阅读说明：本技术 用于非均匀介质的非侵入性光学表征的方法和系统 (Method and system for non-invasive optical characterization of heterogeneous media ) 是由 A·奥布里 A·巴顿 V·巴罗尔 C·博卡拉 L·科布斯 M·芬克 W·兰伯特 于 2019-07-16 设计创作，主要内容包括：本发明涉及一种用于非均匀介质的非侵入性光学表征的方法,所述方法包括：借助于一系列入射光波照射被定位在显微镜的透镜(30)的焦平面中的所述非均匀介质的给定视场的步骤；在所述焦平面(FP)的共轭平面与观测平面之间定义的观测基础中确定第一失真矩阵(D-(ur)、D-(rr))的步骤,所述第一失真矩阵在所述焦平面的共轭平面与像差校正平面之间定义的校正基础中,对应于在所述校正基础中确定的所述视场的第一反射矩阵(R-(ur))借助于在所述校正基础中针对模型介质定义的参考反射矩阵的相位共轭矩阵的逐项矩阵乘积；以及根据所述第一失真矩阵确定所述非均匀介质的物理参数的至少一个制图的步骤。(The present invention relates to a method for non-invasive optical characterization of heterogeneous media, the method comprising: a step of illuminating a given field of view of said inhomogeneous medium positioned in the focal plane of a lens (30) of a microscope by means of a series of incident light waves; determining a first distortion matrix (D) in an observation basis defined between a conjugate plane and an observation plane of the Focal Plane (FP) ur 、D rr ) In a correction basis defined between a conjugate plane of the focal plane and an aberration correction plane, the first distortion matrix corresponding to a distortion in a plane defined by the conjugate plane of the focal plane and the aberration correction planeA first reflection matrix (R) of said field of view determined on the basis of said correction ur ) A term-by-term matrix product of a phase conjugate matrix of a reference reflection matrix defined for the model medium in the correction basis; and determining at least one mapping of physical parameters of the inhomogeneous medium based on the first distortion matrix.)

1. A method for non-invasive optical characterization of heterogeneous media, the method comprising:

-a step of illuminating a given field of view of the inhomogeneous medium positioned in the focal plane of the microscope objective by means of a series of incident light waves;

-determining a first distortion matrix (D) in an observation basis defined between a conjugate plane of said focal plane and an observation plane_ur、D_rr) In a correction basis defined between a conjugate plane of the focal plane and an aberration correction plane, corresponding to a first reflection matrix (R) of the field of view determined in the correction basis_ur) A itemized matrix product with a phase conjugate matrix of a reference reflection matrix defined for a model medium in the correction basis;

-a step of determining at least one mapping of physical parameters of the inhomogeneous medium on the basis of the first distortion matrix.

2. Method according to claim 1, wherein the first distortion matrix (D) is determined_ur、D_rr) The method comprises the following steps:

-experimentally determining said first reflection matrix (R) in said observation basis_ur、R_rr) A step (2);

-constructing the first distortion matrix on the basis of the first reflection matrix and the reference reflection matrix defined in the same basis.

3. The method of claim 2, wherein the observation basis is the correction basis and the first distortion matrix is determined from the first reflection matrix (R) of the field of view determined in the correction basis_ur) A term-by-term matrix product construction with a phase conjugate matrix of the reference reflection matrix defined in the same basis.

4. The method of claim 2Method, wherein the observation basis is a focus basis defined between two conjugate planes of the focal plane, and the first distortion matrix is formed by the focus reflection matrix (R) defined in the focus basis_rr) Is constructed with a spatial correlation between each row and/or column of the reference reflection matrix defined in the same basis and the same row and/or column of the reference reflection matrix.

5. The method of claim 1, wherein:

-the illuminating step comprises illuminating an objective arm and a reference arm of an interferometer by means of the same spatially coherent optical wave, the objective arm comprising the microscope objective (30) with the inhomogeneous medium positioned in its focal plane and the reference arm comprising a reference mirror (123);

-determining said first distortion matrix (D) in said correction basis_ur) And determining the first distortion matrix comprises the steps of:

o for a point (r) incident on said focal plane_in) Each optical wave of (a), acquiring in said correction plane an interferogram resulting from the interference between the electromagnetic field reflected by said point and the electromagnetic field reflected by said reference mirror;

o constructing the first distortion matrix for a point (r) focused at the focal plane_in) Each column of the first distortion matrix corresponds to an electromagnetic field associated with a cross-interference term of the interferogram.

6. The method of claim 1, wherein:

-the illuminating step comprises illuminating an objective arm and a reference arm of a first interferometer by means of spatially incoherent light waves, the objective arm comprising the microscope objective (30) with the inhomogeneous medium positioned in its focal plane and the reference arm comprising a reference mirror (153, 185), the waves reflected by the inhomogeneous medium and the reference mirror at the exit of the first interferometer showing a spatial shift in a plane conjugate to the focal plane, the shift being variable;

-determining said first distortion matrix (D) in a focus basis defined between two conjugate planes of said focal plane_rr) And determining the first distortion matrix comprises the steps of:

o for each spatial shift (r)_out-r_in) Acquiring an interferogram resulting from the interference between the waves reflected by the non-uniform medium and the reference mirror and spatially displaced in a conjugate plane of the focal plane;

o constructing the first distortion matrix, each row of the first distortion matrix corresponding to an electromagnetic field associated with a cross-interference term of the interferogram for a spatial shift value.

7. The method of any of the preceding claims, wherein determining at least one mapping of a physical parameter of the heterogeneous medium comprises:

-determining invariants in the focal plane of the first distortion matrix in order to identify at least one first isoplanar domain in the focal plane;

-for each first isoplanatic domain identified, determining a mapping of at least one first aberration law in the correction plane.

8. The method of claim 7, wherein determining the invariant in the focal plane of the first distortion matrix comprises a singular value decomposition of at least one of a set of matrices, the set of matrices comprising: the first distortion matrix, the first normalized distortion matrix, a normalized correlation matrix of the first distortion matrix.

9. The method of any of claims 7 and 8, further comprising determining, in the observation basis, a reflection matrix for the field of view corrected by the one or more first aberration laws.

10. The method of claim 9, further comprising:

-determining a second distortion matrix in the correction basis corresponding to a term-by-term matrix product of the corrected reflection matrix determined in the correction basis and a phase conjugate matrix of the reference reflection matrix.

11. The method of claim 10, further comprising:

-determining invariants in the focal plane of the second distortion matrix in order to identify at least one second halation domain in the focal plane;

-for each identified second aplanatic domain, determining a mapping of a second aberration law in the correction plane.

12. The method of any of the preceding claims, wherein determining at least one mapping of physical parameters of the non-uniform medium comprises determining, for the identified at least one first isoplanar domain, a first Point Spread Function (PSF) in the focal plane.

13. A system for non-invasive optical characterization of heterogeneous media, the system comprising:

-a first microscope objective (30) defining a focal plane in which the inhomogeneous medium is intended to be positioned;

-a light emitting device (110) for emitting a series of incident light waves intended to illuminate a given field of view of the heterogeneous medium through the microscope objective;

-a two-dimensional acquisition detector (130) arranged in an observation plane;

-a first interferometer coupled to the light emitting device and to the two-dimensional collecting detector, comprising an objective arm with the microscope objective (30) and a reference arm comprising a reference mirror at a focal point of a second microscope objective (123, 152, 184), the first interferometer being configured to create interference at the observation plane between the waves reflected by the inhomogeneous medium and the reference mirror,

-a calculation unit (140) coupled to the two-dimensional acquisition detector and configured to determine a first distortion matrix (D) in an observation basis defined between a conjugate plane of the focal plane and the observation plane on the basis of the interferogram resulting from the interference_ur、D_rr) A first distortion matrix corresponding to a first reflection matrix (R) of the field of view determined in a correction basis defined between a conjugate plane of the focal plane and an aberration correction plane in the correction basis_ur) A itemized matrix product with a phase conjugate matrix of a reference reflection matrix defined for a model medium in the correction basis;

determining at least one mapping of physical parameters of the inhomogeneous medium on the basis of the first distortion matrix.

14. The system for non-invasive optical characterization of heterogeneous media according to claim 13, wherein:

-the light emitting device (110) is configured to illuminate the objective arm and the reference arm by means of the same spatially coherent light wave;

-the observation plane is an aberration correction plane and the two-dimensional acquisition device is configured to be in the correction plane and for a point (r) incident in the focal plane_in) Each light wave at which an interferogram resulting from interference between the electromagnetic field reflected by the point and the electromagnetic field reflected by the reference mirror is acquired;

-the calculation unit is configured to construct the first distortion matrix for a point (r) focused at the focal plane_in) Each column of the first distortion matrix corresponds to an electromagnetic field associated with a cross-interference term of the interferogram.

15. The system for non-invasive optical characterization of heterogeneous media according to claim 13, wherein:

-the light emitting device (110) is configured to illuminate the entire field of view on the objective and reference arm by means of spatially incoherent light waves;

-the first interferometer is configured to form, at an exit of the first interferometer, waves reflected by the inhomogeneous medium and the reference mirror, the waves being mutually coherent and exhibiting a spatial shift in a plane conjugate to the focal plane, the shift being variable;

-the observation plane is a plane conjugate to the focal plane and the two-dimensional acquisition device is configured to acquire, in the observation plane and for each spatial shift, an interferogram resulting from the interference between the waves reflected by the non-homogeneous medium and the reference mirror and spatially shifted;

-the calculation unit is configured to construct the first distortion matrix, each row of which corresponds to an electromagnetic field associated with a cross-interference term of the interferogram for a spatial shift value.

16. The system for non-invasive optical characterization of heterogeneous media according to claim 15, wherein:

-the first interferometer comprises a first beam splitter (121) configured to form the objective arm (160) and the reference arm (150);

-the reference arm (150) comprises a second beam splitter (151) configured to send the illumination wave to the reference mirror (153) and to a second mirror (154) arranged in a plane conjugate to a pupil plane of the microscope objective and exhibiting a variable inclination (θ x) with respect to an optical axis defined by the optical axis of the microscope objective;

-the objective arm (160) comprises a third beam splitter (161) configured to send the illuminating wave to the heterogeneous medium (SMP) and to a third mirror (162), the third mirror (162) being arranged in a plane conjugate to a pupil plane of the microscope objective, perpendicular to an optical axis defined by the optical axis of the microscope objective.

17. The system for non-invasive optical characterization of heterogeneous media according to claim 15, further comprising:

-a second illumination interferometer (170) configured to receive the spatially incoherent light waves from the light-emitting device (110) and to form illumination waves of two polarizations having orthogonal polarizations and exhibiting a spatial shift in a plane conjugate to the focal plane; and wherein

-the first interferometer (180) comprises a polarizing beam splitting element (181) configured to send each of the polarized waves with orthogonal polarization and exhibiting a spatial shift to the objective arm and the reference arm, respectively.

Technical Field

The present description relates to methods and systems for non-invasive optical characterization of heterogeneous media, particularly biological media.

Background

The resolution of an optical imaging system is related to its ability to identify small details of an object. In a perfect optical system, resolution is limited in an absolute manner by diffraction to λ/2 (where λ is the wavelength used), and more generally by the maximum collection angle (i.e., numerical aperture) of the rays. The design of mirrors and aspherical lenses means that it is now known how to manufacture optical systems that operate at the diffraction limit, with several hundred years of improvement in polishing, from spectacles to microscopes and telescopes. However, the propagation medium between the optical imaging system and the plane to be imaged is not always uniform and may introduce aberrations, which may severely degrade the quality of the image.

To improve the quality of the image, astronomers have proposed to measure and compensate for these aberrations: this is the principle of adaptive optics proposed in the fifties of the twentieth century. This requires a loop that operates in real time between the wavefront measuring device and the wavefront correction device, all devices having response times on the order of milliseconds. With respect to wavefront measurement, Shack-Hartmann analyzers have taken advantage of advances in microfabrication and are now used primarily with CCD or CMOS cameras. With respect to wavefront correction, deformable mirrors now have available hundreds of actuators and speeds sufficient to correct aberrations produced by atmospheric disturbances in real time.

At the same time, on another scale, optical microscopy has made great progress in the quality of optics with increasingly larger numerical apertures and in imaging methods, with the advent of virtual field "slicing" techniques: confocal microscopy, structured illumination microscopy and non-linear microscopy. These techniques make it possible to obtain deep tissue images. In addition to these techniques, there are OCT (optical coherence tomography) from ophthalmology (which makes it possible to select a signal from a given depth by using the coherence of a light source), which is routinely used in medical practice to obtain 2D and 3D images of the retina. In all these cases, light passes through the tissue or deformed surface where the refractive index changes, and the quality of the image is reduced. However, only recently adaptive optics have been used in biomedical imaging (see, e.g., m.j.booth, Light sci.appl.3, e165 (2014)).

Although an "artificial star" can be generated in some cases by focusing a laser on the surface of the retina (as in astronomy), measuring the wavefront from the depth of a biological sample is more complex than measuring the wavefront from a star, particularly because it results from the incoherent superposition of echoes associated with unresolved scatterers, forming a speckle image.

The second method consists in correcting the aberrations without measuring the wavefront, simply by optimizing the quality of the image, i.e. by deforming the wavefront in a controlled manner so as to converge towards the optimal image. A disadvantage of this type of method is the choice of criteria for converging towards an optimized image.

In addition, the aberration experienced by the wavefront differs depending on the position on the image. These regions, which are referred to as isohalo domains and are described, for example, in the article by J.Mertz et al ("field of view adaptive optics in microscopics", application. Opt.54,3498-3506,2015), are often impossible to determine by inference. When the field of view or ("field of view" or "FOV") contains a plurality of iso-halo fields, correction of aberrations based on techniques known from the prior art often proves problematic.

The concept of an isoplanatic domain is illustrated in FIGS. 1A-1D. Imagine an aberrator membrane 11 placed between a microscope objective 10 and the focal plane of the microscope objective, which focal plane is represented by images 12a-12D, respectively, for each of fig. 1A-1D. In the embodiment of fig. 1A, the wavefront 13a incident on the microscope objective is uncorrected. It is thus distorted behind the aberrator membrane (wavefront 14a), which results in a focal spot 15a that is enlarged relative to the diffraction limit. In the embodiment of fig. 1B, the incident wavefront 13B is corrected, for example by means of adaptive optics, such that the wavefront 14B at the exit of the aberrator is perfectly corrected (spherical wave). This results in a diffraction-limited focal spot 15b at a given point r of the focal plane. If this same corrected wavefront is slightly angled (13C, FIG. 1C) to allow focusing at point r ', so that r-r' |<l_cWherein l is_cIs a characteristic parameter of the aberrator, called coherence length of the aberrator, the wavefront 14c from the aberrator remains corrected and focused at r' (focal spot 15c) is always diffraction limited. Points r and r' belong to the same iso-halo field of the field of view. However, if the corrected incident wave is further angled (13D, FIG. 1D) to allow focusing at point r ', such that r-r' |>l_cThen the wavefront 14d from the distorter is distorted and the applied correction does not allow diffraction-limited focusing at r' (focal spot 15 d). The points r and r' in this case belong to different iso-halo fields of the field of view.

In the context of the present description, a third approach is proposed which is neither based on the generation of artificial stars nor on the optimization of the wavefront based on any image quality criterion. The invention is based on a matrix-based approach to optical imaging and aberration correction.

For the purpose of communication, in particular, through highly scattering media, matrix-based methods of propagating light waves within non-uniform media were first developed in transmission — see the article by s.m. popoff et al (phys.rev.lett.104,100601, 2010). More recently, matrix-based methods have been used for depth imaging through highly scattering media (see A. Badon et al, "Smart optical coherence tomography for ultra-deep imaging through high elevation staining media", Sci. adv.2016; 2: e 1600370). This method, called "smart OCT" in the article, comprises experimentally determining a reflection matrix (or "focal plane" reflection matrix) in real space by means of an experimental setup, a diagram of which is shown in fig. 2.

The laser beam from the femtosecond laser source 21 is spatially shaped by a Spatial Light Modulator (SLM)22 as a dynamic diffraction grating. A set of plane waves is then emitted by the SLM, which are focused at different focal points r of the object focal plane of the microscope objective 23_inTo (3). For each focal point r_inReflection field E_r(u_out,r_inT) is collected by the same microscope objective 23 and is brought to the reference wave E on a two-dimensional acquisition device 24 (for example a CCD camera) conjugated to the pupil plane of the microscope objective₀(u_out0, t) interference. The temporally windowed reflection matrix R can be obtained by the interference pattern between the two waves integrated over time t_urCoefficient R (u) of column(s)_out,r_in)：

In practice, each coefficient R (u) is recorded by phase-shift interferometry_out，r_in) Amplitude and phase of (d). The time of flight τ is controlled by the length of the reference arm of the interferometer by means of a mirror 25, the position of which is adjusted by a piezoelectric actuator (PZT). For most applications envisaged, the time of flight is adjusted to the ballistic time in order to eliminate multiple scattered photonsAnd only those photons that are scattered individually by the reflector contained in the focal plane of the sample. For each incident focal point r in the focal plane_inCoefficient of reflection R (u)_out，r_in) Is recorded in the pupil of the objective lens of the exit microscope (by vector u)_outIdentified) in a plane conjugate to the focal point. Coordinate u_outThe two-dimensional Fourier transform of (a) makes it possible to determine the sum-of-vectors r_outReflection coefficient R (R) in a plane conjugate to the exit focal plane of the mark_out，r_in). For each incident focal point r in the focal plane_inThe reflection coefficient R (R) is recorded and stored along the column vector_out，r_in). Finally, the set of column vectors forms a reflection matrix R in the focal plane_rr. What is thus obtained is a temporally windowed "focal plane" reflection matrix whose diagonal elements (r)_in＝r_out) The "front" part of the image of the sample is formed because it is obtained in OCT (see for example published patent application US20040061867 for a description of full field OCT imaging). The "smart OCT" approach then consists in applying a filter to the focal plane reflection matrix in order to filter the off-diagonal elements of the reflection matrix that are mainly associated with the effect of multiple scattering. This mathematical operation thus amounts to digitally generating a confocal image with a virtual aperture of adjustable size determined according to the width of the aberration focal spot and the size of the object to be imaged. By combining the first input and output singular vectors, decomposing the resulting filtered matrix into singular values makes it possible to reconstruct an image of the focal plane from which most of the multiple scattering noise has been removed.

Thus, the "smart OCT" described in the article by a.badon et al makes it possible to increase the depth of penetration into highly scattering media by a factor of two with respect to OCT techniques and by means of matrix-based discrimination of single and multiple scattered photons. However, the methods developed so far only allow the detection of targets buried in a multiple scattering medium, and do not allow the correction of aberrations introduced by the optical system or by the medium itself, let alone the imaging of a field of view containing a plurality of isoplanar domains.

The present invention presents a novel matrix-based method for optical imaging and for simultaneous correction of aberrations over multiple isoplanatic regions of a field of view.

Disclosure of Invention

According to a first aspect, the present description relates to a method for non-invasive optical characterization of a sample formed from a heterogeneous medium, the method comprising:

-a step of illuminating a given field of view of the inhomogeneous medium positioned in the focal plane of the microscope objective by means of a series of incident light waves;

-a step of determining a first distortion matrix in an observation basis defined between a conjugate plane of the focal plane and an observation plane, the first distortion matrix being a term-by-term matrix product of, in a correction basis defined between a conjugate plane of the focal plane and an aberration correction plane, a first reflection matrix corresponding to the field of view determined in the correction basis and a phase conjugate matrix of a reference reflection matrix defined for a model medium in the correction basis;

-a step of determining at least one mapping of physical parameters of the inhomogeneous medium on the basis of the first distortion matrix.

Each coefficient or "element" of the first reflection matrix corresponds to a complex reflection coefficient of the sample determined at a point of the correction plane for a given focused illumination. It can be obtained via a cross interference term between the wave reflected by the sample for said focused illumination and the reference wave. The term-by-term matrix product or "Hadamard product" of the first reflection matrix multiplied by the phase conjugate matrix of the reference reflection matrix corresponds to subtracting the phase of the corresponding element of the reflection matrix defined for the model medium from the phase of each element of the reflection matrix. The expected ballistic component (defined by the model medium) is therefore subtracted from the phase of each element of the first reflection matrix, which makes it possible to isolate the distortion component for each illumination point of the field of view. The applicant has shown that analyzing the distortion matrix makes it possible in particular to identify the isohalo fields contained in the field of view and to determine, in the observation plane, the aberration laws associated with each isohalo field.

The model medium or "reference medium" is, for example, a homogeneous medium having an optical index equal to the effective index (or average index) of the propagation medium. Depending on the degree of a priori knowledge of the propagation medium, the model medium may take a more elaborate form (e.g., a multilayer medium, etc.).

Inhomogeneous media within the meaning of the present specification include any medium having a spatially inhomogeneous optical index and reflecting a part of an incident light wave. As an example, such a medium may in particular consist of layers of different optical indices, including layers of air when it is sought to observe it, such as elements located behind scattering objects; this may be a biological medium such as skin, retina or tissue resulting from a biopsy, but may also be other media which may be examined by microscopy, for example in metallography (sheet metal) or in petrography (rock analysis). The methods and systems described in this specification particularly allow for non-invasive deep optical characterization of such heterogeneous media.

Physical parameters of the heterogeneous medium may include, for example: aberration laws associated with each isoplanatic region contained in the field of view ("FOV"), a characteristic parameter of the optical reflectivity of the medium, a characteristic parameter of the refractive index of the medium, or a multiple scattering rate.

The aberrations of a wavefront propagating through a medium and/or an optical system correspond to the difference between the wavefront from this medium and/or optical system and the wavefront that would be expected in an ideal case. These aberrations may for example be related to imperfections of the optical imaging system (e.g. spherical aberration, coma, astigmatism, etc.). In the context of the present description, the aberration caused by the propagation medium itself, i.e. by spatial fluctuations in its optical refractive index, is mainly targeted.

The observation plane is for example an aberration correction plane, for example when a mapping of the aberration laws is sought. The aberration correction plane may be a plane conjugate to the pupil plane of the microscope objective or, when the plane of the aberrator may be considered as a two-dimensional phase screen, a plane conjugate to the plane of the aberrator. In a more general case, it is sought to find a correction plane that maximizes the size of the isohalo field contained in the field of view. The observation plane may also be a plane conjugated to the focal plane when seeking to plot a map of the point spread function of the imaging system (or the spatial impulse response of the imaging system) or a map of the multiple scattering rate.

The applicant has shown that the distortion matrix may comprise a preliminary step of determining said first reflection matrix, or be directly obtained by means of a specific experimental setup.

Thus, according to one or more exemplary embodiments, determining the first distortion matrix comprises the preliminary steps of: the first reflection matrix is determined in an observation basis (a reflection matrix windowed in time or determined in the frequency domain) and then the first distortion matrix is constructed on the basis of the first reflection matrix defined in the same basis and the reference reflection matrix.

According to one or more exemplary embodiments, the observation basis is a correction basis and the first distortion matrix is constructed from a itemized matrix product of said first reflection matrix of said field of view determined on the correction basis and a phase conjugate matrix of a reference reflection matrix defined in the same basis. According to one embodiment, the first reflection matrix can be determined experimentally in a different basis than the correction basis, and then the reflection matrix can be determined in the correction basis by merely changing the basis.

According to one or more exemplary embodiments, the observation basis is a focusing basis defined between two conjugate planes of the focal plane, and said first distortion matrix is constructed by a spatial correlation between each row and/or column of the "focal plane" and the same row and/or column of a reference reflection matrix defined in the same basis.

According to one or more exemplary embodiments, the reference medium is a homogeneous medium having an optical index equal to the effective index (or average index) of the propagation medium. A plane mirror in the focal plane of the microscope objective can be used theoretically to establish a reference reflection matrix for this reference medium. Depending on the degree of a priori knowledge of the propagation medium, the reference medium may take a more elaborate form (e.g., a multilayer medium, etc.). In this case, the reference matrix can be numerically calculated. The construction of the distortion matrix amounts to subtracting the phase of the corresponding element of the reference reflection matrix from the measured phase of each element of the first reflection matrix.

According to one or more exemplary embodiments, the determination of the first distortion matrix is obtained directly without the need to predetermine a reflection matrix.

According to one or more exemplary embodiments, determining the first distortion matrix is performed experimentally by means of at least one first interferometer illuminated with coherent light. The method is then characterized in that:

-the illuminating step comprises illuminating an objective arm and a reference arm of a first interferometer by means of the same spatially coherent optical wave, the objective arm comprising a microscope objective with the inhomogeneous medium positioned in its focal plane and the reference arm comprising a reference mirror;

-determining the first distortion matrix in the correction basis, and determining the first distortion matrix comprises the steps of:

acquiring, in the correction plane, for each light wave incident at a point of the focal plane, an interferogram resulting from the interference between the electromagnetic field reflected by said point and the electromagnetic field reflected by the reference mirror;

constructing the first distortion matrix, each column of which corresponds to the electromagnetic field associated with the cross-interference term of the interferogram for the incident light wave focused at a point of the focal plane.

By illuminating the objective arm and the reference arm with the same incident light wave, the applicant has shown that the electromagnetic fields associated with the cross interference terms of the interferogram thus obtained are directly associated with the distortion components of the reflected electromagnetic fields. The reference medium may be air or a more complex medium obtained, for example, by introducing a gel into the reference arm. The first interferometer is for example a linnic interferometer with two objectives on each arm, advantageously two identical objectives. The determination of the cross-interference term of the interferogram is obtained, for example, by phase-shifting interferometry. Thus, for an incident light wave focused at a point of the focal plane, each column of the first distortion matrix corresponds to a cross-interference term of the interference pattern produced by interference between the electromagnetic field measured in the observation plane and reflected by said point in the object mirror arm and the electromagnetic field reflected by a point conjugate to said point on the reference mirror. The correction plane is for example the conjugate plane of said plane of the exit pupil of the microscope objective. Focal plane scanning allows the reconstruction of the entire distortion matrix.

According to one or more exemplary embodiments, the first distortion matrix is experimentally determined by full-field low coherence interferometry in a focusing basis referred to as being defined between two conjugate planes of the focal plane. The method is then characterized in that:

-the illuminating step comprises illuminating the objective arm and the reference arm of the first interferometer with a full field of spatially incoherent light waves, the objective arm comprising a microscope objective with the inhomogeneous medium positioned in its focal plane and the reference arm comprising a reference mirror, the waves reflected by the inhomogeneous medium and the reference mirror at the output of the first interferometer exhibiting a spatial shift in the plane conjugate to the focal plane, which shift is variable;

-determining the first distortion matrix in a focus basis defined between two conjugate planes of a focus plane, and determining the first distortion matrix comprises the steps of:

acquiring, for each spatial shift, an interferogram produced by interference between said waves reflected by the inhomogeneous medium and the reference mirror and spatially shifted in a conjugate plane of the focal plane;

constructing the first distortion matrix, each row of the first distortion matrix corresponding to an electromagnetic field associated with a cross-interference term of the interferogram for a spatial shift value.

The applicant has shown that each row of said first distortion matrix thus determined is a diagonal of the "focal plane" reflection matrix. The distortion matrix can thus be determined under incoherent illumination and without focal plane scanning.

According to one or more exemplary embodiments, determining at least one mapping of a physical parameter of the heterogeneous medium comprises:

-determining invariants in the focal plane of the first distortion matrix in order to identify at least one first isoplanar domain in the focal plane;

-determining, for each first identified infinitesimal field, a mapping of a first aberration law in the aberration correction plane.

The correction plane in which the basis of the correction of said first distortion matrix is defined is advantageously a plane containing the field of view in which the size of the isoplanatic domain is maximized, for example a plane conjugate to the plane of the distorter in the case where the plane of the distorter is two-dimensional, or for example a plane conjugate to the pupil plane of the microscope objective. The first distortion matrix may be obtained directly in the observation basis or by changing the basis according to a distortion matrix determined in another basis, for example a "focal plane" distortion matrix.

To determine the invariant of the first distortion matrix, it can be implemented by several known methods. According to one or more exemplary embodiments, determining the invariant in the focal plane of the first distortion matrix comprises singular value decomposition of the first distortion matrix, singular value decomposition of the first normalized distortion matrix (that is to say that the modulus of each element thereof will have been normalized but the phase thereof will have been preserved), or singular value decomposition of a normalized correlation matrix of the first distortion matrix (that is to say a correlation matrix of the first distortion matrix whose modulus of each element thereof will have been normalized).

Given that this is often the case at optical frequencies by specular reflection from a non-uniform medium, the applicant has shown that a mapping of the reflectivity of the non-uniform medium over the entire field of view can be obtained by means of a linear combination of the singular vectors of said first distortion matrix.

The applicant has also shown that the singular value decomposition of the distortion matrix makes it possible to filter the noise subspace (random matrix without correlation between its rows and columns) of the signal subspace (matrix characterized by substantial correlation between its rows and/or its columns), which contains both experimental noise and the incoherent contribution of the reflected field caused by multiple scattering events occurring upstream of the focal plane.

According to one or more exemplary embodiments, the method according to the present description further comprises determining a point spread function of the imaging system. The point spread function (or impulse response or "PSF") of the imaging system corresponds to the spatial fourier transform of the aberration law measured in the pupil plane. It is spatially invariant over each isoplanatic domain. According to one embodiment, it may be obtained from the singular value decomposition of a "focal plane" distortion matrix.

According to one or more exemplary embodiments, the method according to the present description further comprises determining, in the observation basis, a first reflection matrix of the field of view corrected by the one or more first aberration laws. This makes it possible to determine a map of the reflectivity of the medium or "image" for aberration correction, especially when random scatter reflections by the sample are assumed.

On the basis of said corrected first reflection matrix of the field of view, according to one or more exemplary embodiments, a second distortion matrix can be determined. The second distortion matrix corresponds in the correction basis to a itemized matrix product of the corrected reflection matrix determined in the correction basis and a phase conjugate matrix of the reference reflection matrix. The second distortion matrix makes it possible to refine the correction in the identified first isocronous domain by determining its invariant in the focal plane. It also makes it possible to identify at least one second equihalo field in the focal plane and, for each second equihalo field identified, determine a mapping of a second aberration law in the correction plane. The method can therefore be iterated as many times as necessary, depending on the number of iso-halo fields contained in the field of view, in order to obtain a map of the reflectivity of the medium or "image" for aberration correction. This iterative process applies more particularly when random scattering or intermediate reflections, i.e. mixed specular and random scattered reflections, are assumed.

According to one or more exemplary embodiments, the method according to the present description further comprises identifying and/or eliminating reflection fields and/or specular components of multiple reflections occurring between various interfaces of the heterogeneous medium. For this purpose, the distortion matrix can be projected into the fourier plane both at the input and at the output. In this basis, specular and multiple reflection components are brought out of the field to obtain accurate reflection and angle of incidence pairs. They can therefore be easily filtered and only the random scattered component (speckle) of the reflected field is retained. This discrimination of the random scatter component then makes it possible to directly access the aberration laws to be applied at the input and output in order to correct the reflection matrix and obtain an optimal image of the medium. In particular, if the specular component is dominant, only the cumulative aberration law is accessed for the incident wave to go out and the reflected wave to return, which prevents the optimal correction of the random scattered component of the object. In addition, filtering the distortion matrix in the fourier plane makes it possible to eliminate multiple reflections between interfaces that may contaminate the optical coherence tomography image.

According to a second aspect, the present description relates to a system for implementing one or more exemplary embodiments of the method for non-invasive optical characterization of heterogeneous media according to the first aspect.

In particular, the present description relates to a system that allows to determine the first distortion matrix directly without having to predetermine the first reflection matrix by means of a suitable interferometric arrangement.

Thus, according to one or more exemplary embodiments, the present description relates to a system for non-invasive optical characterization of heterogeneous media, the system comprising:

-a first microscope objective defining a focal plane in which the inhomogeneous medium is intended to be positioned;

-a light emitting device for emitting a series of incident light waves intended to illuminate a given field of view of the heterogeneous medium through the microscope objective;

-a two-dimensional acquisition detector arranged in an observation plane;

a first interferometer coupled to the light emitting device and to the two-dimensional collecting detector, comprising an objective arm with the microscope objective and a reference arm comprising a reference mirror at a focus of the second microscope objective, the first interferometer being configured to form an interference at the observation plane between the waves reflected by the inhomogeneous medium and the reference mirror,

-a calculation unit coupled to the two-dimensional acquisition detector and configured to

Determining, on the basis of an interferogram produced by the interference, a first distortion matrix in an observation basis defined between a conjugate plane of the focal plane and the observation plane, the first distortion matrix being in a correction basis defined between a conjugate plane of the focal plane and an aberration correction plane, a term-by-term matrix product of a first reflection matrix corresponding to the field of view determined in the correction basis and a phase conjugate matrix of a reference reflection matrix defined for a model medium in the correction basis;

determining at least one mapping of physical parameters of the non-homogeneous medium on the basis of the first distortion matrix.

According to one or more exemplary embodiments, the light emitting device is configured to illuminate the objective arm and the reference arm by means of the same spatially coherent light wave.

According to this embodiment, the observation plane is an aberration correction plane and the two-dimensional acquisition device is configured to acquire, in said correction plane and for each light wave incident at a point of the focal plane, an interferogram resulting from interference between the electromagnetic field reflected by said point and the electromagnetic field reflected by the reference mirror. The calculation unit is configured to construct said first distortion matrix, each column of which corresponds to an electromagnetic field associated with a cross-interference term of said interferogram for an incident light wave focused at a point of the focal plane.

According to one or more exemplary embodiments, the light emitting device is configured to illuminate the entire field of view on the objective and reference arm by means of spatially incoherent light waves ("full field" illumination).

According to this embodiment, the system is configured to form, at the exit of said first interferometer, waves reflected by said inhomogeneous medium and said reference mirror, said waves being mutually coherent and exhibiting a spatial shift in a plane conjugate to the focal plane, which shift is variable. The observation plane is a plane conjugate to the focal plane and the two-dimensional acquisition device is configured to acquire, in said observation plane and for each spatial shift, an interferogram resulting from interference between said waves reflected by the inhomogeneous medium and the reference mirror and spatially shifted. The calculation unit is configured to construct the first distortion matrix, each row of the first distortion matrix corresponding to an electromagnetic field associated with a cross-interference term of the interferogram for a spatial shift value.

Such a system makes it possible to omit scanning of the field of view, relative to a system with coherent illumination.

The applicant has developed several systems that make it possible to achieve a variable spatial shift between the reflected wave and the reference wave.

Thus, according to a first exemplary embodiment, the first interferometer comprises a first beam splitter configured to form the objective lens and a reference arm. The reference arm comprises a second beam splitter configured to send the illumination wave to the reference mirror and to a second mirror arranged in a plane conjugate to a pupil plane of the microscope objective and exhibiting a variable inclination with respect to an optical axis defined by an optical axis of the microscope objective; the objective arm comprises a third beam splitter configured to send the illumination wave to the inhomogeneous medium and to a third mirror arranged in a plane conjugate to a pupil plane of the microscope objective, perpendicular to an optical axis defined by the optical axis of the microscope objective. The first interferometer includes a fourth beam splitter configured to combine waves from the objective lens and the reference arm reflected by the foreign-body medium and the reference mirror.

According to a second exemplary embodiment, the optical characterisation system further comprises a second illumination interferometer configured to receive said spatially incoherent light waves from the light emitting device and to form an illumination wave having two polarizations, orthogonal polarizations and exhibiting a spatial shift in a plane conjugate to the focal plane; the first interferometer includes a polarizing beam splitting element configured to transmit each of the polarized waves having orthogonal polarizations and exhibiting a spatial shift to an objective arm and a reference arm, respectively.

The orthogonal polarizations may be linear polarizations, circular polarizations or any other polarizations making it possible to form two orthogonal polarizations.

Such a system is advantageous in that it allows the two interferometers to be adjusted individually, which provides greater ease of use.

Drawings

Other advantages and features of the techniques presented above will become apparent from reading the following detailed description provided with reference to the drawings, in which:

FIGS. 1A-1D (already described) schematically illustrate the concept of an isoplanatic domain;

figure 2 (already described) schematically shows an experimental system for imaging by a scattering medium according to the prior art;

fig. 3A shows a simplified diagram of the various symbols that the system according to the present description allows to introduce, and fig. 3B shows a diagram illustrating a convention for representing a four-dimensional matrix;

fig. 4 and fig. 5A-5D show diagrams illustrating the concept of a distortion matrix;

6A to 6C illustrate (FIG. 6A) a first exemplary reflection matrix for a sample introducing specular reflection and for defocused defects (single isoplanar regions), (FIG. 6B) a corresponding focal plane reflection matrix and an exemplary point spread function obtained on the basis of the focal plane reflection matrix, and (FIG. 6C) a distortion matrix obtained on the basis of the reflection matrix of FIG. 6A, respectively;

FIGS. 7A to 7C illustrate the frequency spectrum of the normalized singular values of the distortion matrix shown in FIG. 6C, the first output eigenvector (U), respectively₁) And a first input feature vector (V)₁) Mapping of the modulus of (a);

figures 8A-8D illustrate (figures 8A, 8B) the focal plane reflection matrix before and after correction and (figures 8C, 8D) the confocal image deduced from the two matrices, respectively for the same embodiment as illustrated by means of figures 6A-6C (single isoplanar field);

9A-9D illustrate a second exemplary use of a distortion matrix (in the case of multiple isohalo fields), and more precisely, FIG. 9A, a diagram of an experimental setup; FIG. 9B, an embodiment of a measured planar reflection matrix and focal spots and confocal images extracted from the focal planar reflection matrix; FIG. 9C, a spectrum of normalized singular values of a distortion matrix corresponding to the measured reflection matrix; and FIG. 9D, output feature vector (U)_i) Mapping of the phase of (A), input eigenvectors (V)_i) A mapping of the moduli of (a), a conventional OCT image, an image obtained by adaptive optics and an image obtained by means of a combination of the input feature vectors;

10A-10D illustrate results obtained from numerical simulations of distortion matrices in the case of random phase resolution test patterns (random scatter reflections) imaged by distorters; thus, fig. 10A shows a confocal image of an object according to the prior art, and fig. 10B shows a first eigenvector U in the distortion matrix₁10C-D present the two first eigenvectors of the normalized correlation matrix at D (1)Andon the basis of which the image obtained after the iteration is corrected;

11A, 11B schematically illustrate a first embodiment of a characterization system (coherent illumination) according to the present description;

figures 12, 13 illustrate other embodiments of the characterization system according to the present description (incoherent illumination);

fig. 14A, 14B show a distortion matrix (fig. 14B) experimentally obtained by means of an experimental setup of the type of fig. 12 for a sample (resolution test pattern) (fig. 14A) observed through a diseased cornea;

FIGS. 15A-15E and FIGS. 16A-16E illustrate, on the one hand, the use of the distortion matrix shown in FIG. 14B to obtain a corrected image;

17A-17D illustrate the application of the method according to the present description to depth imaging of biological media under mixed specular and random scattering modes (experimental setup of the type of FIG. 13).

In various embodiments, which will be described with reference to the figures, similar or identical elements have the same reference numerals.

Detailed Description

In the following detailed description, only some embodiments are described in detail in order to ensure clarity of the description, but these examples are not intended to limit the general scope of the principles revealed from this specification.

The various embodiments and aspects described in this specification may be combined or simplified in a number of ways. In particular, unless otherwise specified, the steps of the various methods may be repeated, reversed, or performed in parallel.

When reference is made in this specification to computing or processing steps, particularly method steps, for embodiments, it should be understood that each computing or processing step may be implemented by software, hardware, firmware, microcode, or any suitable combination of these techniques. When software is used, each calculation or processing step may be implemented by computer program instructions or software code. The instructions may be stored in or transferred to a storage medium readable by a computer (or computing unit) and/or executed by the computer (or computing unit) to perform the calculations or process steps.

(definition of distortion matrix)

The present specification describes methods and systems for non-invasive optical characterization of non-uniform samples placed in the focal plane of a microscope objective. These methods and systems are based on the determination of at least one first matrix, referred to as "distortion matrix" in the remainder of the description.

The notation used in this description to identify the various planes of the optical system used for characterization of the sample is defined with the aid of fig. 3, fig. 3 illustrating only some of the elements of the system for the sake of simplicity.

Thus, a microscope objectThe focal plane of mirror 30 is referenced as FP and is intended to receive the sample. Let r denote the point of the focal plane FP, which is defined by its cartesian coordinates (x, y). Let InP denote the plane of the entrance pupil of the microscope objective or any plane conjugate to the plane of the entrance pupil of the microscope objective. The entrance pupil is intended to receive the incident light wave for illuminating the field of view of the sample it seeks to characterize. Let u_inThe point of the plane InP representing the entrance pupil, which is defined by its Cartesian coordinates (v)_in,w_in) And (4) defining. Let OutP denote the plane of the exit pupil of the microscope objective or any plane conjugate to the plane of the exit pupil of the microscope objective. The exit pupil is intended to receive light waves reflected by the field of view of the sample it seeks to characterize. Let u_outThe point of the plane OutP of the exit pupil, which point is represented by its Cartesian coordinates (v)_out,w_out) And (4) defining. The entrance and exit paths, which comprise an entrance pupil and an exit pupil, respectively, are separated in this embodiment by a beam splitter element 31. On the incident path, SP denotes the source plane of the optical system, which is conjugate to the focal plane of the microscope objective, in this embodiment forming the arrangement 4f together with the microscope objective 30 by means of the optics 32. Let r be_inA point representing the source plane SP, the point being represented by its Cartesian coordinates (x)_in,y_in) And (4) defining. On the exit path, ImP denotes the image plane of the optical system, which is conjugate to the focal plane of the microscope objective, in this embodiment forming the arrangement 4f together with the microscope objective 30 by means of the optics 33. Let r be_outA point representing the image plane ImP, the point being represented by its cartesian coordinates (x)_out,y_out) And (4) defining.

The distortion matrix corresponds to a term-by-term matrix product of a reflection matrix of the field of view determined in the correction basis and a phase conjugate matrix of a reference reflection matrix defined for a model medium in the correction basis defined between a conjugate plane of the focal plane and an aberration correction plane.

Experimentally, the reflection matrix can be measured actively by using a Spatial Light Modulator (SLM) illuminated by a spatially coherent light source at the time of emission, as explained with reference to prior art fig. 2. The cross-interference term between the field reflected by the sample in the observation plane and the reference field can then be measured on a CCD or CMOS camera by means of interferometric techniques ("four-image phase-shift" methods, off-axis holography, etc.). The reflection matrix thus corresponds in this case to a set of impulse responses between each pixel of the SLM and each pixel of the camera.

Note that the interferogram can also be formed in the frequency domain (e.g., using a spectrometer coupled to a CCD or CMOS camera). The reflection matrix can then be measured in the fourier domain and then reconstructed for each depth in the medium by summing over a given spectral band. In this case, a deep scan of the sample is obtained by recombining the matrices obtained at the different frequencies, rather than by means of a motorized translation of the sample along the optical axis.

The distortion matrix can then be numerically calculated on the basis of the reflection matrix. However, as will be described in more detail below, the distortion matrix may also be determined experimentally directly, without the need to predetermine the reflection matrix.

Furthermore, the reflection matrix and/or distortion matrix may be measured and studied between different planes of the optical component, and in the remainder of the description reference will be made to the reflection matrix and/or distortion matrix, regardless of the basis of the use. Thus, if the SLM and CCD camera have their surfaces conjugated to the pupil of the microscope objective lens that is sought to image the sample, the reflection matrix and/or distortion matrix may be defined, for example, in the pupil plane at transmission (InP) and in the pupil plane at reception (OutP). A reflection matrix and/or a distortion matrix may also be defined between the Source (SP) and receiver (ImP) planes conjugate to the plane of the object to be imaged. Finally, the reflection matrix and/or the distortion matrix may connect so-called "reciprocal" planes: a pupil plane at emission and a plane conjugate to the plane of the object at reception, and vice versa. In this specification, one or the other of these bases may be used, and the transition from one plane to another can be performed by a matrix operation involving a simple discrete spatial fourier transform.

It should also be noted that in this specification, the experimentally measured reflection matrix and/or distortion matrix is typically measured between 2D arrays of sensors (e.g. SLM and CCD cameras). The measured matrix thus has a 4D structure. To manipulate and represent these matrices, 2D arrays of sensors are cascaded according to input and output vectors such that the reflection matrix and/or distortion matrix ultimately take a two-dimensional form that is easier to manipulate and visualize.

As an example, FIG. 3B illustrates cascading matrices to form an input vector 36 having N elements (SLMs) and an output vector 37 having N elements (CCDs) based on²×N²A matrix 35 of individual elements. Each input vector r_in36N²The elements are arranged on columns of a matrix 35, whereas each output vector r_out37N²The elements are arranged on rows of the matrix 35.

Fig. 4 illustrates the concept of a distortion matrix by means of a simplified diagram.

A simplified diagram of a system for characterizing a sample similar to that of figure 3A is illustrated on the left hand side of figure 4. In this embodiment, the first transverse mode 41 is passed_aThe first incident light wave characterized in the entrance pupil InP of the microscope objective 30 is applied, for example, by means of an SLM (not shown) so as to be focused on the focal plane of the microscope objective. This transverse mode is focused at a point r with the source plane SP (not shown)_inaAt the focus of the conjugate focal plane FP. By the second transverse mode 41_bThe second incident light, characterized in the entrance pupil InP of the microscope objective 30, is focused at a point r from the source plane SP_inbAt the focus of the conjugate focal plane FP. The reflected electromagnetic field is measured in fourier space (in this embodiment the exit pupil plane OutP) by a CCD camera (not shown), for example by means of known interferometric techniques (not shown). Image 42_aAnd 42_bRespectively illustrate an incident point r_inaAnd r_inbThe phase of the reflected electromagnetic field. These two-dimensional fields are represented by a vector u_outAnd (5) identifying. After cascading, they form a reflection matrix R between the exit pupil plane OutP and the source plane SP_ur(not shown) two columns. This matrix R_urEach column of (a) thus corresponds to a column for focusing at the focal planePoint r_inAt the pupil plane OutP (by u)_outMarkers) are detected.

The reflected electromagnetic field has a geometric component (plane wave) and a distortion component, the projections of which on the CCD camera pass through the respective incident focal points r_inaAnd r_inbImage 43 of_aAnd 43_bIllustrating that the distortion component is generated, for example, by a distorter schematically illustrated by an aberration layer 40 in fig. 4. Image 44_aAnd 44_bIllustrating a reflection of an electromagnetic field 42_aAnd 42_bA distortion component of the wavefront of each of the first and second sets. After cascading, wavefront 44_aAnd 44_bForming a distortion matrix D_urTwo columns (image 45 of fig. 4). Distortion matrix D_urIs thus determined by the vector u measured in the observation plane_outIdentified, different focal points r of the field of view_inDistortion components of the reflected electromagnetic field are formed.

In practice, to isolate the distortion component of the reflected wavefront, the phase that would ideally be obtained for the model medium in the absence of aberrations is subtracted from the phase of the reflected electromagnetic field, as illustrated in FIGS. 5A-5D.

As illustrated in fig. 5A, in the presence of the distorter 40, is formed so as to be in the focal point r_inAn emitted incident wavefront 52 focused in the focal plane FP of the microscope objective 30_aDue to aberrator membranes (wavefront 53)_a) While distorting and creating an aberration focal spot 54 in the focal plane FP_a. This incident field is reflected by the medium (fig. 5B). Reflected wavefront 55_aAgain through the aberrator membrane and then at the pupil plane OutP (wavefront 56), for example by means of interferometric techniques_a) Is measured. This reflected field R (u)_out,r_in) Having a diffraction-related geometric component and a distorter-related distortion component. To separate these two components, imagine the same experiment without distorter, with the reference medium and the plane mirror in the focal plane (fig. 5C, 5D). The same incident wavefront 52_bIs formed so as to be focused at a focal point r_inGenerating a non-aberrated focal spot 52 at and in the focal plane FP_b. This is toThe field is reflected by a mirror in the focal plane (fig. 5D). Eventually at the pupil plane OutP (wavefront 56)_b) To determine the reflected wavefront 55_b. By subtracting the phase of this ideal field from the phase of the experimentally measured field, the distortion component D (u) of the field is extracted_out,r_in) Which will form a matrix D_urThe column (c). By repeating this operation for each point of the focal plane, a distortion matrix D is obtained_ur。

In the case of a model medium that is homogeneous and a perfect mirror placed in the focal plane, by G₀(u_out,r_in) Shown ideal reception field 56_bContains only the geometrical components associated with diffraction and is simply a plane wave. G₀Is the propagation matrix between the source plane SP and the pupil plane OutP, where:

where j is the unit of an imaginary number,is a constant phase term, f is the focal length of the microscope objective and λ is the wavelength of the incident wavefront. Equation (1) reflects the spatial fourier transform relationship between the fields from the source plane SP (and its conjugate plane) and the exit pupil plane OutP.

Thus, the distortion matrix D can be constructed in the observation plane by means of the following Hadamard matrix product (i.e. term-by-term matrix product):

whereinIs G₀And o denotes a term-by-term matrix product (Hadamard matrix product). Recall that matrix G is₀Phase conjugate matrix ofIs an element having a structure of₀The same modulus but opposite complex number of arguments.

In the case of heterogeneous model media, G₀Becomes more complex than the expression given in equation (1). For example, in the case of a multilayer medium of variable optical index, the matrix G may be analytically calculated by a matrix product between different transmission matrices associated with the propagation of waves in each layer₀. For more complex model media, typically media that are not translationally invariant (e.g., curved interfaces), the matrix G may be determined by numerical simulation or semi-analytical calculations₀。

The distortion matrix can also be studied in the focal plane. Can be changed in the observation plane D via the following basis_urObtaining a 'focal plane' distortion matrix D on the basis of the distortion matrix expressed in_rr：

I.e. by matrix coefficients

Wherein the indexDenotes a conjugate transpose matrix operation and C is a constant. D_rrCorresponds to the column at the focal point r_inUp to the reflected field in the re-centered image plane. Matrix D_rrThus giving a change in the reflection point spread function of the imaging system at each point of the field of view, which is the impulse response of the imaging system, that is to say the focal spot which is re-centered on the irradiated point. As will be described below, this makes it possible to quantify and characterize the aberrations caused by the sample upstream of the focal plane.

In order to further analyze the distortionMatrix D_urIt is advantageously possible to consider, on the one hand, the case in which the reflection by the sample is predominantly specular, and, on the other hand, the case in which the reflection is predominantly random scattering. The two modes can be determined by determining a parameter delta representing a characteristic dimension of the aberration focal spot_ACharacterizing the dimension of spatial variation L of the disordered potential associated with the heterogeneous medium. More precisely, δ can be modeled in the case of a distorter that can be modeled as a two-dimensional random phase screen_AThe writing method comprises the following steps:

wherein l_cIs the coherence length of the aberrator and z is the distance between the aberrator plate and the focal plane PF. If L is>δ_AAn approximation of the specular reflection mode can be made (as is often the case in the mode of light wavelengths). In the opposite case, the sample causes random scattered reflections. In practice, it is often the intermediate case of combining random scattered reflection and specular reflection. In the case of specular reflection, the distortion matrix D_urVisually presenting the correlation between its columns. As will be described below, these correlations correspond to repetitions of the same distortion pattern for wavefronts from the same halo field. For samples causing random scattered reflections, e.g. speckle type (random distribution of unresolved scatterers), the distortion matrix D can be studied_urTo reveal these same correlations. In either case, as will be described in more detail below, the matrix D is searched, for example by means of Singular Value Decomposition (SVD)_urMakes it possible to extract the complex transmittance of the distorter for each point of the focal plane, thereby optimally correcting the aberration included in each of the isoplanar regions in the field of view.

Fig. 6A to 6C illustrate an exemplary reflection matrix, a corresponding focal plane reflection matrix and a distortion matrix, respectively, determined experimentally for a 10 μm defocus defect in the case of a sample causing specular reflection (resolution test pattern). The experimental set-up is the experimental set-up shown in figure 2. Using 3136 poly (N)Focus illumination (spatial resolution 4.5 μm) to scan 250X 250 μm²The field of view of (a).

FIG. 6A illustrates a reflection matrix R measured between a focal plane (SP) at emission and a pupil plane (OutP) at reception_urThe phase of (image 61). Each column of this matrix includes for a given point r in the pupil plane_inThe field reflected by the illumination. Image 610 shows the image with R_urThe column of (a) corresponds to the phase of this complex field. The phase measured here corresponds to the phase G of the field expected in the ideal case₀(u_out,r_in) (611) are greatly different. To isolate aberration-related distortions of the wavefront, the expected ideal phase (611) may be subtracted from the experimentally measured phase (610). The phase mask (612) thus obtained corresponds to the distortion matrix D_urColumn of (equation 2). Which collects together the aberrations experienced by the incident and reflected waves through the microscope objective. Here, these are fresnel ring characteristics of defocusing defects.

Focal plane reflection matrix R_rrShown (as modulus) in fig. 6B (image 613). The focal plane reflection matrix is a reflection matrix R measured between a focal plane (SP) at emission and a pupil plane (OutP) at reception by merely changing the basis_urObtained on the basis of (1). The focal spot (image 614) for focusing the incident wave in the center of the field of view is a reflection matrix R from the focal plane_rrIs obtained from the central column of (1). Energy in R_rrBeyond the extension of one pixel (i.e., resolution unit) the dispersion (image 613) and focal spot (image 614) outside the diagonal and quantify the level of aberration present in the experiments described herein.

In the reflection matrix R_rrBased on the formed distortion matrix D_urIs shown in fig. 6C (image 62). It shows substantial correlation, either along its rows or columns, as evidenced by the close-up of some of its elements shown in image 621. The correlation along the column is related to the fact that: distortion of wavefront and reflectivity of object according to focus r_inSlowly changing. Images 622 and 623 illustrate D in two-dimensional form_urTwo radically different columns of associated phasesBit distortion. The similarity between these two images demonstrates the spatial invariance property of defocus defects. This means that these points of the field of view are associated with the same wavefront distortion; in other words, they are located in the same isohalo domain. Matrix D_urIs inherent to the deterministic nature of the aberration laws (fresnel rings) associated with defocus defects.

Still assuming that the sample causes specular reflection, an exemplary use of determining a map of one or more laws of aberrations in the observation plane, in particular a distortion matrix that establishes a map of the reflectivity of the sample, is described below.

For this purpose, invariance of the distortion matrix, in other words the aberration law, which is spatially invariant over the isohalo field of the field of view, is sought. Various methods for searching invariants of such matrices, such as, for example, singular value decomposition (or "SVD") or principal component analysis ("PCA"), are known to those skilled in the art.

Singular value decomposition is a powerful tool for extracting the correlation between rows or columns of a matrix. Mathematically, the size is N²×N²Matrix D of_urThe SVD of (1) is written as follows:

u and V are dimensions N²×N²Of the unit matrix of_iAnd V_iCorresponding to the output feature vector and the input feature vector. Index of refractionRepresenting a conjugate transpose matrix. Each output feature vector U_iIs defined by a vector u_outIn the identified pupil plane. Each input feature vector V_iAnd is thus defined in the focal plane identified by the vector r. Size N²×N²A matrix whose diagonal elements only are non-zero:

the diagonal element of the matrix Σ is the matrix D_urSingular value of_iThey are real, positive and ranked in descending order:

matrix D_urCoefficient D (u) of_out,r_in) Thus written as the sum:

SVD mainly decomposes the matrix into two subspaces: a signal subspace (a matrix characterized by substantial correlation between its rows and/or its columns) and a noise subspace (a random matrix with no correlation between its rows and columns). The signal subspace is associated with the largest singular values, whereas the noise subspace is associated with the smallest singular values. On the one hand, the SVD of D will thus make it possible to filter a noise subspace containing both experimental noise and incoherent contributions of the reflected field caused by multiple scattering events. On the other hand, each singular state of the signal subspace will make it possible to derive the output eigenvectors U from them_iThe distortion experienced by the wave in the pupil plane is extracted for each region of the image which itself will be represented by the input feature vector V_iAnd (5) identifying.

FIGS. 7A-7C illustrate the distortion matrix D shown in the image 62 under the experimental conditions described above (FIGS. 6A-6C), respectively_ur(FIG. 6C) normalized singular value spectra, first output eigenvectors U₁And a first input eigenvector V of the assumed defocused defect₁The modulus of (a).

As illustrated in FIG. 7A, the distribution of normalized singular values is represented by the first singular value σ₁And (6) determining. Associated feature vector U₁And V₁Is shown in FIG. 7B (U)₁Phase of) and fig. 7C (V)₁Modulus of (d). At defocused defectsIn this case, the distortion of the wavefront does not vary depending on the focal point in the field of view. In other words, the field of view contains only one isoplanar region. In the case of specular reflection, the output eigenvector U can be expressed₁Given the distortion caused by the distorter cumulatively going out and returning:

U₁(u_out)＝A(u_out)A(u_in)δ(u_out+u_in) (10)

wherein A (u)_out) And A (u)_in) Is the distortion experienced by the wavefront going out and back and projected into the pupil plane (identified by vector u). The dirac distribution δ in the preceding equation reflects the fact that in the specular reflection mode, at incidence, comes from a point u in the pupil plane_inWill generate a focus on u upon emergence_out＝-u_inThe reflected wave of (2). In FIG. 7B, the first output feature vector U₁Does take the form of a fresnel ring, which is characteristic of the aberration law associated with defocus defects. Additionally, an input feature vector V can be declared₁Reflectance ρ for which an object can be directly accessed:

V₁(r_in)＝ρ(r_in) (11)

FIG. 7C shows the input feature vector v₁An image of a given object. This corrected image will be compared with the original image subjected to the defocus defect shown in fig. 8C.

By following the output feature vector U₁Correcting the measured reflection matrix R by extracting the distorted phase conjugate of the wavefront_ur(61, FIG. 6A). Physically, the phase conjugation operation consists in re-transmitting the wavefront modulated by a phase opposite to that of the measured distortion. This operation then makes it possible to perfectly compensate for the phase distortion accumulated by the wave on its outward and backward travel. Mathematically, here by pairing matrices R_urThe following correction is applied to perform the phase conjugation operation:

R′_uw＝exp(-j×arg{U₁})cR_ue (12)

wherein arg { U }₁Denotes U₁The phase of (c).

R 'may then be driven by varying the basis upon exit from the pupil plane (OutP) to the image plane (ImP)'_urDeducing a corrected matrix R'_rr. May be from matrix R'_rrDiagonal line (r) of_in＝r_out) The corrected confocal image I' is deduced:

I′(r_in)＝R′(r_in，r_in) (13)

I′(r_in) Then the reflectance of the sample ρ (r)_in) A reliable estimator of (1).

Fig. 8A to 8D illustrate the effect of such correction by comparing the reflection matrices before and after correction and the confocal image obtained in each case, respectively. FIG. 8A shows the focal plane reflection matrix R before comparative calibration_rr(image 811) and applying vector exp (-jar { U) from the pupil plane upon exit₁}) followed by a reflection matrix R'_rr(image 813). And R_rrComparative energy at R'_rrThe concentration around the diagonal line of (a) shows the effect on aberration correction. From the reflection matrix R_rrFocal spot 812 inferred from the column of (image 811) and from the corrected reflection matrix R'_rrThe same column inferred focal spot 814 (fig. 8B) of (image 813) is compared. Obtaining a focal spot (image 814) whose size is only diffraction limited also demonstrates the quality of aberration correction. From corrected matrix R'_rrDeduced confocal image (FIG. 8D) and slave matrix R_rrThe deduced initial confocal images (fig. 8C) were compared. The image obtained (FIG. 8D) is associated with the vector V₁The image provided (fig. 7C) is of equal quality. Figure 8 thus illustrates the success of the method for imaging a specular object in the presence of aberrations.

In the previous embodiments illustrated by means of fig. 6 to 8, an embodiment of the experimental determination and analysis of the distortion matrix has been seen, in particular comprising the calculation of the aberration law for defocus defects; the field of view contains only one isoplanatic domain. Attention is now directed to the general case where the field of view includes multiple iso-halo fields.

Fig. 9A to 9D illustrate an embodiment in which the distorter is formed of a plastic film in this example. As illustrated in the inset 90 of fig. 9A, the plastic aberrator membrane 40 is positioned between the microscope objective 30 and the focal plane FP at which the sample (resolution test pattern) is arranged in its horizontal plane.

The rough and irregular surface of the plastic film causes substantial deformation of the incident and reflected wavefronts. The measurement of the reflection matrix is performed for N441 incident illuminations, making it possible to pair 240 × 240 μm at a spatial interval δ r of 12 μm²Is imaged.

Effect of aberrations the reflection matrix R measured in the focal plane (911, FIG. 9B)_rrThe above is particularly significant. Although in the ideal case this matrix is near diagonal, a substantial expansion of the reflected field outside this diagonal is observed here. Under these conditions, the point spread functionality of the imaging system is heavily degraded, such as by the slave matrix R_rrRandom aspects of the inferred characteristic focal spot (fig. 9B, 911). The confocal image (fig. 9B, 913) deduced from this reflection matrix also shows completely random aspects independent of the reflectivity of the resolution test pattern.

From R_urThe (equation 2) inferred distortion matrix is analyzed in the form of SVD. By σ₁The spectrum of the normalized singular values is shown in fig. 9C. A continuum of singular values is obtained, demonstrating that the prior field of view contains a plurality of isoplanar domains. Three first eigenvectors in the pupil plane and the focal plane are shown in images 91-93 and 94-96, respectively (FIG. 9C). Output feature vector U_iIndicating that the distortion caused by the wavefront is complex and associated with high spatial frequencies, and defocus defects [ FIG. 7B]The situation is different. Input feature vector V_iObjects (images 94-96) in the focal plane are resolved throughout the different iso-halo regions. They therefore differ from one another in the pupil plane by the law of aberration U_iAssociation [ images 91-93]. By associated characteristic valuesWeighted feature vector V_iCan ultimately access an image of the field of view corrected for the upstream induced aberrations

Where Q is the number of iso-halo fields contained in the field of view. Three first eigenvectors V_iThe combination of (a) gives a high contrast and well resolved image of the resolution test pattern (image 99). Comparison with the original confocal image (image 97) is striking and demonstrates the success of the method. The benefit of local aberration correction (image 99) is also revealed by comparison with image 98 which would be obtained by means of conventional adaptive optics techniques (prior art).

After dealing with the case of specular reflection, which is typically caused by an extended object, the problem of random scattered reflection is now addressed. Random scatter reflections are usually caused by a random distribution of under-resolved scatterers, i.e. especially the situation encountered in biological tissue. An iterative method (post-processing) which still performs aberration correction based on the distortion matrix is therefore suitable.

Step #0 of the process is equivalent to the specular reflection case presented above. By a distortion matrix D_urFirst feature vector U of (equation 10)₁To correct the matrix R at the output_ur. The resulting corrected matrix is composed ofAnd (4) showing. This initial step makes it possible to perform an overall correction for aberrations throughout the entire field of view.

Step #1 consists in recalculating the value defined from this time between the entrance pupil plane and the exit focal planeInferred new distortion matrixThe stochastic nature of the object now means that the study is in the pupil planeIn (2) correlation ofMatrix, i.e.Becomes more significant. The matrix B⁽¹⁾Is used to decompose the singular value of the phase of (exp jarg { B)⁽¹⁾}]Giving a new set of feature vectors associated with each isohalo region of the field of viewThe corresponding reflection matrix can thus be corrected at the input at this time:

the following step consists in reproducing the same process by correcting the residual aberrations alternately at the input (even iterations) and at the output (odd iterations). However, in each step, the correlation matrix exp [ jar { B } of the distortion matrix in the pupil plane is still used⁽ⁿ⁾}]First eigenvector of phase (D)The correction is performed. Specifically, selection of the isoplanarity is performed in step # 1. Depending on whether the correction is at the input or at the output, the pupil plane B⁽ⁿ⁾The correlation matrix in (a) is given by: for even number n (output)And for odd n (input)At each step of the process, the reflection matrix, which may be expressed in the focal plane, may be derived fromThe diagonal of (a) infers the image of the field of view. In practice, several iterations are sufficient to obtain the best correction for the selected isohalo region. An image of the entire field of view can then be obtained by combining the corrections determined for each of the iso-halo regions.

Fig. 10 illustrates the benefits of the method according to the present description by means of numerical simulations involving an object whose reflectivity is that of the resolution test pattern in absolute value, but whose phase is random (which gives rise to a diffuse reflection pattern). A reflection matrix is simulated for an aberrator generating an approximately five-fold amplification of the focal spot and the iso-halo field covering the field of view 1/10. Fig. 10A shows an initial confocal image subjected to aberration. FIG. 10B shows the use of the vector U being enabled₁Reflection matrix after step #0 of overall correcting aberrationThe confocal image of (1). In the next step, the correlation matrix exp [ jarg { B ] is normalized⁽ⁱ⁾}]Feature vector ofRank i to select the isohalo field. FIGS. 10C and 10D show the vectorAndon the basis of confocal images obtained after iterations of correcting aberrations. As expected, these images are associated with different iso-halo fields of the field of view and give a real image of the object in each of these fields.

Knowing the aberration at each point of the sample can be used not only very well for imaging, but also for focusing the light at any point of the sample. For example, on the experimental setup of fig. 2, it may be necessary to apply phase modulation to the SLM that aggregates: (1) a geometric phase law associated with the model medium for focusing on the target point; (2) the conjugate of the aberration law determined on the basis of the distortion matrix for the isohalo region containing the target point. In the specular reflection mode, the applied aberration correction law will correspond to the iso-halo region V containing the target point_iAssociated distortion matrix D_urOutput feature vector U of_iThe phase of (c). In the random powderIn the case of shots, it would be the problem of aggregating all corrections for the aberrations obtained at the input of the sample according to the vector W:

in addition to the knowledge of the reflectivity of the medium or of the law of aberrations at each point of the sample, the distortion matrix also makes it possible to perform 3D tomography on the optical index of the sample under investigation. From the "focal plane" distortion matrix D_rrThe point spread function in the sample can be accessed as well as the iso-halo region. Instead of correcting the image directly, the idea is to change the reference medium on which the distortion matrix is calculated from the reflection matrix. This leads to an iterative approach to the distortion matrix, where the reference medium is made to change in the direction of a more complex model (e.g., a multi-layer medium) in order to reduce the spatial extent of the point spread function and increase the size of the isoplanar regions. By going deeper and deeper into the sample, it is possible to reconstruct gradually a three-dimensional map of the refractive index, while obtaining an image of the reflectivity of the medium, which is more realistic the closer the reference medium is to reality.

"focal plane" distortion matrix D_rrAccess to the point spread function of the imaging system at any point of the field of view is provided. Thus, even after correction for aberrations, a residual incoherent background remains in the matrix D_rrOn each column of (a). This incoherent background is caused by multiple scattering events occurring upstream of the focal plane. And therefore can be at the level of the incoherent background (| r)_out-r_in| > δ) and D_rrCentral row (r) of_out＝r_in) The multiple scattering power gamma (r) is locally measured on the basis of the ratio of the signal levels above_in)：

Wherein the symbol < … > represents the center element (| r)_out-r_in| > δ) along D_rrAverage value of each column of (1). Attached withAdditionally, by taking longer than the ballistic time, for example by controlling the reference arm in the interferometer of fig. 2, the point spread function may also make it possible to follow the growth of the diffuse halo within the medium and derive therefrom a local measurement of the transmission parameter of the multiply scattered wave (scattering coefficient or mean free transmission path). Studying a diffuse halo in a short time allows access to a finer spatial resolution than that obtained by the prior art in random scatter optical tomography [ A.Badon et al, Optica 3,1160-]。

According to one or more exemplary embodiments, the characterization method further includes identifying and/or eliminating specular components of the reflected field and/or multiple reflections occurring between various interfaces of the heterogeneous medium. In particular, the reflector is never perfectly specular and its random scatter components will then not be optimally corrected by iterating equations (12) and (15). In addition, specular reflectors can cause multiple reflections between their interfaces, which can blur the image. It is therefore necessary to be able to separate the specular and random scattered components of the field reflected by the medium. To this end, the distortion matrix can be projected both at the input and at the output into the basis defined by the aberration correction plane. Can be derived from the original distortion matrix D by means of the following basic variations_urObtaining a "Fourier plane" distortion matrix D_uu：

D_uu＝D_ur ^tG₀ (18)

The previous equation is therefore rewritten in terms of matrix coefficients as follows:

specular and multiple reflection components for exact pairs u_inAnd u_outOccur such that

u_in+u_out＝u (20)

Where u/λ f is the spatial frequency of the specular object. If the specular reflector is arranged perpendicular to the optical axis, u is, for example, zero. The specular and multi-reflection components can thus be easily filtered and only the random scattered components (speckle) of the reflected field can be retained in order to accurately determine the induced aberrations and correct them. This discrimination of the random scatter component then allows direct access to the aberration laws to be applied iteratively at the input and output in order to correct the reflection matrix and obtain the best image of the medium (iterative correction at the output and input according to equations (12) and (15)), which is not possible in the case of a dominance of the specular component [ a single correction applied at the output according to equation (12) ]. In addition, filtering the distortion matrix in the fourier plane makes it possible to eliminate multiple reflections that contaminate, for example, the image close to the interface (multiple echoes between the interfaces of the medium).

As explained above, an experimental setup such as described in the article of a.badon et al cited in the "prior art" section of the present application may be used to determine the reflection matrix of the field of view in the basis defined between the conjugate plane of the focal plane and the observation plane, e.g. the plane conjugate to the pupil plane of the microscope objective. Each column of the reflection matrix then corresponds to a cross-interference term measured in the observation plane between the wave reflected by the sample and a reference wave for the incident wave focused at a given point of the focal plane. As described above, the distortion matrix may then be calculated on the basis of the reflection matrix thus determined and the reference reflection matrix.

Of course, other arrangements known from the prior art may be used for the measurement of the reflection matrix. For example, in the article by Kang et al ("Imaging depth with a patterned reflective accumulation of single-patterned waves" nat. photonics 9,253-258(2015)), the optical setup allows the reflection matrix in the pupil plane to be measured at the input and output. By applying the basic changes at the input for projection into a plane conjugate to the focal plane, a distortion matrix can be constructed on the basis of such a reflection matrix.

The applicant has also shown that it is possible to implement an experimental setup that allows to directly measure the first distortion matrix without having to go through a predetermined determination of the reflection matrix.

Exemplary settings are presented with the aid of fig. 11 to 13.

Fig. 11A and 11B thus present a first exemplary embodiment of a system for non-invasive optical characterization of heterogeneous media, allowing for the experimental determination of a distortion matrix. In this embodiment, the light source is spatially coherent and the distortion matrix is measured in the basis defined between a source plane conjugated to the focal plane and an observation plane conjugated to the plane OutP of the exit pupil of the microscope objective. Of course, another viewing plane can be chosen, as explained above.

More precisely, the system 100 schematically shown in fig. 11A and 11B comprises a microscope objective 30 defining a focal plane FP in which a sample SMP formed from a heterogeneous medium is intended to be positioned.

The system 100 comprises a light emitting device 110 configured to emit a series of incident light waves intended to illuminate a given field of view of the sample through the microscope objective 30. More precisely in this embodiment, the light emitting device 110 comprises a spatially coherent light source (not shown) positioned, for example, in the object focal plane or source plane SP of a lens 111 for illuminating a Spatial Light Modulator (SLM)112 by means of a beam splitter 113. The SLM acts as a dynamic diffraction grating and forms a set of plane waves intended to be focused at the same number of focal points r of the focal plane of the microscope objective lens 30_inTo (3). FIGS. 11A and 11B illustrate the formation of two plane waves by SLM 112, respectively, whose phases are represented by images 114, respectively_a、114_bTwo focal points r representing and intended to be focused in the focal plane FP of a microscope objective_in,aAnd r_in,bTo (3). The spatially coherent light source is advantageously a broadband light source, such as a superluminescent diode or a femtosecond laser.

The system 100 further comprises an interferometric measuring device 120, in this embodiment a linnik interferometer, a two-dimensional acquisition detector 130, for example a CCD or CMOS camera, and a calculation unit 140, in particular receiving a photoelectric signal from the detector 130.

The linnik interferometer 120 includes a beam splitter element 121 that allows the formation of an objective arm and a reference arm. The microscope objective 30, at the focal point of which the sample SMP is arranged, is located on the objective arm. A second microscope objective 122, which may be identical to the microscope objective 30, and a reference mirror 123, which is arranged in the focal plane of the second microscope objective 122, are located on the reference arm. The linnik interferometer 120 is coupled to the light emitting device 110 to scan incident waves focused in the focal plane of the microscope objectives 30 and 122. A two-dimensional collection detector 130 is used to record the interference (interferogram) between the beams from the objective and reference arm for each focus in the pupil plane of the microscope objective.

For each focal point r_inMultiple interferograms are recorded for different positions of the reference mirror. By means of phase-shifting interferometry [ A. Dubois et al, "" High resolution full field optical coherence tomography with a Linnik microscope, appl. Opt.41,805(2002)]The computing unit 140 reconstructs the cross interference term between the complex electromagnetic field (131A, 131B in fig. 11A, 11B, respectively) reflected by the sample SMP and the reference wave; it corresponds to the distortion matrix D_ur＝[D(u_out,r_in) The column (c). In particular, by measuring the beam from the objective arm E in the pupil plane, rather than in the image plane conjugate to the focal plane_r(u_out，r_inField E of t)_r(u_out，r_inT) and the field E from the reference arm_r(u_out，r_inT), the applicant has shown that it is possible to determine the distortion matrix D directly_ur：

If nothing is between the microscope objective and the mirror, the reference medium is air. If a gel is introduced between the microscope objective and the mirror, the reference medium will be a homogeneous medium with an optical index close to that of the biological tissue.

The calculation unit 140 is further particularly configured to determine at least one mapping of physical parameters of the inhomogeneous medium forming the sample on the basis of said distortion matrix thus obtained, as has been described in detail in the preceding embodiments. The calculation unit 140 may be connected to a control unit (not shown) for controlling in particular the SLM or the like. The calculation unit and the control unit may be integrated into the same device (computer).

The optical characterization system as illustrated in fig. 11A and 11B has the advantage of allowing the distortion matrix to be determined experimentally without the need to predetermine the reflection matrix, which makes it possible to save computation time, since the Hadamard products on the reflection matrix are performed physically rather than numerically. There is also a gain in accuracy because the same degree of accuracy is not numerically reached as compared to the accuracy obtained by interferometry.

Fig. 12 and 13 present two other exemplary systems for optical characterization of non-uniform media that also allow for direct determination of the distortion matrix (without the need to predetermine the reflection matrix) and also make it possible to omit the focal plane scanning necessary in the embodiments of the systems illustrated in fig. 11A, 11B.

The systems described in fig. 12 and 13 use spatially incoherent illumination (e.g., light emitting diodes, halogen lamps, etc.) and are derived from full-field OCT as described, for example, in a [ a. dubois et al, "High resolution full field optical coherence tomography with a line micro scope, appl. opt.41,805(2002) ].

Recall that full-field OCT as described, for example, in the above-mentioned references is based on the use of experimental equipment comprising, for example, a michelson interferometer with a microscope objective placed in both arms thereof (known as a linnik configuration). The interferometer illumination apparatus uses a tungsten halogen lamp or a Light Emitting Diode (LED). With the very broad spectrum of this type of illumination, interference occurs if the path difference in the interferometer is very close to zero. The length of the reference arm of the interferometer determines a slice of thickness set by the width of the spectrum of the light source (typically 1 μm) at the level of the sample to be imaged. Only light reflected by structures of the sample located in this slice creates interference. If the amplitude of the interference signal can be extracted, these structures can be imaged. For this purpose, a plurality of interferometric images are combined, which are detected by means of a CCD or CMOS matrix arrayCollected by the detectors and phase-shifted relative to each other by means of the oscillation of the reference mirror. What is thus obtained is an image of the coherent volume in real time (at a rate of several hundred hertz), that is to say an image of a thin slice oriented transversely. The lateral resolution of the full-field OCT image is similar to that provided by a microscope, i.e., about 1 μm. The axial resolution is for its part much better than in conventional microscopes, since it is set by the width of the spectrum of the light source and not by the depth of the field of the microscope objective. One of the advantages of full-field OCT is the ability to access an image of a slice of the medium in one measurement without having to scan the field of view as is the case, for example, in confocal microscopes. In full-field OCT, each pixel of the camera is conjugated to a point of the focal plane of the reference arm and a point of the focal plane of the objective arm. It therefore measures the mutual coherence function between these two points. Since each focal plane is spatially and temporally illuminated by an incoherent field, such a coherent function has access to the impulse response (or green's function) between these conjugate points. Each pixel of the full-field OCT image thus corresponds to an impulse response to be measured between the point source and a point detector placed at the same position r in the source plane and the image plane. Returning to the matrix form adopted in the present application, a device of the full-field OCT type therefore allows to acquire simultaneously the reflection matrix R associated with the sample_rrAll diagonal elements of R (R)_in,r_in)。

According to an exemplary embodiment of the present description, in order to access the whole reflection matrix, at the radically different illumination points rin and detection points r_outThe impulse response is measured. To do this, the fields from the objective and reference arms of the interferometer are translated relative to each other.

This is what is implemented in the original systems 101 and 102 shown in fig. 12 and 13.

The system 101 schematically illustrated in fig. 12 comprises an illumination device 110 capable of emitting a series of incident light waves intended to illuminate a given field of view of the sample through the microscope objective 30. However, in this embodiment, the illumination device 110 comprises a spatially incoherent light source 115 as in full-field OCT, for example a tungsten halogen lamp or a light emitting diode arranged in this embodiment at the focus of a lens 116 in order to form the incident light waves. In practice, uniform illumination is achieved, for example, by means of a kohler illumination system.

The system 101 comprises, as in full-field OCT, a low coherence interferometer having a beam splitter element 121, making it possible to split the incident wave from the illumination device in the direction of the reference arm 150 and the objective arm 160.

In the reference arm 150, the incident wave is first sent by a beam splitter 151 to a mirror 153 placed in the focal plane of a second microscope objective 152. The microscope objective 152 may be similar to the microscope objective 30. The wave reflected by the mirror 153 is then redirected using a beam splitter element 151 towards a mirror 154 conjugated with the pupil plane of the microscope objective 152 by means of afocal lenses 155, 156. The mirror 154 constitutes the main inventive element of the device, since its inclination will make it possible to spatially shift the reference beam on the camera.

The objective arm of the device is symmetrical to the reference arm in order to obtain the same path difference. The incident wave is sent to the sample SMP by the beam splitter element 161. Sample SMP and mirror 153 are in an optically conjugate plane. The reflected wave is then redirected by a beam splitter 161 to a mirror 162 which is conjugated with the pupil plane of the microscope objective 30 and with the mirror 154 of the reference arm by means of afocal lenses 165, 166. Unlike the mirror 154, which may be tilted, this mirror remains perpendicular to the optical axis.

Thus, at the exit of the reference arm 150 and objective arm 160, the waves reflected by the reference mirror and sample, respectively, are spatially displaced in a plane conjugate to the focal plane. The reflected waves thus formed are recombined by means of the beam splitter 132. The lens 133 makes it possible to cause them to interfere on the CCD or CMOS camera 130 placed in the image focal plane of the sample. A piezoelectric element (PZT)163 placed on the mirror 162 makes it possible to extract the cross-interference term by acquiring interferograms for multiple values of the phase, e.g. three or more phase values, as described in the references mentioned above for full-field OCT.

As shown in FIG. 12, the tilt of mirror 154 brings the reflected beams from the reference and objective arms into focusSpatially displaced relative to each other in planes conjugate to the plane. Unlike full-field OCT, it is therefore possible to measure a radically different point r_inAnd r_inIn time of the pulse response. Their relative position r'_outAs determined by the inclination of the mirror(s),

r'_out＝r_out-r_in＝G tanθ_x e_x+G tanθ_y e_y (22)

where thetax and thetay are relative to the unit vector e_xAnd e_yThe angle of inclination of the axis of the load. G ═ f '/f is the magnification of the system, where f' is the focal length of the lens 133 placed in front of the camera.

The applicant has thus shown that, for each inclination angle (θ)_x、θ_y) The relative position r 'of the matrix for and between the reference beam and the objective beam is recorded'_outCoefficient R (R) of (equation 22)_out–r_in,r_in) The corresponding minor diagonal. Due to D (r'_out，r_in)＝R(r_out-r_in，r_in) (equation 4), this measurement therefore amounts to directly measuring the distortion matrix in the focal plane.

Matrix D in the focal plane_rrCorresponds to illuminating a point r_inA central focal spot R (R)_out–r_in,r_in) I.e. the image forming apparatus at point r_inThe point spread function of (a). The apparatus presented in fig. 12 thus allows direct measurement of the distortion matrix in real space. As above, unless a gel or another material having an optical index close to that of the biological medium is introduced into the reference arm, the reference medium is air.

As explained above, the matrix D_rrThen makes it possible to enter the exit pupil plane and obtain the matrix D_θrIn order to determine the isoplanatic domain of the field of view and the associated aberration laws. Relative to the reflection matrix R_rrCoherent measurement of, directly acquiring the matrix D_rrOffering great advantages. Specifically, acquisition D_rrThe number of required measurement points is of the order of the number of resolution cells contained in the aberrated focal spot：N_A＝(δ_A/δ)². It is independent of the size of the field of view. In contrast, the coherent method requires N ═ (FOV/δ)²And a focused illumination. For typical aberration levels in biological media, N is acquired_A10 images are sufficient to access the entire distortion matrix using the non-coherent setup of FIG. 12. Conversely, for 1mm²Will necessarily scan for N10 in a coherent setting like the coherent settings presented in the articles by a. badon et al and Kang et al⁶A field of view of a pixel.

Another exemplary system for optical characterization of a heterogeneous medium according to the present description is schematically illustrated in fig. 13. Fig. 13 presents a system 102 that is more compact and more efficient in terms of signal-to-noise ratio than the system shown in fig. 12.

The system 102, like in the embodiment of fig. 12, comprises an illumination device 110 comprising a spatially incoherent light source 115 arranged at the focal point of a lens 116 and adapted to emit a series of incident light waves intended to illuminate a given field of view of the sample SMP by means of the microscope objective 30. The system 102 further comprises a two-dimensional acquisition device 130 arranged at the focus of the lens 133 and in particular a calculation unit 140 receiving the photoelectric signal from the detector 130.

However, in this embodiment, the system 102 includes two interferometers placed in series. The first interferometer, referenced 170, is for example a michelson interferometer of air wedge configuration, making it possible to generate at its output two illumination beams inclined with respect to each other and having orthogonal polarizations. The second interferometer, designated 180, is for example a linnic interferometer with a polarizing beam splitter 181 and quarter wave plates 182, 183 on each arm. The afocal systems 191, 192 make it possible to combine the planes of the mirrors 175 and 176 of the first interferometer 170 with the pupil planes of the microscope objectives 30 and 184 of the second interferometer 180.

The operation of this system will now be described in detail. The spatially and temporally incoherent incident field is first of all linearly polarized by 45 degrees in the parallel (e | |) and normal (e |) directions with respect to the device plane by means of a polarizer 171. The components of this wave polarized along the directions e | | and e | |, respectively, are transmitted and reflected by the polarizing beam splitter 172. Each arm of interferometer 170 contains a quarter wave plate (173, 174) and a mirror (175, 176). On one of the arms, a mirror (176) is tilted with respect to the optical axis. On its return, the two waves from each arm exit the interferometer in the form of two orthogonally polarized oblique beams. However, the two beams are coherent with each other because they come from the same incident wave.

In the second interferometer, the two beams are again separated by a polarizing beam splitter 181. The beam polarized along e | is transmitted in the reference arm. The beam polarized along e ″) is reflected in the objective arm. The presence of quarter wave plates 182, 183 on each of the two arms makes it possible to transmit the two beams optimally once they have been reflected by the mirrors on the sample and reference arms in the objective arm. The two beams are recombined at the output of the interferometer using an analyzer 187 polarized at 45 degrees with respect to e | | and e |. They may therefore interfere in the focal plane of the lens 133. The CCD or CMOS camera records the corresponding interference pattern. As above, the phase shift method performed using the piezoelectric element 186 of the mirror 182 attached to the reference arm of the interferometer 180 makes it possible to extract the interference term from the image recorded by the camera. As shown in fig. 13, the inclination of the mirror 175 shifts the reference beam and the objective beam relative to each other on the camera. As for the above setup, a radically different point r is thus measured_inAnd r_outIn time of the pulse response. Their relative position r'_outIs determined by the inclination of the mirror according to equation 22.

Fig. 14-16 show first experimental results obtained with a characterization system such as that described in fig. 12, and fig. 17 shows experimental results obtained with a characterization system such as that described in fig. 13.

Fig. 14 to 16 illustrate results obtained for the test pattern (sample SMP) observed through the abnormal monkey cornea 40 (fig. 14A). The test pattern is positioned in the focal plane FP of the microscope objective 30 (fig. 12). The experimental set-up is the experimental set-up depicted in figure 12. The sample was measured at 1.5X 1.5 with a spatial resolution of 5 μm (300X 300 pixels)mm²Is imaged by a microscope objective with the aid of a light-emitting diode (850nm, 480mW) at a magnification of 4. Distortion matrix D_rrBy aiming at each point r of the field of view over an area of 17 x 17 pixels_inThe measurement point spread function is obtained experimentally, i.e. 289 acquisitions instead of the 90000 acquisitions that would be necessary in the case of the coherence setup of fig. 2.

FIG. 14B illustrates a distortion matrix D measured using the setup of FIG. 12 according to the method described above_rr。

According to the distortion matrix D additionally shown in FIG. 15A_rrThe focal plane reflection matrix R can be determined by rearranging the data as indicated by equation (4)_rr. Can be derived from matrix D_rrThe central row of (a) infers a frontal OCT image, however at each point r of the field of view_inThe point spread function of (b) corresponds to D_rrEach column of (a). Fig. 15E shows the modulus of this point spread function averaged over the entire field of view. At D_rrThe two-dimensional spatial fourier transform at the output of (a) can access the distortion matrix D on the basis of which the law of aberrations can be determined as described above_ur(FIG. 15D).

FIG. 16A illustrates the aberration laws measured in the pupil plane (three first output feature vectors U shown in images (a), (b), (c), respectively)₁、U₂、U₃). Correlated image in the focal plane, i.e. input eigenvector V₁、V₂、V₃Are shown in images (a), (B), (c) of fig. 16B, respectively. From the corrected matrix D 'averaged over each iso-halo field'_rrAnd D'_rrThe inferred point spread functions are illustrated in images (a), (b), (C) of fig. 16C. And D_rrThe OCT image corresponding to the central row of (fig. 16D) is compared with the image corrected by the linear combination of the 10 first eigenvectors (image 16E).

This first embodiment shows how the experimental setup of fig. 12 or 13 allows direct measurement of the matrix D across a millimeter field of view at micron resolution_rr. It also shows how the higher order aberrations that produce multiple isohalo regions in the field of view can be corrected simultaneously.

Fig. 17A to 17D illustrate, still using an experimental setup of the type of fig. 13, the application of the method according to the present description to a second embodiment, namely depth imaging of biological media. Unlike the first case, which corresponds to a specular reflection mode, it is an intermediate mode between the specular reflection mode and the random scattering mode in this example.

The biological sample imaged here is leaves. The field of view is 2X 2mm²(400 × 400 pixels) and the focal plane is located at a depth of 70 μm with respect to the surface of the leaf (fig. 17A).

FIG. 17B shows the measured matrix D_rrThe central row of (a) 'front face' OCT image. This image suffers from poor contrast due to the optical index discontinuity between the air at its surface and the leaf and due to aberrations induced by the leaf itself. It is difficult to see some veins of the leaves. Analyzing the distortion matrix may access a set of eigenvectors V_iTwo examples thereof V₂And V₃Shown in images (a) and (b) of 17C, respectively. The two images indicate that the two feature vectors are associated with different regions of the image. V₂Giving contrast images of the veins with the highest reflectivity, however V₃Giving a sharper image of the speckle in the background of the image. FIG. 17D is a graph of fifteen first eigenvectors V through the distortion matrix_iThe linear combination of (a) and (b). As evidenced by comparison with the initial OCT image shown in fig. 17B, the matrix correction for aberrations gives a sharp and higher contrast image of the cross section of the leaf.

This embodiment, as in the previous embodiment, shows the feasibility of the method according to the present description by means of an arrangement allowing, on the one hand, the acquisition of large-size reflection and distortion matrices and, on the other hand, the correction of higher-order aberrations at micrometer resolution throughout a millimeter field of view.

Although described with respect to a number of detailed exemplary embodiments, the method and system for non-invasive optical characterization includes various modifications, adaptations and refinements that will be apparent to those skilled in the art, and it is to be understood that such various modifications, adaptations and refinements fall within the scope of the present invention as defined by the following claims.