Method for determining properties of particles in a medium

Abstract

A method for determining a property of at least one particle (P) in a medium (M), comprising: emitting a coherent light beam (6) to illuminate a sample (5) of the medium (M); recording an interference image (10) of a first portion of the light beam (6) scattered by the at least one particle (P) and a second portion of the light beam (6) not scattered by the particle (P); calculating (S1) an electric field (E1) of the first portion from the interference image (10) for a plurality of positions (13) within the sample (5); generating (S2) a representation (16) comprising, for each position (13), a phase value (ξ) and an intensity value (I), the phase value being determined from the calculated electric field (E1) and from an estimated electric field (E2) of the second portion, the intensity value being determined from the intensity (I1) of the first portion and from the phase value (ξ); and determining (S3) the property thereby.

Description

Technical Field

[0001] The invention relates to a method for determining a property of at least one particle in a medium. Background Art

[0002] The background of the present invention lies in the field of observing the properties of one or more particles in colloids, such as emulsions, cell cultures, and bacteria in media, for example, to study the bacterial pathogenesis of urinary tract infections. Furthermore, it is possible to observe plastic particles in seawater, impurities in liquid foods or pharmaceuticals, cells or their organelles in body fluids, etc. The properties can be intrinsic to the particles, such as their size, shape, structure, propulsion mechanism, dry mass, etc., or medium-dependent, such as the position, velocity, or diffusion of the particles in the medium. Furthermore, it is possible to determine the properties of several particles, such as their distribution in the medium, their mutual distances, their interactions, etc.

[0003] It is known to observe, for example, the distribution or movement of bacteria in a medium by means of digital holographic microscopy. In such a method, a sample containing the bacteria is illuminated with coherent light to obtain its interference image. From this, a three-dimensional model of the bacteria and their distribution in the medium can be calculated in turn by applying a reconstruction algorithm, such as a forward or backward propagation or projection algorithm, to the interference image. However, experiments have shown that the three-dimensional models obtained in this way are generally not qualitatively suitable for detailed analysis due to the inevitable background signal in the interference image. The background signal is sensed by a portion of the light scattered in the medium, i.e. not by the particles, but by other (usually smaller) objects in the medium (e.g. by Mie scattering), and reduces the contrast between the light scattered by the particles and the light not scattered by the particles.

[0004] To address this impairment, Cheong FC et al., "Rapid, high-throughput tracking of bacterial motility in 3D by phase-contrast holographic video microscopy," Biophysical Journal, Volume 108, pp. 1248-1256, March 2015, proposed digitally introducing a phase shift in the reconstruction algorithm between light scattered by the medium and light not scattered by either the particles or the medium. As a result, background signal is reduced and contrast is enhanced.

[0005] However, the contrast achieved by current holographic microscopy methods and related analysis algorithms is sometimes still too low to adequately resolve the properties of each particle, for example, its position in the medium. The low contrast leads to the erroneous identification of artifacts as particles in the three-dimensional model. This is particularly true when analyzing samples with a high density of particles and / or with small or weakly scattering particles. On the other hand, particles with a high refractive index interact with light in a lens-like manner and therefore appear to be located at their focus rather than their true position and appear to have a different size and other properties. This is called the "lensing effect". In this case, it is impossible to resolve the true particle properties compared to the contrast obtained by current holographic microscopy methods. Summary of the Invention

[0006] It is an object of the present invention to provide a method for determining a property of at least one particle in a medium which allows obtaining a higher contrast, enabling a more accurate determination of said property.

[0007] This object is achieved by a method for determining a property of at least one particle in a medium, the method comprising:

[0008] providing a sample of a medium containing the at least one particle;

[0009] emitting a coherent light beam with a light source to illuminate the sample, wherein a first portion of the light beam is scattered by the at least one particle to produce a scattered light beam;

[0010] recording, with a camera, an interference image of the scattered light beam and a second portion of the light beam that is not scattered by the at least one particle;

[0011] calculating, with a processor, for each of a plurality of locations three-dimensionally distributed within the sample, an electric field of the first portion of the light beam at that location based on the interference image;

[0012] generating, with the processor, a representation of the sample, the representation covering the plurality of locations and including, for each of the plurality of locations, a phase value determined from the calculated electric field at that location and from the estimated electric field of the second portion of the light beam at that location, and an intensity value determined from the determined phase value at that location and from the intensity of the first portion of the light beam at that location; and

[0013] The property is determined using the representation with the processor.

[0014] It should be noted that the electric field of a beam is usually complex-valued and can therefore be described by its real and imaginary parts or by its magnitude and phase. Furthermore, a beam has an intensity proportional to the square of the magnitude of the electric field, ie, the power per unit area.

[0015] The applicant has discovered that, according to the present method, a phase value, which is not conventionally determined solely from the phase of the scattered light beam, but rather from the light beam scattered by the plurality of particles in the medium and the light beam not scattered by the plurality of particles in the medium, produces a higher contrast. This higher contrast is also based on the determination of intensity values, each of which is determined based on the intensity of the first portion of the light beam and based on the corresponding phase value. Thus, the properties of even weakly scattered or small particles or high-density particles in the medium can be resolved in the representation. Furthermore, artifacts can be largely eliminated, and the properties of the plurality of particles exhibiting lensing effects can be distinguished from their focal point, allowing for a more accurate determination of the properties of at least one particle in the medium.

[0016] In order to calculate the electric field of the first portion of the light beam, the plurality of positions can be distributed within the sample as desired, for example as a regular grid representing, for example, contiguous cubic areas within the sample, or as an irregular grid representing, for example, arbitrarily formed spatial areas within the sample. However, in an advantageous embodiment, the plurality of positions are located in a plurality of virtual planes perpendicular to the direction of the second portion of the light beam, and the calculation step is performed plane by plane along said direction. This distribution of the plurality of positions allows the electric field to be calculated efficiently and allows the phase and intensity values ​​to be determined plane by plane along the beam direction, i.e., in the beam direction or in the opposite direction. Since the planes are perpendicular to the direction of the light beam, it can be estimated that the electric field of the second portion of the light beam has the same phase at all positions within the corresponding plane.

[0017] The interference image carries information about the first and second portions of the light beam. To facilitate differentiation between the first and second portions of the light beam during the calculation step, it is advantageous to normalize the interference image based on a reference image of the coherent light beam without scattering by the at least one particle before the calculation step. The normalized interference image enables a more precise calculation of the electric field of the first portion, thereby further improving the determination of phase and intensity values ​​and, consequently, enhancing contrast.

[0018] Advantageously, in said generating step the electric field of the second portion of the beam is estimated from corresponding values ​​of a reference image of the coherent beam in the absence of scattering by particles, which provides an easy and more accurate estimation of the electric field of the second portion of the beam.

[0019] The reference image can be generated in various ways known in the art, for example as a low-pass filtered version of an interference image, by repeating the emission and recording steps to obtain several interference images, the average of which is generated as the reference image, etc. Advantageously, the reference image is generated by emitting a coherent light beam with a light source in the absence of a sample of the medium containing the at least one particle, and recording a reference image thereof with a camera. In this variant, the reference image can be easily generated from a sample of the medium that does not contain any of the particles or from a sample, both options being encompassed by the phrase "without a sample of the medium containing the at least one particle."

[0020] A particularly high contrast ratio can be achieved when, in the step of generating, for each of the plurality of positions, a minimum difference angle between the phase of the calculated electric field and the phase of the estimated electric field is identified and the phase value is determined as part of the difference angle. According to this embodiment, a smaller difference angle between the phases can result in even smaller intensity values, so that the contrast ratio is further enhanced.

[0021] Advantageously, in the generating step, the phase value is determined as the phase of a weighted sum of the calculated electric field and the estimated electric field. This determination is simple and computationally inexpensive, and requires only determining two weights: a weight for the calculated electric field and a weight for the estimated electric field. For example, the weights can be determined iteratively or based on prior experience to maximize contrast, suppress background signals, etc.

[0022] In a particularly preferred variant of the aforementioned embodiment, in the step of generating, for each of the plurality of positions, a phase value is determined according to

[0023] ξ(r,z)=arctan2(Re(E1(r,z)+1),Im(E1(r,z)+1))

[0024] in

[0025] r, z are coordinates of a position, where z is a coordinate in a direction opposite to the direction of the second portion of the light beam, and r represents a pair of coordinates in a plane perpendicular to said opposite direction,

[0026] E1(r,z) is the calculated electric field of the first portion of the beam at position,

[0027] ξ(r, z) is the phase value at position,

[0028] Re, Im represent the real and imaginary part operators, and

[0029] arctan2 represents the four-quadrant inverse tangent function.

[0030] In this variant, the electric field of the second portion of the light beam is estimated as real and has a particularly accurate magnitude in embodiments with a normalized interference pattern. Thus, the first and second portions of the light beam are weighted equally, making it easy to determine that the intensity value is small at locations where the phase difference between the calculated and estimated electric fields is small; as a result, the contrast can be further enhanced.

[0031] In a preferred embodiment, in the step of generating, for each of the plurality of positions, an intensity value is determined according to

[0032] I(r,z)=2·I1(r,z)·(1+cos(π+ξ(r,z)))

[0033] in

[0034] r, z are coordinates of a position, where z is a coordinate in a direction opposite to the direction of the second portion of the light beam, and r represents a pair of coordinates in a plane perpendicular to said opposite direction,

[0035] I1(r,z) is the intensity of the first portion of the light beam at position ,

[0036] ξ(r,z) is the phase value at position , and

[0037] I(r,z) is the intensity value at position.

[0038] In this embodiment, the intensity values ​​are efficiently calculated. The additional phase shift of π further attenuates the background signal, making it easier to distinguish light scattered by the particles from light not scattered by the particles in the representation of the intensity values.

[0039] In order to more easily distinguish between light scattered by particles and light not scattered by particles, it is advantageous to calculate an intensity threshold using the intensity values ​​before the determining step, preferably the intensity threshold being the average of two or more of the intensity values, and in the determining step, for each of the plurality of positions, when the intensity value is less than the calculated intensity threshold, neither the phase value nor the intensity value comprised by the representation of that position is used. In addition to being easier to distinguish, this allows for a faster determination of the particle distribution due to the reduced amount of data to be considered. In this embodiment, the intensity threshold can be calculated as known to those skilled in the art, for example as a predetermined percentage of a (general, typical, expected or currently determined) maximum intensity value, as an average of the intensity values ​​at several positions, as an overall average of all intensity values ​​of the representation, etc.

[0040] In another embodiment of the present invention, in the step of emitting, two or more coherent light beams are emitted, wherein the steps of recording, calculating, and generating are performed for each of the two or more coherent light beams to obtain a corresponding representation of the sample, and wherein the property is determined using the two or more obtained representations. Thus, the property can be determined more accurately based on the additional information provided by the two or more representations. Furthermore, if the emission is delayed, properties such as particle velocity, particle diffusion, electrophoresis, etc. can be studied.

[0041] According to an advantageous embodiment, two or more representations are averaged to form an average representation, and in the step of determining, the property is determined based on the average representation. By performing such an averaging of a plurality of representations, the background signal is effectively attenuated in the average representation, thereby facilitating the determination of the property of at least one particle in the medium, for example a three-dimensional particle distribution, in particular when the particle is stationary.

[0042] In another embodiment, during the emitting step, each of the two or more coherent light beams is emitted using a respective light source from two or more light sources. In this case, the sample can be illuminated at different angles, which provides additional information, for example, further facilitating the distinction between a particle position common to all beams and a particle focus, each focus being different for the positions of these beams. This allows the application of techniques to increase the resolution of the representation, for example by multiplexing spatial frequency bands, known in the art as "super-resolution." Furthermore, when using a respective light source for each beam, the coherent light beams can be emitted simultaneously and are therefore easily correlated.

[0043] In the above-described embodiment, it is advantageous when, during the step of emitting, each of the two or more coherent light beams is emitted at a different frequency. This allows, for example, obtaining a colored and / or more accurate particle distribution by averaging the two or more representations. Furthermore, additional information is generated regarding the properties of the particles, such as their color, dispersion properties, the color of their discharge, etc.

[0044] In a particularly preferred embodiment, three coherent light beams are emitted during the step of emitting, and the respective frequencies of the three coherent light beams correspond to the colors red, green, and blue. This takes advantage of the high sensitivity of conventional camera sensors to red, green, and blue light (RGB sensors) and allows for easy acquisition of color representations. In some cases, other particle properties, such as the oxidation state of iron in hemoglobin particles, the color of particle secretions such as toxins, etc., can also be determined through color representations. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The present invention will now be explained in more detail below based on preferred exemplary embodiments of the invention with reference to the accompanying drawings, in which:

[0046] Figure 1 shows a schematic side view of an in-line interferometer used in the method according to the invention;

[0047] Figure 2 The flow chart shows the process of Figure 1 The interference image generated by the interferometer determines the three-dimensional particle distribution;

[0048] Figure 3 Shows that in the complex plane according to Figure 2 determination of a determined phase value of; and

[0049] Figure 4 and 5 The graphs show the direction opposite to the beam direction ( Figure 4 )

[0050] and in the direction perpendicular to the beam ( Figure 5 ) of the medium sample. DETAILED DESCRIPTION

[0051] Figure 1 An inline interferometer 1 is shown comprising a light source 2 and a camera 3. The inline interferometer 1 is used to determine properties of at least one (microscopic) particle P in a medium M, such as the position, size, shape, structure, elasticity, dry mass, secretion, velocity, propulsion mechanism, diffusion, shape of a vesicle and / or the distribution, mutual distances, interactions, etc. of one or more particles. In the embodiment shown, a three-dimensional particle distribution 4 ( Figure 2 To determine this property, a sample 5 of a medium M containing one or more particles P is provided between a light source 2 and a camera 3. The one or more particles P may be cells, bacteria, charged particles, microplastics, organelles, etc., and the medium M may be water, oil, body fluids (e.g., blood), solutions, etc. In general, any particle P in any colloid may be analyzed.

[0052] To this end, the light source 2 emits a coherent light beam 6 to illuminate the provided sample 5. The light source 2 may be any type of light source capable of emitting a coherent light beam 6, such as a laser diode.

[0053] In the sample 5, a first part of the light beam 6 is scattered by the one or more particles P, thereby generating a scattered light beam 7. However, a second part of the light beam 6 is not scattered by the particles P and passes through the sample 5 as an unscattered light beam 8 in a beam direction 9. In the context of the present specification, the scattered light beam 7 relates to scattering by the one or more particles P in the medium M, whereas the unscattered light beam 8 is not scattered by the particles P in the medium M. Furthermore, scattering can mean diffraction, refraction or reflection and depends on the choice of interferometer 1 used, which in turn can depend on the properties of the particles P, such as their transparency, reflectivity or refractive index, and the properties of the medium M.

[0054] The scattered light beam 7 and the unscattered light beam 8 interfere with each other. At the end of the path of the light beam 6, the camera 3 records an interference image 10 of the scattered light beam 7 and the unscattered light beam 8 ( Figure 2 ). For the present purpose, the camera 3 may be any analog or digital camera, for example having a complementary metal oxide semiconductor (CMOS) or charge coupled device (CCD) image sensor.

[0055] However, it should be noted that a portion of the scattered light beam 7 and of the unscattered light beam 8 may also be scattered in the medium M, for example by other (usually smaller) objects (e.g. via the Tyndall effect), and that this portion of the unscattered light beam 8 deviates slightly from the beam direction 9. In the interference image 10, said portions of the scattered light beam 7 and of the unscattered light beam 8 result in an unavoidable, albeit undesirable, background signal, which generally impairs the determination of the particle distribution 4 in the medium M.

[0056] The interferometer 1 may include one or more other optical devices known in the art of holographic microscopy, such as an attenuator ring for improving the signal-to-noise ratio, a microscope objective, a phase plate, one or more lenses (e.g., a diverging lens for magnifying the interference image 10), etc. In addition, the interferometer 1 may also be embodied as another type of interferometer other than an in-line interferometer, for example, as an interferometer 1 using a beam splitter.

[0057] The interference image 10 recorded by the camera 3 is then forwarded to a processor 11 via an interface 12. The processor 11 processes the interference image 10 to derive therefrom a property of at least one particle P in the medium M (here: a three-dimensional particle distribution 4), as will now be described with reference to Figure 2-5 Explained.

[0058] When the camera 3 records the interference image 10 (at Figure 2 As a purely two-dimensional image (in the example of lysogenic E. coli in liquid culture), the interference image 10 encodes the intensity and phase information of the light beam 6. This information allows the processor 11 to "reconstruct" the sample 5 of the medium M containing the particles P in three steps S1-S3.

[0059] In a first step S1, for each of the plurality of positions 13, the processor 11 calculates the electric field E1 of the first part of the light beam 6, ie the scattered light beam 7, from the interference image 10. The plurality of positions 13 are three-dimensionally distributed within the sample 5. Figure 2 In the example, the plurality of positions 13 are located on several virtual planes 141, 142, ... generally 14 i In this example, the plurality of positions 13 are perpendicular to the beam direction 9 of the unscattered light beam 8. i In other examples, the plurality of locations 13 may be three-dimensionally distributed within the sample 5, for example in a regular grid arrangement representing adjacent cubic regions or in an irregular grid arrangement representing adjacent arbitrarily formed spatial regions.

[0060] To calculate the electric field E1 of the scattered light beam 7, for each position 13, the processor 11 applies a reconstruction algorithm to the interference image 10. For each position 13, the electric field E1 of the scattered light beam 7 is complex valued, so its real and imaginary parts or their phases are calculated separately. and amplitude. In this example, the processor 11 applies the reconstruction algorithm plane by plane in a direction 15 opposite to the beam direction 9. However, this is optional, and other reconstruction algorithms may be applied. Many variations of such reconstruction algorithms are known in the art, such as forward or backward propagation or projection algorithms, such as the inverse Radon transform, Fourier domain reconstruction algorithms, iterative reconstruction algorithms, and the like.

[0061] In a subsequent second step S2, the processor 11 generates a representation 16 of the samples 5 covering all positions 13 and comprising for each position 13 a corresponding phase value ξ ( Figure 3 ) and the corresponding intensity value I( Figure 4 and 5 ). The phase value ξ represents the phase shift of the scattered light beam 7, which phase shift is caused only by scattering by the particles P. For each position 13, the phase value ξ is determined from the electric field E1 of the scattered light beam 7 at that position 13 and the estimated electric field E2 of the unscattered light beam 8 at that position 13. For this purpose, the electric field E2 of the unscattered light beam 8 can be estimated as is known in the art, i.e. from measurements, as will be explained in further detail below. The intensity value I represents the intensity of the light beam 6. For each position 13, the intensity value I is determined from the intensity I1 of the scattered light beam 7 calculated for that position 13 (e.g. as the square of the amplitude of the electric field E1) and from the phase value ξ determined for that position 13.

[0062] After step S2, in a third step S3, the processor 11 uses the representation 16 of the sample 5 obtained in step S2 to determine the properties of the at least one particle P in the medium M (here: the particle distribution 4). This is done by evaluating the determined plurality of intensity values ​​I and / or phase values ​​ξ, as is known in the art. For example, the intensity and / or phase values ​​I, ξ and the corresponding positions 13, i.e., their three-dimensional coordinates in a given coordinate system 17, can be input to a pattern recognition algorithm, a neural network, or the like.

[0063] In one embodiment, the property of the at least one particle P in the medium M (here the particle distribution 4) can be determined using the processor 11 (in this embodiment, with the aid of the processor 11), for example, by manual inspection of a visualization of the intensity value I representing 16, wherein the visualization is provided by the processor 11.

[0064] Returning to step S2 of generating the representation 16 , both the phase value ξ and the intensity value I at each position 13 may be determined in different ways as follows.

[0065] exist Figure 3 In an exemplary embodiment, the phase of the calculated electric field E1 is identified and the phase of the estimated electric field E2 The minimum difference angle between That is, one of the two difference angles is less than π. Then, the phase value ξ is determined as the difference angle This can be achieved in various ways; for example, the phase value ξ can be determined as the minimum difference angle identified It will be appreciated that when the phase of the unscattered light beam 8 is When it is estimated to be zero (which is usually the case by definition), the difference angle and the calculated phase of the scattered beam 7 In another example, the electric fields E1 and E2 at each location 13 are mixed to obtain a mixed field E m , its phase The phases of the calculated and estimated electric fields E1 and E2 are and In yet another example, the phase value ξ is determined as the mixed field E m Phase With the phase and Specifically, the electric field E2 can be estimated as a real number and have a magnitude of one, in which case the phase value ξ can be determined according to the following equation:

[0066] ξ(r,z)=arctan2(Re(E1(r,z)+1),Im(E1(r,z)+1)) (Equation 1)

[0067] in:

[0068] r, z are coordinates at the position 13, where z is a coordinate in a direction 15 opposite to the direction 9 of the second portion of the light beam 6, and r represents a pair of coordinates in a plane x, y perpendicular to said opposite direction 15,

[0069] E1(r,z) is the calculated electric field of the first portion of the beam 6 at position 13,

[0070] ξ(r, z) is the phase value at position 13,

[0071] Re, Im represent the real and imaginary part operators, and

[0072] arctan2 represents the four-quadrant inverse tangent function.

[0073] In another embodiment, in the generating step S2, the phase value ξ is determined as the phase of the weighted sum of the calculated electric field E1 and the estimated electric field E2. In this embodiment, the weights are determined, for example, based on known optical parameters of the particles P and / or the medium M, based on iteratively maximizing the contrast between high intensity values ​​I and low intensity values ​​I in the resulting representation 16, etc.

[0074] Figure 4 and 5 The graph in FIG shows the direction 15 (ie, along the z-axis of the coordinate system 17 ( Figure 4 )) and the direction perpendicular thereto (here: along the y-axis of the coordinate system 17, Figure 5 ) is determined by the intensity value I. The solid line 18 represents the intensity value determined according to the following equation:

[0075] I(r,z)=2·I1(r,z)·(1+cos(π+ξ(r,z))) (Equation 2)

[0076] in:

[0077] r, z are the coordinates of the position 13, where z is the coordinate in the direction 15 opposite to the direction 9 of the second portion of the light beam 6, and r represents a pair of coordinates in a plane x, y perpendicular to said opposite direction 15,

[0078] I1(r,z) is the intensity of the first part of the beam 6 at position 13,

[0079] ξ(r,z) is the phase value at position 13, and

[0080] I(r,z) is the intensity value at position 13.

[0081] exist Figure 4 and 5 In FIG. 1 , the dashed line 19 represents the intensity value I determined according to the prior art (here: based on the interference image of silicon dioxide particles recorded in “Milli Q” deionized water). Figure 4 and 5 As shown, the solid line 18 is at the corresponding maximum intensity I max It is narrower nearby and shows smaller fluctuations overall.

[0082] Alternatively, in a more general embodiment, an additional phase shift θ between the portion of the light beams 7, 8 scattered by the medium and the unscattered light beam 8 may be introduced and fitted, modeled, simulated, iterated, etc., to maximize the contrast between high intensity values ​​I and low intensity values ​​I in the representation 16. In this case, the intensity value I is determined, for example, according to the following equation:

[0083] I(r,z)=2·I1(r,z)·(1+cos(Θ+ξ(r,z))) (Equation 3)

[0084] In an alternative embodiment, an intensity threshold I is introduced before step S3 of the processor. th The intensity threshold I th is calculated using the intensity value I representing 16. Therefore, in step S3, the intensity value I determined at which is less than the calculated intensity threshold value I is not used. th The intensity values ​​I and phase values ​​ξ of those positions 13 are, for example, not input to the pattern recognition algorithm. th It can be, for example, the maximum intensity value I max ( Figure 4 and 5 ), a percentage of, a moving average, an average of two or more intensity values, or even an average of all intensity values ​​I included in representation 16.

[0085] In another alternative embodiment, a reference image 20 of the coherent light beam 6 not scattered by the at least one particle P is generated, so that it is correlated with the unscattered light beam 8. The reference image 20 can be generated in different ways known to those skilled in the art, for example as a low-pass filtered interference image 10. In one variant, the reference image 20 is generated by emitting the coherent light beam 6 with the light source 2 in the absence of a sample 51 of the medium M containing the at least one particle P, and recording its reference image 20 with the camera 3. The expression "sample 5 of the medium M without the particles P" means that there is no sample 5 at all, or that a different sample comprising the medium M without the particles P is arranged between the light source 2 and the camera 3 of the interferometer 1.

[0086] Based on the reference image 20, the processor 11 may normalize the interference image 10 before said calculation step S1 as known in the art. This results in calculation of a normalized calculated electric field E1 in step S1 which is used as the electric field E1 in the subsequent step S2.

[0087] In step S2, the electric field E2 of the unscattered light beam 8 can be estimated based on corresponding values, for example based on the intensity of the reference image 20. Figure 3 In the example of FIG, the magnitude of the electric field E2 of the unscattered light beam 8 is calculated as the square root of the intensity I2 of the unscattered light beam 8 estimated from the corresponding intensity of the reference image 20. In addition, by simulating the light beam 8, by forward or backward propagating the reference image 20 and / or by performing a multi-step ... Iterate step S2 and / or step S3, the phase of the electric field E2 is estimated to be, for example, zero to maximize the contrast in the representation 16 or to achieve a known particle size in the particle distribution 4 .

[0088] In the above-described embodiments, steps S1-S3 are performed on a single recorded interference image 10. However, the method is not limited to these embodiments.

[0089] In another embodiment, several interference images 10 are recorded, each based on a corresponding coherent light beam 6 emitted from the light source 2. Each of these interference images 10 can optionally all be normalized by a common or each by a separate reference image 20. In this case, the common reference image 20 can be generated by averaging the recorded interference images 10.

[0090] Subsequently, for each of the plurality of interference images 10, the electric field E1 of the corresponding scattered light beam 7 is calculated in step S1, and a corresponding representation 16 of the sample 5 is generated in step S2. These representations 16, obtained by performing the steps of recording, calculating S1, and generating S2 for each light beam 6, can then be used to determine the properties of the at least one particle P in the medium M; to this end, these representations 16 can optionally be averaged into an average representation comprising a plurality of averaged intensity and phase values, which are used in step S3 to determine, for example, a three-dimensional particle distribution 4 as described above. As is known in the art, the plurality of averaged intensity and phase values ​​can be averaged, for example, as a geometric mean, an arithmetic mean, etc. Alternatively, step S3 can be performed separately for each of the plurality of representations 16 to determine how the properties of the one or more particles P change over time, for example, to determine a number of particle distributions 4 to study the movement of one or more particles P in the medium M.

[0091] Back to Figure 1As an example, the interferometer 1 can optionally include (here: two) additional light sources 2', 2". Each light source 2, 2', 2" emits a corresponding coherent light beam 6, 6', 6" at the same or a different frequency to illuminate the sample 5. The coherent light beams 6, 6', 6" are emitted simultaneously or successively and are scattered by the at least one particle P. The corresponding interference images 10 are recorded by means of one camera 3 or by means of several cameras, one interference image for each light beam 6, 6', 6".

[0092] In an alternative embodiment of this example, the three frequencies of the light beams 6, 6' and 6" correspond to the colors red, green and blue; however, other frequencies may be chosen, even frequencies of light that are invisible to the human eye.

[0093] Subsequently, as described above, steps S1-S3 are performed in the processor 11 for each of the light beams 6, 6', 6", wherein in step S3, for example, the colored particle distribution 4 can be determined. Furthermore, an average representation 16 can optionally be calculated as described above. Thereby, the property of the at least one particle P (here the particle distribution 4) can be determined.

[0094] Depending on the position of the light sources 2, 2', 2" and the optional optics in the interferometer 1, a set of different spatial frequencies can be recorded with the camera(s), if desired. In this case, the resulting average representation 16 includes more information about each position 13 and therefore has a higher resolution (known in the art as "super-resolution").

[0095] Furthermore, the coherent light beams 6, 6', 6" can illuminate the sample 5 at different angles, which can be taken into account, for example, by applying a corresponding forward or backward propagation along the direction of each beam to the interference image respectively obtained therefrom. In an alternative variant thereof, instead of using several light sources 2, 2', 2", only the light source 2 can emit several coherent light beams 6 at different frequencies, which are recorded and processed as described above.

[0096] The present invention is not limited to the specific embodiments described above, but includes all variations, modifications, and combinations thereof that fall within the scope of the appended claims.

Claims

1. A method for determining a property of at least one particle (P) in a medium (M), comprising: providing a sample (5) of a medium (M) comprising said at least one particle (P); emitting a coherent light beam (6) using a light source (2) to illuminate the sample (5), wherein a first portion of the light beam (6) is scattered by the at least one particle (P) to generate a scattered light beam (7); recording, with a camera (3), an interference image (10) of the scattered light beam (7) and a second portion of the light beam (6) not scattered by the at least one particle (P); calculating (S1) with a processor (11) for each of a plurality of positions (13) three-dimensionally distributed within the sample (5) an electric field (E1) of the first portion of the light beam (6) at that position (13) based on the interference image (10); generating (S2) with the processor (11) a representation (16) of the sample (5), the representation (16) covering the plurality of positions (13) and comprising, for each of the plurality of positions (13), a phase value (ξ) determined from the calculated electric field (E1) at that position (13) and from the estimated electric field (E2) of the second portion of the light beam (6) at that position (13), and an intensity value (I) determined from the determined phase value (ξ) at that position (13) and from the intensity (I1) of the first portion of the light beam (6) at that position (13); and The property is determined (S3) using the representation (16) by the processor (11).

2. The method according to claim 1, wherein the plurality of positions (13) are located in a plurality of virtual planes (14) perpendicular to the direction (9) of the second portion of the light beam (6). i ), and wherein the step of calculating (S1) is performed plane by plane along said direction (9).

3. The method according to claim 1, wherein Prior to the step of calculating (S1), the interference image (10) is normalized based on a reference image (20) of the coherent light beam (6) in the absence of scattering by the at least one particle (P).

4. The method according to claim 1, wherein In the step of generating (S2), the electric field (E2) of the second portion of the light beam (6) is estimated based on corresponding values ​​of a reference image (20) of the coherent light beam (6) in the absence of scattering by the at least one particle (P).

5. The method according to claim 3 or 4, wherein: The reference image (20) is generated by emitting the coherent light beam (6) with the light source (2) in the absence of the sample (5) of the medium (M) containing the at least one particle (P) and recording a reference image (20) thereof with the camera (3).

6. The method according to claim 1, wherein In the step of generating (S2), for each of the plurality of positions (13), the phase of the calculated electric field (E1) is identified. The phase of the estimated electric field (E2) The minimum difference angle between And the phase value (ξ) is determined as the difference angle part of.

7. The method according to claim 1, wherein In the step of generating (S2), the phase value (ξ) is determined as the phase of a weighted sum of the calculated electric field (E1) and the estimated electric field (E2).

8. The method according to claim 6 or 7, wherein In the step of generating (S2), for each of the plurality of positions (13), the phase value (ξ) is determined according to ξ(r,z)=arctan2(Re(E1(r,z)+1),Im(E1(r,z)+1)) in r,z are coordinates of a position (13), wherein z is a coordinate in a direction (15) opposite to the direction (9) of the second portion of the light beam (6), and r represents a pair of coordinates in a plane (x, y) perpendicular to the opposite direction (15), E1(r,z) is the calculated electric field of the first portion of the light beam (6) at position (13), ξ(r, z), which is the phase value at position (13), and arctan2 represents the four-quadrant inverse tangent function.

9. The method according to claim 1, wherein: Before the step of determining (S3), the intensity threshold (I th ) and wherein, in the step of determining (S3), for each of the plurality of positions (13), when the intensity value (I) is less than the calculated intensity threshold value (I th ), neither the phase value (ξ) nor the intensity value (I) comprised by said representation (16) of that position (13) is used.

10. The method according to claim 1, wherein In the step of generating (S2), for each of the plurality of positions (13), an intensity value (I) is determined according to I(r,z)=2·I1(r,z)·(1+cos(π+ξ(r,z))) in r,z are coordinates of a position (13), wherein z is a coordinate in a direction (15) opposite to the direction (9) of the second portion of the light beam (6), and r represents a pair of coordinates in a plane (x, y) perpendicular to the opposite direction (15), I1(r,z) is the intensity of said first portion of said light beam (6) at position (13), ξ(r, z) is the phase value at position (13), and I(r,z) is the intensity value at position (13).

11. The method according to claim 1, wherein In the step of emitting, two or more coherent light beams (6, 6', 6") are emitted, wherein the steps of recording, calculating (S1) and generating (S2) are performed for each of the two or more coherent light beams (6, 6', 6") to obtain a corresponding representation (16) of the sample (5), and wherein the property is determined using the two or more representations (16) obtained.

12. The method according to claim 11, wherein The two or more representations (16) are averaged into an average representation, and wherein, in the step of determining (S3), the property is determined from the average representation.

13. The method according to claim 11 or 12, wherein: In the step of emitting, each of the two or more coherent light beams (6, 6', 6") is emitted using a respective light source of two or more light sources (2, 2', 2").

14. The method according to claim 11, wherein In the step of emitting, each of the two or more coherent light beams (6, 6', 6") is emitted at a different frequency.

15. The method according to claim 14, wherein In the step of emitting, three coherent light beams (6, 6', 6") are emitted, and wherein respective frequencies of the three coherent light beams (6, 6', 6") correspond to the colors red, green and blue.

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