Method for holographic generation of an array of focusing points

Abstract

The invention relates to a method for holographic generation of an array of focusing points arranged according to multiple positions of the field of an optical system, which comprises: (S10) detecting images formed by the optical system at a plurality of calibration points arranged according to multiple positions of the field of the optical system; (S20) estimating aberrations introduced by the optical system onto the optical field from the detected images; (S30) applying a phase mask to the optical beam in order to generate a plurality of focusing points arranged according to multiple positions in the field of the optical system; wherein the phase mask is calculated from the estimated aberrations in order to simultaneously compensate for the aberrations at each focusing point. The invention also relates to a holographic generation system which carries out this method.

Description

Method for holographic generation of a focal point array Background of the invention

[0001] The present description relates to a method for holographically generating focal points. In addition, the present description relates to a system for holographically generating focal points implementing said method.

[0002] Holographic focus point generation systems generally consist of generating an array of focus points from an optical beam by means of an optical system and phase modulation of the wavefront composing the optical beam generally applied by means of a spatial light modulator.

[0003] However, the optical systems used are generally imperfect and introduce aberrations into the optical beam that degrade the quality of the focal points. In particular, the intensity homogeneity of the different focal points may be reduced. In addition, the fidelity of the shape of the focal points to a desired shape may also be reduced.

[0004] Typically, it has been found that when applying these systems to the generation of optical tweezers, aberrations of the optical system lead to deformations of the optical tweezers which reduce the performance of said tweezers for various applications such as the manipulation of atomic arrays.

[0005] Solutions have been proposed to reduce the impact of aberrations in optical systems on the quality of focal points.

[0006] For example, it has been proposed to measure the wavefront distortions introduced by the optical system and then to compensate for these distortions by applying a corrected phase mask to the optical beam, see [REF 1], [REF 2], [REF 3]. However, in these methods, the aberrations of the optical system are only evaluated at one point, generally a point located on the optical axis, and the characterization of the aberrations does not take into account the fact that the aberrations introduced by optical systems at a point in the optical field depend on the position of this point in the said field. Thus, existing methods do not do not allow to correct all the aberrations introduced by the optical system for all the focal points generated.

[0007] There is therefore a need for a method that solves the problems of the state of the art. References [REF 1] US 2008 / 0316575 A1 [REF 2] WO 2010 / 109241 [REF 3] WO 2023 / 132865 [REF 4] HANSER, Bridget M., GUSTAFSSON, Mats GL, AGARD, David A., et al. Phase retrieval for high-numerical-aperture optical systems. Optics letters, 2003, vol. 28, no. 10, pp. 801-803. [REF 5] DI LEONARDO, Roberto, IANNI, Francesca, and RUOCCO, Giancarlo. Computer generation of optimal holograms for optical trap arrays. Optics Express, 2007, vol. 15, no. 4, pp. 1913-1922. [REF 6] BORN, Max and WOLF, Emil. Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. Chap. V, Elsevier, 2013. [REF 7] KIM, Donggyu, KEESLING, Alexander, OMRAN, Ahmed, et al. Large-scale uniform optical focus array generation with a phase spatial light modulator. Optics letters, 2019, vol. 44, no. 12, p. 3178-3181. Object and summary of the invention

[0008] This description aims to remedy at least in part the drawbacks of the state of the art.

[0009] To this end, the present description relates to a method for holographic generation of a network of focusing points arranged in several positions in the field of an optical system comprising the detection of images formed by the optical system at a plurality of calibration points arranged in several positions in the field of the optical system; the estimation of the aberrations introduced by the optical system over the entire field of the optical system from the detected images; the application of a phase mask to an optical beam entering the optical system, in order to generate a plurality of focusing points arranged in several positions in the field of the optical system; in which the phase mask is calculated, from the estimated aberrations, in order to simultaneously compensate for aberrations at each focus point.

[0010] In the present description, a focal point is to be understood as a convergence zone of an optical beam with a desired light distribution. The shape and extent of the focal point depend in particular on the type of optical beam considered. For example, the optical beam may be a beam with a light intensity profile with Gaussian distribution (Gaussian beam), in which case the focal point is an optical spot having a Gaussian light distribution. In some examples, the optical beam is an optical bottle beam, in which case the focal point is an optical spot having an annular light distribution. Other types of optical beam may be considered, such as Laguerre-Gauss modes, Hermite-Gauss modes or optical vortices.

[0011] For example, Gaussian or bottle-type focusing points are particularly suitable for generating optical tweezers to trap particles and / or atoms.

[0012] It is understood that by focal point array is meant an arrangement of several focal points arranged in two spatial dimensions or in three spatial dimensions. Such arrangements can also be referred to as focal point matrices or focal point arrays (from the English term "optical spot array").

[0013] With the present invention, it is possible to correct the aberrations induced by the optical system at each focal point of the array of focal points. In addition, the focal points can be placed arbitrarily at any point in the optical field, i.e. at any point in the focal plane of the optical system considered.

[0014] Simultaneous correction of aberrations at any desired set of focal points is made possible by the complete characterization of the aberrations introduced by the optical system using a set of aberration coefficients. In particular, the position dependence of the aberrations introduced by the optical system is characterized by these aberration coefficients. This approach is based on the decomposition of imperfections of an optical system according to the Seidel expansion. The method allows to estimate aberration coefficients derived from the Seidel decomposition coefficients from the measured aberrations. For this reason, the aberration coefficients calculated in the present method are called modified Seidel coefficients.

[0015] Advantageously, the set of coefficients is sufficient to characterize the optical system and it is therefore possible, with a single calibration, to produce several different focal point networks using several masks. The calibration therefore does not need to be redone each time a new focal point network is generated. The calibration points are calibration focal points used to characterize the aberrations of the optical system.

[0016] According to certain examples, the images formed by the optical system at a plurality of calibration points arranged at several positions in the optical field are formed by phase modulation of an optical beam passing through the optical system, said phase modulation comprising a superposition of phase ramps each allowing the formation of a calibration point at one of said positions in the field of the optical system.

[0017] According to certain examples, the method according to the present description further comprises the detection of images formed by the optical system at a plurality of calibration points arranged in several positions on either side of the image focal plane of the optical system, said images being formed by phase modulation of an optical beam passing through the optical system, said phase modulation comprising a superposition of phase terms corresponding to Fresnel lenses and each allowing the formation of a calibration point at one of said positions on either side of the focal plane of the optical system.

[0018] According to certain examples, the present method therefore makes it possible to move a calibration point in three dimensions of space by modulating the phase of the optical beam and to acquire the images formed at the level of said calibration points.

[0019] According to some examples, the step of estimating the aberrations introduced by the optical system over the entire optical field (i.e. for any position in the optical field) comprises, for each calibration point at a given position in the optical field, the calculation of a wavefront deformation introduced by the optical system at the pupil of the optical system for said given position in the optical field; and the decomposition of said wavefront deformation into a sum of Zernike polynomials weighted by Zernike coefficients of different indices, said Zernike coefficients being associated with said given position in the optical field.

[0020] According to certain examples, the method further comprises: calculating, from the Zernike coefficients of the same given index obtained for calibration points corresponding to different positions in the optical field, a function of dependence of said Zernike coefficient of given index with the position in the field of the optical system.

[0021] In some examples, the dependence function of a Zernike coefficient on the position in the field of the optical system is obtained by polynomial regression from the Zernike coefficients of the same index obtained for calibration points corresponding to different positions in the optical field. The regression can, for example, be linear or quadratic.

[0022] According to certain examples, the aberrations introduced by the optical system over the entire optical field are expressed according to a decomposition comprising a sum of Zernike polynomials of different indices weighted by the dependence functions of said Zernike polynomials on the optical field previously calculated.

[0023] In some examples, the focus points correspond at least partially to different positions in the optical field relative to the calibration points.

[0024] In some examples, a new array of focus points is generated at different positions of the optical field by applying a new phase mask simultaneously compensating for aberrations introduced by the optical system at each of the positions of the new array of focus points, wherein the new phase mask is calculated from the estimation of the aberrations already performed.

[0025] In some examples, the phase mask is calculated iteratively to maximize the amplitude or intensity of light at the focus points.

[0026] In some examples, the phase mask is iteratively calculated to minimize the difference between the intensity distribution of light detected at the image focal plane of the optical system and the intensity distribution of light corresponding to the desired focus point array.

[0027] In some examples, the array of focus points is configured to generate an array of optical tweezers for trapping particles and / or atoms.

[0028] The present disclosure also relates to a holographic focus point generation system comprising: an optical source configured to emit an optical beam; a converging optical system configured to converge the optical beam into an image focal plane (of the optical system); a spatial phase modulator, arranged between the optical source and the optical system, configured to modulate the phase of the optical beam so as to generate an array of focus points at the image focal plane (of the optical system), the points of the array of focus points corresponding to several positions in the field of the optical system; a detector configured to detect the intensity of light at each focus point;a computing unit configured to simultaneously correct aberrations induced by the optical system at the focal points by means of the spatial light modulator using the method according to the present description. The optical beam emitted by the optical source has a spatial coherence (over the extent of the spatial phase modulator) and a coherence length compatible with the holographic generation of the focal points. In some examples, the optical beam has a plane wavefront. Brief description of the drawings;

[0029] Other features and advantages of the invention will emerge from the following description of embodiments of the invention, given in by way of non-limiting examples, with reference to the appended figures, in which: − [Fig 1] Figure 1 is a schematic view of a holographic generation system according to the present description; − [Fig 2] Figure 2 is a block diagram of an example of aberration correction method according to the present description; − [Fig 3] Figure 3 is a set of images illustrating advantages of the method according to the present description, based on experimental results obtained for Gaussian focal points; − [Fig 4] Figure 4 is a set of images illustrating advantages of the method according to the present description, based on experimental results obtained for bottle-type focal points. Detailed description of the invention

[0030] Figure 1 shows a holographic generation system for implementing the method according to the present description.

[0031] The holographic generation system comprises an optical source 101, a spatial light modulator (SLM) 102, a converging optical system 103, an imaging system 104 and a control unit 105. The optical source 101 emits an optical beam towards the SLM 102. The optical beam is modulated by the SLM 102 and enters the optical system 103 which converges it at the image focal plane 106 of the optical system 103.

[0032] Depending on the modulation applied by the SLM 102, the optical beam is focused according to different light distributions in the focal plane of the optical system 103. In particular, it is possible to choose a phase modulation allowing the focusing of the optical beam in one or more focusing points by means of known techniques, see for example [REF 5]. The light intensity of the optical field in the focal plane 106 of the optical system 103 is detected by the imaging system 104.

[0033] The control unit 105 acquires and processes the imaging data from the image detected by the imaging system 104. In addition, the control unit 105 controls the modulation applied by the SLM 102.

[0034] The optical source 101 may comprise different types of optical sources, for example a laser source or any other source that is spatially coherent over the extent of the SLM and has a coherence length compatible with the holographic generation of the focal points. For example, a spectral lamp (filtered or not) or a filtered incandescent lamp whose spectrum is filtered by a narrow band filter may be used.

[0035] The SLM 102 may comprise any type of spatial light modulator enabling at least the modulation of the phase of an optical beam emitted by the optical source 101. In particular, although the SLM 102 shown in FIG. 1 is used in reflection, other SLMs are suitable for implementing the method according to the present description, such as for example spatial light modulators in transmission. It is also possible to add non-modulatable diffracting elements, or micromirror modulators (DMD) performing Lohman coding to modulate the phase. In some examples, the SLM 102 is arranged at the entrance pupil of the optical system or a plane conjugate with the plane of the entrance pupil of the optical system.

[0036] The optical system 103 is generally a centered optical system. The optical system 103 may consist of a single converging lens. In other examples, the optical system 103 may be more complex and consist of multiple optical elements, such as multiple converging lenses or a set of converging and diverging lenses or any other assembly of multiple optical elements. The optical system may also include elements such as diaphragms, polarizers, mirrors, and / or semi-reflecting plates or any other optical elements conventionally used in optical assemblies.

[0037] As illustrated in Figure 1, in some examples contemplated in this disclosure, the optical system 103 may be an afocal telescope 132, 133 imaging the SLM 102 onto a lens aspherical 131, for example an aspherical lens with a centimeter or millimeter focal length.

[0038] The imaging system 104 comprises a detector 141, such as a camera, comprising an acquisition surface configured to convert the light signal of the optical beam transmitted by the optical system 103 into an electrical signal. The imaging system 104 may also comprise one or more additional optical elements 142, 143. In some examples, the detector 141 is arranged such that its object focal plane coincides with the image focal plane 106 of the optical system 103.

[0039] As illustrated in FIG. 1, the detector may comprise a magnifying optical device 143 free of aberrations between the focal plane 106 of the optical system 103 and the acquisition surface of the detector. This arrangement is particularly advantageous in the case where the images (i.e. the optical spots) generated in the image focal plane 106 of the optical system 103 comprise details smaller than the size of a pixel of the detector 141.

[0040] Figure 2 illustrates steps of an exemplary method according to the present description. The method according to the present description comprises in particular the following steps: S10 detecting images formed by the optical system at a plurality of calibration points arranged at several positions in the field of the optical system; S20 estimating the aberrations introduced by the optical system over the entire field of the optical system from the detected images; and S30 applying a phase mask in order to generate a plurality of focusing points arranged at several positions in the field of the optical system, the phase mask simultaneously compensating for the aberrations at each focusing point.

[0041] In step S10 of the present method, a plurality of calibration points are generated using several phase modulations of the optical beam passing through the optical system whose aberrations are to be estimated, for example via a known phase mask calculated for this purpose, see for example [REF 5]. As an example, the holographic generation system illustrated in Figure 1 can be used.

[0042] The measurement points are chosen so as to probe several points of the optical field, i.e. corresponding to several inclinations of the optical beam entering the optical system and several depths of field, that is to say corresponding to several shifts on either side of the focal plane of the optical system.

[0043] Advantageously, a number of measuring points between 20 and 30 is sufficient for the present method.

[0044] It is important to note that the positions of the calibration points are independent of the positions of the focus points whose generation is desired. In particular, the positions of the measurement points are not necessarily different or identical to the positions of the focus points.

[0045] According to certain examples, the positions of the calibration points may be characterized by coordinates, (^^^^^^, ^^), where ^^ is the longitudinal coordinate on the optical axis of the optical system 103, the reference of which is taken relative to the focal plane 106 of the optical system 103 for which ^ = 0, and where ^^^^^^ is the transverse position vector characterizing the position of the calibration point in the plane transverse to the optical axis located at ^ = ^^.

[0046] It is possible to focus the optical beam at the calibration points, (^^^^^^, ^^), by applying phase masks of the type F is a phase mask corresponding to a Fresnel lens converging the beam at a certain distance ^ ^ on the longitudinal axis, and where R is a phase mask corresponding to a phase ramp converging the beam at a transverse position defined by the vector ^^^^ ^ ^. The vector ^^^ is the vector characterizing the coordinates of an element on the pupil of the optical system 103. Thus, to obtain a calibration point of given position, (^^^^^^, ^^), the phase masks applied are functions which vary with the pupil coordinate, ^^^, therefore with the position in the plane of the SLM used.

[0047] In some examples, the detector acquires an image for each calibration point, (^^^^^^, ^^) in the vicinity of the image focal plane of the optical system. The imaging system remains fixed at the image focal plane of the optical system during acquisition.

[0048] In step S20 of the method, the aberrations induced by the optical system at the pupil of the optical system are calculated by the control unit from the imaging data obtained with the detector.

[0049] For a given field coordinate, all the images obtained for calibration points positioned at different depths, ^^ ^ ^^, is processed to reconstruct the wavefront deformations, ^(^^^^^^^, ^^^^)^, existing in the plane of the SLM 102 (i.e. the wavefront deformations in the pupil plane that lead to the different aberrant optical spots). This reconstruction can be carried out, for example, using the method described in [REF 4].

[0050] In particular, in some examples, the wavefront deformation at the pupil is decomposed on the basis of Zernike polynomials, ^^ ^(^^^)^^, where ^ is the index of the Zernike polynomial.

[0051] The wavefront deformation can therefore be expressed according to the following expression.

[0052] [Math 1]

[0054] Thus, for a given position calibration point, calculating the wavefront deformation amounts to finding the Zernike coefficients, ^ ^ (^^^^ ^ ^), verifying the expression [Math 1].

[0055] Zernike coefficients are understood in the sense that the optical system degrades the optical beam passing through it by producing^^(^^^^^^) radian(s) of aberration of the type characterized by the index ^ of the polynomial. Each Zernike coefficient of a given index corresponds to a type of aberration. The types of aberration are, for example, horizontal coma, vertical coma, straight astigmatism, oblique astigmatism, defocus, and so on. The relationship between the index ^ and the type of aberration depends on the convention used, for example, the Noll convention or the American Optical Society convention.

[0056] In other examples, the wavefront distortion at each calibration point is obtained by other methods, for example by means of interference, or a Shack-Hartman type wavefront analyzer.

[0057] Once the wavefront deformation in the pupil plane is obtained in terms of Zernike coefficients for all calibration points, the optical field dependence (i.e., according to the transverse position coordinate ^^) of the Zernike coefficients, ^ ^ ( ^^^^ ^ ^ ) ^, is estimated from the values ​​of the Zernike coefficients obtained for several calibration points of different coordinates in the optical field, ^^^^ ^ ^^ ^ .

[0058] More precisely, for a given index j, the set of coefficients ^^ ^ (^^^^ ^ ^)^^ corresponding to several positions, ^^^^ ^ ^, in the field of the optical system is fitted by a polynomial function defined according to the following expression.

[0059] [Math

[0060] ^^^^ ^^^

[0061] The variation of each coefficient, ^ ^ (^^^^ ^^), with the position in the field of the optical system is therefore adjusted by determining the parameters, ^ ^ And ^ ^ ^^ ^ ^^ . The parameter, ^ ^ , is a weighting coefficient of the polynomial function, ^^(^^), in the decomposition. The parameter,^ ^^^^^^, is a centering parameter of the polynomial function, ^^(^^). The centering parameter can for example be equal to 0 in the case of a centered optical system, and different from 0 in the case of an optical system that is not strictly centered.

[0062] The functions ^^ ^(^^)^ are polynomial functions having as argument the coordinate vector in the image focal plane 106 of the optical system 103. According to some examples, the polynomial functions,^^^(^^)^, are functions of two variables, x and y, in which x and y are the Cartesian coordinates corresponding to the vector, ^^ , in the image focal plane 106 of the optical system 103.

[0063] In particular, the ^^ functions ^ ( ^^ ) ^^can be expressed as follows.

[0064] [Math 3]

[0066] The inventors observed that it is sufficient to limit oneself to a decomposition going up to an index lower than five (j≤5), that is to say comprising five Zernike coefficients adjusted with five functions adjustment polynomials, so that the method produces satisfactory results.

[0067] Once the adjustment is made, it is possible to re-express the aberrations as a wavefront deformation depending on both the position in the field of the optical system, ^^, and the coordinates in the pupil of the optical system, ^^^, as in the following expression.

[0068] [Math 4]

[0070] The general idea of ​​the present method is to use the characterization of the aberrations of an optical system in the form of a Seidel decomposition from the wavefront deformations obtained for several calibration points in the optical field (see for example [REF 6]).

[0071] According to the Seidel decomposition, the wavefront deformation produced at any point ^^(-, .) of the image focal plane 106 of the optical system 103 by a pupil element of coordinate ^^^^( / , 0) can be written in the form of a Seidel expansion as defined in the following expression.

[0072] [Math 5]

[0074] In the expression [Math 5], the coefficients T, C, K are Seidel coefficients generally named coma, astigmatism, and field curvature, respectively. These coefficients are therefore associated with types of aberrations introduced by the optical system.

[0075] To avoid confusion, it should be noted that, although some Seidel coefficients have the same name as some Zernike coefficients, the information they convey is different. Zernike coefficients characterize any wavefront, while Seidel coefficients characterize a centered optical system by providing information on the amount of aberration produced when moving away from the optical axis (i.e., in particular, information on the field dependence of aberrations). The amount of aberrations indicated by the Seidel expansion is commonly expressed in radians per meter or radians per square meter. The Seidel expansion emphasizes in particular the simple (polynomial) dependence of aberrations on the pupillary radial coordinate, r.

[0076] With the method according to the present description, the adjustments defined in [Math 2] make it possible to reveal the Zernike polynomials, ^^(^^^)^, depending on the pupil coordinates ^^^^( / , 0) in a decomposition close to the Seidel decomposition.

[0077] The adjustment coefficients, ^ ^ , are therefore related to Seidel coefficients. Thus, in this description, the coefficients,^^ ^, are called modified Seidel coefficients.

[0078] In particular, with the method according to the present description, once the modified Seidel coefficients are obtained, the aberrations introduced by the optical system are completely characterized, including the aberrations dependent on the optical field. Thus, it is possible to take these aberrations into account to generate a focusing point network which is not degraded by these aberrations. In addition, it is not necessary for the positions of these focusing points in the optical field to coincide with the positions of the calibration points.

[0079] In step S30 of the present method, a phase mask is applied to the optical beam so as to generate a network of focusing points which is not degraded by the aberrations which would normally be introduced at these points by the optical system. This is made possible by taking into account, in the expression of the phase mask, the aberrations of the optical system thanks to the characterization of the aberrations previously carried out.

[0080] To calculate the phase modulation required for holographic generation of the dot array, an augmented version of the Gerchberg-Saxton iterative algorithm is used, as described for example in [REF 5]. With the basic iterative algorithm, a phase mask is calculated to generate a network of focusing bridges whose intensities are homogeneous, however the aberrations of the optical system are not taken into account.

[0081] Thus, with the algorithm according to the present description, a phase mask 9 is calculated ( ^^^ ) equal to a sum of plane waves weighted by amplitudes, : ; ^, and phases, . ; ^, so that after passing after the optical system, at each coordinate point, in the focal plane image of the optical system, the light amplitude 6 ; forms a desired focal point (or more generally a desired intensity distribution) while freeing itself from the aberrations induced by the optical system at this point.

[0082] The phase mask calculation algorithm used in the method according to the present description can be expressed with the following expressions.

[0083] [Math 6]

[0085] [Math 7]

[0086] ^9(^^^) = arg^∑; :; exp <J^.<^^^^;^, ^^^= + J.;= ^

[0087] [Math 8]

[0088] 6; = KL^^^ expMJ^9(^^^) − J^.<^^^^;^, ^^^=N

[0089] In the expressions [Math 6], [Math 7] and [Math 8], O is the wavelength of the light emitted by the optical source (e.g. the average or maximum wavelength of the optical spectrum of the light emitted by the optical source), and P is the focal length of the optical system crossed by the optical beam. In the case of the example illustrated in Figure 1, given that the telescope preceding the aspherical lens has a magnification equal to 1, P is the focal length of the aspherical lens.

[0090] With the present method, a special phase term showing the Zernike polynomials and the modified Seidel coefficients is therefore introduced into the phase mask for each plane wave. This phase term can be defined according to the following expression.

[0091] [Math 9] ^

[0093] The addition of the above term makes it possible to simultaneously compensate for aberrations introduced by the optical system at all desired focusing points.

[0094] The iteration is performed in the same way as with the algorithm described in [REF 5]. Thus, the weighting coefficients are modified over the iterations by improving the intensity distribution. In particular, according to some examples, the amplitude weighting coefficients are initialized to :; = 1 and the phase weighting coefficients are randomly initialized such that, .; ∈ [0, 2T[. Moreover, at each iteration, the weighting coefficients are updated according to the following expression.

[0095] [Math 10]

[0097] In the expression [Math 10], W ; is the target value for the site amplitude p. In some examples, all W ; are worth 1 but this is optional. In addition, is an average value of the intensity distribution at the focal point of index p.

[0098] In some examples, these successive iterations may optionally include a display of the phase mask on the SLM and a measurement of the power of each spot with the camera (see for example [REF 5]).

[0099] In some examples, successive iterations may include updating the target optical power values ​​at each focus point as described in [REF 7].

[0100] The inventors have validated the contribution of the present method by obtaining experimental results illustrated in Figures 3 and 4. The aforementioned results are obtained in the context of an application to the correction of the aberrations of the field of an aspherical lens with a focal length PZ = 16.3 mm and a numerical aperture NA = 0.35. In this application, a holographic generation system as shown in Figure 1 is used to generate a two-dimensional network of 10 x 10 Gaussian focal points at the image focal plane of the optical system distributed over a field of 500 micrometers by 500 micrometers in the focal plane of the optical system (this corresponds to the results presented in Figure 3).

[0101] The inventors have also validated the method according to the present description for the generation of a two-dimensional array of 20 x 20 bottle-like focus points (this corresponds to the experimental results illustrated in Figure 4). For the generation of bottle-like focus points, a second phase mask is applied in addition to the iteratively obtained phase mask, as described in [REF 5].

[0102] In the aforementioned holographic generation system, the optical system used to converge the optical beam to the image focal plane comprises the aforementioned aspherical lens and an afocal telescope containing two converging lenses each having a focal length of P \ =500 mm. The two lenses are arranged so as to be in a 2f-2f configuration, that is to say that they are in particular spaced 4 times their focal length P \ .

[0103] Tests (not shown in the figures) were also carried out for an optical system including a lens with numerical aperture NA=0.48.

[0104] In the above examples, the optical source is a Toptica brand "DLC pro" laser with a wavelength of 821 nm and a nominal power of 2.5 W injected into a polarization-maintaining single-mode fiber. When taking images, a very small part of the total available optical power is used.

[0105] In the above examples, the SLM is a Hamamatsu LCOS-SLM X15213-02 model. The SLM's element matrix size is 1272x1024 elements and the dynamic range is 8 bits.

[0106] The afocal telescope images the SLM plane onto the aspherical lens. In addition, the focal plane of the aspherical lens is imaged onto the camera using a microscope objective with a numerical aperture of NA=0.5 followed by a projection lens with a focal length of f=300 mm.

[0107] Figure 3 shows images of the focus points generated at the focal plane of the optical system and conjugated on the camera by means of the entire microscope objective and the projection lens. The intensity profiles of the images are represented in logarithmic scale. On the one hand, Figure 3 shows the reference images 300 which are obtained by considering only the method as described in [REF 5], these reference images 300 include the total image 301 of the Gaussian focus point array and an enlarged portion 302 of the image showing corresponding to a field far from the optical axis. On the other hand, Figure 3 shows the enhanced images 310 obtained with the method and system according to the present description. These enhanced images 310 include the total image 311 of the focus point array and an enlarged portion 312 of the image corresponding to a field far from the optical axis.

[0108] To obtain the improved images 310, the method according to the present description is used, that is to say that the aberrations produced by the optical system are characterized for several calibration points, then that this information is used to modify the phase masks of the SLM in order to correct the aberrations.

[0109] The reference images 300 show that, in the case of the state-of-the-art method, as soon as we consider focal points moving away from the center of the image (i.e. moving away from the optical axis of the optical system by exploring the field of the optical system) the focal points (optical spots) become deformed under the increasing influence of the aberrations introduced by the optical system.

[0110] The improved images 310, which are obtained with the method according to the present description, show that the focal points are not distorted regardless of their deviation from the center of the image, that is to say regardless of the exploration of the optical field that they represent. In particular, the inventors observed that with the method according to the present description, the focal points have a minimal diameter limited by diffraction over the entire observed field. This observed field was calculated with the Oslo software and has a vertical and horizontal extension of 50 micrometers. The experimental results show that with the present method, it is even possible to correct aberrations for transverse positions up to more than 500 micrometers.

[0111] The results illustrated in Figure 3 therefore show that the method according to the present description makes it possible to overcome the aberrations induced by the optical system during the holographic generation of a network of focusing points, in particular concerning Gaussian focusing points generated in an optical field of at least 500 micrometers.

[0112] Figure 4 shows experimental images of the bottle-like focusing points generated at the focal plane of the optical system and conjugated on the camera by means of the entire microscope objective and projection lens. On the one hand, Figure 4 shows the reference experimental images 400 which are obtained by considering only the method as described in [REF 5]. On the other hand, Figure 4 shows the improved experimental images 410 obtained with the method according to the present description.

[0113] The reference experimental images 400 comprise the total image 401 of the bottle-type focus point array and two enlarged portions 402, 403 of the image 401 corresponding respectively to a field far from the optical axis (enlarged portion 402), and to a field close to the optical axis (enlarged portion 403).

[0114] The enhanced experimental images 410 comprise the total image 411 of the bottle-type focus point array and two enlarged portions 412, 413 of the image 411 corresponding respectively to a field far from the optical axis (enlarged portion 412), and to a field near the optical axis (enlarged portion 413).

[0115] The experimental results in Figure 4 show that when generating bottle-like focus points, even focus points close to the center of the optical axis are distorted when only the state-of-the-art method is applied. On the contrary, when applying the method according to the present description, the points are not distorted regardless of the optical field considered, including for focus points far from the optical axis.

[0116] The experimental results illustrated in Figure 4 therefore show that the method according to the present description makes it possible to overcome the aberrations induced by the optical system during the holographic generation of a network of focusing points, in particular concerning bottle-type focusing points generated in an optical field of at least 500 micrometers. It is noted in particular that it would be impossible to generate bottle-type focusing points which are homogeneous throughout the optical field without using the method according to the present description.

[0117] Although the present disclosure has been described with reference to a specific exemplary embodiment, it is obvious that various modifications and changes may be made to these examples without departing from the general scope of the invention as defined by the claims. Furthermore, individual features of the various embodiments recited may be combined in additional embodiments. Therefore, the description and drawings should be considered in an illustrative rather than restrictive sense.

Claims

CLAIMS 1. A method for holographic generation of a network of focusing points arranged in several positions in the field of an optical system comprising: - (S10) detecting images formed by the optical system at a plurality of calibration points arranged in several positions in the field of the optical system; - (S20) estimating aberrations introduced by the optical system over the entire field of the optical system from the detected images; - (S30) applying a phase mask to an optical beam entering the optical system, in order to generate a plurality of focusing points arranged in several positions in the field of the optical system; wherein the phase mask is calculated, from the estimated aberrations, in order to simultaneously compensate for the aberrations at each focusing point. 2.Method according to claim 1, in which the images formed by the optical system at a plurality of calibration points arranged at several positions in the optical field are formed by phase modulation of an optical beam passing through the optical system, said phase modulation comprising a superposition of phase ramps each allowing the formation of a calibration point at one of said positions in the field of the optical system. 3.Method according to claim 1 or 2, further comprising the detection of images formed by the optical system at a plurality of calibration points arranged in several positions on either side of the image focal plane of the optical system, said images being formed by phase modulation of an optical beam passing through the optical system, said phase modulation comprising a superposition of phase terms corresponding to Fresnel lenses and each allowing the formation of a calibration point at one of said positions on either side of the focal plane of the optical system.

4. Method according to any one of the preceding claims, in which the step (S20) of estimating the aberrations introduced by the optical system over the entire optical field comprises, for each calibration point at a given position in the optical field: - calculating a wavefront deformation introduced by the optical system at the pupil of the optical system for said given position in the optical field; - decomposing said wavefront deformation into a sum of Zernike polynomials weighted by Zernike coefficients of different indices, said Zernike coefficients being associated with said given position in the optical field. 5.Method according to claim 4, further comprising: - calculating, from the Zernike coefficients of the same given index obtained for calibration points corresponding to different positions in the optical field, a function of dependence of a Zernike coefficient of given index with the position in the field of the optical system.

6. Method according to claim 5, in which the function of dependence of a Zernike coefficient of given index with the position in the field of the optical system is obtained by polynomial regression from the Zernike coefficients of the same index obtained for calibration points corresponding to different positions in the optical field. 7.Method according to any one of claims 5 to 6, in which the aberrations introduced by the optical system over the entire optical field are expressed according to a decomposition comprising a sum of Zernike polynomials of different indices weighted by the dependence functions of said Zernike polynomials on the optical field previously calculated.

8. Method according to any one of claims 1 to 6, in which the focal points correspond at least partially to. different positions in the optical field relative to the calibration points.

9. Method according to any one of claims 1 to 8, in which a new array of focusing points is generated at different positions in the optical field by applying a new phase mask simultaneously compensating for the aberrations introduced by the optical system at each of the positions of the new array of focusing points, wherein the new phase mask is calculated from the estimation of the aberrations already carried out.

10. Method according to any one of claims 1 to 9, wherein the phase mask is calculated iteratively so as to maximize the intensity of the light detected at the focusing points. 11.A method according to any one of claims 1 to 10, the phase mask is calculated iteratively so as to minimize the difference between the intensity distribution of the light detected at the image focal plane of the optical system and the intensity distribution of the light corresponding to the desired array of focal points.

12. A method according to any one of claims 1 to 11, wherein the array of focal points is configured to generate an array of optical tweezers for trapping particles and / or atoms. 13.Holographic focal point generation system comprising: - an optical source (101) configured to emit an optical beam; - a converging optical system (103) configured to converge the optical beam into an image focal plane (106); - a spatial phase modulator (102), arranged between the optical source (101) and the optical system (103), configured to modulate the phase of the optical beam so as to generate a network of focal points at the image focal plane (106), the points of the network of focal points corresponding to several positions in the field of the system. optical; - a detector (104) configured to detect the intensity of the light at each focal point; - a computing unit (105) configured to simultaneously correct the aberrations induced by the optical system (103) at the focal points by means of the spatial light modulator (102) using the method according to any one of claims 1 to 12.

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