Optical system

Abstract

Disclosed is an optical system comprising a microscope admitting an optical axis, a light source for the microscope and a self-referenced phase-imaging system. The light source is configured to illuminate an object space. The microscope is configured to conjugate an object plane of the object space with an image plane, the self-referenced phase-imaging system being placed in or in the vicinity of the image plane. The self-referenced phase-imaging system is configured to produce a real intensity and phase image of the object plane. The temporal coherence (CT) of the light source is between 0.4% and 6% and the spatial coherence (CS) of the light source, at the self-referenced phase-imaging system, is between 0.4% and 10%. The optical system further includes a processing unit configured to digitally propagate the real image along the optical axis.

Description

Optical system

[0001] This application relates to an optical system. Such a system makes it possible, in particular, to measure the concentration of nanoparticles without prior knowledge of the nanoparticles and without having to modify the particles or their environment. Background

[0002] In the prior art, the optical measurement of a nanoparticle concentration is hampered by the provision of a tool to determine a measurement volume in which the nanoparticles are imaged. Indeed, the volume in which the nanoparticles are detectable depends on the size and nature of the nanoparticles as well as the optical system. The optical measurement of a nanoparticle concentration, without a priori knowledge of the physical nature of the nanoparticles, is therefore difficult and there is a need for an optical system to facilitate this measurement.

[0003] For the purposes of this application, the following terms are understood to mean:- "Temporal coherence CT" of a light source: the ratio of the wavelength extent of the source divided by its central wavelength.- "Spatial coherence CS" of a light source in an optical system: the ratio of the illumination numerical aperture of an optical system to the collection numerical aperture.- "Self-referenced phase imaging system": a self-referenced detection system, or detector, providing, in addition to the optical intensity, the phase of an incident wave. The system is self-referenced because it does not use a separate optical arm as a reference. "Real image": image of the intensity and phase of the wave field in an object plane, captured by the self-referenced phase imaging system used.“Digitally propagated image”: image of the intensity and phase of the wave field in a plane parallel to the object plane, it is calculated numerically from the real image using classical propagation methods to solve the wave equation. “Image volume”: volume imaged by digital propagation of the real image. “Imaged nanoparticle” or “imaged particle”: nanoparticle that forms a sharp image or one with maximum spatial energy density in the real image (this is particularly the case for a nanoparticle in the object plane) or in digitally propagated images (this is particularly the case for a nanoparticle outside the object plane). “Digital depth of field”: thickness, along the direction of the optical axis, of the volume imaged by digital propagation, particularly centered on the real image, in which nanoparticles can be faithfully imaged.This is the thickness in which the reconstruction of the volume imaged by digital propagation, from the real image, is valid. That is to say, the digitally propagated images are the reflection of the reality of the object space. The objects physically present in the object space, and only these objects, are imaged on the digitally propagated images considered to be faithful. "White laser" or "super-continuum laser": a source with strong spatial coherence and almost zero temporal coherence.

[0004] The digital depth of field defined above depends on the signal-to-noise ratio for detecting the imaged objects. In addition, the digital depth of field is less than or equal to the depth of field (hereinafter referred to as the "optical" depth of field for clarity) of the optical system used. The optical depth of field, in turn, depends on the spatial and temporal coherence of the light used for imaging.

[0005] Thus, for a spatial and temporal coherence optical system (CS, CT) tending towards (0, 0), the limit to the optical depth of field imposed by these two parameters tends towards infinity but the noise level increases, which makes any digital propagation of the real image difficult, if not impossible, and therefore limits the digital depth of field. Conversely, for a CS and / or CT optical system tending towards infinity, the noise drops but the optical depth of field tends towards 0. Only perfectly focused objects appear on the real image. This also makes any digital propagation of the real image difficult, if not impossible, and therefore limits the digital depth of field.

[0006] Furthermore, with a fixed optical system, the signal-to-noise ratio of an imaged nanoparticle depends on its size and nature. Thus, the digital depth of field depends on the size and nature of the nanoparticles.

[0007] There is therefore a need for an optical system that can be used to produce a real image of nanoparticles, ideally without the need for a priori knowledge of the size and / or nature of the nanoparticles, and which is such that, for this real image, the digital depth of field is satisfactory. General presentation

[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-referenced phase imaging system. The illumination source is configured to illuminate an object space. The microscope is configured to conjugate an object plane of the object space with an image plane, the self-referenced phase imaging system being arranged in the image plane or in the vicinity of the image plane. The self-referenced phase imaging system is configured to produce a real intensity and phase image 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 self-referenced phase imaging system, is between 0.4% and 10%. The optical system further comprises a processing unit configured to digitally propagate the real image, along the optical axis.

[0009] 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 self-referenced phase imaging system, is close to 2.5%.

[0010] In some embodiments, the illumination source is a white laser illuminating a bandpass filter. Alternatively, the illumination source may be a white plasma source illuminating a bandpass filter or a laser diode.

[0011] In some embodiments, the illumination source is configured to illuminate an object space in a nanoparticle solution, and the processing unit is configured to:count the number of imaged nanoparticles in the real image,digitally propagate the real image, along the optical axis, in an image volume of predetermined thickness,count the number of imaged nanoparticles in the digitally propagated images,calculate the size of the object volume corresponding to the image volume,calculate the concentration of the nanoparticles based on the number (N) of imaged nanoparticles counted and the size of the object volume.

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

[0013] In some embodiments, to determine the digital depth of field, the processing unit is configured to:count the number of nanoparticles in a real image of a nanoparticle solution, obtained with the self-referenced phase imaging system;digitally propagate the real image in image volumes of increasing variable thickness;count the number of imaged nanoparticles in the digitally propagated images;analyze the variation in the number of imaged particles counted as a function of the variable thickness of the image volume and identify a limit 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,determine the digital depth of field as a function of the identified limit thickness.

[0014] In some embodiments, the optical system further comprises a computer memory in which is recorded an abacus indicating, for different types of nanoparticle, the correspondence between the amplitude, hereinafter referred to as "amplitude R", of a field formed from the information of the real and / or imaginary parts of the wave field generated by an imaged nanoparticle and a digital depth of field. The amplitude R may correspond, in particular, to the amplitude of a Rytov field.

[0015] In some embodiments, the processing unit refers to the chart to determine the digital depth of field from the amplitude R of an imaged nanoparticle in the real image.

[0016] In some embodiments, for a solution comprising a mixture of nanoparticles, the illumination source is configured to illuminate an object space in the solution and the processing unit is configured to: count the imaged nanoparticles in the real image, measure the amplitudes R of these imaged nanoparticles and determine, by referring to an abacus as previously described, the digital depth of field associated with each of these imaged particles;digitally propagate the real image, along the optical axis, in an image volume of predetermined thickness, denoted D, for each of the nanoparticles imaged in the images digitally propagated in planes of the image volume, check using the abacus whether the amplitude R of the nanoparticle corresponds to a digital depth of field, denoted H, greater than or equal to twice the distance between the digitally propagated image in which the nanoparticle is imaged and the real image, if so, keep the particle for counting and if not, do not keep it for counting; for each nanoparticle counted, calculate the associated object volume corresponding, if H≥D, to the image volume of thickness D or, if H <D, à un volume image d'épaisseur égale à la profondeur de champ numérique H associée à la nanoparticule;andcalculate the concentration of nanoparticles which is equal to the sum, over all the nanoparticles counted, of the inverses of the associated object volumes.;

[0017] The foregoing and other features and advantages will become apparent from the following detailed description. This detailed description refers to the accompanying drawings.

[0018] This figure is a graph representing the number N of imaged particles in an image volume of variable thickness Dv, in micrometers (µm).This figure is a graph representing the digital depth of field H, in micrometers (µm), as a function of the amplitude R, in arbitrary units (au), of the Rytov peaks of the imaged nanoparticles.This figure represents an example of a spatial coherence domain CS and a temporal coherence domain CT. Detailed description

[0019] An example of an optical system according to the invention comprises a microscope having an optical axis, an illumination source, a self-referenced phase imaging system more simply called a "detector", and a processing unit configured to digitally propagate the real image. The illumination source illuminates the microscope which combines an object plane and an image plane containing the detector. The detector produces phase and intensity images.

[0020] The spatial coherence domain CS and temporal coherence domain CT of the source is chosen to allow faithful digital propagation from the real image of a nanoparticle solution in order to determine the position of the nanoparticles in the object volume. Digital propagation consists of digitally propagating the real image, along the optical axis, in an image volume of predetermined thickness less than or equal to the digital depth of field.

[0021] Digital propagation is only accurate up to a certain thickness of the image volume, distributed symmetrically on either side of the real image. Beyond this thickness limit, digitally propagated images exhibit artifacts and no longer represent the reality of the solution sample. This thickness limit corresponds to the digital depth of field.

[0022] In particular, a lighting source is used whose spatial coherence CS and temporal coherence CT is chosen or modified to operate the source in the desired coherence domain. L represents the coherence domain (CS and CT) chosen for the lighting source. This domain is limited as follows: from 0.4% to 6% in temporal coherence CT and from 0.4% to 10% in spatial coherence CS. This domain includes the operating mode CT=2.2% and CS=2.5%, considered optimal.

[0023] For the implementation of the invention, the skilled person may consider in particular the following lighting sources: - a laser diode (Thorlabs L405P150: wavelength 405nm and power 150mW), with temporal coherence estimated at CT = 0.25% (1nm spectral width on a central wavelength of 405nm). A modulation of the wavelength during the integration interval of the detector used (for example 1 ms) can be applied to approach the temporal coherence CT = 2.2% considered optimal; - a white laser also referred to as a "super continuum laser", filtered by a bandpass filter (reference super-continuum laser Leukos ELECTRO VIS 430); - a white plasma source, sufficiently powerful so that the signal from the nanoparticles is greater than the noise, filtered by a bandpass filter; - a lighting source which is a source of temporal coherence CT tending towards 0 (ega laser diode), in combination with a method of adjusting the temporal coherence by high-frequency variation of wavelength (electronic trigger);- a lighting source which is a source of spatial coherence CS tending towards 0 (eg a source with a collimation system), in combination with a method of adjusting the spatial coherence such as in particular: by a system for focusing or diversifying the beam, by coupling with a multimode optical fiber, by high-frequency movement (rotation / vibration / scanning) of the optical elements;- a superluminescent diode.

[0024] It will be noted that a spatial coherence of the order of 2% (therefore close to the value CS=2.5% considered optimal) with known microscopes proves satisfactory for implementing the invention. The teaching of the present application, when it presents a domain of spatial and temporal coherence, does not establish a link of equivalence between these two notions which are different by nature. The constraints of belonging to intervals of temporal and spatial coherence are therefore understood as cumulative conditions which must be simultaneously fulfilled.

[0025] Furthermore, it is understood that a point of zero spatial coherence (CS=0) or zero temporal coherence (CT=0) is without physical meaning. Therefore, in the present application, an interval of spatial or temporal coherence extending between 0 and an upper bound is an open interval not including the value 0.

[0026] The spatial and temporal coherence domain represented on the is hereinafter referred to as the “main domain”. As previously indicated, the operating mode considered optimal for the invention, within the main domain, is obtained for CT=0.022 (2.2%) and CS=0.025 (2.5%).

[0027] Making CT or CS tend towards 0 is not a preferred embodiment because the presence of optical noise due to spatial and temporal coherence (speckle, speckle or laser granularity) degrades particle detection by raising the background noise level, which decreases the number of particles detected and the possible propagation volume. A domain suitable for implementing the invention is therefore a domain excluding CT=0 or CS=0.

[0028] In the present application, the temporal coherence CT of the illumination source is considered to be close to 2.2% and the spatial coherence CS of the illumination source at the level of the self-referenced phase imaging system is considered to be close to 2.5%, if these two parameters CT, CS are respectively in an interval containing the value CT=2.2% and in an interval containing the value CS=2.5%, these two intervals being strictly included, respectively, in the intervals of the main domain mentioned above and represented on the, that is to say between 0.4% and 6% for CT and between 0.4% and 10% for CS. In other words, the combination CT=2.2% and CS=2.5% being considered as an “optimum point” of operation of the system, a neighborhood of the optimum point within the meaning of the present application is any sub-domain of the main domain which contains the optimum point. For example, a subdomain with a range of 1.7% to 2.7% for CT and a range of 2% to 3% for CS can be cited.

[0029] In the prior art, a low but relatively common value for spatial coherence is typically CS = 0.1%. A prior art document that would teach to minimize spatial coherence or to make it tend towards 0 must therefore be interpreted as teaching to choose CS values ​​lower than 0.1%. This would therefore not correspond to the conditions for implementing the invention in the interval [0.4%; 10%] of spatial coherence CS.

[0030] In the prior art, a low but relatively common value for temporal coherence is typically CT = 0.02% (without this value being related to the common low value of spatial coherence CS mentioned above). A prior art document which would teach to minimize temporal coherence CT must therefore be interpreted as teaching to choose CT values ​​lower than 0.02%. This would therefore not correspond to the conditions of implementation of the invention in the interval [0.4%; 6%] of temporal coherence CT.

[0031] To create such an optical system, it will be sufficient for a given lighting source to either verify that it corresponds to the aforementioned spatial and temporal coherence domain, or to verify that the signal-to-noise ratio that it provides on a detector allows the detection of nanoparticles and the digital propagation of the real image.

[0032] In the present application, a detector producing phase and intensity images is understood as a detector producing a phase measurement itself but also equivalently a quantity capable of reconstructing the phase information as a quantity proportional to the phase, as an optical path difference, or as one or more gradients of the phase which allow it to be reconstructed by integration.

[0033] For example, the following devices can be used as detectors: - a multi-lateral shift interferometry device using a modified Hartmann mask, for example by superimposing an amplitude grating of given period p and a phase grating of period 2.p such as for example a detector referenced under the name "SID4" and marketed by the company "Phasics"; - wavefront analyzers, making it possible to establish a phase mapping of a wavefront, combined with an intensity detector to analyze simultaneously and with a common spatial reference, the phase and intensity of a wave; - a wavefront analyzer or imager known from the prior art such as a curvature analyzer, a Shack-Hartmann sensor, a quantitative phase microscopy assembly such as for example a self-referenced digital holography device.

[0034] The determination of the digital depth of field to calculate the nanoparticle concentration is based on the digital propagation of the real image to calculate the wave field in the object volume. To solve the wave equation in an inhomogeneous medium (as is the case of a medium containing a population of nanoparticles) and perform a digital propagation, several approaches or methods known from the prior art can be applied, among them in particular: the ray method (or geometric optics), the Born weak perturbation method, the Rytov approach, the parabolic approximation and the intensity transfer equation.

[0035] In certain embodiments, a microscope of revolution around an optical axis coincident with the z axis of an orthonormal reference frame (O, x, y, z) in an image space is used, and a surface detector S, arranged in the image plane z=0 and providing a measurement of the intensity and phase of the complex field incident on this detector. A real image in intensity and phase, also called holographic, of nanoparticles arranged in the object volume around an object plane optically conjugated to the detector plane is thus formed on the detector.

[0036] We can count the number of imaged nanoparticles n(z=0) in the real image, then by digital propagation in steps of thickness d, symmetrically with respect to the image plane (i.e., the plane of the real image), obtain images of planes distant by d / 2 from the detector and distant from each other by d. We can then count the number of imaged nanoparticles n(-d / 2) and n(d / 2) in these two planes. By addition we obtain a number of imaged particles N(d) = n(0) + n(-d / 2) + n(d / 2) in the volume, image of thickness d, that is to say by summing the particles imaged in planes inside the image volume (here, the plane of the detector) and on the surface of the image volume of thickness d.

[0037] It is easy to demonstrate that by propagating the image in –d / 2 in the plane in –d and the image in +d / 2 in the plane in +d, that is to say by increasing symmetrically with respect to the image, the image volume by steps of thickness d, we can count the number of particles imaged by two digital propagations in two new planes located outside the image volume for which the number of particles is previously known. We add the number of particles imaged known in the interior volume to the new planes and the number of particles imaged in these new planes, step by step. Thus for a variable thickness Dv=k*d (k being a positive integer) of image volume, we have: N((k+1)*d)=N(k*d)+n(k*d / 2)+n(-k*d / 2).

[0038] We can then plot the graph or curve N(Dv) representing the number N of particles imaged as a function of the variable thickness Dv for an experiment or an average curve for several experiments (several real images of the same nanoparticle solution).

[0039] For a given population of nanoparticles (fixed size and nature), we observe for a controlled source of spatial and temporal coherence, that the number N of imaged particles (which can be an average number if several experiments are carried out) present in an increasingly large image volume does not increase linearly but peaks at a constant value on a plateau or plateau zone P which extends in projection on the axis of thicknesses Dv, over a range of thicknesses k1*d ≤ Dv ≤ k2*d with k1 <k2 et sur l’axe des N en gardant une valeur sensiblement constante aux erreurs de mesure près. Il est alors possible de déterminer la valeur H=k1*d comme étant la profondeur de champ numérique pour le dispositif expérimental utilisé et pour la population de nanoparticules imagées.

[0040] The preceding explanations are illustrated by the example of the. In this example, the particles used are polystyrene particles of 100nm diameter. La is a graph representing the number N of particles imaged in an image volume V of variable thickness Dv in micrometers (µm) after the digital propagation of the real image in the image volume V. This image volume V is centered on the plane of the real image and its thickness Dv increases symmetrically on either side of the real image. The imaged particles are counted in digitally propagated images spaced from each other to reconstruct the image volume V. This operation was carried out for several real images of the same sample (light lines), the relationships are then averaged to obtain the curve N(Dv) in thick lines.This curve N(Dv) shows a monotonic growth up to a plateau on a plateau zone P (surrounded by dotted lines on the) within which the number N of imaged particles is substantially stable with Dv. There is thus a limiting thickness from which the number N of imaged particles peaks in the zone P at a certain value noted N(H). In the example in the figure, N(H) is close to 16. The digital depth of field H corresponds to said limiting thickness. In the example in the figure, the digital depth of field H is estimated to be equal to 25 µm.

[0041] For thicknesses Dv greater than H, the reconstruction of the volume by digital propagation is considered to no longer be faithful to the reality of the object volume. Indeed, the capping of N then its growth with Dv (for Dv>H) does not correspond to a physical reality for a homogeneous sample of nanoparticles (for which N must constantly increase with Dv). For Dv>H, digital propagation therefore no longer allows the reconstruction of images of objects physically present in the object volume but creates images of objects not present in the object volume.

[0042] To avoid or limit counting artifacts as much as possible, digital propagation over a distance (i.e. a predetermined thickness D of image volume) chosen to be less than or equal to the digital depth of field H determined with reference nanoparticles will be a preferred method of implementation to determine the concentration of a population of nanoparticles without a priori knowledge of them.

[0043] The step d is chosen to be less than the axial resolution of the microscope and to allow faithful sampling of the volume.

[0044] The value of the numerical depth of field for a nanoparticle depends on the volume of the particle and the modulus of the complex index difference between the particle and the surrounding medium at a given wavelength, at a given CS and CT, and a given imaging system (illumination and collection numerical aperture).

[0045] The inventors discovered that Rytov's approach was particularly relevant for calculating nanoparticle concentrations. Indeed, calculating the complex Rytov field, and in particular its intensity, facilitates the detection of imaged nanoparticles in the real image and in digitally propagated images.

[0046] The Rytov approach described here is valid in the spatial CS and temporal CT coherence domains of the illumination source mentioned earlier.

[0047] From the intensity I(x,y,zi) and the phase phi(x,y,zi) in the plane of the detector (real image) (zi=0) or in the plane of a digitally propagated image (zi different from zero), the complex Rytov field r(x,y,zi) is formed by formulas known from the prior art, in other fields of application.

[0048] We then form a Rytov intensity image R(x,y,zi) in the zi plane by the square of the modulus in this plane of the complex Rytov amplitude according to the formula: R(x,y,zi)=|r(x,y,zi)|2. Alternatively, a Rytov amplitude image can be obtained for the same purposes, by forming the square root of R as a function of x, y in the zi plane.

[0049] Using Rytov intensity is particularly effective for detecting imaged nanoparticles in both real and propagated images. Indeed, the Rytov intensity or amplitude makes it possible to obtain, for a nanoparticle, clear in the plane considered, a positive signal on a zero background, whatever 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).

[0050] Using the Rytov intensity is therefore a preferred way to identify and count the imaged nanoparticles in the image volume after digital propagation (by calculating the Rytov field for each digitally propagated image in the image volume and performing the detection on the corresponding image of the Rytov intensity or amplitude), as described above. Calculating the Rytov field is therefore useful for counting the imaged nanoparticles. In addition, the inventors discovered that the intensity or amplitude of the Rytov field is characteristic of the associated digital depth of field.Indeed, when the complex amplitude information is expressed in the form of the Rytov field, for an optical system adapted to the CT and CS coherence regime, we obtain the result that the digital depth of field is no longer a function of the Rytov intensity or amplitude, in the sense that nanoparticles having the same Rytov intensity or amplitude are detectable in the same digital depth of field even if their optical index or volume are different. This result is illustrated by the. This figure is a graph representing the digital depth of field H, in micrometers (µm), as a function of the average amplitude R of the Rytov peaks, in arbitrary units (au), of the imaged nanoparticles. Here, the chosen observable is the amplitude of the Rytov field of the digitally propagated complex field, in the image volume of thickness equal to the digital depth of field H.Each point and its associated statistic correspond to homogeneous samples of different nanoparticles, the nanoparticles of each sample having a fixed diameter and nature.

[0051] Thus, the value of the average Rytov amplitude R for samples of different nanoparticles (each sample is homogeneous in composition and size) is presented as a function of the numerical depth of field H determined by the method of determining the plateau P (see) previously described. Each point corresponds to a different sample, i.e. to a different pair (average diameter, materials). The following samples are represented: - Polystyrene (PS) 60nm, PS 80nm, PS 100nm, PS 150nm, PS 200nm, - Gold 60nm, Gold 100nm - Silver 100nm and - Diamond 80nm.

[0052] It is observed that there is a relationship between the digital depth of field H and the amplitude R of the Rytov peaks, or Rytov amplitude. This relationship can be approximated by the dotted line of the graph. This graph can therefore be used as a nomogram since, for a given optical system, operating in a given CS and CT regime, it is possible to determine the digital depth of field H associated with an unknown nanoparticle by a simple measurement of the Rytov amplitude R of this nanoparticle. This avoids having to systematically carry out the process of determining the digital depth of field H by propagation of the real image, counting the imaged nanoparticles and determining the plateau P (see). Such a nomogram makes it possible to determine a calibration of the digital depth of field of a fixed optical system as a function of the Rytov amplitude of the objects imaged by this system.

[0053] Thus, using the Rytov approach, the digital depth of field can be determined directly by measuring the Rytov amplitude with reference to an abacus, i.e., a graph or table indicating the correspondence between the Rytov amplitude R and the digital depth of field H. The Rytov amplitude is therefore a measure of choice for the digital depth of field for a type of nanoparticle in an optical system for the purpose of measuring the concentration of nanoparticles.

[0054] It follows that for an optical system whose correspondence between the Rytov amplitude R and the digital depth of field H is known by an abacus as previously described, we can, for a single nanoparticle imaged in intensity and phase on the detector, know by forming the image of the Rytov amplitude, and by looking for a signal peak in the Rytov image, both locate the imaged nanoparticle and deduce the digital depth of field associated with this nanoparticle.

[0055] The Rytov field can be replaced by another combination of information from the real and imaginary parts of the wave field or, if a priori knowledge about the particle response is known, by only the real component or the imaginary component. In other words, instead of the Rytov field, other fields formed from information from the real and / or imaginary parts of the wave field can be used.

[0056] The proposed optical system and measurement method therefore make it possible to obtain a measurement of the concentration of any nanoparticles regardless of the physical nature of the nanoparticles and their size and without the need to calibrate the system with samples of known concentrations.

[0057] Indeed, determining the digital depth of field makes it possible to delimit the image volume in which the reconstruction by digital propagation from the real image is faithful to the reality of the imaged sample. The digital propagation is therefore carried out for this volume, the imaged nanoparticles are counted for this volume and the concentration of the nanoparticles is calculated as being equal to the number of nanoparticles counted divided by the volume. This volume is controlled and defined digitally and is not the result of an assumption or calibration to define this volume. This concentration measurement is carried out solely from the optical signal coming from the sample and does not require prior calibration with samples of known concentrations.

[0058] Knowing the digital depth of field makes it possible to avoid digitally propagating the real image over excessively large image volume thicknesses, which gives a better measurement of the concentration (propagation artifacts are not counted as imaged nanoparticles) while limiting the digital propagation calculation time.

[0059] The use of the abacus, characteristic of a given optical system, makes it possible to determine the digital depth of field from the measurement of the Rytov amplitude of a nanoparticle imaged in the real image. This further limits the calculation time since the initial propagation step, on an increasing thickness Dv () which is used to determine the digital depth of field H, is not necessary. Only propagation on a thickness D less than or equal to the depth H is carried out to allow counting.

[0060] For samples of heterogeneous nanoparticles (in composition and size) it is also possible to calculate the concentration of the sample by the methods previously described. In such a mixture the nanoparticles have different digital depths of field. Care must be taken to ensure that the imaged particles of the image volume that contribute to the calculation of the concentration are not digital propagation artifacts. This is achieved by checking using the abacus, for each of the nanoparticles imaged in the successive digitally propagated images of the image volume (of thickness D), that the amplitude R of the nanoparticle corresponds to a digital depth of field H greater than or equal to twice the distance between the digitally propagated image in which the nanoparticle is imaged and the real image. If this condition is verified the particle is retained, if it is not verified, the nanoparticle is not retained.When calculating the concentration, it is also necessary to take into account, for each nanoparticle, the image volume in which it was counted. For the nanoparticles retained: - if H <D alors ce volume a pour épaisseur H;- si H≥D alors ce volume a pour épaisseur D.

[0061] The final concentration is equal to the sum, on the retained particles, of the inverse of these volumes.

[0062] Under the assumption that the lateral and axial magnification is known between the object space and the image space, the following relation 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 the axial magnification in the vicinity of the detector plane in the z direction of the optical axis of the optical system used for the conjugation, assumed to be of revolution.

[0063] To calculate an object volume from the image volume, it is useful to use the surface of the detector and the lateral and axial magnification of the optical system to complete the dimensions of the image volume and then obtain the object volume.

[0064] This application is susceptible to industrial application, particularly in the field of measuring the concentration of nanoparticles.

[0065] The proposed device and method are particularly suitable for measuring the concentration of nanoparticles in solution, subjected to Brownian motion, because the availability of the intensity and the phase in a self-referenced manner over time (production of a film) makes it possible to envisage tracking and refocusing of the nanoparticles in the propagated images outside the plane of the real image within the meaning of the present application and to obtain a signal-to-noise ratio capable of implementing the teaching of the present application, by averaging the successive digitally propagated images of the same particle.

Claims

An optical system comprising a microscope having an optical axis, an illumination source for the microscope, and a self-referenced phase imaging system, wherein the illumination source is configured to illuminate an object space, wherein the microscope is configured to conjugate an object plane of the object space with an image plane, the self-referenced phase imaging system being disposed in or near the image plane, and wherein the self-referenced phase imaging system is configured to produce a real intensity and phase image of the object plane, wherein the temporal coherence (CT) of the illumination source is between 0.4% and 6% and the spatial coherence (CS) of the illumination source, at the self-referenced phase imaging system, is between 0.4% and 10%, the optical system further comprising a processing unit configured to digitally propagate the real image along the optical axis. Optical system according to claim 1, wherein the temporal coherence (CT) of the illumination source is close to 2.2% and the spatial coherence (CS) of the illumination source, at the level of the self-referenced phase imaging system, is close to 2.5%. An optical system according to any one of claims 1 or 2, wherein the illumination source is a white laser illuminating a bandpass filter. An optical system according to any one of claims 1 or 2, wherein the illumination source is a white plasma source illuminating a bandpass filter. An optical system according to any one of claims 1 or 2, wherein the illumination source is a laser diode. An 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:count the number of imaged nanoparticles in the real image,digitally propagate the real image, along the optical axis, in an image volume of predetermined thickness,count the number of imaged nanoparticles in the digitally propagated images,calculate the size of the object volume corresponding to the image volume,calculate the concentration of the nanoparticles based on the number (N) of imaged nanoparticles counted and the size of the object volume. An optical system according to claim 6, wherein the processing unit is configured to:- count the number of nanoparticles in a real image of a nanoparticle solution, obtained with the self-referenced phase imaging system;- digitally propagate the real image in image volumes of increasing variable thickness (Dv);- count the number of imaged nanoparticles in the digitally propagated images;- analyze the variation in the number (N) of imaged nanoparticles counted as a function of the variable thickness (Dv) of the image volume and identify a limit thickness of the image volume for which the number (N) of imaged nanoparticles no longer increases with the variable thickness (Dv) of the image volume and reaches a plateau (P), and- determine a digital depth of field (H) as a function of the identified limit thickness; andwherein the predetermined thickness is less than or equal to the digital depth of field (H). Optical system according to claim 6 or 7 in which the system further comprises a computer memory in which is recorded an abacus indicating for different types of nanoparticle, the correspondence between a digital depth of field (H) and the amplitude, noted amplitude R, of a field formed from the information of the real and / or imaginary parts of the wave field generated by an imaged nanoparticle. Optical system according to claim 8 wherein the processing unit refers to the abacus to determine a digital depth of field (H) from the amplitude R of a nanoparticle imaged in the real image, and wherein the predetermined thickness is less than or equal to the digital depth of field (H). Optical system according to any one of claims 1 to 6, further comprising a computer memory in which is recorded an abacus indicating, for different types of nanoparticle, the correspondence between a digital depth of field and the amplitude, denoted amplitude R, of a field formed from the information of the real and / or imaginary parts of the wave field generated by an imaged nanoparticle,in which the illumination source is configured to illuminate an object space in a solution comprising a mixture of nanoparticles,in which the processing unit is configured to:count the imaged nanoparticles in the real image, measure their amplitude R and determine, with reference to the abacus, the digital depth of field associated with each of these imaged nanoparticles;digitally propagate the real image, along the optical axis, in an image volume, of predetermined thickness, denoted D;for each of the nanoparticles imaged in the digitally propagated images of the image volume, check using the abacus, if the amplitude R of the nanoparticle corresponds to a digital depth of field, noted H, greater than or equal to twice the distance between the digitally propagated image in which the nanoparticle is imaged, and the real image, if so, keep the nanoparticle for counting and if not, do not keep it for counting; for each nanoparticle counted, calculate an associated object volume corresponding, if H≥D, to the image volume of thickness D or, if H <D, à un volume image d'épaisseur égale à la profondeur de champ numérique H associée à la nanoparticule; etcalculer la concentration des nanoparticules qui est égale à la somme, sur toutes les nanoparticules comptées, des inverses des volumes objet associés.;

Images