Method for determining the focal length of particles in a medium

Abstract

A method for determining the focal length (d) of particles (P) in a medium (M), comprising: providing a sample (4); emitting a coherent light beam (6) to irradiate the sample (4), wherein a first part of the light beam (6) is scattered by the particles (P); recording an interference image (11); calculating (S1) an electric field (E1) for a set (H) of a plurality of positions based on the interference image (11); generating (S2) a representation (16), for, the representation including an intensity value (I) of the coherent light beam (6) calculated based on the calculated electric field (E1) for each of the plurality of positions (H); finding (S3) two positions (HP, HF), wherein a first position (HP) of the two positions is located in the sample (4), and a second position (HF) of the two positions is located after or before the first position (HP) in the beam direction (9); and determining (S4) the focal length (d) based on the found two positions (HP, HF).

Description

Technical Field

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

[0002] The background of the present invention lies in the field of observing colloids in a medium such as emulsions, cell cultures, and bacteria, for example, for studying bacterial contamination of water or the pathogenesis of bacteria in urinary tract infections. In addition, it is possible to observe plastic particles in seawater, impurities in liquid foods or drugs, cells or their organelles in body fluids, etc. When observing transparent particles that scatter focused light, their focal length provides valuable information: the focal length can be related to other properties of the particles, such as their size, shape, refractive index, and thus to the dry mass, the amount of water or sugars in bacteria, etc., or for distinguishing between classes and subclasses of particles in the medium.

[0003] Common methods for determining the optical properties of particles, such as their refractive index, are flow cytometry or phase contrast microscopy. Flow cytometry is well-suited for extracting statistical information about particles in high throughput. However, it has the disadvantage of low precision in determining the optical properties of individual particles and cannot observe particles in a static medium. On the other hand, phase contrast microscopy provides high precision but only the visualization of individual particles at limited throughput and focal depth. In addition, difficult and demanding interpretation of two-dimensional images is required to extract the refractive index and, if necessary, the focal length of the particles.

[0004] Another possible method is digital holographic microscopy. In this method, a sample containing the particles is irradiated with a coherent light beam to obtain an interference image. Based on the interference image, a three-dimensional model of the irradiated light beam is calculated by applying a reconstruction algorithm, such as a forward or backward propagation or projection algorithm, to the interference image. In the three-dimensional model, the position of the particles and their foci can be determined, as well as the focal length, which is the difference between them.

[0005] However, experiments have shown that the three-dimensional models obtained by ordinary digital holographic microscopy are not suitable in quality for reliably determining the focal length of particles. On the one hand, the intensity of the light beam at the focus usually far exceeds the intensity at the particles, such that especially in the case of small focal lengths, the particles cannot be distinguished from their foci. On the other hand, an inevitable background signal generated by a part of the light scattered in the medium (i.e., not by the particles but by other (usually smaller) objects in the medium, such as through micro-scattering) is recorded in the interference image. This background signal weakens the contrast between the light scattered by the particles and the light not scattered by the particles, and thus deteriorates the determination of their position in the model. In order to still accurately determine the particle position, a long and computationally demanding comparison of the reconstruction model with a scattering model, such as with Mie theory, would have to be performed.

[0006] The object of the present invention is to overcome the limitations of the prior art and to provide a method for determining the focal length of transparent particles in a medium in an effective and precise manner. Summary of the Invention

[0007] This object is achieved by a method for determining the focal length of transparent particles in a medium, the method comprising:

[0008] providing a sample of the medium containing the particles;

[0009] using a light source to emit a coherent light beam to irradiate the sample, wherein a first part of the beam is scattered by the particles to produce a scattered beam, and the scattered beam has a focal point behind or in front of the particles in the beam direction;

[0010] using a camera to record an interference image of the scattered beam and a second part of the beam that is not scattered by the particles;

[0011] using a processor, for each position in a set of a plurality of positions three-dimensionally distributed in a space including the particles and the focal point, calculating the electric field of the first part of the beam based on the interference image;

[0012] using the processor to generate a representation of the beam that covers the plurality of positions and includes the intensity value of the coherent beam calculated based on the calculated electric field at each of the plurality of positions;

[0013] using the processor to find two positions, wherein a first position of the two positions is in the sample, a second position of the two positions is behind or in front of the first position in the beam direction, and the intensity value of each of the two positions is greater than the corresponding intensity value of its neighboring positions; and

[0014] using the processor to determine the focal length based on the two found positions;

[0015] wherein, in the generating step, the intensity at each position is calculated according to the following

[0016] value

[0017]

[0018] where

[0019] r, z are the coordinates of the position, where z is the coordinate in the opposite direction of the beam direction, and r represents a pair of coordinates in a plane perpendicular to the opposite direction,

[0020] I(r, z) is the intensity value of the position,

[0021] I1(r, z) is the intensity of the first part of the beam at the position,

[0022] Θ is the phase shift parameter,

[0023] k, l are summation indices,

[0024] C k , D l are spreading parameters,

[0025] E1(r, z) is the calculated electric field at the position, and

[0026] arctan2 represents the four - quadrant arctangent function.

[0027] It should be noted that the electric field of the beam is usually a complex value, and thus can be described by its real and imaginary parts or by its amplitude and phase. In addition, the beam has an intensity proportional to the square of the electric field amplitude, i.e., the power per unit area.

[0028] The first position corresponds to the particle position and the second position corresponds to the focal position, such that the focal length can be determined as their difference. The applicant has found that the calculation of each intensity value allows for a high contrast between the light scattered by the particle and the light not scattered by the particle and a reliable discrimination between the particle and its focus; thus, the two positions can be found precisely. Therefore, the focal length can be effectively determined directly from a complex comparative representation presenting the intensity or the electric field of the beam using a model of the scattering distribution.

[0029] In addition, the phase shift and spreading parameters used to calculate each intensity value allow for the precise determination of the corresponding focal lengths for a large set of different particles and media. For example, any one of the phase shift and spreading parameters can be predetermined, e.g., for similar samples or measurements, or estimated based on existing knowledge. For example, the phase shift parameter can be set to π to reduce the background signal. On the other hand, these parameters can be adapted to a specific situation, e.g., to precisely determine the focal length of a specific bacterium in water. To this end, in one embodiment, for example, by applying an iterative optimization algorithm known in the art, such as the quasi - Newton algorithm, etc., which can terminate, for example, when the particle and focal positions converge, one or more of the phase shift and spreading parameters can be determined iteratively to optimize the generated representation.

[0030] In an advantageous variant of this embodiment, at least one of the phase shift and the spreading parameter is determined by repeating the generating step, wherein the at least one parameter is changed to increase the difference between the higher intensity values and the lower intensity values comprised by the representation. This optimization reduces the influence of the background, which is typically represented by the lower intensity values, and results in more prominent higher intensity values. The difference can be, for example, the difference between the sum of all higher intensity values and the sum of all lower intensity values, the RMS (root mean square) contrast, etc. For example, using the latter results in a smaller number of more distinct intensity value maxima, which can be considered first in the step of finding the two positions.

[0031] In an alternative or additional variant, at least one of the phase shift and the spreading parameter is determined by repeating the generating and finding steps, wherein the at least one parameter is changed to increase the difference between the intensity value of the first position and the corresponding intensity values of its neighboring positions and / or to increase the difference between the intensity value of the second position and the corresponding intensity values of its neighboring positions. This determination particularly emphasizes the corresponding intensity values of the particle and / or the focal position compared to the intensity values of the corresponding neighboring positions, thereby enhancing the local contrast.

[0032] According to another advantageous variant, at least one of the phase shift and the spreading parameter is determined by repeating the generating and finding steps, wherein the at least one parameter is changed to increase the ratio of the intensity value of the first position to the intensity value of the second position. This facilitates the distinction of the intensity value of the particle position from the corresponding intensity values of the focal position and its neighboring positions, which is particularly suitable for accurately determining a small focal length.

[0033] In a particularly preferred embodiment, at least one of the phase shift and the spreading parameter is determined by

[0034] simulating the providing, emitting, recording, calculating, and generating steps to obtain a simulated representation in the generating step and the intensity of the simulated light beam at each position covered by the simulated representation; and

[0035] repeating the simulation of the generating step, wherein the at least one parameter is changed to reduce the difference between the intensity values comprised by the simulated representation and the intensity of the simulated light beam at the corresponding positions.

[0036] The medium, additional scatterers in the medium, the surroundings of the particles, their shape, size, orientation, refractive index, etc. can be simulated separately and, if necessary, adjusted. Thus, at least one of the phase shift and the spreading parameter can be easily determined, for example, by performing a simulation of a sample comprising a number of particles with different local environments, for a specific sample or for a more general case. Additionally, this embodiment can be for pre-determining at least one of the plurality of parameters and / or setting at least one of the plurality of parameters to an initial value for iteration according to one of the above variants.

[0037] In another advantageous embodiment, at least one of the phase shift and the spreading parameter depends on the position in the representation. This allows different local neighboring regions to be taken into account separately by pre-determining or determining the at least one parameter differently when calculating the intensity value at the corresponding position, namely, especially the vicinity of the particle position and the focus position. Thereby, an improved accuracy in determining both the particle and the focus positions and thus the focal length can be achieved.

[0038] To facilitate the distinction between the light scattered by the particles and the light not scattered by the particles, it is advantageous when, in the searching step, only those positions with intensity values greater than a predetermined threshold are considered. Besides being easier to distinguish, this allows for a faster search for the two positions due to the reduced amount of data to be considered. In this embodiment, the threshold can be pre-determined as known to those skilled in the art, for example, as a percentage of the (general, typical, expected or currently determined) maximum intensity value, as the average of the intensity values of a number of positions, as the overall average of all the intensity values of the representation, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The invention will now be explained in more detail below with reference to the preferred exemplary embodiments of the invention based on the accompanying drawings, wherein:

[0040] Figure 1 A schematic side view of an in-line interferometer for a method according to the invention is shown;

[0041] Figure 2 is shown in a flowchart for determining the focal length from an interference image recorded by an interferometer according to the invention; and Figure 1 The intensity values of the light beam determined according to the method shown in

[0042] Figure 3 will be shown as a graph in a direction opposite to the direction of the light beam. Figure 1 and Figure 2 DETAILED DESCRIPTION

[0043] Figure 1 ​Figure 1 shows an in-line interferometer 1 including a light source 2 and a camera 3. The in-line interferometer 1 is used to determine the focal length d of (microscopic) transparent particles P in a medium M. To determine the focal length d, a sample 4 of the medium M containing the particles P (or a number of particles P) is provided in the optical path 5 between the light source 2 and the camera 3. Each particle P can be a cell, a bacterium, a charged particle, a microplastic particle, an organelle, etc., and the medium M can be water, oil, a body fluid (such as blood), a solution, etc. Generally, the focal length d of any transparent particle P that focuses light in the medium M can be determined.

[0044] To this end, the light source 2 emits a coherent light beam 6 to irradiate the provided sample 4. The light source 2 can be any type of light source capable of emitting a coherent light beam 6, such as a laser diode.

[0045] In the sample 4, a first portion of the light beam 6 is scattered by the particle P, thereby generating a scattered light beam 7 having a focal point 8, which in Figure 1 the example is located behind the particle P in the beam direction 9, i.e., at a distance corresponding to the focal length d behind the particle P. In other cases where the particle P acts as a diverging lens, when observed in the beam direction 9 (not shown), the focal point is in front of the particle P.

[0046] However, a second portion of the light beam 6 is not scattered by the particle P and passes through the sample 4 as an unscattered light beam 10. In the context of this specification, the scattered light beam 7 refers to scattering by the particle P in the medium M, while the unscattered light beam 10 is not scattered by the particle P in the medium M.

[0047] The scattered light beam 7 and the unscattered light beam 10 interfere with each other. At the end of the optical path 5, the camera 3 records an interference image 11 of the scattered light beam 7 and the unscattered light beam 10 ( Figure 2 ). For the present purpose, the camera 3 can be, for example, any analog or digital camera having a complementary metal oxide semiconductor (CMOS) or a charge-coupled device (CCD) image sensor.

[0048] However, it should be noted that a portion of both the scattered light beam 7 and the unscattered light beam 10 can also be scattered in the medium M, for example, by other (usually smaller) objects (e.g., via the Tyndall effect), and this portion of the unscattered light beam 10 is slightly deviated from the beam direction 9. In the interference image 11, this portion of the scattered light beam 7 and the unscattered light beam 10 results in an inevitable, although undesirable, background signal that impairs the determination of the focal length d.

[0049] The interferometer 1 may include one or more other optical devices known in the field of holographic microscopy, for example, an attenuator loop for improving the signal-to-noise ratio, a microscope objective, a phase plate, one or more lenses, etc. In addition, the interferometer 1 may also be implemented as an interferometer of a different type from an in-line interferometer, for example, an interferometer 1 that utilizes a beam splitter.

[0050] Then, the interference image 11 recorded by the camera 3 is transmitted to the processor 12 through the interface 13. Optionally, the processor 12 may preprocess the interference image 11 as known in the art, for example, in order to numerically correct aberrations. Subsequently, the processor 12 processes the interference image 11 to determine the focal length d therefrom, as will now be explained with reference to Figure 2 and 3 explained.

[0051] When the camera 3 records the interference image 11 as a pure two-dimensional image, the interference image 11 encodes both the intensity and phase information of the light beam 6. This information allows the processor 12 to "reconstruct" the light beam 6 in three dimensions.

[0052] In a first step S1, for each position in a set of a plurality of positions H from the interference image 11, the processor 12 calculates the electric field E1 of a first portion of the light beam 6 (i.e., the scattered light beam 7). The plurality of positions H are three-dimensionally distributed in a space R that includes the particle P and the focal point 8. In the Figures 1 to 3 example, since the known or expected focal point 8 (in the light beam direction 9) is located behind the particle P, the space R extends from within the sample 4 to the camera 3. In another embodiment, when the known or expected focal point 8 (in the light beam direction 9) is located in front of the particle P, the space R extends from within the sample 4 to (or even beyond) the light source 2. In yet another embodiment, the space R extends, for example, from the camera 3 to (or beyond) the light source 2.

[0053] In Figure 2 the example, the plurality of positions H are located in a plurality of virtual planes 141, 142,... generally 14 i in, and these virtual planes are perpendicular to the light beam direction 9 of the unscattered light beam 10. In this example, the plurality of positions H are identically arranged in each virtual plane 14 i ; however, this is optional. In other examples, the plurality of positions H may be differently distributed in the space R, for example, in a regular grid arrangement representing adjacent cubic regions or in an irregular grid arrangement representing arbitrarily formed adjacent spatial regions.

[0054] To calculate the electric field E1 of the scattered light beam 7, for each position H in the set, the processor 12 applies a reconstruction algorithm to the interference image 11. The electric field E1 of the scattered light beam 7 for each position H is a complex value, and thus, its real and imaginary parts or its phase are calculated separately And amplitude. In this example, the processor 12 applies the reconstruction algorithm plane by plane in the direction 15 opposite to the beam direction 9. However, this is optional. Thus, as is known in the art, multiple variants of the reconstruction algorithm can be applied, such as forward or backward propagation or projection algorithms, such as inverse Radon transform, Fourier transform reconstruction algorithm, iterative reconstruction algorithm, etc.

[0055] In a subsequent second step S2, the processor 12 generates a representation 16 of the sample 4 that covers all positions H and includes the corresponding intensity value I( Figure 3 ), where the intensity value I represents the intensity of the beam 6 at that position H. Based on the intensity I1 and electric field E1 of the scattered 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

[0056]

[0057] There is

[0058] r, z are the coordinates of the position H, where z is the coordinate in the direction 15 opposite to the beam direction 9, and r represents a pair of coordinates in the plane x, y perpendicular to the opposite direction 15,

[0059] I(r, z) is the intensity value at the position H,

[0060] I1(r, z) is the intensity of the first part of the beam 6 at the position H,

[0061] Θ is a phase shift parameter that has been predetermined or will be determined as shown below,

[0062] k, l are the exponents of the summation, which iterate over the sets of k, l values respectively,

[0063] C k , D l are expansion parameters that have been predetermined or will be determined as shown below, E1(r, z) is the calculated electric field at the position H, and

[0064] arctan2 represents the four-quadrant arctangent function.

[0065] It should be understood that the summation excludes all cases where the expansion parameters C k , D l are zero and arctan2 only produces the phase of the electric field E1 of the scattered beam 7 . In addition, the exponents k, l of the summation need not be limited to integers, i.e., each of the sets of k, l can also include real numbers, for example.

[0066] In a third step S3 after step S2, the processor 12 looks for two positions HP , H F :First position H P , which is the particle position and is located in sample 4, and the second position H F , which is the focal position and is located at the particle position H when viewed in the beam direction 9 P Afterwards (or in other cases, at the particle position H P Before), that is, inside the sample 4 or between the sample 4 and the camera 3 (in the other case, inside the sample 4 or between the sample 4 and the light source 2 or even beyond the light source 2). Two positions H are found according to the following criteria P and H F :For these two positions H P , H F For each of the P ,I F is a local maximum, i.e., each intensity value I P ,I F Greater than the nearby position H NP , H NF The corresponding intensity value I NP ,I NF ( Figure 3 ). Nearby location H NP is located at particle position H P The position H in a neighboring area, for example a sphere or a box. This applies correspondingly to the focus position H F Nearby location H NF .

[0067] To find two locations H P , H F , the processor 12 may apply any search algorithm; for example, it may first determine all intensity values I showing a local maximum and then compare the various positions H in order to find two positions H that are far from each other in the beam direction 9. P , H F If several pairs of first and second positions H P , H F If the selection criteria are met, then in sample 4 ( Figure 1 ) there are several particles P; in addition, additional selection criteria can optionally be used, for example, the position H with the highest intensity value I is taken as the focus position H F , or the position H with the distribution of intensity values I around it is taken as the particle position H P , which shows a known (eg, a distribution derived from Mie scattering theory) particle scattering distribution, and so on.

[0068] In the final step S4, the processor 12 calculates the position H of the two locations found in step S3.P , H F to determine the focal length d of the particles P in the medium M, for example, as their mutual distance calculated according to their respective coordinates x, y, z in a given coordinate system 18( Figure 3 ).

[0069] Now various embodiments for calculating the intensity value I in step S2 will be explained with reference to Figure 3 .

[0070] Figure 3 The exemplary curve of k , D l shows the intensity value I that has been calculated along the direction 15 and is represented by the solid line 17. In the first embodiment, at least one of the phase shift and expansion parameters Θ, C k , i.e., the phase shift parameter Θ, one or more of the plurality of first expansion parameters C l and / or one or more of the plurality of second expansion parameters D

[0071] In an alternative or additional embodiment, the phase shift and expansion parameters Θ, C k , d l are iteratively determined for the recorded interference image 11 of the sample 4.

[0072] In its first variant, step S2 is iteratively repeated ( Figure 2 the dashed branch b1 in k ), and in each iteration, the at least one parameter Θ, C l is changed to increase the difference between the higher intensity value I and the lower intensity value I included in the representation 16. The higher intensity value I can be, for example, higher than the average intensity value I avg , higher than the intensity threshold I th (e.g., a certain percentage of the highest intensity value I (here I F )) or can be a fixed number (e.g., ten) of local maxima of the calculated intensity values I included in the representation 16, etc. Similarly, the lower intensity value I can be lower than (or different from) the above intensity threshold I th , the average intensity value I avg , etc.

[0073] In this example, the difference between the higher intensity value I and the lower intensity value I is calculated as the absolute deviation ΔI between each intensity value I and the average intensity value I avg . avgThe sum, thus increasing the variance of all intensity values I included in representation 16. Alternatively, other differences can be used, such as the difference between the sum of all higher intensity values I and the sum of all lower intensity values I, etc.

[0074] In Figure 3 the example, the at least one parameter Θ, C k , D l The result of the iterative determination is represented by the solid line 17, while the dashed line 17' represents 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 distinct maximum I P , I F , in addition, the dashed line shows the maximum I' P , H' F of the intensity values at different particle and focal positions H' P , I' F .

[0075] It should be noted that Figure 3 depicts the intensity value I in the direction 15, i.e., the z - direction, while the at least one parameter Θ, C k , D l usually affects representation 16 in all three dimensions. It should also be noted that the determination of the expansion parameters C k , D l includes the determination of the corresponding sets K, L, i.e., the sets K, L can be pre - determined, and the expansion parameters C k , D l can be determined iteratively, or the sets K, L can also be determined iteratively.

[0076] In the second variant, steps S2 and S3 ( Figure 2 the dashed - line branch b2 in) are repeated, and the at least one parameter Θ, C k , D l is changed to increase the difference ΔI P between the intensity value I P of the particle position H NP and the corresponding intensity value I NP of its neighboring position H P-NP , where the intensity value I NP of the neighboring position H NP is optionally averaged to an average intensity value I NP,avg . Alternatively, any other combination of the intensity value I P and the neighboring intensity value I NP can be used, such as the difference between the intensity value I NP and the weighted sum. Similarly, the at least one parameter Θ, C k , D lAdditionally or alternatively vary to increase the focus position H F of the intensity value I F and the focus position H F of the nearby position H NF of the corresponding intensity value I NF , for example their average I NF,avg the difference ΔI between F-NF .

[0077] In a third variant, steps S2 and S3 are repeated, wherein the at least one parameter Θ, C k , D l is varied to increase the ratio of the intensity value I P of the particle position H P and the intensity value I F of the focus position H F .

[0078] In another additional or alternative embodiment, the processor 12 simulates a beam irradiating the sample, scatters it and records its intensity in an interference image. This simulation can be performed, as is known in the art, for example using a field tracing method, for a supposed particle sample or for a more general sample, each sample containing one or more particles. From the interference image of this simulation, intensity values I of another set of positions, different or equal to the set of the plurality of positions H, are calculated by performing steps S1 and S2 as described above, to obtain a simulated representation. Thus, the steps of providing, recording, emitting, calculating and generating are simulated. Then, a repeated simulation of the step of generating S2 is performed, wherein the at least one parameter Θ, C k , D l is varied to reduce the difference between the intensity values included in the simulated representation and the intensity of the simulated beam at the corresponding positions. Of course, the simulation can optionally be performed for different particles in different media, and the resulting parameters Θ, C k , D l can be combined, for example averaged, to be applicable to various particles P and media M.

[0079] Optionally, at least one of the phase shift and expansion parameters Θ, C k , D l depends on the position H in the representation 16, such that different values of the at least one parameter Θ, C k , D l are used to calculate the intensity values I of different positions H. For example, the value of the at least one parameter Θ, C k , D l , for example C2, can be predetermined or determined for the particle position H P and its nearby position H NP to be different from the focus position H Fand the nearby position H NF of the same at least one parameter Θ, C k , D l .

[0080] Any of the above embodiments and variations can be performed using an optimization algorithm with stopping criteria known in the art. For example, when the particle and the focal position H P , H F converge, the quasi - Newton algorithm stops. In addition, the above embodiments and variations can be combined while optimizing the parameters Θ, C k , D l individually or different parameters among them.

[0081] In an alternative embodiment, before step S3 of the processor, an intensity threshold I th is introduced. Thus, in step S3, positions H where the determined intensity value I is less than the calculated intensity threshold I th should not be considered and used. The intensity threshold I th can be estimated, for example, or be a percentage representing the maximum intensity value I included in 16 ( Figure 3 the I in F ), a moving average, an average of two or more intensity values, or even an average of all intensity values I.

[0082] In another alternative embodiment, a reference image 19 of the coherent beam 6 that is not scattered by the particle P is generated, and thus it is related to the non - scattered beam 10. Based on this, the processor 12 can normalize the interference image 11 before the calculation step S1 as known in the art, such that the normalized calculated electric field E1 is calculated in step S1 and used as the electric field E1 in the subsequent step S2.

[0083] It goes without saying that the method can be performed using multiple beams and / or multiple light sources of different frequencies, for example, to study the focal length and / or the dispersion of the particle P from different illumination angles. In addition, in addition to the focal length d, the particle position H P and the intensity I F at the focal position H P , I F can also be used, for example, to characterize or distinguish the particle P from other particles in the sample 4.

[0084] The present invention is not limited to the above - described specific embodiments, but includes all variations, modifications, and their combinations falling within the scope of the appended claims.

Claims

1. A method for determining the focal length d of transparent particles P in a medium M, the method comprising: providing a sample (4) of the medium M containing the particles P; using a light source (2) to emit a coherent light beam (6) to irradiate the sample (4), wherein a first part of the coherent light beam (6) is scattered by the particles P to produce a scattered light beam (7), and the scattered light beam has a focal point (8) located before or after the particles P in the light beam direction (9); recording, with a camera (3), an interference image (11) of the scattered light beam (7) and a second part of the coherent light beam (6) that is not scattered by the particles P; using a processor (12) to calculate, for each position H in a set of a plurality of positions (H) three-dimensionally distributed in a space S including the particles P and the focal point (8), an electric field E1 of the first part of the coherent light beam (6) based on the interference image (11); using the processor (12) to generate a representation (16) of the coherent light beam (6) that covers the plurality of positions H and includes an intensity value I of the coherent light beam (6) calculated based on the calculated electric field E1 at each of the plurality of positions H; Using the processor (12) to find two positions H P , H F , where a first position H of the two positions P is located in the sample (4), and a second position H of the two positions F is located after or before the first position H in the beam direction (9), and the intensity value I P of each of the two positions is greater than the corresponding intensity value I P , I F of nearby positions H NP , H NF ; and NP , I NF ; and Using the processor (12) to determine the focal length d according to the two found positions H P , H F ; wherein, in the generating step, the intensity value I for each position H is calculated according to where r, z are the coordinates of the position H, where z is the coordinate in the opposite direction (15) of the light beam direction (9), and r represents a pair of coordinates in a plane x, y perpendicular to the opposite direction (15); I(r, z) is the intensity value at the position H; I1(r, z) is the intensity of the first part of the coherent light beam (6) at the position H; Θ is a phase shift parameter; k, l are summation indices; C k and D l are expansion parameters E1(r, z) is the calculated electric field for the position H; and arctan2 represents the four-quadrant arctangent function.

2. The method according to claim 1, wherein the phase shift and the expansion parameters Θ, C k , D l are determined by repeating the generating step, wherein at least one of the parameters Θ, C k , D l is changed to increase the difference between the higher intensity value I and the lower intensity value I included in the representation (16).

3. The method according to claim 1, wherein, Determine the phase shift and the expansion parameters Θ, C by repeating the steps of generating and searching k , D l at least one of, wherein the at least one parameter Θ, C k , D l is changed to increase the intensity value I of the first position H P and the difference ΔI between the corresponding intensity values I of its neighboring positions H P , and / or increase the intensity value I of the second position H NP and the difference ΔI between the corresponding intensity values I of its neighboring positions H NP . P-NP , F and the corresponding intensity value I of its neighboring positions H F , NF and the difference ΔI between the corresponding intensity values I of its neighboring positions H NF . F-NF .

4. The method according to claim 1, wherein Determine the phase shift and the expansion parameters Θ, C by repeating the steps of generation and search k , D l at least one of them, wherein at least one of the parameters Θ, C k , D l is changed to increase the intensity value I of the first position H P and the ratio between the intensity value I of the second position H P and the intensity value I of the second position H F and the intensity value I of the second position H F .

5. The method according to claim 1, wherein The phase shift and expansion parameters Θ, C k , D l are determined at least in part by the following simulating the providing, emitting, recording, calculating, and generating steps to obtain a simulated representation in the generating step and the intensity of the simulated light beam at each position covered by the simulated representation; and Repeat the simulation of the generated steps, wherein the at least one parameter Θ, C k , D l is changed to reduce the difference between the intensity value included in the representation of the simulation and the intensity of the simulated light beam at the corresponding position.

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

7. The method according to any one of claims 1 to 6, wherein In the step of the search, only those positions H where the intensity value I is greater than a predetermined threshold I th are considered.

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