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 that makes it possible, in particular, to measure the concentration of nanoparticles without prior knowledge of the nanoparticles and without the need to modify the nanoparticles or their medium. [Background technology]

[0002] In the prior art, the optical measurement of nanoparticle concentration encounters the problem of providing a tool to determine the measurement volume in which the 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 on the optical system. Therefore, since it is difficult to optically measure the concentration of nanoparticles without prior knowledge of the physical properties of the nanoparticles, there is a need for an optical system that makes it possible to facilitate this measurement.

[0003] For purposes of this application, the following definitions apply. - "Temporal coherence TC" of the illumination source: the ratio of the wavelength range of the illumination source divided by its central wavelength. - "Spatial coherence SC" of an illumination 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 the incident wave in addition to the 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 the wave field at the 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 surface. It is calculated numerically based on a real image using conventional propagation methods to solve the wave equation. "Image Volume": A volume that is imaged by numerical propagation of a real image. "Imaging nanoparticle" or "imaging particle": a nanoparticle that forms a sharp image, or an image with a maximum spatial energy density, in the real image (this is particularly the case when the nanoparticle is in the object plane) or in the numerically propagated image (this is particularly the case when the nanoparticle is outside the object plane). "Numerical depth of field": the thickness in the direction of the optical axis of the volume imaged by numerical propagation, in particular the volume centered on the real image in which nanoparticles can be faithfully imaged. This is the thickness for which the 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 the object space. The numerically propagated image is such that objects physically present in the object space, and only these objects, are imaged onto the numerically propagated image, which is considered faithful. "White laser" or "supercontinuum laser": an illumination source with high spatial coherence and quasi-zero temporal coherence.

[0004] The numerical depth of field as 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 the "optical" depth of field for clarity). The optical depth of field, in turn, 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) approach (0,0), the optical depth of field limit imposed by these two parameters approaches infinity, but the noise level increases, which makes it difficult or even impossible to achieve any numerical propagation of the real image, and therefore the numerical depth of field is limited. On the other hand, in an optical system where at least one of SC and TC approach 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 therefore the numerical depth of field is limited.

[0006] Furthermore, in fixed optics, the signal-to-noise ratio of the imaging nanoparticles depends on their size and properties, and therefore the numerical depth of field depends on the size and properties of the nanoparticles.

[0007] Therefore, what is needed is an optical system that can be used to generate real images of nanoparticles, ideally without requiring prior knowledge of the nanoparticles' size and / or properties, and that provides a satisfactory numerical depth of field for this real image. Summary of the Invention [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 an object space. The microscope is configured to couple an object plane and an image plane of the object space. The self-referencing phase imaging system is arranged in or near the image plane, and is configured to generate 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 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.

[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 the self-referenced phase imaging system is around 2.5%.

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

[0011] In some embodiments, an illumination light source is configured to illuminate an object space in a nanoparticle solution, and a processing unit is configured to count the number of imaged nanoparticles in a real image, to numerically propagate the real image along an optical axis within an image volume of a predetermined thickness, to count the number of imaged nanoparticles in the numerically propagated image, to calculate dimensions of an object volume corresponding to the image volume, and to calculate a concentration of nanoparticles based on the number of counted imaged 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, to determine the numerical depth of field, the processing unit: configured to count the number of imaged nanoparticles in a real image obtained using a self-referencing phase imaging system of the nanoparticle solution; configured to numerically propagate a real image within an image volume of increasing variable thickness; configured to count the number of imaged nanoparticles in the numerically propagated image; configured to analyze the variation in the number of imaged nanoparticles counted as a function of the varying thickness of the image volume and identify a critical thickness of the image volume where the number of imaged nanoparticles no longer increases with the varying thickness of the image volume and reaches a plateau; The method is configured to determine a numerical depth of field based on the identified critical thickness.

[0014] In some embodiments, the optical system further includes a computer memory storing a chart showing, for various types of nanoparticles, a correspondence between the amplitude, hereinafter referred to as "amplitude R," of a field formed from information about the real and / or imaginary parts of the wave field generated by the imaging nanoparticles and the numerical depth of field. The amplitude R may correspond in particular to the amplitude of a Ritov 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 real image.

[0016] In some embodiments, for a solution containing a mixture of nanoparticles, an illumination light source is configured to irradiate an object space in the solution, and the processing unit counts the imaged nanoparticles in the real image, measures the amplitude R of these imaged nanoparticles, refers to the chart as described above, and is configured to determine the numerical depth of field associated with each of these imaged nanoparticles, configures the real image to numerically propagate within an image volume of a predetermined thickness denoted by D along the optical axis, and for each imaged nanoparticle in the numerically propagated image at each plane of the image volume, uses the chart to check whether the amplitude R of the nanoparticle corresponds to a numerical depth of field denoted by H that is more than twice the distance between the numerically propagated image in which the nanoparticle is imaged and the real image, and if it corresponds, retains the nanoparticle for counting, and if it does not correspond, is configured not to retain the nanoparticle for counting, for each counted nanoparticle, if H≧D, calculates the associated object volume corresponding to the image volume of thickness D, and if H<D, calculates the associated object volume corresponding to the image volume of a thickness equal to the numerical depth of field H associated with the nanoparticle, is configured to calculate the concentration of nanoparticles equal to the sum of the reciprocals of the associated object volumes for all counted nanoparticles.

[0017] Reading the following embodiments for carrying out the invention will clarify the above-described features and advantages, as well as other features and advantages. The embodiments for carrying out this invention refer to the accompanying drawings.

Brief Description of the Drawings

[0018] [Figure 1] This figure is a graph showing the number N of nanoparticles imaged within 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 lithographic, peak amplitude R in arbitrary units (au) of the imaged nanoparticles. [Figure 3] This figure shows an example of spatial coherence (SC) and temporal coherence (TC) regions. DETAILED DESCRIPTION OF THE INVENTION

[0019] 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, more simply called a "detector", and a processing unit configured to numerically propagate a real image. The illumination source illuminates the microscope, which combines an object plane and an image plane that includes a detector. The detector produces phase and intensity images.

[0020] To determine the location of the nanoparticles within the object volume, the spatial coherence SC and temporal coherence TC of the illumination source are selected to enable faithful numerical propagation of the nanoparticle solution based on 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.

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

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

[0023] To implement the invention, the person skilled in the art can take into account, inter alia, the following illumination sources: - Laser diode (Thorlabs L405P150: wavelength 405 nm and power 150 mW), estimated temporal coherence TC = 0.25% (spectral width 1 nm over a central wavelength of 405 nm). By applying wavelength modulation during the integration period of the detector used (e.g. 1 ms), it is possible to approach the optimal temporal coherence TC = 2.2%. - white lasers, also called "supercontinuum lasers", filtered by bandpass filters (supercontinuum lasers referenced in Leukos Electro VIS430); - a band-pass filtered white plasma source that is strong enough so that the nanoparticle signal outweighs the noise; an illumination source (e.g. a laser diode) whose temporal coherence TC approaches 0 in combination with a method of temporal coherence regulation based on high-frequency wavelength fluctuations (electronic trigger); - an illumination source whose spatial coherence SC approaches 0 (for example an illumination source with a collimation system) in combination with a spatial coherence adjustment method, for example in particular based on a system for focusing or diverging the beam, based on coupling with a multimode optical fiber, based on high-frequency movements (rotation / oscillation / scanning) of optical elements, -Superluminescent diodes.

[0024] It should be noted that with known microscopes, a spatial coherence of the order of 2% (hence a value SC=2.5%, considered to be optimal) has proven to be sufficient for implementing the invention. The teachings herein, in presenting spatial and temporal coherence regions, do not establish an equivalence between these two distinct concepts, and therefore the constraints pertaining 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 the point of zero spatial coherence (SC=0) or the point of zero temporal coherence (TC=0) has no physical meaning. Therefore, in this application, a spatial or temporal coherence interval extending between 0 and an upper value is an open interval that does not include the value 0.

[0026] The spatial and temporal coherence region shown in Figure 3 is hereinafter referred to as the "primary region." As indicated above, the operating mode within the primary region that is considered optimal for the present invention is obtained with TC = 0.022 (2.2%) and SC = 0.025 (2.5%).

[0027] Setting TC or SC close to 0 is not a preferred embodiment, since the presence of optical noise (speckle or laser granularity) due to spatial and temporal coherence degrades nanoparticle detection due to an increased background noise level, 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 these two parameters TC and SC are within the interval including the value TC=2.2% and the value SC=2.5%, respectively, and these two intervals are strictly within the intervals of the aforementioned main regions shown in FIG. 3 , i.e., between 0.4% and 6% for TC and between 0.4% and 10% for SC, respectively, then the temporal coherence TC of the illumination source at the level of the self-referenced phase imaging system is considered to be near 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 near 2.5%. In other words, the combination of TC=2.2% and SC=2.5% is considered to be the “optimum operating point” of this optical system. For the purposes of this application, “close to the optimum point” refers to any subregion of the main region that includes the optimum point. For example, the subregions ranging from 1.7% to 2.7% for TC and from 2% to 3% for SC can be mentioned.

[0029] In the prior art, a low but relatively common value of spatial coherence is usually SC=0.1%. Therefore, prior art documents that teach minimizing or approaching zero spatial coherence should be interpreted as teaching the selection of SC values ​​below 0.1%. Therefore, it is assumed that this does not 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 low but relatively common value for temporal coherence is typically TC=0.02% (this value is unrelated to the common low spatial coherence value SC mentioned above). Therefore, prior art documents that teach minimizing the temporal coherence TC should be interpreted as teaching the selection of a TC value less than 0.02%. Therefore, it is assumed that this teaching does not correspond to the conditions for implementing the present invention, which are within the temporal coherence TC interval [0.4%; 6%].

[0031] To create such an optical system, it would be sufficient to ensure that, for a given illumination source, either it corresponds to the spatial and temporal coherence region mentioned above, or it provides a signal-to-noise ratio on the detector that allows the detection of nanoparticles and the numerical propagation of a real image.

[0032] In this application, a detector that produces phase and intensity images is understood to be a detector that not only produces actual phase measurements, but equally produces a quantity from which phase information can be reconstructed, either as a quantity proportional to phase, as an optical path difference, or as one or more phase gradients that allow reconstruction by integration.

[0033] By way of example, the following devices can be used as detectors: multi-way shift interferometer devices using a Hartmann mask modified, for example, 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 by the name "SID4" and sold by the company "Phasics", a wavefront analyzer used to establish a phase map of the wavefront, combined with an intensity detector for analyzing the phase and intensity of the wave simultaneously and with a common spatial reference; Wavefront analyzers or imagers known from the prior art, such as curvature analyzers, Shack-Hartmann sensors, quantitative phase microscope assemblies, for example self-referencing numerical holography devices.

[0034] The determination of the numerical depth of field for calculating the concentration of nanoparticles relies on the numerical propagation of real images to calculate the wave field in the object volume. To solve the wave equation in an inhomogeneous medium (as in the case where the medium contains a population of nanoparticles) and perform the numerical propagation, many techniques or methods known from the prior art can be applied, including, inter alia, the ray method (or geometric optics), the Born weak scattering method, the Rytov approximation, the parabolic approximation, and the intensity transport equation.

[0035] In some embodiments, a microscope is used that pivots around its optical axis coinciding with the z-axis of an orthogonal reference frame (O, x, y, z) in image space, and a surface detector S that is placed in the image plane z = 0 and provides measurements of the intensity and phase of the complex field incident on the detector, thereby forming a real image on the detector of the intensity and phase of the nanoparticles placed in the object volume around an object plane that is optically conjugate to the plane of the detector, also called a holographic image.

[0036] The number of imaging nanoparticles n (z=0) in the real image is counted, and then, using numerical propagation by thickness d symmetrically with respect to the image plane (i.e., the plane of the real image), an image of a plane d / 2 away from the detector and an image of a plane at a distance d from each other can be obtained. The numbers of imaging nanoparticles n(-d / 2) and n(d / 2) in these two planes can then be counted. Addition is performed to obtain a certain number of imaging nanoparticles N(d)=n(0)+n(-d / 2)+n(d / 2) in the image volume of thickness d. That is, the addition is performed by summing the imaging nanoparticles in the plane (here, the plane of the detector) in the image volume and the imaging nanoparticles on the surface of the image volume of thickness d.

[0037] It is easy to show that by gradually propagating the image of -d / 2 into the plane of -d and the image of +d / 2 into the plane of +d, i.e., by increasing the image volume by thickness d symmetrically with respect to the image, it is possible to count the number of nanoparticles imaged by two numerical propagations in two new planes located outside the image volume, where the number of nanoparticles is known a priori. The known number of imaged nanoparticles in the internal volume are added to the new planes and gradually added to the number of imaged nanoparticles in these new planes. Thus, 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).

[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 of a certain experiment, or the average curve of a plurality of experiments (a plurality of real images of the same nanoparticle solution).

[0039] For a given population of nanoparticles (constant dimensions and properties), with an illumination source whose spatial and temporal coherence is controlled, the number of imaged nanoparticles N (which may be an average if multiple experiments are performed), present within an increasingly large image volume, does not increase linearly, but rather, over the thickness range k1*d ≦ Dv ≦ k2*d (k1 < k2), it projects along the thickness axis Dv and reaches a peak at a constant value beyond a flat portion or flat zone P that spreads out to maintain a substantially constant value within the range of measurement error, along the N axis. And it is possible to determine the value H = k1*d as the numerical depth of field of the experimental apparatus used and of the population of imaged nanoparticles.

[0040] The above description is illustrated by the example of FIG. 1. In this example, the nanoparticles used are polystyrene particles with a diameter of 100 nm. FIG. 1 shows a graph of the number N of imaged nanoparticles in an image volume V of 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 imaged nanoparticles are counted in the numerically propagated images spaced apart from one another to reconstruct the image volume V. This operation was performed for multiple real images (thin lines) of the same sample. These relationships are then averaged to obtain the thick curve N(Dv). This curve N(Dv) exhibits monotonic growth beyond a plateau zone P (encircled by a dotted line in FIG. 1) up to an upper limit. Within the plateau zone, the number N of imaged nanoparticles is approximately stable with respect to Dv. Thus, within the zone P there is a limit thickness from which the number N of imaged nanoparticles starts and peaks at a certain value, denoted N(H). In the illustrated example, N(H) is around 16. A numerical depth of field H corresponds to said limit thickness. In the illustrated example, the numerical depth of field H is estimated to be equal to 25 μm.

[0041] If the thickness Dv is greater than H, the reconstruction of the volume by numerical propagation is considered to no longer be faithful to the reality of the object volume. In fact, the fact that N peaks and then increases with Dv (if Dv>H) does not correspond to the physical reality of a homogeneous sample of nanoparticles (for which N must always increase with Dv). If Dv>H, numerical propagation is no longer able to reconstruct images of objects physically present in the object volume, and instead creates images of objects that are not present in the object volume.

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

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

[0045] We have found that the Rytov approximation is particularly relevant and applicable to the calculation of nanoparticle concentrations. Indeed, by calculating the complex Rytov field, and in particular its intensity, it becomes easier to detect imaged nanoparticles in real and numerically propagated images.

[0046] The Rytov approximation described here is valid in the previously mentioned spatial coherence SC domain and temporal coherence TC domain of the illumination source.

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

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

[0049] The use of the Rythov intensity is particularly effective for detecting imaged nanoparticles, whether in real or propagated images: indeed, a nanoparticle that is sharp in the considered plane will make it possible to obtain a positive signal on a zero background, regardless of the nature of the nanoparticle, by virtue of its Rythov intensity or amplitude (this signal will be visible in the Rythov field intensity or amplitude, whether it is included in the real or imaginary part of the real or propagated image).

[0050] Therefore, as described above, using the Rytov intensity is a preferred method for identifying and counting imaged nanoparticles within an image volume after numerical propagation (by calculating the Rytov field for each numerically propagated image within the image volume and detecting the Rytov intensity or amplitude in the corresponding image). Thus, calculating the Rytov field is useful for counting imaged nanoparticles. Furthermore, the inventors have discovered that the Rytov field intensity or amplitude is a relevant characteristic of the numerical depth of field. Indeed, when complex amplitude information is expressed in the form of a Rytov field, for optical systems suitable for the TC and SC coherence regimes, it now follows that the numerical depth of field is only a function of the Rytov intensity or amplitude, in the sense that nanoparticles with the same Rytov intensity or amplitude can be detected at the same numerical depth of field even if their optical indices or volumes are different. This result is illustrated in Figure 2. The figure is a graph showing the numerical depth of field H in micrometers (μm) as a function of the average amplitude R in arbitrary units (au) of the Ritov peaks of the imaged nanoparticles. Here, the observable quantity chosen is the Ritov field amplitude of the numerically propagated complex 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 of each sample have a consistent diameter and properties.

[0051] Thus, Figure 2 shows the values ​​of the average Ritz amplitude R of different nanoparticle samples (each sample is homogeneous in terms of composition and size) as a function of the numerical depth of field H, determined using the method described above for determining the plateau 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 100 nm, and -Diamond 80nm.

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

[0053] Therefore, using the Rythov approximation, the numerical depth of field can be determined directly by measuring the Rythov amplitude with reference to a chart, i.e., graph or table, showing the correspondence between the Rythov amplitude R and the numerical depth of field H. The Rythov amplitude is therefore 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 the Rytov amplitude R and the numerical depth of field H is known from a chart such as that described above, for a single nanoparticle imaged on a detector in terms of intensity and phase, it is possible to both identify the position of the imaged nanoparticle and, from the identified position, derive the numerical depth of field associated with this nanoparticle by forming an image of the Rytov amplitude and by looking for signal peaks in the Rytov image.

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

[0056] The proposed optical system and measurement method therefore make it possible to obtain measurements of the concentration of any nanoparticle, regardless of the nanoparticles' physical properties and their dimensions, and without the need to calibrate the optical system with samples of known concentration.

[0057] In fact, determining the numerical depth of field allows defining an image volume in which the reconstruction by numerical propagation based on the actual image is faithful to the reality of the imaged sample. Numerical propagation is then performed on this image volume, imaged nanoparticles are counted on this volume, and the nanoparticle concentration is calculated as equal to the number of counted nanoparticles divided 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 solely based on the optical signal from the sample and does not require prior calibration using samples of known concentration.

[0058] Knowing the numerical depth of field makes it possible to avoid numerical propagation of the real image through excessively large image volume thicknesses, which gives better concentration measurements (propagation artifacts are not counted as imaging nanoparticles) and at the same time limits the numerical propagation calculation time.

[0059] The use of a chart specific to a given optical system enables the determination of the numerical depth of field based on the measurement of the lithographic amplitude of the imaged nanoparticles in the real image. This further limits the calculation time, provided that the initial propagation step over the increasing thickness Dv (Figure 1) used to determine the numerical depth of field H is not required. Only propagation over a thickness D below the depth H is performed to enable counting.

[0060] Even in the case of a sample where the nanoparticles are not uniform (with respect to composition and dimensions), it is possible to calculate the concentration of the sample using the above method. In such a mixture, the nanoparticles have different numerical depths of field. Care must be taken to ensure that the imaged nanoparticles within the image volume contributing to the concentration calculation are not numerical propagation artifacts. This is achieved by using the chart to confirm that for each imaged nanoparticle within the continuous 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 more than 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, it is not. 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 the 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 lateral and longitudinal magnifications between object space and image space are known, the correspondence between object volume V1 and image volume V2 is given by the following relationship: 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 longitudinal magnification of the optical system used for conjugation, near the plane of the detector, in the direction of the optical axis z, assumed to be the pivot axis.

[0063] To calculate the object volume based on the image volume, it is convenient to use the detector surface and the lateral and longitudinal magnifications of the optical system to complete the dimensions of the image volume and then obtain the object volume.

[0064] The present application is industrially applicable, 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 solutions undergoing Brownian motion, since the availability of intensity and phase in a self-referencing manner over time (producing a film) makes it possible to envisage within the scope of this application the tracking and refocusing of nanoparticles in an image that propagates out of the plane of the real image, and by averaging successive numerically propagated images of the same nanoparticle, to obtain a signal-to-noise ratio that allows the implementation of the present teachings.

Claims

1. 1. 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 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 a real intensity and phase image of the object plane; 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-referenced 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.

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

3. 3. The optical system according to claim 1, wherein the illumination light source is a white laser that illuminates a bandpass filter.

4. 3. The optical system of claim 1, wherein the illumination source is a white plasma source illuminating a bandpass filter.

5. 3. The optical system according to claim 1, wherein the illumination light source is a laser diode.

6. 6. The optical system according to claim 1, wherein the illumination source is configured to illuminate an object space in a nanoparticle solution, and the processing unit comprises: configured to count the number of imaged nanoparticles in the real image; configured to numerically propagate the real image along the optical axis within an image volume of a predetermined thickness; configured to count the number of imaged nanoparticles in the numerically propagated image; configured to calculate dimensions of the object volume corresponding to the image volume; an optical system configured to calculate the concentration of nanoparticles based on the number of imaged nanoparticles counted (N) and the dimensions of the object volume.

7. 7. The optical system of claim 6, wherein the processing unit: configured to count the number of imaged nanoparticles in a real image obtained using the self-referencing phase imaging system of the nanoparticle solution; configured to numerically propagate the real image into an image volume of increasing and variable thickness (Dv); configured to count the number of imaged nanoparticles in the numerically propagated image; configured to analyze the variation of the number of imaging nanoparticles (N) counted as a function of the variable thickness (Dv) of the image volume and identify a critical thickness of the image volume at which the number of imaging nanoparticles (N) no longer increases as a function of the variable thickness (Dv) of the image volume and reaches a plateau (P); configured to determine a numerical depth of field (H) based on the identified critical thickness; The optical system, wherein the predetermined thickness is equal to or less than the numerical depth of field (H).

8. 8. The optical system according to claim 6 or 7, further comprising a computer memory storing a chart showing, for different types of nanoparticles, the correspondence between the numerical depth of field (H) and the amplitude, denoted as amplitude R, of a field formed from information about the real and / or imaginary parts of the wave field generated by the imaging nanoparticles.

9. 9. The optical system according to claim 8, the processing unit determines a numerical depth of field (H) based on the amplitude R of the imaged nanoparticles in the real image by referring to the chart; The optical system, wherein the predetermined thickness is equal to or less than the numerical depth of field (H).

10. The optical system according to any one of claims 1 to 6, further comprising a computer memory storing a chart showing, for different types of nanoparticles, a correspondence between the numerical depth of field and the amplitude, denoted as amplitude R, of a field formed from information relating to the real and / or imaginary part of the wave field generated by the imaging nanoparticles, the illumination source is configured to illuminate an object space in a solution containing a mixture of nanoparticles; The processing unit 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 reference to the chart; configured to numerically propagate the real image along the optical axis within an image volume of a predetermined thickness, denoted D; for each imaging nanoparticle in the numerically propagated image of the image volume, using the chart to determine whether the amplitude R of the nanoparticle corresponds to a numerical depth of field, denoted H, that is at least twice the distance between the numerically propagated image and the actual image at which the nanoparticle is imaged, and if so, retaining the nanoparticle for the counting, and if not, not retaining the nanoparticle for the counting; configured to calculate, for each counted nanoparticle, an associated object volume corresponding to said image volume of thickness D if H≧D, or corresponding to an image volume of thickness equal to said numerical depth of field H associated with said nanoparticle if H<D; an optical system configured to calculate, for all of the counted nanoparticles, the concentration of nanoparticles equal to the sum of the reciprocals of the associated object volumes.

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