Optical system

Abstract

The invention relates to an optical system comprising a microscope having an optical axis, an illumination source for the microscope, and a self-reference phase imaging system. The illumination source is configured to illuminate the object space. The microscope is configured to conjugate an object plane of an object space with an image plane, and the self-reference phase imaging system is arranged in or near the image plane. The self-referencing phase imaging system is configured to produce real images of the object plane in intensity and phase. 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-reference phase imaging system is between 0.4% and 10%. The optical system also includes a processing unit configured to propagate the real image value along the optical axis.

Description

Technical Field

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

[0002] In the prior art, optical measurement of nanoparticle concentrations has encountered the problem of providing tools to determine the measurement volume within which the nanoparticles are imaged. In practice, the volume within which nanoparticles can be detected depends on the size and properties of the nanoparticles, as well as the optical system. Therefore, without prior knowledge of the nanoparticles' physical properties, optically measuring nanoparticle concentrations is difficult, and an optical system capable of facilitating this measurement is needed.

[0003] For the purposes of this application, the following definitions apply:

[0004] - "Temporal coherence TC" of a light source: the ratio of the wavelength range of the light source divided by its central wavelength.

[0005] - "Spatial coherence SC" of a light source in an optical system: the ratio of the numerical aperture of the illumination to the numerical aperture of the collection of the optical system.

[0006] - "Self-referencing phase imaging system": A self-referencing detection system or detector that provides the phase of the incident wave in addition to the light intensity. The system is self-referencing because it does not use a separate optical arm as a reference.

[0007] “Real image”: an image of the intensity and phase of the wavefield in the object plane captured by the self-referencing phase imaging system used.

[0008] "Numerical propagation image": An image of the intensity and phase of the wave field in a plane parallel to the object plane; it is numerically calculated based on the real image using conventional propagation methods to solve the wave equation.

[0009] "Image volume": the volume imaged by numerically propagating a real image.

[0010] “Imaged nanoparticles” or “imaged particles”: nanoparticles that form a sharp image or an image with maximum spatial energy density in a real image (especially for nanoparticles in the object plane) or in a numerical propagation image (especially for nanoparticles outside the object plane).

[0011] "Numerical depth of field" refers to the thickness of the volume imaged by numerical propagation along the optical axis, specifically centered on the real image, within which the nanoparticles can be faithfully imaged. This is the thickness within which reconstruction of the volume imaged by numerical propagation based on the real image is valid. In other words, the numerically propagated image reflects the reality of object space. Objects physically present in object space (and only those objects) are imaged in the numerically propagated image, which is considered to be faithful.

[0012] "White light laser" or "supercontinuum laser": a light source with high spatial coherence and quasi-zero temporal coherence.

[0013] The numerical depth of field defined above depends on the signal-to-noise ratio used to detect the imaged object. In addition, the numerical depth of field is less than or equal to the depth of field of the optical system used (hereinafter referred to as the "optical" depth of field for clarity). The optical depth of field depends on the spatial and temporal coherence of the light used for imaging.

[0014] Thus, for an optical system whose spatial and temporal coherence (SC, TC) approaches (0, 0), the limit on 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 limiting the numerical depth of field. On the other hand, for an optical system where SC and / or TC approaches infinity, the noise decreases, but the optical depth of field approaches 0. The real image only contains objects that are perfectly focused. This also makes it difficult or even impossible to achieve any numerical propagation of the real image, and thus limits the numerical depth of field.

[0015] Furthermore, with fixed optical systems, the signal-to-noise ratio of imaged nanoparticles depends on their size and properties. Consequently, the numerical depth of field depends on the size and properties of the nanoparticles.

[0016] Therefore, there is a need for an optical system that can be used to produce a real image of nanoparticles, ideally without requiring a priori knowledge of the size and / or properties of the nanoparticles, and such that the numerical depth of field is satisfactory for the real image. Summary of the Invention

[0017] Against this background, 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 an object space. The microscope is configured so that an object plane of the object space is conjugate to an image plane, and the self-referencing phase imaging system is arranged in or near the image plane. The self-referencing phase imaging system is configured to generate a real image of the object plane in terms of intensity and phase. 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 comprises a processing unit configured to numerically propagate the real image along the optical axis.

[0018] In some embodiments, the temporal coherence of the illumination source is close to 2.2%, and the spatial coherence of the illumination source at the level of the self-referencing phase imaging system is close to 2.5%.

[0019] In some embodiments, the illumination source is a white light laser that illuminates a bandpass filter. Alternatively, the illumination source may be a white plasma source or a laser diode that illuminates a bandpass filter.

[0020] In some embodiments, the illumination source is configured to illuminate an object space in the nanoparticle solution, and the processing unit is configured to:

[0021] Count the number of nanoparticles imaged in the real image,

[0022] numerically propagating a real image in an image volume of predetermined thickness along the optical axis,

[0023] Count the number of nanoparticles imaged in the numerical propagation image,

[0024] Calculate the size of the object volume corresponding to the image volume,

[0025] The concentration of nanoparticles was calculated based on the calculated number of imaged nanoparticles (N) and the size of the object volume.

[0026] In some embodiments, the predetermined thickness is less than or equal to the numerical depth of field.

[0027] In some embodiments, to determine the numerical depth of field, the processing unit is configured to:

[0028] counting the number of nanoparticles in a real image of a nanoparticle solution obtained using a self-referencing phase imaging system;

[0029] numerically propagating a real image in an image volume of increasing variable thickness;

[0030] Counting the number of nanoparticles imaged in the numerical propagation image;

[0031] analyzing the variation of the number of imaged particles calculated as a function of the variable thickness of the image volume and identifying a limiting thickness of the image volume for which the number of imaged nanoparticles no longer increases with the variable thickness of the image volume and reaches a plateau,

[0032] A numerical depth of field is determined based on the identified limiting thickness.

[0033] In some embodiments, the optical system further includes a computer memory storing a graph that indicates, for various types of nanoparticles, the correspondence between the amplitude of a field formed by information on the real part and / or the imaginary part of the wave field generated by the nanoparticles with respect to imaging (hereinafter referred to as "amplitude R") and the numerical depth of field. The amplitude R can particularly correspond to the amplitude of the Rytov field.

[0034] In some embodiments, the processing unit refers to the graph to determine the numerical depth of field based on the amplitude R of the nanoparticles imaged in the real image.

[0035] In some embodiments, for a solution containing a mixture of nanoparticles, the illumination source is configured to irradiate the object space in the solution, and the processing unit is configured to:

[0036] count the nanoparticles imaged in the real image, measure the amplitude R of these imaged nanoparticles, and refer to the graph described above to determine the numerical depth of field associated with each of these imaged particles;

[0037] numerically propagate the real image along the optical axis in an image volume of a predetermined thickness (denoted as D);

[0038] for each nanoparticle imaged in the numerically propagated image in the plane of the image volume, use the graph to verify whether the amplitude R of the nanoparticle corresponds to a numerical depth of field (denoted as H) that is greater than or equal to twice the distance between the numerically propagated image in which the nanoparticle is imaged and the real image, and if it corresponds, retain the particle for counting, and if it does not correspond, do not retain the particle for counting;

[0039] for each counted nanoparticle, if H≥D, calculate the associated object-space volume corresponding to the image volume of thickness D, or if H<D, calculate the associated object-space volume corresponding to the image volume of thickness equal to the numerical depth of field H associated with the nanoparticle; and

[0040] calculate the concentration of the nanoparticles, which is equal to the reciprocal sum of the associated object-space volumes for all counted nanoparticles.

[0041] The above features and advantages, as well as other features and advantages, will become apparent by reading the following detailed description. The detailed description refers to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The figure is a graph showing the number N of particles imaged in an image volume having a variable thickness Dv, in units of micrometers (μm).

[0043] Figure 2 ​​]The figure is a graph showing the numerical depth of field H in micrometers (μm) as a function of the amplitude R of the Rytov peak of imaged nanoparticles in arbitrary units (au).

[0044] Figure 3 The figure shows an example of spatially coherent (SC) and temporally coherent (TC) domains. DETAILED DESCRIPTION

[0045] An example of an optical system according to the present invention includes a microscope having an optical axis, an illumination source, a self-referencing phase imaging system (referred to as a "detector"), and a processing unit configured to numerically propagate a real image. The illumination source illuminates the microscope, which is conjugated to an object plane and an image plane containing the detector. The detector generates phase and intensity images.

[0046] The spatial coherence (SC) and temporal coherence (TC) domains of the light source are selected to enable faithful numerical propagation of the nanoparticle solution based on the real image, thereby determining the position of the nanoparticles in the object volume. The numerical propagation consists in numerically propagating the real image along the optical axis within an image volume of a predetermined thickness less than or equal to the numerical depth of field.

[0047] Numerical propagation is faithful only up to a certain thickness of the image volume, which is symmetrically distributed on either side of the real image. Beyond this limiting thickness, the numerically propagated image exhibits artifacts and no longer represents the reality of the solution sample. This limiting thickness corresponds to the numerical depth of field.

[0048] In particular, an illumination source is used having a spatial coherence SC and a temporal coherence TC which are selected or modified so that the light source operates in the desired coherence domain. Figure 3 The coherence domain (SC and TC) selected for the illumination source is shown. This domain is limited as follows: from 0.4% to 6% in the temporal coherence (TC) domain and from 0.4% to 10% in the spatial coherence (SC) domain. This domain includes the operating mode TC = 2.2% and SC = 2.5%, which is considered optimal.

[0049] In order to implement the present invention, those skilled in the art may particularly consider the following illumination sources:

[0050] - a laser diode (Thorlabs L405P150: wavelength 405 nm and power 150 mW) with an estimated temporal coherence of TC = 0.25% (1 nm spectral width at a central wavelength of 405 nm). Wavelength modulation within the integration interval of the detector used (e.g. 1 ms) can be applied to get closer to the temporal coherence TC = 2.2%, which is considered optimal;

[0051] - White light laser, also called "supercontinuum laser", filtered by a bandpass filter (supercontinuum laser reference Leukos Electro VIS 430);

[0052] - a white plasma source with sufficient power to make the nanoparticle signal larger than the noise, filtered by a bandpass filter;

[0053] - an illumination source (e.g. a laser diode) with a temporal coherence TC approaching zero, combined with a temporal coherence adjustment method based on high-frequency wavelength variation (electronic triggering);

[0054] - an illumination source with a spatial coherence SC tending to zero (for example a source with a collimation system), combined with a spatial coherence modulation method, for example, in particular: based on a system for focusing or spreading the light beam, based on coupling with a multimode fiber, based on high-frequency movement of optical elements (rotation / vibration / scanning);

[0055] -Superluminescent diodes.

[0056] It should be noted that for implementing the invention, a spatial coherence of the order of 2% of the known microscope (thus close to the value SC=2.5% considered to be optimal) has proven to be satisfactory.

[0057] When proposing spatial and temporal coherence domains, the teachings in this application do not establish any equivalence link between these two essentially different concepts. Therefore, constraints belonging to temporal and spatial coherence intervals are understood as cumulative conditions to be satisfied simultaneously.

[0058] Furthermore, it should be understood that the point of zero spatial coherence (SC=0) or zero temporal coherence (TC=0) has no physical meaning. Therefore, in this application, the spatial or temporal coherence interval extending between 0 and the upper limit is an open interval that does not include the value 0.

[0059] Figure 3 The spatial and temporal coherence domain shown in is hereinafter referred to as the "primary domain." As described above, for TC=0.022 (2.2%) and SC=0.025 (2.5%), the operating mode considered to be the best for the present invention is obtained within the primary domain.

[0060] It is not a preferred embodiment to drive TC or SC towards 0, because the presence of optical noise due to spatial and temporal coherence (speckle or laser graininess) degrades particle detection by increasing the background noise level, thereby reducing the number of detected particles and the possible propagation volume. Therefore, the domain suitable for implementing the present invention is the domain that does not include TC=0 or SC=0.

[0061] In this application, the temporal coherence TC of the illumination source is considered to be close to 2.2%, and the spatial coherence SC of the illumination source at the level of the self-referenced phase imaging system is considered to be close to 2.5% if the two parameters TC, SC are respectively within the interval containing the value TC = 2.2% and within the interval containing the value SC = 2.5%, and these two intervals are strictly included in Figure 3 , that is, between 0.4% and 6% for TC and between 0.4% and 10% for SC. In other words, if the combination of TC = 2.2% and SC = 2.5% is considered the "optimal operating point" of the system, a sub-range close to the optimal point within the meaning of this application is any sub-range of the main range that contains the optimal point. For example, a sub-range with a TC range of 1.7% to 2.7% and a SC range of 2% to 3% can be mentioned.

[0062] In the prior art, a low but relatively common value of spatial coherence is typically SC = 0.1%. Therefore, prior art documents that teach minimizing spatial coherence or causing it to approach 0 should be interpreted as teaching the selection of SC values ​​less than 0.1%. Therefore, this would not correspond to the conditions for implementing the present invention within the spatial coherence SC interval of [0.4%, 10%].

[0063] In the prior art, a low but relatively common value of temporal coherence is typically TC = 0.02% (this value is not related to the common 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%. Therefore, this would not correspond to the conditions for implementing the present invention within the temporal coherence TC interval of [0.4%, 6%].

[0064] To generate such an optical system, for a given illumination source, it is sufficient to verify that it corresponds to the above-mentioned spatial and temporal coherence domain or that it provides a signal-to-noise ratio on the detector allowing the detection of nanoparticles and the numerical propagation of the real image.

[0065] In this application, a detector producing phase and intensity images is understood to be a detector that produces actual phase measurements, but equivalently also a detector that is able to reconstruct the phase information as a quantity proportional to the phase, the optical path difference or one or more phase gradients, which allows reconstruction by integration.

[0066] For example, the following devices can be used as detectors:

[0067] - multi-lateral phase-shift interferometry devices using a modified Hartmann mask, for example by superimposing an amplitude grating with a given period p and a phase grating with a period 2p, such as the detector sold under the name "SID4" by the company "Phasics";

[0068] - a wavefront analyzer for building up a phase map of the wavefront combined with a detector for simultaneously analyzing the phase and intensity of the wave and having a common spatial reference;

[0069] - Wavefront analyzers or imagers known from the prior art, such as curvature analyzers, Shack-Hartmann sensors, quantitative phase microscopy assemblies (such as, for example, self-referencing numerical holographic devices).

[0070] The determination of the numerical depth of field for calculating the nanoparticle concentration is based on the numerical propagation of the real image to calculate the wave field in the object volume. To solve the wave equation in an inhomogeneous medium (such as the case of a medium containing a population of nanoparticles) and perform the numerical propagation, a number of approaches or methods known in the art can be applied, including, in particular, the ray method (or geometric optics), the Born weak scattering method, the Rytov method, the parabolic approximation, and the intensity transfer equation.

[0071] In some embodiments, a microscope is used that rotates about an optical axis that coincides with the z-axis of an orthogonal reference system (O, x, y, z) in image space, and a surface detector S that is arranged in the image plane z = 0 and provides measurements of the intensity and phase of the complex field incident on the detector. This results in the formation of a true intensity and phase image of the nanoparticles, also called a holographic image, on the detector, which is arranged in the object volume about an object plane that is optically conjugated to the plane of the detector.

[0072] The number of nanoparticles imaged in the real image, n(z=0), can be calculated, and then numerical propagation with steps of thickness d can be used symmetrically about the image plane (i.e., the plane of the real image) to obtain images of planes spaced d / 2 from the detector and d from each other. The number of nanoparticles imaged in these two planes, n(-d / 2) and n(d / 2), can then be calculated. An addition is performed to obtain the number of particles imaged in the image volume of thickness d, N(d)=n(0)+n(-d / 2)+n(d / 2), that is, by summing the particles imaged in a plane within the image volume (here, the plane of the detector) and on the surface of the image volume of thickness d.

[0073] It is easy to show that by gradually propagating the image at -d / 2 in the -d plane and the image at +d / 2 in the +d plane, that is, by increasing the image volume symmetrically with respect to the image by steps of thickness d, the number of particles imaged by the two numerical propagations in two new planes located outside the image volume where the number of particles is known in advance can be calculated. The known number of particles imaged in the internal volume is gradually added to the number of particles imaged in these new planes. Therefore, for a variable image volume thickness Dv = k*d (k is a positive integer): N((k+1)*d) = N(k*d) + n(k*d / 2) + n(-k*d / 2).

[0074] Then, for a single experiment, a graph or curve N(Dv) representing the number N of imaged particles as a function of the variable thickness Dv can be plotted, or an average curve can be plotted for multiple experiments (multiple real images of the same nanoparticle solution).

[0075] For a given nanoparticle population (fixed size and properties), for a light source with controlled spatial and temporal coherence, it is observed that the number N of imaged particles present in an increasingly large image volume (which can be an average value if multiple experiments are performed) does not increase linearly, but peaks at a constant value on a plateau or plateau region P that extends over a thickness range k1*d ≤ Dv ≤ k2*d (where k1 < k2) projected along the thickness axis Dv and remains substantially constant along the N axis within the measurement error. Then the value H = k1*d can be determined as the numerical depth of field of the experimental setup used and the nanoparticle population being imaged.

[0076] The above explanation is illustrated by the example of Figure 1 In this example, the particles used are polystyrene particles with a diameter of 100 nm. Figure 1 is a graph showing the number N of particles imaged in an image volume V of variable thickness Dv in micrometers (μm) after numerical propagation of the real image in the image volume V. The 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 imaged particles are counted in numerically propagated images spaced apart from each other in order to reconstruct the image volume V. This operation is performed on multiple real images (bright lines) of the same sample, and then the relationships are averaged to obtain the coarse curve N(Dv). This curve N(Dv) shows a monotonic increase up to the upper limit of the plateau region P (enclosed by the dashed line in Figure 1 ), within which the number N of imaged particles remains substantially stable as Dv increases. Thus, there is a limiting thickness from which the number N of imaged particles peaks at a certain value in the region P, denoted as N(H). In the example in the figure, N(H) is close to 16. The numerical depth of field H corresponds to the limiting thickness. In the example in the figure, the estimated numerical depth of field H is equal to 25 μm.[[ID=,15]]

[0077] For a thickness Dv greater than H, the reconstructed volume by numerical propagation is considered to no longer be faithful to the reality of the object space volume. In fact, the fact that N peaks and then increases as Dv increases (for Dv > H) does not correspond to the physical reality of a homogeneous sample of nanoparticles where N must continuously increase as Dv increases. For Dv > H, numerical propagation no longer makes it possible to reconstruct an image of an object physically present in the object space volume, but creates an image of an object that does not exist in the object space volume.

[0078] In order to avoid or limit counting artifacts as much as possible, numerical propagation over a distance chosen to be less than or equal to the numerical depth of field H determined using reference nanoparticles (i.e. a predetermined image volume thickness D) would be a preferred embodiment for determining the concentration of a nanoparticle population without a priori knowledge thereof.

[0079] The step distance d is chosen to be smaller than the axial resolution of the microscope and to allow faithful sampling of the volume.

[0080] For given SC and TC and a given imaging system (illumination and collection numerical apertures), the value of the numerical depth of field of a nanoparticle depends on the volume of the particle and the modulus of the complex refractive index difference between the particle and the surrounding medium at a given wavelength.

[0081] The inventors have found that the Rytov method can be applied in a particularly relevant way to the calculation of nanoparticle concentrations. In fact, calculating the complex Rytov field and in particular its intensity makes it easier to detect nanoparticles imaged in real and numerical propagation images.

[0082] The Rytov method described here is valid in the spatially coherent SC and temporally coherent TC domains of the aforementioned illumination sources.

[0083] In other areas of application, the intensities I(x,y,zi) and phases phi(x,y,zi) in the plane of the detector (real image) (zi=0) or the plane of the numerical propagation image (zi non-zero) are used as the basis for forming the complex Rytov field r(x,y,zi) using formulas known in the prior art.

[0084] The intensity Rytov image R(x,y,zi) is then formed in plane z using the square of the modulus of the complex Rytov amplitude in that plane, according to the formula R(x,y,zi)=|r(x,y,zi)|2. Alternatively, a Rytov amplitude image can be obtained for the same purpose by forming the square root of R as a function of x and y in plane z.

[0085] The use of Rytov intensity is particularly effective for detecting imaged nanoparticles, whether in the real or propagated image. In fact, for nanoparticles that are sharp in the plane of consideration, the Rytov intensity or amplitude makes it possible to obtain a positive signal above zero background, regardless of the nature of the nanoparticle (whether the signal is contained in the real or imaginary part of the real or propagated image, it will be visible in the intensity or amplitude of the Rytov field).

[0086] Therefore, as described above, the use of Rytov intensity is a preferred way to identify and count nanoparticles imaged in the image volume after numerical propagation (by calculating the Rytov field for each numerically propagated image in the image volume and by detecting the Rytov intensity or amplitude in the corresponding image). Therefore, the calculation of the Rytov field is useful for counting imaged nanoparticles. In addition, the inventors found that the intensity or amplitude of the Rytov field is characteristic of the associated numerical depth of field. In fact, when the complex amplitude information is represented in the form of a Rytov field, for optical systems suitable for TC and SC coherence mechanisms, the result is that the numerical depth of field is now only a function of the Rytov intensity or amplitude, in such a sense that nanoparticles with the same Rytov intensity or amplitude can be detected in the same numerical depth of field even if their optical refractive index or volume is different. This result is shown in FIG. Figure 2 . This figure shows the numerical depth of field H in micrometers (μm) as a function of the mean amplitude R of the Rytov peaks in arbitrary units (au). Here, the chosen observable is the amplitude of the Rytov field of the complex field numerically propagated in an image volume with a thickness equal to the numerical depth of field H. Each point and its associated statistics corresponds to a homogeneous sample of different nanoparticles, each sample having nanoparticles of fixed diameter and properties.

[0087] therefore, Figure 2 The values ​​of the average Rytov amplitude R for samples of different nanoparticles (each sample being homogeneous in composition and size) are shown as a function of the numerical depth of field H, determined using the method described above for determining the platform P (see Figure 1 ). Each point corresponds to a different sample, that is to say to a different pair (mean diameter, material). The following samples are shown:

[0088] -Polystyrene (PS) 60nm, PS 80nm, PS 100nm, PS 150nm, PS 200nm,

[0089] -Gold 60nm, Gold 100nm

[0090] -Silver 100nm and

[0091] -Diamond 80nm.

[0092] It is observed that there is a relationship between the numerical depth of field H and the amplitude R of the Rytov peak (or the Rytov amplitude). This relationship can be approximated by the dashed line on the graph. Therefore, the graph can be used as a diagram because, for a given optical system operating under given SC and TC conditions, the numerical depth of field H associated with an unknown nanoparticle can be determined by simply measuring the Rytov amplitude R of that nanoparticle. This avoids having to systematically perform the method for determining the numerical depth of field H by propagating a real image, counting the imaged nanoparticles, and determining the platform P (see Figure 1 ). Such a diagram makes it possible to determine the calibration of the numerical depth of field of a fixed optical system as a function of the Rytov amplitude of the object imaged by the system.

[0093] Thus, using the Rytov method, the numerical depth of field can be determined directly by measuring the Rytov amplitude with reference to a graph (i.e., a diagram or table indicating the correspondence between the Rytov amplitude R and the numerical depth of field H). Therefore, the Rytov amplitude is the measure of choice for the numerical depth of field of a nanoparticle in an optical system for the purpose of measuring nanoparticle concentration.

[0094] The result is that for an optical system in which the correspondence between the Rytov amplitude R and the numerical depth of field H is known from the diagram described above, for a single nanoparticle imaged on a detector according to intensity and phase, the imaged nanoparticle can be located by forming an image of the Rytov amplitude and by looking for signal peaks in the Rytov image and thereby deriving the numerical depth of field associated with the nanoparticle.

[0095] The Rytov field can be replaced by another combination of information about the real and imaginary parts of the wavefield, or, if a priori knowledge about the particle response is known, by only the real part or only the imaginary part. In other words, other fields formed from information about the real and / or imaginary parts of the wavefield can be used instead of the Rytov field.

[0096] The proposed optical system and measurement method therefore make it possible to obtain measurements of any nanoparticle concentration, regardless of the physical properties of the nanoparticles and their size, and without having to calibrate the system with samples of known concentration.

[0097] In practice, determining the numerical depth of field allows defining an image volume within which the reconstruction, based on numerical propagation of the real image, remains faithful to the reality of the imaged sample. Thus, numerical propagation is performed for this volume, the imaged nanoparticles are counted for this volume, and the nanoparticle concentration is calculated as the number of counted nanoparticles divided by this volume. This volume is numerically controlled and defined and is not the result of assumptions or calibrations used to define it. This concentration measurement is based solely on the optical signal from the sample and does not require prior calibration with samples of known concentration.

[0098] Understanding the numerical depth of field allows avoiding numerical propagation of the real image over an excessive image volume thickness, thereby providing better concentration measurements (propagation artifacts are not counted as imaged nanoparticles), while limiting the numerical propagation calculation time.

[0099] The use of a graph characteristic of a given optical system allows determining the numerical depth of field based on the measurement of the Rytov amplitude of the nanoparticles imaged in the real image. This further limits the calculation time because the initial propagation step over an increasing thickness Dv ( Figure 1 ) for determining the numerical depth of field H is unnecessary. Only the propagation over a thickness D less than or equal to the depth H is performed to allow counting.

[0100] For a heterogeneous (in terms of composition and size) sample of nanoparticles, the above method can also be used to calculate the concentration of the sample. In such a mixture, the nanoparticles have different numerical depths of field. Care must be taken to ensure that the imaged particles in the image volume contributing to the concentration calculation are not numerical propagation artifacts. This is achieved by, for each nanoparticle imaged in the successive numerically propagated images in the image volume (thickness D), using the graph to verify that the amplitude R of the nanoparticle corresponds to a numerical depth of field H (which is greater than or equal to twice the distance between the numerically propagated image in which the nanoparticle is imaged and the real image). If this condition is verified, the particle is retained; if not verified, the nanoparticle is not retained. When calculating the concentration to be considered, for each nanoparticle, the image volume in which it is counted also needs to be considered. For the retained nanoparticles:

[0101] - If H < D, the volume has a thickness H;

[0102] - If H ≥ D, the volume has a thickness D.

[0103] The final concentration is equal to the sum of the reciprocals of these volumes for the retained particles.

[0104] Assuming that the lateral and axial magnifications between the object space and the image space are known, the following relationship gives the correspondence between the object volume V₁ and the image volume V₂ = V₁·gx·gy·gz, where gx = gy is the lateral magnification of the optical system between the object plane and the image plane, and gz is the axial magnification near the detector plane in the z direction of the optical axis (assumed to be the rotation axis) of the optical system used for conjugation.

[0105] To calculate the object volume based on the image volume, it is advantageous to use the surface of the detector and the lateral and axial magnifications of the optical system to complete the sizing of the image volume and then obtain the object volume.

[0106] The present application is particularly applicable to the field of measuring nanoparticle concentration in industry.

[0107] The proposed device and method are particularly suitable for measuring the concentration of nanoparticles undergoing Brownian motion in solution, since the availability of intensities and phases obtained over time in a self-referenced manner (production of movies) makes it possible to envisage tracking and refocusing nanoparticles in images propagating outside the plane of the real image within the meaning of the present application, and to obtain a signal-to-noise ratio enabling the teachings of the present application to be implemented by averaging consecutive numerically propagated images of the same particle.

Claims

1. An optical system comprising a microscope having an optical axis, an illumination source for the microscope, and a self-referencing phase imaging system, wherein the illumination source is configured to illuminate the object space, wherein the microscope is configured such that an object plane of the object space is conjugated to an image plane, the self-referencing phase imaging system is arranged in or near the image plane, and wherein the self-referencing phase imaging system is configured to generate a real image of the object plane in intensity and phase, wherein 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 comprises a processing unit configured to numerically propagate the real image along the optical axis.

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

3. The optical system of claim 1 or 2, wherein the illumination source is a white light laser illuminating a bandpass filter.

4. The optical system of claim 1 or 2, wherein the illumination source is a white plasma source that illuminates a bandpass filter.

5. The optical system of claim 1 or 2, wherein the illumination source is a laser diode.

6. The optical system according to any one of claims 1 to 5, wherein the illumination source is configured to illuminate an object space in a nanoparticle solution, and wherein the processing unit is configured to: counting the number of nanoparticles imaged in the real image, numerically propagating the real image in an image volume of predetermined thickness along the optical axis, Count the number of nanoparticles imaged in the numerical propagation image, Calculate the size of the object volume corresponding to the image volume, The concentration of nanoparticles is calculated based on the calculated number (N) of the imaged nanoparticles and the size of the object volume.

7. The optical system according to claim 6, wherein the processing unit is configured to: - counting the number of nanoparticles in a real image of the nanoparticle solution obtained with the self-referencing phase imaging system; - numerically propagating said real image in an image volume of increasing variable thickness (Dv); - Counting the number of nanoparticles imaged in the numerical propagation image; - analyzing the variation of the number (N) of said imaged nanoparticles calculated as a function of the variable thickness (Dv) of the image volume and identifying a limiting thickness of the image volume for which the number (N) of said imaged nanoparticles no longer increases with the variable thickness (Dv) of the image volume and reaches a plateau (P), and - determining a numerical depth of field (H) based on the identified limiting thickness; and The predetermined thickness is less than or equal to the numerical depth of field (H).

8. The optical system according to claim 6 or 7, wherein the system further includes a computer memory storing a graph that indicates, for various types of nanoparticles, the correspondence between the amplitude of a field formed by information on the real part and / or the imaginary part of the wave field generated by the nanoparticles regarding imaging and the numerical depth of field (H), the amplitude being represented as amplitude R.

9. The optical system according to claim 8, wherein the processing unit refers to the graph to determine the numerical depth of field (H) based on the amplitude R of the nanoparticles imaged in the real image, and wherein the predetermined thickness is less than or equal to the numerical depth of field (H).

10. The optical system according to any one of claims 1 to 6, further including a computer memory storing a graph that indicates, for various types of nanoparticles, the correspondence between the amplitude of a field formed by information on the real part and / or the imaginary part of the wave field generated by the nanoparticles regarding imaging and the numerical depth of field, the amplitude being represented as amplitude R, wherein the illumination source is configured to illuminate an object space in a solution containing a mixture of nanoparticles, wherein the processing unit is configured to: count the nanoparticles imaged in the real image, measure their amplitude R, and refer to the graph to determine the numerical depth of field associated with each of these imaged nanoparticles; numerically propagate the real image along the optical axis in an image volume having a predetermined thickness, the predetermined thickness being represented as D; for each nanoparticle imaged in the numerically propagated image of the image volume, use the graph to verify whether the amplitude R of the nanoparticle corresponds to a numerical depth of field, which is represented as H, and which is greater than or equal to twice the distance between the numerically propagated image and the real image in which the nanoparticle is imaged, and if it corresponds, retain the nanoparticle for counting, and if it does not correspond, do not retain the nanoparticle for counting; for each counted nanoparticle, if H≥D, calculate the associated object-space volume corresponding to the image volume having thickness D, or if H<D, calculate the associated object-space volume corresponding to the image volume having a thickness equal to the numerical depth of field H associated with the nanoparticle; and calculate the concentration of the nanoparticles, which is equal to the reciprocal sum of the associated object-space volumes for all counted nanoparticles.

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