Method for representing the dispersion of focal points of a lens
Patent Information
- Application Number
- PCT/FR2025/050210
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- Filing Date
- 2025-03-18
- Publication Date
- 2026-09-24
Smart Images
Figure FR2025050210_24092026_PF_FP_ABST
Abstract
Description
[0001] DESCRIPTION
[0002] TITLE: Method for representing the dispersion of focal points of a lens
[0003] technical field
[0004] The present invention relates to a method of representing the dispersion of focal points of a lens and / or a method of defining a function describing an optical response at the output of a lens.
[0005] The field of the invention is more particularly, but not exclusively, that of optical lenses, especially for the correction of images obtained by such a lens.
[0006] Prior art
[0007] The point spreading function (PSF) of an optical lens depends on a large number of parameters, for example:
[0008] The position within the image field, i.e., 2 parameters,
[0009] The distance between the lens and the sensor (Doc)
[0010] The distance to the point on the scene
[0011] The wavelength
[0012] So, at this stage, there are 5 parameters.
[0013] But it also depends, for each Doc distance (Objective Sensor Distance), on a field of 2 intensity values, over a more or less wide neighborhood, in two dimensions, around the ideal focal point.
[0014] Therefore, we have a total of no fewer than 7 parameters. A calculation with a certain discretization of each parameter can, for example, lead to considering no less than 7 Terabytes (7.10 12 ), which is gigantic, and even close to what can reasonably be recorded in onboard memory. Furthermore, acquiring this enormous data field could take an equally enormous and impractical amount of time.
[0015] This makes using PSF data to correct image acquisition defects difficult to consider, especially over a very wide PSF range, for example when the Doc distance is far from the beam convergence Doc distance (because the resulting optical spot is large and consumes even more data).
[0016] - The invention aims to overcome limitations compared to the state of the art, in particular by enabling the representation of the dispersion of focal points of a lens and / or defining a function describing an optical response at the output of a lens, preferably but not limited to:
[0017] - drastically limiting the size of the data to be recorded to represent the PSF, while still being able to obtain it in a very wide area, and / or
[0018] - limiting the number of experiments to be conducted and their duration to physically acquire this very broad PSF on a target, and / or
[0019] - limiting the number of simulations to be carried out to obtain this PSF, which otherwise could also lead to large and very long calculations, making it unrealistic to do so.
[0020] Description of the invention
[0021] A first aspect of the invention relates to a method for representing the dispersion of focal points of a lens comprising an input and an output, implemented by technical means, and comprising:
[0022] - Obtaining or defining at least one function describing the optical response at the lens output as a function of the light input parameters at the lens input,
[0023] - For several propagated beams of light whose direction, curvature and / or phase vary on an input surface at the lens input, a decomposition of the input surface into several non-zero finite area input cells, each input cell corresponding to the shape, on the input surface, of one of the propagated beams,
[0024] - For each input cell, a calculation of at least one parameter of an output cell on an output surface at the output of the lens corresponding to the passage of one of the beams emitted through the lens from that input cell to the output surface, each output cell corresponding to the shape, on the output surface, of this propagated beam, the at least one parameter of the output cell including the position of that output cell on the output surface, said calculation being based on the at least one function describing the optical response at the output of the lens as a function of input light parameters at the lens input,
[0025] - For each propagated beam, a determination of: o a modification of the curvature and / or phase and / or direction of the propagated beam at the level of the output cell corresponding to this propagated beam relative to the input cell of this propagated beam, this modification being induced by the lens between the input surface and the output surface, and / or o a curvature and / or phase and / or direction of the propagated beam at the level of the output cell corresponding to this propagated beam,
[0026] said determination being based on at least one function describing the optical response at the output of the lens as a function of input light parameters at the lens input,
[0027] - for at least one position of an imaging surface of a sensor located on the output side of the lens, a summation, on the imaging surface, of the beams from the output cells.
[0028] The method according to the first aspect of the invention may include determining a decomposition step in the input cells as a function of a choice of decomposition step in the output cells or determining a decomposition step in the output cells as a function of a choice of decomposition step in the input cells.
[0029] The input cells may be disjoint and / or partially overlap.
[0030] The method according to the first aspect of the invention may include, for each propagated beam, the determination of the modification of the curvature and / or phase and / or direction of the propagated beam at the level of the output cell corresponding to this propagated beam with respect to the input cell of this propagated beam, this modification being induced by the lens between the input surface and the output surface, said determination being based on at least one function describing the optical response at the output of the lens as a function of input light parameters at the input of the lens.
[0031] The method according to the first aspect of the invention may include, for each propagated beam, determining the curvature and / or phase and / or direction of the propagated beam at the output cell corresponding to that propagated beam, said determination being based on at least one function describing the optical response at the output of the lens as a function of the light input parameters at the lens input. The method according to the first aspect of the invention may include determining the position of a mean point on the imaging surface of the sensor for each propagated beam and / or input cell.
[0032] The summation, on the imaging surface, of the beams from the output cells may include a summation, on the imaging surface, of the complex amplitudes corresponding to the amplitudes and phases of all the propagated beams.
[0033] The function describing the optical response at the lens output as a function of the input light parameters at the lens input can be obtained or defined:
[0034] based on a known lens design. The function describing the optical response at the lens output as a function of the light input parameters at the lens input can be further optimized by taking into account deviations between lens realization parameters and the known lens design.
[0035] - according to the fifth aspect of the invention set forth below.
[0036] A second aspect of the invention relates to a data processing device comprising means and / or a processor adapted and / or configured to implement the steps of the process according to the first aspect of the invention.
[0037] A third aspect of the invention relates to a computer program comprising instructions which, when executed by a computer, lead the computer to carry out the steps of the process according to the first aspect of the invention.
[0038] A fourth aspect of the invention relates to a computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to perform the steps of the process according to the first aspect of the invention.
[0039] A fifth aspect of the invention relates to a method for defining a function describing an optical response at the output of a lens as a function of light input parameters at the lens input, characterized in that it comprises: - the lens is placed between a light source and an image sensor - technical processing means control a calibration sequence:
[0040] o by emitting, from the light source, different distinct beams of light which pass through the lens to the sensor so that when the light beams reach an input surface at the lens, each beam is distributed on the input surface in the form of a calibration cell distinct from the calibration cells of the other emitted beams, then
[0041] o by imaging these beams emitted onto the sensor,
[0042] the calibration sequence being repeated by varying all or part of the following parameters of the emitted beams: collimation or focusing of the emitted beams on the input surface, angle of incidence of the emitted beams on the input surface, position of incidence of the emitted beams on the input surface, wavelength of the emitted beams, number and / or position(s) of the calibration cell(s), distance between the lens and the sensor,
[0043] - the processing means process the images obtained by the sensor during the calibration sequence in order to construct the function describing the optical response at the output of the lens as a function of the input light parameters at the lens input.
[0044] The light source may include a projector and an opaque mask with at least one passage hole, so that at any given time, each passage hole corresponds to an emitted beam.
[0045] The opaque mask can be fitted with several passage holes, so that at any given moment, each passage hole corresponds to one of the emitted beams.
[0046] The calibration sequence may include a mask displacement controlled by the processing means so as to create new emitted beams.
[0047] The processing of images obtained by the sensor may include associating data obtained from the sensor with:
[0048] - one of the emitted beams, and
[0049] - the parameters of this emitted beam. During the calibration sequence, the objective can be illuminated simultaneously by several emitted beams in such a way as to:
[0050] - create an interference pattern on the sensor and,
[0051] - during the processing of images obtained on the sensor, decode phase differences between different angles of incidence and incidence positions of beams emitted on the input surface.
[0052] Each emitted beam can have, on the input surface:
[0053] a Gaussian profile with an elliptical intensity distribution, and,
[0054] - a wavefront having two curvatures along two principal axes independent of the axes of the intensity ellipse.
[0055] During at least part of the calibration sequence, a lens with magnifying aberration can be placed upstream of the input surface, which compensates for a magnifying aberration of the objective, in order to present homogeneous curvatures of the emitted beams at the output of the objective.
[0056] A sixth aspect of the invention relates to a device comprising: - a light source (preferably comprising a projector and an opaque mask having at least one passage hole) and an image sensor as defined in the method according to the fifth aspect of the invention
[0057] - processing means (typically including electronic and / or computer technical means and / or a processor) adapted and / or configured to implement the steps of the process according to the fifth aspect of the invention implemented by the processing means, in particular the calibration sequence step and its reiteration, and the step of processing the images obtained.
[0058] A seventh aspect of the invention relates to a computer program comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the process according to the fifth aspect of the invention implemented by the processing means, in particular the calibration sequence step and its reiteration, and the step of processing the images obtained. An eighth aspect of the invention relates to a computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the process according to the fifth aspect of the invention implemented by the processing means, in particular the calibration sequence step and its reiteration, and the step of processing the images obtained.
[0059] Description of the figures and embodiments Other advantages and features of the invention will become apparent upon reading the detailed description of implementations and embodiments, which are by no means limiting, and the following attached drawings:
[0060] [Fig. 1] Figure 1 is a flowchart of a first embodiment of process 1 according to the invention, which is the preferred embodiment of the invention,
[0061] [Fig. 2] Figure 2 is a flowchart of a second variant of step 101 of the first embodiment of process 1 according to the invention,
[0062] [Fig. 3] Figure 3 schematically illustrates the optical system considered during the implementation of the first embodiment of process 1 according to the invention, in particular the decomposition of the transmitted light 600, on a functional basis,
[0063] [Fig. 4] Figure 4 illustrates the input reference surface 21 during the implementation of step 102 of the first embodiment of process 1 according to the invention, viewed from the objective 2; the incident wave 600 is decomposed into basic functions, called input cells 8, represented by the circles in this figure,
[0064] [Fig. 5] Figure 5 illustrates the output reference surface 22 during the implementation of step 103 of the first embodiment of process 1 according to the invention, viewed from the objective 2; each basic function is calculated at the output, called output cell 9, from the basic function at the input, and the known relationships representing the transmission in the objective 2,
[0065] [Fig. 6] Figure 6 schematically illustrates the optical system considered during the implementation of the second variant of step 101 of the first embodiment of method 1 according to the invention, in particular for obtaining the transmission functions of the objective 2, [Fig. 7] Figure 7 schematically illustrates the optical system considered during the implementation of the second variant of step 101 of the first embodiment of method 1 according to the invention, in particular for recovering the relative phase shifts in the objective 2 (to construct the TPROP function),
[0066] [Fig. 8] Figure 8 illustrates, on its different parts a, b, c, d, e, f, different physical parameters relating to the propagated beams 6,
[0067] [Fig. 9] Figure 9 schematically represents the modeling of the screening effects by division, with polygons 16, of the input surface 21 of the lens 2, and [Fig. 10] Figure 10 illustrates a determination of the direction ao, po of the beam 6 at the output 22 of the lens 2, by moving the sensor 4 to different positions illustrated on part a of this figure so as to form on the sensor 4 a series of ellipses 14 illustrated on part b of this figure.
[0068] These embodiments are not exhaustive; in particular, variants of the invention may be considered that comprise only a selection of features described or illustrated hereafter, isolated from the other described or illustrated features (even if this selection is isolated within a sentence including these other features), provided that this selection of features is sufficient to confer a technical advantage or to differentiate the invention from the prior art. This selection includes at least one preferably functional feature without structural details, and / or with only a portion of the structural details if this portion alone is sufficient to confer a technical advantage or to differentiate the invention from the prior art.
[0069] We will first describe, with reference to figures 1 to 7:
[0070] - an embodiment of method 1 for representing the dispersion of focal points of an objective 2
[0071] - in the second variant of step 101 of process 1, an embodiment of a method for defining a function describing an optical response at the output of a lens according to the invention.
[0072] For each of these two processes, the embodiment of this process will be associated with: - a device according to the invention to implement all or part of this process,
[0073] - a computer program according to the invention comprising instructions which, when executed by a computer, lead the computer to implement all or part of the steps of this process, and
[0074] - a computer-readable storage medium according to the invention comprising instructions which, when executed by a computer, cause the computer to execute all or part of the steps of this process.
[0075] Objective 2 includes an input 21 and an output 22.
[0076] The process 1 is implemented by technical means, typically comprising a processing unit 3 according to the invention which forms a data processing device comprising means and / or a processor adapted and / or configured to implement the steps of the process 1.
[0077] Unit 3 comprises at least one computer, a central processing unit or computing unit, an analog electronic circuit (preferably dedicated), a digital electronic circuit (preferably dedicated), and / or a microprocessor (preferably dedicated), and / or software means which may include, for example:
[0078] - a method of implementing a computer program according to the invention comprising instructions which, when executed by a computer, lead the computer to carry out the steps of process 1.
[0079] - An embodiment of a computer-readable storage medium according to the invention comprising instructions which, when executed by a computer, cause the computer to execute the steps of process 1.
[0080] The goal is a method for representing the PSF of a lens 2. By representation of the PSF, it is necessary to understand that we seek to obtain a way to calculate the focal point dispersion of the light for any set of parameters of use of the camera module 2, 4 including the lens 2, among the position in the image field, the lens 2-sensor 4 distance (therefore the focal distance setting), the distance of the scene point 5, the wavelength.
[0081] Step 101 The process 1 first includes obtaining or defining 101 at least one function (preferably a Point Spreading Function (PSF)) describing an optical response at the output of the lens as a function of light input parameters at the lens input.
[0082] These functions can be represented, for example, by:
[0083] - polynomials, algebraic expressions, neural networks, etc., providing a preferably continuous representation modeling the continuity of the objective's response as a function of the input parameters, or - tables of (discrete) values modeling discrete values of these functions at certain points, from which interpolations are generally necessary, or
[0084] - any other suitable form.
[0085] The Gaussian propagation model of a beam is known.
[0086] This propagation can be symmetrical Gaussian beam. More generally, the Gaussian beam can be astigmatic according to a simplified model.
[0087] More generally, the Gaussian beam can be astigmatic according to a generalized model.
[0088] Method 1 proposes to represent not the PSF itself, but to record synthetic data from objective 2, in other words, data representing the overall way in which light is transmitted at the level of objective 2.
[0089] This allows us to calculate the transmission of light at the output 22 of the lens 2, and the superposition of the electromagnetic fields obtained at the level of an image sensor 4, and finally, to calculate the light spots called PSF for each point 51, 52, 53 of the source 10 and / or of the scene 5 illuminating said lens 2 and the image sensor 4.
[0090] In this description, the assembly formed by the lens 2 and the sensor 4 will be referred to as the "camera module".
[0091] We will subsequently consider beams of light 6 which propagate from the scene 5 to the lens 2 and then to the sensor 4, of which various examples 61, 62, 63 are illustrated in figures 3, 6 and 7.
[0092] In this description, a beam of light is defined as light propagating with a non-zero cross-section perpendicular to its direction of propagation. We will then consider the following parameters:
[0093] • Ap is the principal ray of a propagated beam 6 and on which this propagated beam is centered: Api is this principal ray at the input 21 of the objective 2 and Apo is the principal ray at the output 22 of the objective 2.
[0094] • (' / P'): locates the incident beam 6, along its trajectory, relative to the camera module or lens 2:
[0095] oa: is the angle between the beam 6 (or its center or its average direction of propagation) and the optical axis 7 of the lens (central to the lens)
[0096] op: is the angle (between 0 and 360°) around the axis 7 locating the projection of the beam 6 onto a plane perpendicular to the optical axis 7.
[0097] • z or Z is the measurement coordinate along axis 7, illustrated in figures 3, 6 and 7,
[0098] • x (or X) and y (or Y) are coordinates perpendicular to each other and perpendicular to z, in a plane perpendicular to axis 7, illustrated in figures 4 and 5, • (ai, pi) is the value of (a, P) of beam 6 at the level of the entrance 21, illustrated on the left part of figure 8a, • (ri,0i): identifies the point of entry of beam 6 into the objective 2 at the level of the entrance 21:
[0099] where ri is the distance between this entry point and the optical axis 7,
[0100] o 0i is, like angle p, the angle (between 0 and 360°) around axis 7, identifying the projection of this entry point onto a plane perpendicular to the optical axis 7. • The following partial derivatives:
[0101] o (dai / dri) is the curvature of beam 6 in a plane including axis 7 (plane of figure 8), at the level of the inlet 21,
[0102] o (dai / dOi) is the angular curvature of beam 6 in a plane including axis 7 (plane of figure 8), at the level of the inlet 21,
[0103] o (dpi / dri) is the curvature of beam 6 in a plane perpendicular to axis 7, at the level of input 21, o (dpi / d0i) ) is the angular curvature of beam 6 in a plane perpendicular to axis 7, at the level of input 21,
[0104] These four partial derivatives of the beam 6 depend respectively on z the distance between the scene point from which the light comes and the reference point of entry of the optical beam 6 into the lens 2, and the position (x,y) or (<*-, P), in the scene.
[0105] • X is the wavelength of the signal or beam 6, potentially exploring a wavelength range preferably between 400 nm and 800 nm. X can be simplified to only three possible values Xr, Xg, Xb which correspond to the 3 average wavelengths of the three color filters of the sensor 4.
[0106] • (ro,0o): identifies the exit point of beam 6 at the level of the exit 22 of the objective 22.
[0107] o ro is the distance between this exit point and the optical axis 7,
[0108] o 0o is, like angle p, the angle (between 0 and 360°) around axis 7, identifying the projection of this exit point onto a plane perpendicular to the optical axis 7. • ao( ai, pi, ri,0i, X) ; o( ai, pi, ri,0i, X) are the exit angles of beam 6 at the level of the exit 22, as a function of the angles of beam 6 at the entrance 21, and the positions of the entry points:
[0109] o ao, which depends on ( ai, pi, ri, 0i, A), is the value of a at output 22, and is illustrated on the right-hand side of figure 8a,
[0110] oo, which depends on (ai, pi, ri, 0i, A), is the value of p at output 22, and is illustrated on the right-hand side of figure 8a.
[0111] • The following partial derivatives:
[0112] o (dao / dro) is the curvature of beam 6 in a plane including axis 7 (plane of figure 8), at the level of the outlet 22, o (dao / dOo) is the angular curvature of beam 6 in a plane including axis 7 (plane of figure 8), at the level of the outlet 22,
[0113] o (dpo / dro) is the curvature of beam 6 in a plane perpendicular to axis 7, at the level of output 22,
[0114] o (dpo / dOo)) is the angular curvature of beam 6 in a plane perpendicular to axis 7, at the level of outlet 22,
[0115] • Ci: Ci is the entry point of beam 6 (more precisely of ray Api) at the level of the entrance 21. Ci is illustrated on the left part of figure 8a.
[0116] • Co(ai, pi, ri, 0i, X): Co, which depends on (ai, pi, ri, 0i, A), is the exit point of beam 6 (more precisely, of the ray Apo), as a function of the beam's input parameters, at the output 22. Co is equivalent to knowing two parameters (ro, 0o) and a distance z from the point (in the frame of objective 2). The distance z can be arbitrarily fixed or allowed to vary according to (ai, pi, ri, 0i, 7). The two representations are compatible, but depending on the one chosen, the functions Co and TProp may change. This point Co is located on the output surface 22. Co is illustrated on the right-hand side of Figure 8a.
[0117] • Co(ai, pi, ri,0i, A) is possibly differentiated into Cuo(ai, pi, ri,0i, X) and Cvo(ai, pi, ri,0i, X), along 2 main axes Uf (illustrated in figures 8b and 8f) and Vf (illustrated in figures 8c and 8f) local, possibly ideally independent of (ai, pi), but only of (ri,0i), or in practice having to depend on the optical signal according to the coordinates ( ao, po, ro,0o) or (ai, pi, ri,0i, ao, po, ro,0o), or only (ai, pi, ri, 0i) and possibly A to take into account the path of the signal 6 in the objective 2 (as ao, po, ro,0o depend on (ai, pi, ri, 0i), only these 4 variables are necessary).
[0118] • Ucbo((ai, pi, ri,0i, X) (also denoted Ucrbo) and Vcbo(ai, pi, ri,0i, X) (also denoted Vcrbo), both illustrated in figure 8 e , are the main axes of action related to the curvature of the objective.
[0119] • TProp( ai, pi, ri,0i, X ), also noted TPROP, is the propagation time or phase shift between the input point and the output point, (expressed up to a constant, which is not a problem)
[0120] • Fu (ai, pi, ri,0i, X) (illustrated in figure 8b) and Fv (ai, pi, ri,0i, X) (illustrated in figure 8c) are the 2 focal lengths, measured from Cuo and Cvo. These focusing distances (when the incoming beam comes from infinity) can also be expressed in Crbuo and Crbvo which are the curvatures added to the incident beam 6, by the objective 2, along the 2 principal axes llcbo and Vcbo of action of the objective 2, that is to say that these latter parameters are equivalent and redundant if we consider the curvatures and the focal lengths.
[0121] • Finally, it is necessary to add the transformations of the input decomposition cells 21 of the beam 6 to those of the output 22 of the beam 6. That is to say, in the case where the beam 6 is decomposed at the input for example on a basis of Gaussian intensity functions in the reference input surface 21 of the objective 2, we must know how these functions are transformed at the output 22, in terms of intensity profile.Thus, from two beam width parameters (for example Gaussian) wxi (illustrated in Figure 8d) along the X axis and wyi along the Y axis (illustrated in Figure 8d), chosen to be equal by simplification without loss of generality at the input, we obtain 2 wupo (illustrated in Figure 8f) and wvpo (illustrated in Figure 8f) at the output, intensity profile width parameters, with Uwp and Vwp the two principal axes potentially different from those of the action of objective 2 in terms of curvature (the llcbo and Vcbo previously mentioned), but also different from the axes of the output beam (llf, Vf).
[0122] To avoid any potential confusion, there is the curvature of the input / beam wavefront, which is transformed into a certain curvature of the output beam by adding the curvature inherent to lens 2—or the lens's effect—to the path of the light 6. Each of these curvatures can be decomposed along two eigenaxes, which are generally different from each other, except in specific cases. Thus, the eigenaxes of the beam curvature 6 are generally different from those of the effect of lens 2.
[0123] • Vi (ai, pi, ri,0i, X) is the weighting function of the amplitude of the signal transmitted by the sensor 4 due to the reception of the beam 6 having passed through the lens 2.
[0124] This function models the angle and occultation effects of beam 6. It multiplies with the amplitude of beam 6 received locally by sensor 4.
[0125] Thus, the following parameters are defined in relation to beam 6 passing through lens 2:
[0126] • (ao, po, ro,0o) the angles and exit position.
[0127] • ((dao / dro) (dao / dOo) ; (dfto / dro) (dpo / dOo)) the curvature of the output beam.
[0128] • Uf((ai, pi, ri,0i, X) and Vf(ai, pi, ri,0i, X), the principal axes of the beam 6 at the output 22, deduced from the action of the objective 2 on the curvature of the beam 6 at the input 21.
[0129] These parameters allow, for example, the modeling of the propagation of beams originating from each cell 8.
[0130] The input surface 21 is, for example, the physical surface, in the direction of scene 5, of the first lens, in the direction of scene 5, of lens 2, or a reference plane located somewhere in or in front of lens 2 (at a certain z) in the vicinity of this lens.
[0131] The output surface 22 is preferably a locus of points which will serve to define the output conditions of the beam 6. The output surface 22 is for example the physical surface, in the direction of the sensor 4, of the last lens, in the direction of the sensor 4, of the objective 2, or a reference plane located somewhere in or behind the objective 2 (at a certain z) in the vicinity of this lens.
[0132] During this step 101, process 1 defines: - the optical phase shift TProp of propagation between the input surface 21 and the output surface 22,
[0133] - Co, (or Cuo, Cvo if differentiated)
[0134] - ao ie how the beam is deflected by the lens
[0135] - po
[0136] - Vi the output amplitude weighting
[0137] - llcbo the main axes of the curvature added by the lens.
[0138] - Vcbo
[0139] - Cbruo, the intensity of the curvatures
[0140] - Crbvo, (therefore the transform of wxi, wyi into wupo, wvpo, which is a consequence)
[0141] - Fuo, (which is a consequence of the output beam)
[0142] Fvo
[0143] Method 1 considers the incident beam 6 by its origin (i.e., the x, y, z coordinates relative to the objective 2), which translates, for example, into two angles a and p with respect to the optical axis 7, in a plane perpendicular to the optical axis 7, and a certain curvature of the beam 6 depending on its origin ((dai / dri) (dcci / dOi); (dpi / dri) (dpi / dOi)). This beam 6 is assumed to enter the objective 2 at several positions, called entry points.
[0144] First variant of step 101
[0145] In a first variant of step 101, the function describing the optical response at the output of lens 2 as a function of input light parameters at the input of lens 2 is obtained or defined from a known design of lens 2.
[0146] Thus, the transfer function of objective 2 is ideally calculated from a model of objective 2. By ideally, we mean using the design parameters of objective 2, for a realization or manufacture of objective 2 respecting them precisely.
[0147] The function describing the optical response at the output of lens 2 as a function of the input light parameters of lens 2 is preferably further optimized or modified by taking into account discrepancies between the manufacturing parameters of lens 2 and the known design of lens 2. Thus, the transfer function of lens 2 is calculated based on the actual realization from a model of lens 2. To do this, the manufacturing parameters of lens 2 are evaluated. For example, the decentering, the actual gaps, the actual thicknesses of the lenses, the actual refractive indices, the actual shapes of the lenses, and the angles of each plane on each face of each lens are measured. From these actual manufacturing parameters, step 101 further includes a simulation of a light propagation model in the stack of the N lenses of lens 2.
[0148] For example, we know the design data. The achieved objective 2 has deviations from its design. We do not have sufficient metrology to directly determine these deviations. We can then define a number of indirect measures of objective 2.
[0149] These measures can be a game of:
[0150] - Measurements of specific optical response
[0151] - Measures of the type described below in 2 ème variant of step 101
[0152] - Geometric measurements.
[0153] Step 101 will allow us to find the representation of the PSF corresponding to the objective produced 2.
[0154] To this end, it includes a simulation generation with a model comprising variable parameters modeling those likely to vary during the realization of objective 2, and a range of variation of these parameters framing the variations of the physical parameters likely to occur (for example: thickness of a lens of 249pm in the theoretical design, realization at + / -1.5pm, a wider range of + / -3pm is given for example).
[0155] These simulations provide as outputs the DS data (specified data) as specified for the PSF representation.
[0156] They also provide DC data (control data) such as the measurements that will be taken. For example, DC data is the measured thickness of the lens – which in this case directly optimizes or modifies the value of the thickness parameter of that lens.
[0157] It can also be an MTF type response calculation under certain conditions, for example: a position in the image field, and / or a line step serving as a pattern to calculate the MTF, etc.
[0158] This can also be a measure in the sense of the one described below in 2 ème This is a variant of step 101, but partial so as not to have to go through the whole process, which is necessarily longer. Step 101 can then train a neural network, perform regressions, or any method allowing to obtain a model of the variations of the representation, with DCs as input, and DSs as output.
[0159] In the usage phase to generate data relating to a particular camera module, or a particular lens, a set of measurements will be taken, and the representation data of the PSF of this particular lens, as it is made, will be calculated with the neural network.
[0160] From one of these simulation models, it is necessary to extract the data in a form usable for representing the PSF. For this, we create for example a light source limited to the function basis at the input of the objective 2, in the input reference surface 21, and on the output side, we place the simulation analysis location at the desired location, in order to obtain the characteristics of the light beam at this location (intensity distribution, curvature, phase shift or propagation delay relative to the input reference location).
[0161] Second variant of step 101
[0162] In the second variant of step 101, the function describing the optical response at the output of a lens as a function of input light parameters at the input of the lens is defined by means of an embodiment of a method for defining a function describing an optical response at the output of a lens according to the invention, by means of the following steps 1011, 1012, 1013.
[0163] First, in 1011 we place the lens 2 between a light source 10 and an image sensor 4.
[0164] The light source 10 comprises a projector 11 and an opaque mask 12 having at least one passage hole 80 (of which various examples 81, 82, 83, 84 are illustrated in figures 6 and 7), so that at a given instant, each passage hole 80 corresponds to a single beam emitted 6 having a given shape 90 on the exit surface 22 of the lens 2.
[0165] This mask 12, comprising several holes 80 of a certain diameter, allows the definition of source areas, in relation to the decomposition into basis functions of the transmission of the lens 2. The mask 13 is movable via an actuator along the X and Y axes. The source 10 may further include an optional optical element 13 (such as a lens) arranged to change the focus or collimation of the beam 6, generally to simulate that it originates from a point farther away than it actually is. This element 13 can amplify the light onto the sensor 4, and / or can allow a source virtually at infinity or very far away, in a compact device.
[0166] Preferably, the opaque mask 12 is provided with several passage holes 80, so that at a given moment, the projector 11 illuminates (by a main beam 600 grouping the different beams 6, 61, 62, 63) a large area of the mask 12, this illuminated area grouping the plurality of the passage holes, the light of this illumination being blocked by the mask 12 except at the level of the passage holes, so that each passage hole corresponds only to one of the beams 6 emitted by the source 10 to the lens 2. None of these different passage holes overlap.
[0167] At each instant, the plurality of passage holes 80 is defined so that the set of passage holes corresponds to a set of beams 6 making light spots on the sensor 4 whose hole (or holes) of origin is identifiable, in order to know how to establish the relationship between the so-called output beams and those so-called input beams.
[0168] We can aim to have a single beam 6 forming a luminous spot in order to facilitate this identification.
[0169] Thus in one variant, at each instant, the plurality of passage holes 80 is defined so that each passage hole corresponds to a unique beam 6 so that none of the beams 6 overlaps on the input surface 21 of the lens 2 and / or on the output surface 22 of the lens 2 and / or on the sensor 4.
[0170] We can also have at least two beams illuminating the same spot, in order to identify the relative phase shifts between the paths of the different beams.
[0171] Also, a single hole 80 can receive several beams 6 in order to simultaneously create more light spots, this can, at a given hole density, increase the density of spots on the screen, by means of several source points 51, 52, 53 of the source 10 illuminated simultaneously.
[0172] This mask 12 is positioned as close as possible to the objective 2, preferably so that each passage hole is located at or corresponding to the future so-called reference position (i.e., on the inlet surface 21). Thus, depending on the implementation variant of this step 1011, this mask may be located on or outside the reference surface of the inlet 21.
[0173] The central computing unit 3, which controls the control interfaces, is connected to the source 10 (to the projector 11 and the means for moving the mask 12 (to control them)), to the sensor 4 (for acquiring the data from the sensor 4), and to the means for moving the sensor 4 (to control them).
[0174] Next, the technical processing means 3 control 1012 a calibration sequence:
[0175] o by emitting, from the light source, different emitted beams of light 6 distinct beams which pass through the lens to the sensor so that when the light beams reach an input surface at the lens, each beam is distributed on the input surface in the form of a calibration cell distinct from the calibration cells of the other emitted beams, then
[0176] o by imaging these beams emitted onto the sensor,
[0177] the calibration sequence being repeated by varying all or part of the following parameters of the emitted beams: collimation or focusing of the emitted beams on the input surface, angle of incidence of the emitted beams on the input surface, position of incidence of the emitted beams on the input surface, wavelength of the emitted beams, number and / or position(s) of the calibration cell(s), distance between the lens and the sensor.
[0178] The calibration sequence includes a mask movement controlled by the processing means 3 to create new emitted beams by changing the position of the pass-through holes. An alternative is to use a liquid crystal mask 12 in which the position of each pass-through hole can be electronically controlled.
[0179] During at least part of the calibration sequence, a lens with magnifying aberration (not illustrated) is placed upstream of the input surface 21, which compensates for a magnifying aberration of the objective 2, in order to present homogeneous curvatures of the emitted beams 6 at the output 22 of the objective 2.
[0180] Positioned upstream, before mask 12, this lens with magnification aberration, which compensates for that of objective 2, allows for homogeneous (equal) curvatures of the test beam 6 to be presented at output 22 along both axes, thus also restoring symmetry to the ellipsoid, as this eliminates the curvature derivative component. The aim is to facilitate the extraction of local beam parameters, because when there is a curvature derivative, the iso-intensity ellipses are no longer strictly ellipses, nor are they perfectly symmetrical curves, which can lead to errors or inaccuracies.
[0181] Unit 3 can change the color of the emitted beams 6, or emit them simultaneously, and the focus of these emitted beams 6. Unit 3 can move the mask 12 in translation along X, Y and possibly in Z to place it as close as possible to the camera module (a part of the mask may be independent of this movement).
[0182] Doc distances are generated in such a way as to obtain one or more images around the focus, and one or more images further from the focus.
[0183] Unit 3 communicates with camera modules 2 and 4 to receive images, and also to modify the Doc setting, among other things.
[0184] The calibration sequence can be carried out as follows:
[0185] - Setting the source to 10 for an infinite transmission distance,
[0186] - Acquisition of multiple images by sensor 4 at varying distances (Doc), - Other transmission distance settings
[0187] - Etc.
[0188] Each emitted beam 6 has, on the input surface (and also on the output surface 22 of the lens 2 if the shape of each beam 6 on the surface 21 is sufficiently small):
[0189] a Gaussian profile with an elliptical intensity distribution, and
[0190] - a wavefront having two curvatures along two principal axes independent of the axes of the intensity ellipse.
[0191] The emission of beams 6 therefore follows a Gaussian profile, with an elliptical intensity distribution. The emitted wavefront also has two curvatures, but along two principal axes, different from the axes of the intensity ellipse.
[0192] When the distance Doc is shifted, an ellipsoid (the union of intensity surfaces and wavefront curvatures) is observed – or alternatively, ellipses of equal intensity with two principal axes and relative phase shifts varying according to other ellipses with different principal axes. Since the wavefront has differentiated curvatures with different axes, the axes of the ellipsoid rotate when the beam observation point is shifted. Generally, this rotation is most noticeable around the point where the beam is narrowest.
[0193] This allows us to find the parameters of both the major and minor axis values of the ellipsoid, the curvatures of the two axes, and the amplitude values of the ellipses.
[0194] We can also find the direction of the optical axis by moving the Doc and observing the movement of the light spot.
[0195] Thus, a device 10, 11, 12 is used which illuminates the lens 12 at the input 21, according to varying locations and angles. The illumination locations are scanned in a certain number of positions and from a certain number of different angles.
[0196] It is possible to illuminate several light spots simultaneously, allowing, for example:
[0197] - for the same point 51 of the source 10 (more precisely of the projector 11), to generate a luminous spot on the sensor 4, obtained from different apertures 81 and 82 (which can potentially overlap in part) in the mask 12 (which would correspond to the case of Figure 7 but where tl would potentially be separated into two distinct spots tll and tl2 for the two beams 61 and 62),
[0198] - for the same point 51 source 10 (more precisely of the projector 11), to use two different apertures 81 and 82, to obtain a superposition tl of the beams on the sensor 4, capable of recovering the relative phase shifts between these beams, as illustrated in figure 7,
[0199] - for two different points 52, 53 of the source 10 (more precisely of the projector 11), to use a common aperture 82, 83 generating on the sensor 4 a luminous spot t2 for the beam 62 (coming from 82) different from the luminous spot t3 for the beam 63 (coming from 83), as illustrated in figure 6,
[0200] - for two different points 51, 52 of the source 10 (more precisely of the projector 11), to use a different aperture 81, 82 generating on the sensor 4 respectively a luminous spot t1 for the beam 61 (coming from 81) different from the luminous spot t2 for the beam 62 (coming from 82), as illustrated in figure 6,
[0201] For each light spot, the sensor 4 is moved to different positions 41, 42, 43, 44, each with a value equal to zi (i being a position index), along the axis z. Intensity images are recorded for each position zi. From these positions, the parameters of the corresponding typical beam are deduced, for example, a generally shaped astigmatic Gaussian beam.
[0202] We can perform the following:
[0203] - a measurement 1013 according to different input points or angles, simultaneously, and / or
[0204] - a measurement 1013 according to different entry points in the objective 2, The openings 80 of the mask 12 at the entrance 21 can simultaneously receive several beams 6.
[0205] - A single aperture of 80 can potentially allow light from several different points 51, 52, 53, etc. to pass through, thus generating several different light angles, t1, t2, t3, etc., for a simultaneous acquisition. The spots can be analyzed simultaneously, on the same image, during processing 1013.
[0206] Thus, the processing means 3 process 1013 the images obtained by the sensor during the calibration sequence in order to construct the function describing the optical response at the output of the lens as a function of the input light parameters at the lens input.
[0207] Regarding this processing 1013, it is a matter of recognizing, for all the points or spots obtained on the sensor, the parameters of the emitted beams 6, for each hole of passage of the mask 12, and for each angle of incidence of the beam 6. We can seek to recognize Gaussian beams, for example by a least squares method, by finding the parameters of the Gaussian beam providing the images at each Doc closest to the beam obtained from these parameters.
[0208] We thus obtain a collection of light emitters from lens 2, for each emitting point. At each emitting point, we have a set of ((dai / dri) (dai / dOi) ; (dpi / dri) (dpi / dOi)) which depend on the equivalent distance (z) to the point in scene 5.
[0209] The collection of these parameters can directly represent the different functions to be obtained. It can also be used to obtain algebraic expressions, or to train neural networks to obtain a continuous representation from this collection of discrete values.
[0210] The processing of the images obtained by sensor 4 includes associating data obtained on sensor 4 with: - one of the emitted beams 6, and
[0211] - the parameters of this emitted beam 6.
[0212] For each point of light in the mask 12, and for each angle of incidence on the lens 2 of the emitted beams 6, the data from the sensor 4 are associated with data of direction, curvature, and intensity of the incident beam 6 on the input surface 21.
[0213] Advantageously, during the calibration sequence, the lens 2 is illuminated simultaneously by several emitted beams 6 (and therefore via at least one or preferably several holes in the mask) so as to:
[0214] - create an interference pattern on sensor 4, and
[0215] - during the processing of images obtained on the sensor, decode phase differences between different angles of incidence and incidence positions of beams emitted on the input surface.
[0216] Thus, in order to correctly obtain the TPROP function, the following configuration can be used for the light emitters:
[0217] - The same source 11 illuminates the lens simultaneously with several beams through several orifices or holes in the mask 12.
[0218] This allows us to create an interference pattern in order to decode (relatively) the phase differences between the different transmission angles and transmission locations.
[0219] Thus, all these measurement results are analyzed to deduce the different functions, depending on the beam input parameters (ai, pi, ri, 0i, X):
[0220] - variation of the angles between beam 6 entering at the inlet 21 and beam 6 exiting at the outlet 22,
[0221] - correspondence of the exit point of beam 6 at the level of the exit 22 as a function of the entry point of beam 6 at the level of the entry 21 and the entry angles of beam 6 at the level of the entry 21,
[0222] - profile of curvatures encountered by beam 6 passing through objective 2, principal axes of curvature and curvature values,
[0223] - modulation of the width along the principal intensity axes, from the exit point of beam 6 at the output 22, relative to the entry point of beam 6 at the input 21,
[0224] - the direction of these principal intensity axes. In more detail, regarding the interpretation or processing of the images or measurements from sensor 4, the aim is to recover the parameters of the Gaussian beam (if a decomposition of the incoming light onto Gaussian intensity profiles has been used). To do this, one can:
[0225] 1) Consider, around each point of convergence of a light spot on sensor 4, the concentric ellipses of iso-intensity detected. The values of the major axis, minor axis, and angles of these axes with respect to the sensor's coordinate system (axes perpendicular to each other) must be analyzed. Furthermore, by moving sensor 4, the center of these light spots will move on the sensor. From the displacement of this center, we obtain the direction of the central axis of the emitted Gaussian beam 6. From the variation with respect to z of the major and minor axes, as well as the widths of the ellipses of the same intensity as a function of z, and the rotation law of these major axes as a function of z, we obtain a set of data allowing us to determine the generation parameters of the Gaussian beam 6.
[0226] 2) One parameter that cannot be directly extracted from these observations of a particular light spot remains: the phase of the light reaching a location at position z (i.e., a part of the sensor located at z). To resolve this uncertainty, we can intentionally ensure that several apertures in the mask allow light from the same source to pass through, in order to superimpose—at the sensor—at least two Gaussian beams originating from different paths within the lens. This results in an interference zone of two (or more) Gaussian beams. We can also intentionally move one of the mask apertures relative to the other, which remains fixed, to modulate / shift the resulting interference patterns. In this way, varying the interference analysis parameters as a function of the displacement of one of the mask apertures will allow us to reconstruct a phase relationship (without the modulo-2 jumps).n (i.e., an unfolded phase), between the two or more Gaussian beams. Then, by moving said second aperture to a set of points covering a sampling of all the input points, we obtain the relative propagation phase shifts of the different beams in the lens, which allows us to construct the TPROP function (at an absolute time offset that is not determined, but which is not needed). For this, the mask can actually be two different masks, driven by two independent 2-axis movement devices, or even just one of the two masks moved, the other fixed, or even an electronically addressable mask such as an LCD screen. For example, with reference to Figure 7:
[0227] - The through hole 82 can be fixed, and
[0228] The passage hole 81 can be a movable opening relative to the fixed orifice 82, in order to vary the overlapping interferences of the light spots, near the convergence zone of the beams.
[0229] To accelerate the measurement, it is possible to create several apertures in a fixed mask and simultaneously move several apertures in a moving mask. This operation can be repeated in parallel during a single measurement step, thus providing a relative phase shift along multiple lines in the lens's output surface. Next, the relative phases in other directions intersecting the lines should be compared, for example, by rotating both the moving and fixed masks by 90°, in order to determine all the relative phases in every possible direction.
[0230] Therefore, it is not necessary to repeat the operation for all possible fixed points on the sensor surface, the phase relationship obtained on all moving points relative to a fixed point, for example at the center, gives a priori the entire phase shift field over the entire surface.
[0231] We observe that below a certain width ratio (wx ; wy) of a Gaussian (in 2D, in exp( -((x-x0) 2 / wx 2 +(y-y0) 2 / wy 2By considering the distance between Gaussians (the difference between (x0; y0) values of different functions), we can obtain a sum that becomes very close to a flat (constant) function, or that follows a particular shape. This means that we can decompose the input beam 6 into Gaussians, calculate their equivalent transmitted by the lens, and sum these output Gaussians in the plane of the sensor 4 or the sensor surface (possibly arbitrary, non-planar), which reconstructs all the light coming from the lens 2, even if the contours of the decomposition functions are not definable because each of these functions extends into the "domain" of neighboring functions. By taking the intensity of this superposition, we obtain the value of the PSF in the plane of the sensor, for the lens adjustment parameters, and those of the input light beam (x, y, z of the point in the scene).
[0232] The advantage of performing this decomposition on Gaussian functions is numerous:
[0233] First, algebraic expressions for propagation at the lens output for such intensity and phase distributions exist, are rather simple to calculate, and are "quasi-compact support" - a term to say that the function takes significant values only on a fairly localized area. There is therefore no differential equation to solve dynamically, hence a very large economy of calculations at this level.
[0234] The localized area of output intensity, for example near the focusing distance of the output beam, allows calculations to be kept to a minimum. Therefore, the recomposition of beams from each output cell can be calculated with relatively few steps, and without exploring large areas where sums of undamaged electric fields for each basis function eventually cancel each other out due to destructive interference. Thus, the calculations required are generally limited to the areas of interest and extend only slightly beyond them. Schematically, the diameter of the light spot is inversely proportional to the aperture from which it originates. Thus, if we divide the objective lens into, for example, 10 x 10 cells in x and y (100, or rather π / 4 * 10 * 10 = 78 or 79 cells on a circle), we obtain light spots that are "only" 10 times too large at the convergence zone.The superposition of the 79 cells ultimately reduces the effective diameter of the light spot by approximately xl0. Another method generally risks summing over significantly larger areas.
[0235] In addition, step 1013 includes a determination of the direction ao, po of beam 6 at output 22 of objective 2, preferably by moving sensor 4.
[0236] To do this, as illustrated in Figures 10a, for each z-position of sensor 4, at each position (e.g., l, 2, 3, 4, 5 in Figures 10a and 10b), we find the center of the image of beam 6 obtained by sensor 4, which is generally a series of concentric iso-intensity ellipses 14 illustrated in Figure 10b. The position of the centers i is converted into X, Y, Z positions in space: Z is the displacement of sensor 4 along axis 7, and X and Y are the transposition of the U, V coordinates of the center of the light spots (center of the ellipses) into X, Y positions in space.
[0237] From these positions, a curve, preferably a straight line, is deduced, passing as close as possible to all these positions, typically using a least-squares method. This straight line corresponds to the angles ao, po of the beam 6 at output 22 (as a function of the angles ai, pi at the input).
[0238] We note that, if mask 12 has:
[0239] - 80 passage holes that correspond directly to the desired input cells 8, then step 101 directly gives the desired representation of the dispersion of focal points of the objective, and steps 102 to 105 are immediate,
[0240] - passage holes 80 which do not correspond to the desired input cells 8, then steps 102 to 105 described below require more calculations to obtain the desired representation of the dispersion of focus points of objective 2.
[0241] Furthermore, step 1013 may optionally include a survey of the function representing the optical opacifications at the edge of lens 2. Indeed, the image displacement / survey cycle on sensor 4 can be performed with reduced steps (preferably along the radial direction with respect to axis 7) to obtain an equivalent opacification position (generally dependent on the angle of incidence (ai, pi)) in the input surface 21 of the beam 6. The decrease in the summed intensity on the image obtained by sensor 4 is observed. When it reaches a certain ratio, for example 50% of that further from the opacification, the equivalent opacification position is deduced as, for example, the center of the light passage hole for this ratio, at the input 21 of lens 2. This is done as a function of several incidences of the incoming light 6, which gives a position law for this limit depending on this impact.
[0242] The embodiment of the device according to the invention for implementing this embodiment of the method according to the invention for defining a function describing an optical response at the output of a lens, comprises:
[0243] - the light source 10 and the image sensor 4 and the possible magnification aberration lens, - the processing unit 3 adapted and / or configured to implement steps of this process, in particular the calibration sequence step and its reiteration, and the image processing step obtained (including the control of any movements of the sensor 4, the control of any movement of the opaque mask 12 and / of the position of the passage holes 80, the control of the emission of beams by the source 10, the control of the variations of the parameters of the beams emitted by the source 10, etc.).
[0244] Processing unit 3 typically includes:
[0245] - a computer program embodiment according to the invention comprising instructions which, when executed by a computer, lead the computer to implement steps (calibration sequence and its reiteration, and the image processing step) of this process, and
[0246] - an embodiment of computer-readable storage media according to the invention comprising instructions which, when executed by a computer, cause the computer to execute steps (calibration sequence and its reiteration, and the step of processing the images obtained) of this process.
[0247] Step 102
[0248] After step 101, the process 1 includes, for several propagated beams 6 of light whose direction, curvature and / or phase on the input surface 21 at the input of the lens 2 vary, a decomposition 102 of the input surface 21 into several input cells 8 (as many as necessary) of non-zero finite area, each input cell 8 corresponding to the shape, on the input surface, of one of the propagated beams, allowing by contiguity or overlap to describe the input surface of the lens 2.
[0249] The process 1 can determine a decomposition step into the input cells 8 as a function of a choice of decomposition step into the output cells 9, preferably so as to determine a maximum input cell step 8 beyond which the modeling would induce computational artifacts.
[0250] Input cells 8 are disjoint and / or partially overlap.
[0251] Step 103 Next, the process 1 includes, for each input cell 8, a calculation 103 of at least one parameter of an output cell 9 on the output surface 22 at the output of the lens 2 corresponding to the passage of one of the emitted beams 6 passing through the lens 2 from this input cell 8 to the output surface 22, each output cell 9 corresponding to the shape, on the output surface 22, of this propagated beam 6, the at least one parameter of the output cell 9 including the position and shape of this output cell 9 on the output surface 22, said calculation 103 being based on the at least one function describing the optical response at the output of the lens 2 as a function of input light parameters at the input 21 of the lens 2.
[0252] Thus, for each input cell, we calculate the output cell: position Co and other parameters (such as ao, po, wupo, wvpo, llf, Vf, and the curvatures (dao / dro), (dao / d0o), (dpo / dro), (dpo / dOo))), considering that the transition from input cell 8 to output cell 9 depends on the angles of the received beam 6.
[0253] Step 104
[0254] Next, process 1 includes, for each propagated beam 6, a determination 104:
[0255] o a modification of the curvature and / or phase and / or direction of the propagated beam 6 at the output cell 9 corresponding to this propagated beam 6 with respect to the input cell 8 of this propagated beam 6, this modification being induced by the lens 2 between the input surface 21 and the output surface 22 (thus determining the addition of curvature and delay induced by the lens 2, between the incidence positions at the input and output, for each input cell 8), and / or
[0256] o of a curvature and / or phase and / or direction of the propagated beam 6 at the level of the output cell 9 corresponding to this propagated beam 6 (the transformation of the curvature of the beam 6 is determined for each input cell 6),
[0257] said determination being based on at least one function describing the optical response at the output of the lens as a function of input light parameters at the lens input.
[0258] The calculation of the beam parameters 6 is useful for determining a propagation function at the output 22 of the objective 2.
[0259] 105Next, method 1 includes, for at least one position of an imaging surface of the sensor 4 located on the output side 22 of the lens 1, a summation 105, on the imaging surface, of the beams 6 from the output cells 9 (preferably a summation, on the imaging surface, of complex numbers representing the amplitudes and phases of the electric fields of all the propagated beams 6).
[0260] Figure 1 illustrates different positions 41, 42, 43, 44 of value equal to zi (i a position index) along the z-axis, for which the beam 6 at the output 22 is calculated.
[0261] Thus, for each known value of the Doc (distance Sensor 4 to lens 2) of the position of the imaging plane or surface of sensor 4, as well as the parameters of the beam 6 necessary to calculate its propagation, process 1 sums, at the level of this imaging surface of sensor 4, during step 105, the complex amplitudes resulting from the amplitudes and phases of all these propagated beams 6, for each propagation originating from each cell 8 and / or 9. This provides a result whose complex amplitude represents both the value of the photocurrent at each pixel in the sensor (taking the magnitude of the square of the resulting electric field) and thus the PSF of the system formed by lens 2 and sensor 4, for the current parameters (x, y, z), Doc. This also provides an average point (u, v) in the imaging plane or surface of sensor 4 which corresponds to the point (x, y, z) from the scene 5.
[0262] Thus, step 105 includes determining the position of a mean point on the sensor imaging surface for each propagated beam and / or input cell.
[0263] Method 1 further includes, for each passage hole 80 or calibration cell or input cell 8, taking into account the screening effects on the edges 15 of this passage hole 80 or calibration cell or input cell 8, which results in a stronger attenuation coefficient on the edges 15 and also a displacement of the output beam 6 22 and / or a modulation of the curvatures. Thus, and as illustrated in Figure 9, the modeling of the screening effects is done as follows: a division is created, for example with polygons 16 – such as hexagons – of the input surface 21 of the lens 2, and functions (preferably Gaussian) 17 are placed on it.For polygons 16 intercepting the opacity limits of objective 2, more points are created receiving functions (preferably Gaussian) 17, which functions have a smaller spatial extent (perpendicular to the beam) (in the Gaussian representation formula, the wx and wy that divide x. 2 and y 2 are smaller, causing the function to decrease more at a given radius), so as to obtain a sum of the values of these functions modeling the shape of the opaque edge 15, with a certain approximation (for example exponential decay) preferably with a transmitted value of brightness which is close to that which would be obtained with a very dense mesh of these functions 17.
[0264] If necessary, the weighting (typically in the form of a coefficient factoring each function 17) is calculated to obtain a superposition of the values of the functions 17 corresponding to the brightness distribution at the input 21 of the lens 2, for example flat, or for example decreasing when the angle of incidence increases.
[0265] The position of the opaque border 15 depends on the angle of incidence of the beam 6, since there are generally several borders 15 stacked on different planes, which are not all struck simultaneously, depending on the angles of incidence. The determination of the position of each border 15 is preferably carried out during step 101 from the design stage (as in the first variant of step 101), or by surveying it (as in the second variant of step 101).
[0266] The method may further include a correction of the representation thus obtained of the dispersion of focal points of an objective comprising an input and an output, for example by replacing the functions 17 with asymmetric functions along X, Y modeling the obstruction effect of a part of the field (as an alternative or complement to the local use of more tightly packed functions 17, with a smaller spatial amplitude of action).
[0267] Thus, process 1 allows:
[0268] - improved compactness of the PSF representation.
[0269] - faster calculation of the PSF.
[0270] - and, in the case of the 2 èmevariant of step 101, to apply process 1, even without prior knowledge of the realization and stacking design of objective 2. Of course, the invention is not limited to the examples just described and many modifications can be made to these examples without going out of the scope of the invention.
[0271] Of course, the various features, forms, variants, and embodiments of the invention can be combined in various ways, provided they are not incompatible or mutually exclusive. In particular, all the variants and embodiments described above are combinable.
Claims
DEMANDS 1. A method for representing the dispersion of focal points of a lens comprising an input and an output, implemented by technical means, and comprising: - Obtaining or defining at least one function describing the optical response at the lens output as a function of the light input parameters at the lens input, - For several propagated beams of light whose direction, curvature and / or phase vary on an input surface at the lens input, a decomposition of the input surface into several non-zero finite area input cells, each input cell corresponding to the shape, on the input surface, of one of the propagated beams, - For each input cell, a calculation of at least one parameter of an output cell on an output surface at the output of the lens corresponding to the passage of one of the beams emitted through the lens from that input cell to the output surface, each output cell corresponding to the shape, on the output surface, of this propagated beam, the at least one parameter of the output cell including the position of that output cell on the output surface, said calculation being based on the at least one function describing the optical response at the output of the lens as a function of input light parameters at the lens input, - For each propagated beam, a determination: o of a modification of the curvature and / or phase and / or direction of the propagated beam at the output cell corresponding to this propagated beam relative to the input cell of this propagated beam, this modification being induced by the lens between the input surface and the output surface, and / or o of a curvature and / or phase and / or direction of the propagated beam at the output cell corresponding to this propagated beam, said determination being based on at least one function describing the optical response at the output of the lens as a function of input light parameters at the lens input, - for at least one position of an imaging surface of a sensor located on the output side of the lens, a summation, on the imaging surface, of the beams from the output cells.
2. A method according to claim 1, characterized in that it comprises determining a decomposition step in the input cells as a function of a choice of decomposition step in the output cells or determining a decomposition step in the output cells as a function of a choice of decomposition step in the input cells.
3. Method according to claim 1 or 2, characterized in that the inlet cells are disjoint and / or partially overlap.
4. A method according to any one of the preceding claims, characterized in that it comprises, for each propagated beam, the determination of the modification of the curvature and / or phase and / or direction of the propagated beam at the level of the output cell corresponding to this propagated beam relative to the input cell of this propagated beam, this modification being induced by the lens between the input surface and the output surface, said determination being based on at least one function describing the optical response at the output of the lens as a function of input light parameters at the lens input.
5. A method according to any one of the preceding claims, characterized in that it comprises, for each propagated beam, the determination of the curvature and / or phase and / or direction of the propagated beam at the level of the output cell corresponding to that propagated beam, said determination being based on at least one function describing the optical response at the output of the lens as a function of input light parameters at the lens input.
6. A method according to any one of the preceding claims, characterized in that it comprises a determination of a position of a mean point on the imaging surface of the sensor for each propagated beam and / or input cell.
7. A method according to any one of the preceding claims, characterized in that the summation, on the imaging surface, of the beams from the output cells comprises a summation, on the imaging surface, of the complex amplitudes corresponding to the amplitudes and phases of all the propagated beams.
8. A method according to any one of the preceding claims, characterized in that the function describing the optical response at the output of the lens as a function of input light parameters at the input of the lens is obtained or defined from a known design of the lens.
9. Method according to the preceding claim, characterized in that the function describing the optical response at the output of the lens as a function of light input parameters at the lens input is further optimized by taking into account deviations between lens realization parameters and the known lens design.
10. A method according to any one of the preceding claims, characterized in that the function describing the optical response at the output of the lens as a function of the input light parameters at the lens input is obtained or defined by the following steps: - The lens is placed between a light source and the image sensor - technical processing means control a calibration sequence: a. by emitting, from the light source, different distinct beams of light which pass through the lens to the sensor so that when the light beams reach the entrance surface of the lens, each beam is distributed on the entrance surface in the form of a calibration cell distinct from the calibration cells of the other emitted beams, then b. by imaging these beams emitted onto the sensor, the calibration sequence being repeated by varying all or part of the following parameters of the emitted beams: collimation or focusing of the emitted beams on the input surface, angle of incidence of the emitted beams on the input surface, position of incidence of the emitted beams on the input surface, wavelength of the emitted beams, number and / or position(s) of the calibration cell(s), distance between the lens and the sensor, - the processing means process the images obtained by the sensor during the calibration sequence in order to construct the function describing the optical response at the output of the lens as a function of the input light parameters at the lens input.
11. Data processing device comprising means and / or a processor adapted and / or configured to implement the steps of the process according to any one of claims 1 to 10.
12. Computer program comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the process according to any one of claims 1 to 10.
13. Computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the process according to any one of claims 1 to 10.