Method for determining the focal length of a particle in a medium

Abstract

A method for determining the focal length (d) of a particle (P) in a medium (M), the method comprising the steps of providing a sample (4), emitting a coherent light beam (6) to illuminate the sample (4), a first portion of the light beam (6) being scattered by the particle (P), recording an interference image (11), calculating (S1) an electric field (E1) for a set of positions (H) from the interference image (11), and generating (S2) a display (16) comprising, for each of the positions (H), an intensity value (I) of the coherent light beam (6) calculated from the calculated electric field (E1), and P ) is located on the sample (4), and the second position (H F ) is at the first position (H P ) behind or in front of the beam direction (9), at two positions (H P , H F ) and a step (S3) of detecting the two detected positions (H P , H F and (S4) determining the focal length (d) from the (f) by the processor (12).

Description

Detailed Description of the Invention

[0001] The present invention relates to a method for determining the focal length of a transparent particle in a medium.

[0002] The background of the invention is in the field of observing colloids, such as emulsions, cell cultures and bacteria in a medium, for example to study the contamination of water with bacteria or the initiation of bacterial infection in urinary tract infections. One may also observe plastic particles in seawater, impurities in liquid food or medicines, or cells, their organelles, etc. in body fluids. When transparent particles that focus light by scattering are observed, their focal length provides valuable information. The focal length can be used to correlate with other properties of the particle (hence size, shape, refractive index, and dry mass, etc.) with the amount of water or sugars in bacteria, etc., or to distinguish classes and subclasses of particles in a medium.

[0003] Commonly used methods to determine the optical properties of a particle (e.g. its refractive index) are flow cytometry or phase contrast microscopy. Flow cytometry is well suited to extract statistical information about the particles at high throughput. However, it has low accuracy in determining the optical properties of single particles and cannot observe particles in a stationary medium. Phase contrast microscopy, on the other hand, can visualize individual particles with high accuracy only at limited throughput and focal depth. Moreover, difficult and demanding interpretation of two-dimensional images is required to extract the refractive index and, if necessary, the focal length of the particle.

[0004] Another possible method is digital holographic microscopy. First, a coherent light beam is irradiated onto a sample containing the particles to obtain an interference image. A three-dimensional model of the emitted light beam is calculated from the interference image by applying a reconstruction algorithm (e.g., forward propagation, backward propagation, or projection algorithm) to the interference image. In the three-dimensional model, the position of the particle and its focal point, as well as the focal length as their difference, can be determined.

[0005] However, experiments have shown that three-dimensional models obtained by conventional digital holographic microscopy are often qualitatively inadequate to reliably determine the focal length of a particle. On the one hand, the intensity of the light beam at the focal point generally far exceeds that at the particle, so that the particle cannot be distinguished from its focal point, especially for small focal lengths. On the other hand, an unavoidable background signal is recorded in the interference image, which is generated not by the particle but by other (usually smaller) objects in the medium (e.g., by Mie scattering) as a part of the light scattered in the medium. This background signal impairs the localization of the model, since it impairs the contrast between the light scattered by the particle and the light not scattered by the particle. Nevertheless, to accurately determine the particle position, it is necessary to perform a rigorous comparison of the reconstructed model with a model of scattering, using precise and tedious calculations (e.g., using Mie theory).

[0006] It is an object of the present invention to overcome the limitations of the prior art and to provide a method for efficiently and accurately determining the focal length of a transparent particle within a medium.

[0007] The object is to provide a method for determining the focal length of a transparent particle in a medium, comprising: providing a sample of a medium containing said particles; using a light source to emit a coherent light beam and illuminating the sample with the light beam, such that a first portion of the light beam is scattered by the particle to produce a scattered light beam having a focus in a beam direction behind or in front of the particle; recording, with a camera, an interference image of the scattered light beam and a second portion of the light beam that was not scattered by the particle; calculating by a processor an electric field of an initial portion of the light beam from the interference image for each of a set of positions distributed three-dimensionally in space that includes the particle and the focal point; generating, with a processor, a representation of the light beam covering said locations, each of said locations including an intensity value of the coherent light beam calculated from the calculated electric field at that location; detecting, with a processor, intensity values ​​for two locations, a first location on the sample and a second location behind or in front of the first location in the beam direction, the intensity values ​​being greater than the respective intensity values ​​for nearby locations; determining a focal length from the two detected positions by a processor; In the generating step, for each location, the intensity value is calculated according to the following formula:

[0008]

number

[0009] (In the formula, r and z are coordinates of a position, z being a coordinate in a direction opposite to the beam direction, and r being a pair of coordinates in a plane (x, y) perpendicular to said opposite direction; I(r,z) is the intensity value at position, I1(r,z) is the intensity of the first portion of the light beam with respect to position, Θ is the phase shift parameter, k, l are the sum indices, C k , D l teeth, expansion is a parameter, E1(r,z) is the electric field calculated for position, arctan2 is the four-quadrant arctangent function. It is calculated according to:

[0010] Note that the electric field of a light beam is generally complex-valued and therefore can be described by its real and imaginary parts, or by its amplitude and phase. Furthermore, a light beam has an intensity, i.e., power per unit area. The power per unit area is proportional to the square of the amplitude of the electric field.

[0011] From a first position corresponding to the particle position and a second position corresponding to the focus position, the focal length can be determined as their difference. Applicant has found that said calculation of each intensity value allows for achieving high contrast between light scattered by the particle and light not scattered by the particle, and reliable discrimination of the particle from its focus, resulting in accurate detection of said two positions. Thus, the focal length can be determined directly and efficiently from the intensity of the light beam, or a representation that obviates the need for complex comparison of electric field and scattering models.

[0012] Moreover, the phase shift and magnification parameters used to calculate the respective intensity values ​​allow for accurate identification of the respective focal lengths for a large set of different particles and media. For example, any of the phase shift and magnification parameters may be pre-specified, for example, by similar samples or measurements, or by estimation based on prior knowledge. For example, the phase shift parameter may be set to π to reduce background signals. On the other hand, these parameters may be adapted to a particular situation, for example, to accurately identify the focal length of a particular bacterium in water. To this end, in certain embodiments, one or more of the phase shift and magnification parameters may be iteratively identified, for example, by applying an iterative optimization algorithm known in the art (such as the Quasi-Newton algorithm), which may terminate when the particle and focal positions converge, in order to optimize the generated display.

[0013] In a preferred aspect of this embodiment, at least one of the phase shift and the magnification parameters is identified by repeating the generating step, and the at least one parameter is changed to increase the difference between the higher intensity value and the lower intensity value included in the display. This optimization reduces the background effect typically caused by the lower intensity value, resulting in more prominent higher intensity values. This difference can be, for example, the difference between the sum of all higher intensity values ​​and the sum of all lower intensity values, the effective (root mean square) contrast, etc. For example, by adopting the latter, the number of maximum values ​​of the more prominent intensity values ​​can be initially considered in the step of finding the two positions can be reduced.

[0014] In other or further embodiments, at least one of the phase shift and magnification parameters is determined by repeating the generating and detecting steps, and the at least one parameter is changed to increase the difference between the intensity value of the first location and each of its nearby locations and / or to increase the difference between the intensity value of the second location and each of its nearby locations. This determination particularly emphasizes the intensity values ​​of the particles and / or focal locations compared to the intensity values ​​of their nearby locations, such that local contrast is enhanced.

[0015] According to another preferred embodiment, at least one of the phase shift and magnification parameters is determined by repeating the generating and detecting steps, and said at least one parameter is changed to increase the ratio between the intensity value of the first location and the intensity value of the second location. This makes it easier to distinguish the intensity values ​​of the particle location from the intensity values ​​of the focal location and its nearby locations, respectively. This location is particularly suitable for accurately determining small focal distances.

[0016] In a particularly preferred embodiment, at least one of the phase shift and magnification parameters is A simulation of the steps of providing, emitting, recording, calculating and generating to obtain a simulated representation in the generating step, and a simulated light beam intensity at each location covered by the simulated representation; and Identified by repeating a simulation of the generating step; The at least one parameter is altered to reduce a difference between an intensity value contained by the simulated representation and an intensity of the simulated light beam at the respective location.

[0017] The medium, additional scatterers in the medium, the surroundings of the particle, its shape, size, orientation, refractive index, etc. can be simulated separately and adjusted as necessary. In this way, at least one of the phase shift and magnification parameters can be easily identified for a specific sample or for a more general example, for example by performing a simulation of the sample, including several particles with different local environments. Furthermore, i.e. this embodiment is used to pre-identify at least one of said parameters and / or to set at least one of said parameters to an initial value to be used repeatedly according to one of said aspects.

[0018] In another preferred embodiment, at least one of the phase shift and magnification parameters depends on the position in said representation. This makes it possible to take into account different local environments, i.e. positions particularly near the particle position and the focal position, respectively, when calculating the intensity value of each position, by predetermining or specifying said at least one parameter differently. This allows to improve the accuracy in determining both the particle and focal position, and thus the focal distance.

[0019] To facilitate the distinction between light scattered by particles and light not scattered by particles, it is advantageous if in the detection step only positions whose intensity value is greater than a predefined threshold are considered. Apart from easier distinction, this allows faster detection of said two positions, since the amount of data to be considered is reduced. This embodiment allows the intensity threshold to be calculated by methods known to those skilled in the art, for example as a predefined percentage of the highest intensity value (commonly, typically, expected or currently specified), the average of the intensity values ​​at several positions, the overall average of all intensity values ​​of the display, etc.

[0020] The present invention will now be described in detail based on preferred exemplary embodiments with reference to the accompanying drawings, in which: FIG. 1 is a schematic side view of an in-line interferometer used in the method of the present invention; FIG. 2 is a flow chart illustrating the determination of focal length from an interference image recorded by the interferometer of FIG. 1 according to the present invention; FIG. 3 graphically illustrates intensity values ​​of a light beam determined according to the method illustrated in FIGS. 1 and 2 from the direction of the light beam to the opposite direction.

[0021] Fig. 1 shows an in-line interferometer 1 with a light source 2 and a camera 3. The in-line interferometer 1 is used to determine the focal length d of a (microscopic) transparent particle P in a medium M. To determine the focal length d, a sample 4 of the medium M containing a particle P (or several particles P) is placed in the light path 5 between the light source 2 and the camera 3. The particle P can be a cell, a bacterium, a charged particle, a microplastic particle, an organelle, etc., and the medium M can be water, an oil, a body fluid (e.g. blood), a liquid drug, etc. In general, the focal length d of any transparent particle P focusing a light beam in the medium M can be determined.

[0022] For this, the light source 2 emits a coherent light beam 6 for illuminating a provided sample 4. The light source 2 may be of any type capable of emitting a coherent light beam 6, such as, for example, a laser diode.

[0023] In the sample 4, a first portion of the light beam 6 is scattered by a particle P to produce a scattered light beam 7 having a focal point 8 in the beam direction 9 behind the particle P, in the example shown in Figure 1, i.e. at a distance corresponding to the focal length d behind the particle P. In other cases, if the particle P acts as a diverging lens, the focal point is in front of the particle P when viewed in the beam direction 9 (not shown).

[0024] However, a second portion of light beam 6 is not scattered by particle P and traverses sample 4 as unscattered light beam 10. In the context of this specification, scattered light beam 7 refers to scattering by particle P in medium M, whereas unscattered light beam 10 is not scattered by particle P in medium M.

[0025] The scattered light beam 7 and the unscattered light beam 10 interfere with each other. At the end of the light path 5, the camera 3 records an interference image 11 (FIG. 2) of the scattered light beam 7 and the unscattered light beam 10. The camera 3 can be for this purpose any analog or digital camera with, for example, a complementary metal-oxide semiconductor (CMOS) or charge-coupled device (CCD) image sensor.

[0026] However, it should be noted that parts of both the scattered light beam 7 and the unscattered light beam 10 may be scattered into the medium M, for example by other (usually smaller) objects (e.g. via the Tyndall effect), and this part of the unscattered light beam 10 will deviate slightly from the beam direction 9. In the interference image 11, the parts of the scattered light beam 7 and the unscattered light beam 10 will give rise to an unavoidable and undesirable background signal, which will interfere with the determination of the focal length d.

[0027] Interferometer 1 may comprise one or more further optical devices as known in the art of holographic microscopy, such as an attenuator ring for improving the signal-to-noise ratio, a microscope objective lens, a phase plate, one or more lenses, etc. Furthermore, interferometer 1 may be of a different type than an in-line interferometer, such as, for example, an interferometer 1 that utilizes a beam splitter.

[0028] The interferometric image 11 recorded by the camera 3 is transferred to the processor 12 via an interface 13. Optionally, the processor 12 can pre-process the interferometric image 11 as known in the art, for example to numerically correct aberrations. The processor 12 then processes the interferometric image 11 to determine therefrom the focal length d, as will be described with reference to Figures 2 and 3.

[0029] Camera 3 records interference image 11 as a purely two-dimensional image, which encodes both intensity and phase information of light beam 6. This information allows processor 12 to "reconstruct" light beam 6 in three dimensions.

[0030] In a first step S1, the processor 12 calculates the electric field E1 of the first portion of the light beam 6, i.e. the scattered light beam 7, for each of a set of positions H from the interference image 11. The positions H are three-dimensionally distributed in a space R that includes the particle P and the focal point 8. In the example shown in Figures 1-3, the space R extends from within the sample 4 to the camera 3, since the focal point 8 is known or expected to be behind the particle P (in the beam 9 direction). In another embodiment, the space R ranges from within the sample 4 to the light source 2 (or even beyond) when the focal point 8 is known or expected to be in front of the particle P (in the beam 9 direction). In yet another embodiment, the space R extends, for example, from the camera 3 to the light source 2 (or even beyond).

[0031] In the example shown in FIG. 2, the position H is a plane of several imaginary planes 141, 142, . . . , generally 14 i, and some imaginary planes 14 are perpendicular to the light beam 9 of the unscattered light beam 10. In this example, the position H is located at each imaginary plane 14 i In other examples, the locations H may be distributed differently in the space R, for example in a regular grid arrangement representing adjacent cubic regions, or in an irregular grid arrangement representing adjacent arbitrarily shaped spatial regions.

[0032] To calculate the electric field E1 of the scattered light beam 7, the processor 12 applies a reconstruction algorithm to the interferogram 11 for each set of positions H. Since the electric field E1 of the scattered light beam 7 for each position H is complex, its real and imaginary parts, or the phase φ1 and amplitude, respectively, are calculated. In this example, the processor 12 applies the reconstruction algorithm on a plane-by-plane basis in a direction 15 opposite to the beam direction 9, although this is optional. Various examples of such reconstruction algorithms include forward or backward propagation or projection algorithms, such as inverse Radon transforms, Fourier domain reconstruction algorithms, iterative reconstruction algorithms, etc., as known in the art.

[0033] In a subsequent second step S2, the processor 12 generates a representation 16 of the sample 4 covering all positions H and comprising for each position H a respective intensity value I (FIG. 3) representative of the intensity of the light beam 6 at that position H. From the electric field E1 and the intensity I1 of the scattered light beam 7 calculated for that position H, for example as the square of the amplitude of the electric field E1, the intensity value I for each position H is calculated according to the following formula:

[0034]

number

[0035] (In the formula, r, z are coordinates at position H, z is a coordinate in a direction 15 opposite to the beam direction 9, and r is a pair of coordinates in a plane x, y perpendicular to said direction 15, I(r,z) is the intensity value at position H, I1(r,z) is the intensity of the first portion of the light beam 6 for the position H; Θ is a phase shift parameter that is pre-specified or specified as follows: k, l are the indices of the sums repeated over the sets of values ​​K, L, respectively. C k , D l teeth, expansion are parameters, either predetermined or specified as follows: E1(r,z) is the electric field calculated for position H arctan2 represents the four-quadrant arctangent function. It is calculated by:

[0036] The sum is all expansion Parameter C k , D l It should be understood that the trivial case is excluded where {overscore (k), (l)} is zero and only arctan 2 results in the phase φ1 of the electric field E1 of the scattered light beam 7. Furthermore, the summation indices k, l need not be restricted to integers, i.e., each of the sets K, L may, for example, include real-valued values.

[0037] In a third step S3 following step S2, the processor 12 P , H F Detect. H P is a first position located in the sample 4 and being a particle position, and H P is the focal position and a second position that is behind the particle position (or in front of it in other cases) when viewed in the beam direction 9. These points are either in the sample 4 or between the sample 4 and the camera 3 (or in the other cases either in the sample 4 or between the sample 4 and the light source 2, or even beyond). P and H F are detected according to the following criteria: P , H FFor each of the intensity values ​​I P , I F is a maximum, so that each intensity value I P , I F is the nearby position H NP , H NF Each intensity value I NP , I NF (Fig. 3) Position H NP For example, particle position H P This is the position H located near the sphere or box centered at the focal position H F Position H near NF The same applies to.

[0038] To detect the two positions, the processor 12 can apply any detection algorithm. For example, two positions H P , H F To find, first, all intensity values ​​I that exhibit local maxima can be identified and then their respective positions H compared. P , and the second position H F If some pairs of P satisfy this selection criterion, then some particles P are present in the sample 4 (FIG. 1); otherwise, an additional selection criterion can be selected, e.g., the focal position H F or obtain the position H with the highest intensity value I as the particle position H P One can arbitrarily choose a criterion such as taking a location H that has a distribution of intensity values ​​I around it that exhibits a known particle scattering distribution (eg, a distribution derived from Mie scattering theory) as

[0039] In the final step S4, the processor 12 calculates the two positions H P , H F from which we can determine, for example, the focal length d of a particle P in a medium M as its mutual distance calculated from its respective coordinates x, y, z in a given coordinate system 18 (FIG. 3).

[0040] Next, various embodiments for calculating the intensity value I in step S2 will be described with reference to FIG.

[0041] The exemplary graph of FIG. 3 shows intensity values ​​I calculated along a direction 15 and represented by a solid line 17. In a first example, the phase shift and magnification parameters Θ, C k , D l At least one of the following parameters, i.e., the phase shift parameter Θ, the first expansion parameter C k and / or a second expansion parameter D l One or more of may be pre-identified, for example, by similar samples or measurements, or based on prior knowledge. For example, the phase shift parameter Θ may be set to π, where the phase shift parameter generally reduces background signal.

[0042] In other or further embodiments, the phase shift and magnification parameters Θ, C k , D l At least one of these is repeatedly identified for the recorded interference images 11 of the sample 4 .

[0043] In the first embodiment, step S2 is repeated many times (dashed branch b1 in FIG. 2) to determine the at least one parameter Θ, C k , D l is changed with each iteration to increase the difference between the higher intensity value I and the lower intensity value I constituted by the representation 16. For example, the higher intensity value I is changed with each iteration to increase the difference between the higher intensity value I and the lower intensity value I constituted by the representation 16. avg higher than the intensity threshold I th higher than, for example, a certain percentage of the highest intensity value I (here I F ), or may be a fixed value (e.g., 10) of the calculated maximum intensity value I, such as that configured by the display 16. Similarly, the lower intensity value I may be greater than or equal to the intensity threshold I mentioned above (or another). th , the average intensity value I avg etc. may be lower.

[0044] In this example, the difference between the higher intensity value I and the lower intensity value I is the mean intensity value I avg Absolute deviation ΔI between avg , so that the variance of all intensity values ​​I included in the display 16 is increased. Alternatively, other differences may be used, such as the difference between the sum of all the higher and the sum of all the lower intensity values ​​I.

[0045] In the example of FIG. 3, the at least one parameter Θ, C k , D l The particular result of the iteration of step S2 is symbolized by the solid line 17, while the dashed line 17' symbolizes the initial intensity value I', i.e. the intensity value calculated before repeating step S2. As shown in this example, the solid line 17 has a more pronounced maximum value I than the dotted line 17'. P , I F In addition, various particles and focal positions H' P , H' F Intensity value I' at P , I' F Indicates the maximum value of.

[0046] FIG. 3 shows the intensity value I in a direction 15, i.e. in the z-direction, while the at least one parameter Θ, C k , D l Note that changes in generally affect the display 16 in all three dimensions. expansion Parameter C k , D l The identification of includes the identification of respective sets K, L, i.e., the sets K, L may be pre-specified, expansion Parameter C k , D l It should further be noted that may be repeatedly specified, or the sets K, L may also be repeatedly specified.

[0047] In the second embodiment, steps S2 and S3 are repeated (dashed branch b2 in FIG. 2). k , D l is the particle position HP Intensity value of I P and nearby position H NP The respective intensity values ​​of I NP The difference between P-NP is changed to increase the nearby position H NP Intensity value of I NP is optionally the mean intensity value I NP,avg Alternatively, the intensity value I P , and nearby intensity values ​​I NP Any other combination of, for example, the intensity value I NP Similarly, the weighted sum of the at least one parameter Θ, C k , D l Alternatively or additionally, the focal position H F Intensity value of I F and the focal position H F Position H near NF The respective intensity values ​​of I NF , for example, their average I NF,avg The difference between F-NF is modified to increase

[0048] In a third embodiment, steps S2 and S3 are repeated and the at least one parameter Θ,C k , D l is the particle position H P Intensity value of I P and the focal position H F Intensity value of I F The ratio between

[0049] In a further additional or alternative embodiment, the processor 12 simulates the light beam illuminating the sample, its scattering, and its intensity recorded in an interference image. This simulation can be performed, for example, using field tracing methods known in the art, for either the specific sample envisaged or more general samples, each containing one or more particles. From this simulated interference image, intensity values ​​I are calculated for a further set of positions different or equal to the set of positions H by performing steps S1 and S2 exemplified above to obtain a simulated display. Thus, the steps of providing, recording, emitting, calculating, and generating are simulated. A simulation is then performed for an iteration of the generating step S2, where the at least one parameter Θ, C k , D l is modified to reduce the difference between the intensity values ​​constructed by the simulated representation and the intensity of the simulated light beam at each position. Of course, the simulation may optionally be performed for different particles in different media, and the obtained parameters Θ, C k , D l may, for example, be averaged and combined to be applicable to a wide variety of particles P and media M.

[0050] Optionally, phase shift and magnification parameters Θ, C k , D l At least one of the parameters Θ, C depends on the position H in the display 16, so that the intensity values ​​I for different positions H vary depending on the at least one parameter Θ, C k , D l For example, the at least one parameter Θ, C k , D l For example, the value of C2 is P and nearby position H NP is the focal position H F and nearby position H NF C k , Dl The value of the at least one parameter Θ may be predetermined or specified to be different from the values ​​of the at least one parameter Θ of the same.

[0051] Any of the above examples and embodiments may be used, for example, to determine the particle and focal position H P , H F The above-described embodiments and aspects may be implemented using an optimization algorithm with a stopping criterion known in the art, such as a quasi-Newton algorithm that stops when the parameters Θ, C k , D l can be combined with different ones of each of the above while optimizing.

[0052] In any embodiment, the intensity threshold I th is introduced into the processor before step S3, where the identified intensity value I is multiplied by the calculated intensity threshold I th Positions H smaller than the intensity threshold I shall be considered and not used in step S3. th may be estimated, for example, or may be determined by the maximum intensity value I included in the display 16 (I in FIG. 3). F ), a moving average, an average of two or more values, or even a percentage of all intensity values ​​I.

[0053] In a further optional embodiment, a reference image 19 of the coherent light beam 6 is generated for the light beam 10 that is not scattered, i.e. not scattered, by the particle P. On that basis, prior to said step S1 of calculation as known in the art, the interference image 11 can be normalized by the processor 12, such that a normalized calculated electric field E1 is calculated in step S1 and used as the electric field E1 in the subsequent step S2.

[0054] It should be understood that the method may employ multiple light beams at different frequencies and / or multiple light sources, for example to investigate focal lengths from different illumination angles and / or dispersions of particle P. It is also possible to estimate particle and focal position H in addition to focal length d, for example to characterize or distinguish particle P from other particles in sample 4. P , H F Intensity at I P , I F may also be used.

[0055] The present invention is not limited to the particular embodiments described above, but encompasses all variations, modifications and combinations thereof that fall within the scope of the appended claims. [Brief description of the drawings]

[0056] [Figure 1] FIG. 1 is a schematic side view of an in-line interferometer used in the method of the present invention. [Diagram 2] FIG. 2 is a flow chart illustrating the determination of focal length from an interference image recorded by the interferometer of FIG. 1 according to the present invention. [Diagram 3] FIG. 3 graphically illustrates intensity values ​​of a light beam determined according to the method illustrated in FIGS. 1 and 2 from the direction of the light beam to the opposite direction.

Claims

1. A method for determining the focal length (d) of a transparent particle (P) in a medium (M), comprising the steps of: Providing a sample (4) of medium (M) containing said particles (P); using a light source (2) to emit a coherent light beam (6), irradiating a sample (4) with said light beam (6), such that a first portion of the light beam (6) is scattered by a particle (P) to produce a scattered light beam (7) having a focus (8) in a beam direction (9) behind or in front of the particle (P); recording, by means of a camera (3), an interference image (11) of the scattered light beam (7) and a second portion of the light beam (6) that has not been scattered by said particle (P); For each of a set of positions (H) distributed three-dimensionally in the space (S) containing the particle (P) and the focal point (8), the electric field (E １ ) by a processor (12) １ )and, Each of the positions (H) corresponds to a calculated electric field (E １ generating (S) using a processor (12) a representation (16) of the light beam (6) covering said position (H) including an intensity value (I) of the coherent light beam (6) calculated from the intensity value (I) of the coherent light beam (6); ２ )and, The first position (H Ｐ ) is located on the sample (4), and the second position (H Ｆ ) is the first position (H Ｐ ) in the beam direction (9) behind or in front of Ｐ , H Ｆ ) and nearby positions (H ＮＰ , H ＮＦ ) for each intensity value (I ＮＰ , I ＮＦ ) Ｐ , I Ｆ ) using a processor (12), ３ )and, The two detected positions (H Ｐ , H Ｆ A step (S) of determining the focal length (d) by the processor (12) from the ４ ) and The generating step (S ２ ), for each position (H), the intensity value (I) is calculated according to the following formula: [0010] (In the formula, r and z are coordinates of a position (H), z is a coordinate in a direction (15) opposite to the beam direction (9) and r is a pair of coordinates in a plane (x, y) perpendicular to said direction (15), I(r,z) is the intensity value at position (H), I １ (r,z) is the intensity of the first portion of the light beam (6) for the position (H); Θ is the phase shift parameter, k, l are summation indices, C ｋ , D ｌ is the expansion parameter, E １ (r,z) is the electric field calculated for position (H), arctan2 represents the four-quadrant arctangent function. Calculated according to the method.

2. The phase shift and broadening parameters (Θ, C ｋ , D ｌ At least one of the steps (S ２ ) and the at least one parameter (Θ, C ｋ , D ｌ 2. The method of claim 1, wherein the intensity values ​​(I) of the first and second indices (14, 15, 16) are altered to increase the difference between higher and lower intensity values ​​(I) included in the representation (16).

3. The phase shift and broadening parameters (Θ, C ｋ , D ｌ At least one of the generation (S ２ ) and detection (S ３ ) and the at least one parameter (Θ, C ｋ , D ｌ ) is the first position (H Ｐ ) intensity value (I Ｐ ) and its nearby position (H ＮＰ ) ＮＰ ) between Ｐ－ＮＰ ) and / or to increase the second position (H Ｆ ) intensity value (I Ｆ ) and its nearby position (H ＮＦ ) ＮＦ ) between Ｆ－ＮＦ 3. The method of claim 1 or 2, wherein the method is modified to increase

4. The phase shift and broadening parameters (Θ, C ｋ , D ｌ At least one of the generating steps (S ２ ) and a detection step (S ３ ) and the at least one parameter (Θ, C ｋ , D ｌ ) is the first position (H Ｐ ) for the intensity value (I Ｐ ) and the second position (H Ｆ ) for the intensity value (I Ｆ 4. The method of claim 1, wherein the method is modified to increase the ratio between

5. The phase shift and broadening parameters (Θ, C ｋ , D ｌ ) at least one of A simulation of the steps of providing, emitting, recording, calculating and generating to obtain a simulated representation in the generating step, and a simulated light beam intensity at each location covered by the simulated representation; and Identified by repeating a simulation of the generating step; The at least one parameter (Θ, C ｋ , D ｌ 5. The method of claim 1, wherein the intensity values ​​contained by the simulated representation are altered to reduce a difference between the intensity values ​​contained by the simulated light beam at the respective positions.

6. The phase shift and broadening parameters (Θ, C ｋ , D ｌ 6. The method according to claim 1, wherein at least one of the following is dependent on the position (H) in the representation (16).

7. The method according to any one of the preceding claims, wherein in the detecting step (S3) only positions (H) where the intensity value (I) is greater than a predefined threshold (Ith) are taken into account.

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