Method for holographic generation of a network of focal points

Abstract

The invention relates to a method for holographic generation of a network of focal points arranged in several positions of the field of an optical system comprising (S10) the detection of images formed by the optical system at a plurality of calibration points arranged in several positions of the field of the optical system; (S20) the estimation of the aberrations introduced by the optical system on the optical field from the detected images; (S30) the application of a phase mask to the optical beam, in order to generate a plurality of focal 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 the aberrations at each focal point. The invention also relates to a holographic generation system implementing said method. Figure for abstract: Fig. 2

Description

Title of the invention: Method for holographic generation of a network of focal points 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 which 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 with respect 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 of optical systems on the quality of the 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 the optical systems at a point in the optical field depend on the position of this point in said field. Thus, the existing methods 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 solving the problems of the state of the art. References

[0008] [REF 1] US 2008 / 0316575 Al [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, p. 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. Subject matter and summary of the invention

[0009] The present description aims to remedy at least in part the drawbacks of the state of the art.

[0010] For this purpose, 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 the aberrations at each focusing point.

[0011] In the present description, a focusing point should be understood as being a convergence zone of an optical beam with a desired light distribution. The shape and extent of the focusing 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 focusing point is an optical spot having a Gaussian light distribution. In certain examples, the optical beam is an optical bottle beam, in which case the focusing 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.

[0012] For example, Gaussian or bottle type focal points are particularly particularly suitable for the generation of optical tweezers to trap particles and / or atoms.

[0013] It is understood that by focusing point array is meant an arrangement of several focusing points arranged in two spatial dimensions or in three spatial dimensions. Such arrangements can also be referred to as focusing point matrices or focusing point arrays (from the English term "optical spot array").

[0014] 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.

[0015] The 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 in the field of the aberrations introduced by the optical system is characterized by these aberration coefficients. This approach is based on the decomposition of the imperfections of an optical system according to the Seidel expansion. The method makes it possible 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.

[0016] 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 networks of focusing points using several masks. The calibration therefore does not need to be redone each time a new network of focusing points is generated. The calibration points are calibration focusing points used to characterize the aberrations of the optical system.

[0017] 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.

[0018] 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 a beam optical system 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.

[0019] 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.

[0020] According to certain 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.

[0021] 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.

[0022] According to certain examples, the dependence function of a Zemike coefficient with the position in the field of the optical system is obtained by polynomial regression from the Zemike 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.

[0023] 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.

[0024] According to certain examples, the focusing points correspond at least partially to different positions in the optical field relative to the calibration points.

[0025] According to some examples, a new array of focal 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 focal points, wherein the new phase mask is calculated from the estimation of the aberrations already performed.

[0026] In some examples, the phase mask is calculated iteratively so as to maximize the amplitude or intensity of the light at the focus points.

[0027] According to some examples, 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.

[0028] According to some examples, the array of focal points is configured to generate an array of optical tweezers for trapping particles and / or atoms.

[0029] The present disclosure also relates to a holographic focal 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 focal points at the image focal plane (of the optical system), the points of the array of focal points corresponding to several positions in the field of the optical system; a detector configured to detect the intensity of the light at each focal 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.;

[0030] 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 focusing points. According to certain examples, the optical beam has a plane wavefront. Brief description of the drawings

[0031] Other characteristics and advantages of the invention will emerge from the following description of embodiments of the invention, given as non-limiting examples, with reference to the appended figures, in which: • [Fig.l] [Fig.l] is a schematic view of a holographic generation system according to the present description; • [Fig.2] [Fig.2] is a block diagram of an example of a process of correction of aberrations according to this description; • [Fig.3] [Fig.3] is a set of images illustrating the advantages of the method according to the present description, based on experimental results obtained for Gaussian focal points; • [Fig.4] [Fig.4] is a set of images illustrating the advantages of the method according to the present description, based on experimental results obtained for bottle-type focusing points. Detailed description of the invention

[0032] [Fig.l] represents a holographic generation system for implementing the method according to the present description.

[0033] 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.

[0034] 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.

[0035] 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.

[0036] The optical source 101 may comprise different types of optical sources, for example a laser source or any other source spatially coherent over the extent of the SLM and of coherence length compatible with the holographic generation of the focusing 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.

[0037] 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.l] 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.

[0038] 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 several optical elements, such as several converging lenses or a set of converging and diverging lenses or any other assembly of several optical elements. The optical system may also include elements such as diaphragms, polarizers, mirrors, and / or semi-reflecting plates or any other optical element conventionally used in optical assemblies.

[0039] As illustrated in [Fig.l], in certain examples envisaged in the present description, the optical system 103 may be an afocal telescope 132, 133 imaging the SLM 102 onto an aspherical lens 131, for example an aspherical lens with a centimeter or millimeter focal length.

[0040] 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.

[0041] As illustrated in [Fig.l], 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.

[0042] [Fig.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 the detection of images formed by the optical system at a plurality of calibration points arranged according to several positions in the field of the optical system; S20 the estimation of the aberrations introduced by the optical system over the entire field of the optical system from the detected images; and S30 the application of a phase mask in order to generate a plurality of focusing points arranged according to several positions in the field of the optical system, the phase mask simultaneously compensating for the aberrations at each focusing point.

[0043] In step S10 of the present method, a plurality of calibration points is generated using several phase modulations of the optical beam passing through the optical system whose aberrations are to be estimated, for example via a mask known phase calculated for this purpose, see for example [REF 5]. As an example, the holographic generation system illustrated in [Fig.l] can be used.

[0044] 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, i.e. corresponding to several offsets on either side of the focal plane of the optical system.

[0045] Advantageously, a number of measurement points between 20 and 30 is sufficient for the present method.

[0046] 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.

[0047] According to certain examples, the positions of the calibration points can 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 < = O, and where x^ is the transverse position vector characterizing the position of the calibration point in the plane transverse to the optical axis located at ~ A.

[0048] It is possible to focus the optical beam at the calibration points, (xJ, z^), by applying phase masks of the type u) + F^, u) where 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 x^. The vector u 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, (xJ, z,), the phase masks applied are functions which vary with the pupil coordinate, ", therefore with the position in the plane of the SLM used.

[0049] According to some examples, the detector acquires an image for each calibration point, zj) 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.

[0050] 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.

[0051] For a given field coordinate, x^, the set of images obtained for calibration points positioned at different depths, , is processed for reconstruct wavefront deformations, <p(xk , U ) , existantes dans le plan du SLM 102 (c’est-à-dire les déformations du front d’onde dans le plan pupille qui amènent aux différentes taches optiques aberrantes). Cette reconstruction peut être effectuée, par exemple, à l’aide de la méthode décrite dans [REF 4].

[0052] In particular, in some examples, the wavefront deformation at the pupil is decomposed on the basis of the Zernike polynomials, {Z7(u)} , where j is the index of the Zernike polynomial.

[0053] The wavefront deformation can therefore be expressed according to the following expression.

[0054] [Math.l] u ) Zj(u)

[0055] Thus, for a calibration point of given position, the calculation of the wavefront deformation amounts to finding the Zernike coefficients, , verifying the expression [Math 1].

[0056] Zernike coefficients are understood in the sense that the optical system degrades the optical beam passing through it by producing bj(x^) radian(s) of aberration of the type characterized by the index j of the polynomial. Each Zernike coefficient of 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 j and the type of aberration depends on the convention used, for example, the Noll convention or the American Optical Society convention.

[0057] In other examples, the wavefront deformation at each calibration point is obtained by other methods, for example by means of interference, or a Shack-Hartman type wavefront analyzer.

[0058] 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 x) of the Zernike coefficients, bj(x^.), is estimated from the values ​​of the Zernike coefficients obtained for several calibration points of different coordinates in the optical field, -— xk'

[0059] More precisely, for a given index j, the set of coefficients {bj(17)} corresponding to several positions, in the field of the optical system is adjusted by a polynomial function defined according to the following expression.

[0060] [Math.2]

[0061] The variation of each coefficient, bj(x^ ), with the position in the field of the optical system is therefore adjusted by determining the parameters, cJ and Jy. The parameter, CJ, is a weighting coefficient of the polynomial function, Pj{x), in the decomposition. The parameter, Ço, is a centering parameter of the polynomial function, Pj(x). 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 {Py(x)} are polynomial functions having as argument the coordinate vector in the image focal plane 106 of the optical system 103. According to certain examples, the polynomial functions, |Py(x)}, 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 {P^(x) ) can be expressed as follows.

[0064] [Math.3] ' P^X,y)=X P2(^y) -y P3(x, y) = x2-y2 P^x,y)=2xy .P5(x,y) = x2 + y2

[0065] The inventors have 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 adjustment polynomial functions, for the method to produce satisfactory results.

[0066] Once the adjustment is made, it is possible to re-express the aberrations as a wavefront deformation depending both on the position in the field of the optical system, L and on the coordinates in the pupil of the optical system, u, as in the following expression.

[0067] [Math.4] (p(x, U ) -^jCjPj^XX^Zj(u)

[0068] 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]).

[0069] According to the Seidel decomposition, the wavefront deformation produced at any point x(r, a) of the image focal plane 106 of the optical system 103 by a pupil element of coordinate u(p, 0) can be written in the form of a deve- Seidel development as defined in the following expression.

[0070] [Math.5] q>(x, u) = T rp cos(^-a) + C rp^cos^da} - A r2p\x>&(9-a) ~^r2p2+ ...

[0071] In the expression [Math 5], the coefficients T, C, K are Seidel coefficients generally called coma, astigmatism, and field curvature, respectively. These coefficients are therefore associated with types of aberrations introduced by the optical system.

[0072] To avoid confusion, it should be noted that, although some Seidel coefficients have the same name as some Zemike coefficients, the information they convey is different. Zemike 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 the 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 the aberrations on the pupillary radial coordinate, r.

[0073] With the method according to the present description, the adjustments defined in [Math 2] make it possible to reveal the Zemike polynomials, Zy(m), depending on the pupil coordinates u(p, 3) in a decomposition close to the Seidel decomposition.

[0074] The adjustment coefficients, cî , are therefore linked to Seidel coefficients. Thus, in the present description, the coefficients, ci , are called modified Seidel coefficients.

[0075] 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.

[0076] 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.

[0077] To calculate the phase modulation necessary for the holographic generation of the point set, 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.

[0078] Thus, with the algorithm according to the present description, a phase mask w) is calculated equal to a sum of plane waves weighted by amplitudes, wp, and phases, aP, so that after passing after the optical system, at each point of coordinates, , in the image focal plane of the optical system, the light amplitude Ap 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.

[0079] The phase mask calculation algorithm used in the method according to the present description can be expressed with the following expressions.

[0080] [Math.6] u) -^-CjPj^-x^ZjÇu)

[0081] [Math.7] V? ( u ) = arg {( i « ( » ) +iap )}

[0082] [Math. 8] A p = Jc / wexp (i (u) - ia (xJ, u)]

[0083] In the expressions [Math 6], [Math 7] and [Math 8], 2 is the wavelength of the light emitted by the optical source (for example the average or maximum wavelength of the optical spectrum of the light emitted by the optical source), and / 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, / is the focal length of the aspherical lens.

[0084] With the present method, a particular 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.

[0085] [Math.9]

[0086] The addition of the aforementioned term makes it possible to simultaneously compensate for the aberrations introduced by the optical system at all desired focusing points.

[0087] The iteration is carried out 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, in some examples, the amplitude weighting coefficients are initialized to wp — 1 and the phase weighting coefficients are randomly initialized such that, ap G [0, 2æ[- Moreover, at each iteration, the weighting coefficients are updated according to the following expression.

[0088] [Math. 10] =

[0089] In the expression [Math 10], tp is the target value for the amplitude of site p. In some examples, all tp are 1 but this is optional. In addition, ( [ ) is a mean value of the intensity distribution at the focal point of index p.

[0090] According to certain 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]).

[0091] According to certain examples, the successive iterations may comprise an update of the target values ​​of the optical power at each focusing point as described in [REF 7].

[0092] 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 of focal length / 4=16.3mm and numerical aperture NA=0.35. In this application, a holographic generation system as shown in [Fig.l] 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 [Fig.3]).

[0093] 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 [Fig.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].

[0094] 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 / ^=500 mm. The two lenses are arranged in so as to be in a 2f-2f configuration, that is to say that they are in particular spaced 4 times their focal length fL.

[0095] Tests (not shown in the figures) were also carried out for an optical system comprising a lens with a numerical aperture NA=0.48.

[0096] In the above-mentioned examples, the optical source is a “DLC pro” laser from the Toptica brand 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 portion of the total available optical power is used.

[0097] In the above examples, the SLM is a Hamamatsu brand LCOS-SLM XI5213-02 model. The size of the SLM element matrix is ​​1272x1024 elements and the dynamic range is 8 bits.

[0098] 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.

[0099] [Fig.3] represents images of the focal 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, [Fig.3] presents the reference images 300 which are obtained by considering only the method as described in [REF 5], these reference images 300 comprise the total image 301 of the Gaussian focal point array and an enlarged portion 302 of the image showing corresponding to a field far from the optical axis. On the other hand, [Fig.3] presents 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.

[0100] 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.

[0101] The reference images 300 show that, in the case of the state-of-the-art method, as soon as focal points are considered 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.

[0102] The improved images 310, which are obtained with the method according to the present description, show that the focal points are not distorted whatever their deviation from the center of the image, that is, regardless of the exploration of the optical field they represent. In particular, the inventors observed that with the method according to the present description, the focal points have a minimum 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.

[0103] The results illustrated in [Fig.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.

[0104] [Fig.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, [Fig.4] shows the reference experimental images 400 which are obtained by considering only the method as described in [REF 5]. On the other hand, [Fig.4] shows the improved experimental images 410 obtained with the method according to the present description.

[0105] 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).

[0106] 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 close to the optical axis (enlarged portion 413).

[0107] The experimental results of [Fig.4] show that when generating bottle-type 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.

[0108] The experimental results illustrated in [Fig.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. In particular, it is noted 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.

[0109] 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 holographically generating a network of focusing points arranged at several positions in the field of an optical system comprising: - (S 10) 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 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 at 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. A method according to claim 1 or 2, further comprising detecting images formed by the optical system at a plurality of calibration points arranged at 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 position in the given optical field: - the calculation of a wavefront deformation introduced by the system optics at the pupil level of the optical system for said position in the given optical field; - the decomposition of said wavefront deformation into a sum of Zemike polynomials weighted by Zemike coefficients of different indices, said Zemike coefficients being associated with said position in the given 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 dependence function 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. A method according to any one of claims 1 to 6, wherein the focusing 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 of 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, in which the new phase mask is calculated from the estimation of the aberrations already carried out.

10. A 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 detected light at the focus 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 focusing points is configured to generate an array of optical tweezers for trapping particles and / or atoms.

13. A 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 an array of focal points at the image focal plane (106), the points of the array of focal points corresponding to several positions in the field of the optical system; - 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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