image within the image volume, and by detecting the Lithoff intensity or amplitude in the corresponding image). Thus, calculating the Lithoff field is beneficial for counting imaging nanoparticles. Furthermore, the inventors have discovered that the intensity or amplitude of the Lithoff field is a characteristic of the associated numerical depth of field. In fact, when complex amplitude information is expressed in the form of a Lithoff field, in the case of optical systems suitable for TC and SC coherence regimes, it now appears that numerical depth of field is a single function of Lithoff intensity or amplitude, meaning that nanoparticles with the same Lithoff intensity or amplitude can be detected at the same numerical depth of field even if the optical index or volume differs. This result is illustrated in Figure 2. This figure is a graph showing the numerical depth of field H in micrometers (μm) as a function of the average amplitude R of the Lithov peak of the imaged nanoparticles in arbitrary units (au). Here, the selected observable quantity is the amplitude of the numerically propagated complex Lithov field within an image volume of thickness equal to the numerical depth of field H. Each point and its associated statistics correspond to a homogeneous sample of different nanoparticles. The nanoparticles in each sample have a constant diameter and properties.

[0051] Accordingly, Figure 2 shows the average Litoff amplitude R values ​​for different nanoparticle samples (each sample is uniform in composition and dimensions) as a function of numerical depth of field H, determined using the method described above for determining the flat area P (see Figure 1). Each point corresponds to a different sample, i.e., a different pair (average diameter, material). The following samples are shown. - Polystyrene (PS) 60nm, PS80nm, PS100nm, PS150nm, PS200nm, - Gold 60nm, Gold 100nm, - Silver 100nm, and - Diamond 80nm.

[0052] A relationship is observed between the numerical depth of field H and the amplitude R of the Lithov peak or Lithov amplitude. This relationship can be approximated by a dotted line on a graph. Therefore, for a given optical system operating in a given SC and TC regime, this graph can be used as a chart insofar as the numerical depth of field H associated with an unknown nanoparticle can be determined by simply measuring the Lithov amplitude R of this nanoparticle. This avoids the need to systematically perform a method for determining the numerical depth of field H by propagating a real image, counting the imaged nanoparticles, and determining the flat area P (see Figure 1). Such a chart makes it possible to determine the calibration of the numerical depth of field of an optical system as a function of the Lithov amplitude of an object imaged by a fixed optical system.

[0053] Therefore, using the Litoff approximation, the numerical depth of field can be directly determined by measuring the Litoff amplitude by referring to a chart, i.e., a graph or table, that shows the correspondence between the Litoff amplitude R and the numerical depth of field H. Thus, the Litoff amplitude is a measure for selecting the numerical depth of field for a certain type of nanoparticle in an optical system intended to measure the concentration of nanoparticles.

[0054] As a result, in an optical system where the correspondence between Lithov amplitude R and numerical depth of field H is known from a chart as described above, it is possible to both identify the position of an imaged nanoparticle by forming a Lithov amplitude image for a single nanoparticle imaged on the detector in terms of intensity and phase, and by searching for signal peaks in the Lithov image, and to derive the numerical depth of field associated with this nanoparticle from the identified position.

[0055] The Litov field can be replaced with another combination of information regarding the real and imaginary parts of the wave field, or, if prior knowledge about the response of nanoparticles is known, it can be replaced with either the real or imaginary component alone. In other words, instead of the Litov field, another field formed from information regarding at least one of the real and imaginary parts of the wave field can be used.

[0056] Therefore, the proposed optical system and measurement method make it possible to obtain measured values ​​of any nanoparticle concentration, regardless of the physical properties and dimensions of the nanoparticles, and without the need to calibrate the optical system using samples of known concentrations.

[0057] In fact, by determining the numerical depth of field, it becomes possible to define an image volume in which the reconstruction based on numerical propagation of the actual image is faithful to the actual object of the imaged sample. Therefore, numerical propagation is performed on this image volume, the imaged nanoparticles are counted against this volume, and the nanoparticle concentration is calculated by taking the number of counted nanoparticles as equal to the value obtained by dividing the counted nanoparticles by the volume. This volume is numerically controlled and defined, and is not the result of any assumptions or calibrations that define this image volume. This concentration measurement is performed based solely on the optical signal from the sample, and no prior calibration using samples of known concentrations is required.

[0058] Knowing the numerical depth of field makes it possible to avoid numerical propagation of the real image over excessively large image volume thicknesses, resulting in better density measurements (propagation artifacts are not counted as imaging nanoparticles) and simultaneously limiting the numerical propagation calculation time.

[0059] The use of a chart specific to a given optical system makes it possible to determine a numerical depth of field based on measurement of the Rytov amplitude of imaged nanoparticles in a real image. This further limits calculation time, unless an initial propagation step over increasing thickness Dv (Fig. 1) used to determine the numerical depth of field H is required. To enable counting, only propagation over a thickness D less than or equal to the depth H is performed.

[0060] Even in the case of a sample where nanoparticles are not uniform (in terms of composition and size), it is possible to calculate the concentration of the sample using the above method. In such mixtures, nanoparticles have different numerical depths of field. Care must be taken to ensure that the imaged nanoparticles in the image volume that contribute to the concentration calculation are not numerical propagation artifacts. This is achieved by using a chart to confirm that, for each imaged nanoparticle in successive numerically propagated images within the image volume (thickness D), the amplitude R of the nanoparticle corresponds to a numerical depth of field H that is at least twice the distance between the numerically propagated image in which the nanoparticle is imaged and the real image. If this condition is confirmed, the nanoparticle is retained; if not, the nanoparticle is not retained. When calculating the concentration to be considered, it is also necessary to take into account, for each nanoparticle, the image volume in which the nanoparticle was counted. For retained nanoparticles, - if H < D, this volume has a thickness H, - if H ≧ D, this volume has a thickness D.

[0061] The final concentration is equal to the sum of the reciprocals of these volumes for the retained nanoparticles.

[0062] Assuming that the transverse and longitudinal magnifications between the object space and the image space are known, the correspondence between the object volume V1 and the image volume V2 is given by the following relationship: V2 = V1.gx.gy.gz. Here, gx = gy is the transverse magnification of the optical system between the object plane and the image plane, and gz is the longitudinal magnification of the optical system used for conjugate purposes, in the direction z of the optical axis (assumed to be the pivot axis), near the plane of the detector.

[0063] To calculate the object volume based on the image volume, it is convenient that the dimensions of the image volume can be perfected by using the lateral and vertical magnifications of the detector surface and optical system, and then the object volume can be obtained.

[0064] This invention is industrially applicable, particularly in the field of measuring the concentration of nanoparticles.

[0065] The proposed apparatus and method are particularly suitable for measuring the concentration of nanoparticles in a solution undergoing Brownian motion. This is because, by utilizing the intensity and phase in a self-referential manner over time (when the film is formed), it becomes possible to conceive of tracking and refocusing nanoparticles in an image that propagate outside the plane of the real image, within the scope of the present invention, and by averaging consecutive numerically propagated images of the same nanoparticle, it becomes possible to obtain a signal-to-noise ratio that enables the teaching of the present invention.

Claims

1. An optical system for measuring the concentration of nanoparticles in a solution, The system includes a microscope having an optical axis, an illumination source for the microscope, and a self-referencing phase imaging system. The illumination light source is configured to irradiate the object space in the nanoparticle solution, The microscope is configured to merge the object plane and the image plane in the object space, and the self-referencing phase imaging system is positioned within or near the image plane. The self-referencing phase imaging system is configured to generate real images of the intensity and phase of the object surface. The temporal coherence (TC) of the illumination light source is between 0.4% and 6%, and the spatial coherence (SC) of the illumination light source at the level of the self-referencing phase imaging system is between 0.4% and 10%. The optical system further includes a processing unit, and the processing unit is It is configured to count the number of imaged nanoparticles in the aforementioned real image, The actual image is configured to propagate numerically along the optical axis within an image volume of a predetermined thickness. It is configured to count the number of imaged nanoparticles in the image, which are numerically propagated from the actual image. It is configured to calculate the dimensions of the object volume corresponding to the image volume, An optical system configured to calculate the concentration of nanoparticles based on the counted number of imaged nanoparticles (N) and the dimensions of the object volume.

2. The optical system according to claim 1, The predetermined thickness of the image volume is less than or equal to the numerical depth of field (H), and in order to determine the numerical depth of field (H), the processing unit, The system is configured to count the number of imaged nanoparticles in a first real image obtained using the self-reference phase imaging system for a nanoparticle solution. The first real image is configured to propagate numerically within a first image volume of increasing variable thickness (Dv), It is configured to count the number of imaged nanoparticles in the image that have been numerically propagated from the first real image, The system is configured to analyze the variation in the number of imaging nanoparticles (N) counted as a function of the variable thickness (Dv) of the first image volume, and to identify the limit thickness of the first image volume at which the number of imaging nanoparticles (N) no longer increases in accordance with the variable thickness (Dv) of the first image volume and reaches a flat portion (P). An optical system configured to determine the numerical depth of field (H) based on the identified limiting thickness.

3. The optical system according to claim 1, An optical system further comprising computer memory for storing charts, wherein the charts show a correspondence between a numerical depth of field (H) and an amplitude R of a field formed from information about at least one of the real and imaginary parts of a wave field generated by imaging nanoparticles, for various types of nanoparticles.

4. The optical system according to claim 3, An optical system in which the predetermined thickness is less than or equal to the numerical depth of field (H), and the processing unit refers to the chart and determines the numerical depth of field (H) based on the amplitude R of the imaging nanoparticles in the real image.

5. The optical system according to claim 1, The system further includes a computer memory for storing charts, the charts showing the correspondence between numerical depth of field and the amplitude R of a field formed from information about at least one of the real and imaginary parts of the wave field generated by the imaged nanoparticles, for various types of nanoparticles. The illumination light source is configured to irradiate an object space in the nanoparticle solution containing a mixture of nanoparticles, The aforementioned processing unit The system is configured to count the imaging nanoparticles in the real image, measure the amplitude R of the imaging nanoparticles, and determine the numerical depth of field associated with each of these imaging nanoparticles by referring to the chart. The actual image is configured to propagate numerically along the optical axis within the image volume of a predetermined thickness denoted by D. For each of the imaged nanoparticles in the numerically propagated image of the image volume, the system is configured to check, using the chart, whether the amplitude R of the nanoparticle corresponds to a numerical depth of field, denoted by H, which is at least twice the distance between the numerically propagated image in which the nanoparticle is imaged and the actual image. If there is a correspondence, the nanoparticle is held for counting; if there is no correspondence, the nanoparticle is not held for counting. For each counted nanoparticle, the system is configured to calculate an associated object volume corresponding to the image volume of thickness D if H ≥ D, and to an image volume of thickness equal to the numerical depth of field H associated with the nanoparticle if H < D. An optical system configured to calculate the concentration of nanoparticles equal to the sum of the reciprocals of the associated object volumes for all of the counted nanoparticles.

6. The optical system according to claim 1, An optical system in which the temporal coherence (TC) of the illumination light source is 2.2%, and the spatial coherence (SC) of the illumination light source at the level of the self-referencing phase imaging system is 2.5%.

7. The optical system according to claim 1, An optical system in which the illumination light source is a white laser that irradiates a bandpass filter.

8. The optical system according to claim 1, An optical system in which the illumination light source is a white plasma source that irradiates a bandpass filter.

9. The optical system according to claim 1, An optical system in which the illumination light source is a laser diode.

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