EP3201563A1

EP3201563A1 - Diffraction microscope method and device

Info

Publication number: EP3201563A1
Application number: EP15771517.8A
Authority: EP
Inventors: Pierre Bon; Emmanuel Fort; Sandrine Leveque-Fort
Original assignee: Centre National de la Recherche Scientifique CNRS; Universite Paris Sud Paris 11
Current assignee: Centre National de la Recherche Scientifique CNRS; Universite Paris Sud Paris 11
Priority date: 2014-10-03
Filing date: 2015-09-08
Publication date: 2017-08-09
Also published as: FR3026836A1; US10012495B2; WO2016050460A1; CA2963297A1; US20170299375A1; JP6667539B2; JP2017533445A; FR3026836B1

Abstract

According to one aspect, the invention relates to a device (100, 200, 300, 400, 500) for measuring the distance, with respect to a reference plane (P_REF), of a point of light (P_i) of an object (O). The device comprises a two-dimensional detector (30) comprising a detection plane (P_DET) and an imaging system (10) capable of forming an image of a point of light (Pi) situated on an object plane of interest (11) in an image plane (11') arranged close to the detection plane (P_DET) or to a conjugate plane (P'_DET) of the detection plane. The device further comprises a separator element (20) able to form, from a beam emitted by a point of light of the object plane of interest (11) and emerging from the imaging system (10), at least two mutually coherent beams, having a region of special superposition in which the beams interfere, and signal processing means (50) able to determine, from the interference pattern formed in the detection plane and resulting from the optical interference between said mutually coherent beams, the distance from the point of light to the conjugate plane of the detection plane in the object space of the imaging system (10), said conjugate plane of the detection plane forming the reference plane (P_REF).

Description

DIFFRACTIVE MICROSCOPE METHOD AND DEVICE

STATE OF THE ART

TECHNICAL FIELD OF THE INVENTION The present invention relates to a method and an optical telemetry device for determining the three-dimensional position of an object, and is particularly applicable to three-dimensional microscopic imaging in biology but also to passive optical telemetry. (without measurement of flight time).

State of the art Just a few years after their introduction, so-called super-resolution microscopy techniques have taken a considerable step forward in the field of the study of biological specimens, in particular for the study of the structure and the spatial dynamics of protein assemblies (molecular complexes of a few nanometers to a hundred nanometers) within the cell. At present, it is possible to functionalize virtually any protein in an organism by adding a fluorescent marker, the latter being directly synthesized by the cell, or consisting of a fluorescent compound added within the sample . It follows the formation of emitters capable of emitting a number of photons between a few hundred thousand and a few million before being destroyed. Super-resolution techniques, known as PALM for "Photo-Activated Localization Microscopy" or (d) STORM for "(direct) Stochastical Optical Reconstruction Microscopy" for example, combine nanometric localization and control of the number of simultaneously active transmitters. , in order to obtain two-dimensional images of cell samples with a resolution of 10-50 nm, well below the classical limit of diffraction.

However, these techniques are today mainly used for two-dimensional imaging; accessing the 3D organization of cellular structures at the nanoscale continues to present many difficulties. The review article by B. Hajj et al. ("Accessing the third dimension in localization-based super-resolution microscopy", Phys Chem Chem Phys., 2014, 16, 16340-16348) presents a synthesis of the techniques used for three-dimensional super-resolution microscopy and regroups these techniques in several categories: the techniques based on the control of the form of PSF (the acronym of the English expression "Point Spread Function" and representing the impulse response of the imaging system), those based on a so-called "multi plans and techniques using interferometry.

The impulse response shape (PSF) control techniques of the imaging system including the microscope objective aim to break the axial symmetry of the PSF so that there is a one-to-one relationship between the section. of the PSF and the axial position of the transmitter relative to the focal plane of the imaging system. Very recently, it has been described (see A Backer et al, "A bisected pupil for studying single-molecule orientational dynamics and its application to three-dimensional super-resolution microscopy", Applied Physics Letters 104, 193701 (2014)) a mask of particular phase arranged in a pupillary plane of the microscope objective, and for dividing the lateral section of the PSF into two lobes, the relative position of the two lobes for determining the axial position of the transmitter. However, in this technique as in other techniques of this type, it is not possible to simultaneously study a high density of molecules because as soon as the particle density increases, there is a superposition of the lobes or more generally extended PSF . Moreover, optical aberrations naturally introduced by the sample in the case of deep imaging tend to eliminate the bijective relationship between the shape of the PSF and the axial position, which limits the use of these techniques in the first layers. of cells.

The multi-plane approach consists of simultaneously imaging the signal of a transmitter in axially separated planes. The article by S. Abrahamsson et al. For example, "fast multicolor 3D imaging using aberration-corrected multifocus microscopy", Nature Methods, Vol.10 No. 1 (2013) describes the arrangement of a particular network for generating nine images on a single detector corresponding to nine orders of diffraction. However, a limitation of multi-plane techniques is the division of the "photon budget" of the transmitter according to a given number of images, resulting in a loss of sensitivity and therefore of accuracy.

Axial precision in super-resolution microscopy can be significantly improved by interfering the emitted waves from a transmitter at the focus of two microscope objectives (see G. Shtengel et al., "Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure" Proc Natl Acad Sci USA 106, 3125 (2009)). This last technique which implements a measurement system called "4pi", that is to say using two objectives head to tail to collect the light in almost 4pi steradian, combined with a triple interferometric detection of photons emitted, is the one who offers today the best axial location accuracy, but at the cost of considerable experimental complexity that relegates to a very minor use in biology laboratories. This technique is also sensitive to differential aberrations resulting from the passage of the sample forwards or backwards in a 4pi assembly, for any type of sample.

The present invention implements an interferometric technique which does not have the disadvantages of the previously described techniques; in particular, it allows a full-field imaging adapted to the detection of continuums of fluorescent emitters but requiring only one detector. It is applied in super resolution microscopy but also in conventional microscopy and also finds applications in passive optical telemetry, that is to say for determining the distance of an object in a scene without flight time analysis. .

SUMMARY OF THE INVENTION

According to a first aspect, the invention relates to a device for measuring the distance, with respect to a reference plane, from a light point of an object, comprising:

a two-dimensional detector comprising a detection plane;

an imaging system adapted to form an image of a luminous point situated on an object plane of interest in an image plane situated near the detection plane or a conjugate plane of the detection plane;

a separating element making it possible to form, from a beam emitted by a luminous point of the object plane of interest and emerging from the imaging system, at least two coherent beams between them, having a region of spatial superposition in which the beams interfere with each other; ;

signal processing means making it possible to determine from the interference pattern formed on the detection plane and resulting from optical interferences between said beams coherent with each other, the distance from the light point to a conjugate plane of the detection plane in the object space of the imaging system (10), said conjugate plane of the detection plane forming the reference plane.

For the purpose of this description, the notion of "luminous point" of an object or "source point" also extends more broadly to a basic zone of an object in which all the emission points are coherent between them spatially and together form a single image point on the detector. Thus, in the case of super-resolution microscopy application, a source point may be a fluorescent emitter or "quantum dot" whose spatial dimensions are smaller than the diffraction task of the imaging system. In other macroscopic applications, on the other hand, a source point may include a larger and spatially coherent area of an object forming on the detection plane a "picture point" whose dimensions of which are much larger than those of the impulse response (or PSF) of the imaging system.

The device thus described makes it possible in particular to reconstruct an object in 3D without the need to use controlled illumination means of the object; thus, the device described makes it possible, for example, to reconstruct in 3D an object emitting its own light (in the case of a fluorescent emitter in microscopy) or an object re-emitting light without having any control over its illumination (scene of everyday life).

The separating element as defined in the device according to the present description makes it possible to print within the "image point", that is to say the image of a luminous point of the object formed on the plane of detection, a modulation whose period depends on the relative curvature of the wave coming from the luminous point, finally allowing to achieve a relative elevation mapping of the object. The separator element coupled to the detector thus behaves as a curvature sensor of the wave coming from the different light points of the object which prints a modulation within each image point without degrading the resolution. Advantageously, the separator element makes it possible to print a modulation within the image point whose period is sufficiently small to form at least two fringes at the image point and to obtain a sufficient measurement precision.

Advantageously, and particularly in the case of super-resolution microscopy applications, the period of the fringes of the interference pattern formed on the detection plane ("interfrange") is smaller than the diameter of the impulse response of the imaging system. imaging (or PSF), which is the smallest image formed from a bright spot on the detection plane.

According to one variant, the separating element comprises a diffraction grating close to the imaging plane, for example a two-dimensional diffraction grating. According to one variant, the diffraction grating is a transmission network, respectively in reflection, which does not transmit, respectively does not reflect, the zero order. According to one variant, the device is applied to three-dimensional imaging; the imaging system then includes a microscope objective.

Alternatively, the device further comprises a relay optics for forming a conjugate plane of the detection plane in the image space of the imaging system.

According to a second aspect, the invention relates to a method for measuring the distance, with respect to a reference plane, of a light point of an object of interest, comprising:

- forming an image of the light spot in an image plane close to the detection plane of a two-dimensional detector or a conjugate plane of the detection plane;

the formation, by means of a separating element, from a beam emitted by the light spot and emerging from the imaging system from at least two beams coherent with each other and having a region of spatial superposition in which the beams coherent between them interfere;

determining, from the interference pattern formed on the detection plane and resulting from the optical interferences between said coherent beams, the distance from the light point to a conjugate plane of the detection plane in the object space of the imaging system, said conjugate plane of the detection plane forming the reference plane.

According to one variant, the distance from the luminous point to the reference plane is obtained from the measurement of the period of the fringes of the interference pattern.

BRIEF DESCRIPTION OF THE DRAWINGS

Other advantages and characteristics of the invention will appear on reading the description, illustrated by the following figures:

FIGS. 1A and 1B, diagrams illustrating two examples of telemetry device according to the present description;

Figures 2A to 2D, diagrams illustrating the principle of the method implemented according to an example; 3, curves showing according to two particular examples the value of the interfrange (pseudo-period of modulation) as a function of the axial position of the source point relative to the reference plane;

Figures 4A and 4B, diagrams illustrating telemetry devices according to two other examples;

Figure 5 is a diagram illustrating an exemplary device according to the present description, applied to three-dimensional microscopic imaging;

FIGS. 6A to 6C, images illustrating various steps of the telemetry method in a super-resolution microscopy application implemented with a montage of the type of FIG. 5 and with a biological sample comprising CHO cells ("Chinese Hamster Ovary ") and a labeling of tubulin proteins of the cytoskeleton of these cells;

7A to 7C, images showing the appearance of the interference pattern obtained for a single fluorescent emitter (quantum dot), at different axial positions, in a similar configuration (mounting and sample) to that implemented for the obtaining images 6A to 6C;

8A, 8B, respectively a standard fluorescence image and an image of the biological sample obtained in a similar configuration (assembly and sample) to that used to obtain the images 6A to 6C; - Figure 9, a diagram of a device according to the present description, applied to passive optical telemetry in a scene.

For the sake of consistency, the identical elements are identified by the same references in the various figures.

DETAILED DESCRIPTION

FIGS. 1A and 1B illustrate two examples of telemetry device according to the present description, adapted for measuring the distance, with respect to a given reference plane, from a luminous point Pi (or "source point") of a object of interest O in a scene. The telemetry device 100 shown diagrammatically in FIG. 1A generally comprises a two-dimensional detector 30 with a detection plane P _DET connected to signal processing means 50, and an imaging system 10 adapted to form an image of a light point. Pi of an object plane of interest 11, in an image plane 11 'located near the detection plane 31 of the detector. In the telemetry device 200 shown diagrammatically in FIG. 1B, the image plane 11 'is in the vicinity of a plane P' _DET conjugated to the detection plane P _DET , the device further comprising a relay optic 40 making it possible to form in the image space of the imaging system 10 a conjugate plane of the detection plane.

The proximity of the image plane to the detection plane (or the conjugate of the detection plane) depends on the precision sought for the distance measurement.

Indeed, for a given position of the detection plane P _DET (OR of the conjugate plane P ' _DET of the detection plane by the relay optics 40), it is possible to define in the object space of the imaging system 10 an area of defined measure on both sides of an object plane P _REF said "reference plane" and corresponding to the conjugate plane of the detection plane in the object space of the imaging system. The measurement zone corresponds to the zone in which the accuracy of measuring the distance of a light point relative to the reference plane is satisfactory depending on the intended application.

For example, in applications in three-dimensional microscopy, when seeking a location accuracy of an emitter relative to the reference plane well below the object field depth of the imaging system, the measurement zone can be have a total length L _m less than four times the object depth dz of the imaging system and advantageously less than twice the depth of field dz object of the imaging system to ensure a good measurement accuracy.

For a digital aperture imaging system NA, the object depth of field dz can be determined by

dz = - ₂ (1)

NA ² '

With λ the average wavelength of the light collected and n the immersion index of the imaging system, that is to say the index of the medium located just before the first diopter (in the direction of propagation light) of the imaging system 10; typically n = 1 for an imaging system immersed in the air, for example for passive telemetry applications and n¾1.5 for an imaging system immersed in an immersion oil, for example for applications in microscopy of super -resolution.

Consequently, in the case for example applications in three-dimensional microscopy, the detection plane (or the conjugate of the detection plane) and the image plane 11 'conjugate of the object plane of interest 11 by the imaging system 10 may be separated from each other by a distance less than twice the image field of view of the imaging system, and preferably by a distance less than once the image field depth of the imaging system, in order to benefit from a good accuracy in the measurement of the distance of the luminous point.

In other applications on the contrary, as for example in passive telemetry applications, the distance between the detection plane (or the conjugate of the detection plane) and the image plane 11 'conjugate of the object plane of interest 11 by the imaging system 10 can be lengthened to ten times or even twenty times the image depth of field, to the detriment of the localization accuracy which then becomes of the order of depth of field; this mode of operation is mainly interesting for passive telemetry measurement, where to find out where the object is located axially without super-resolution is sufficient.

Thus, in the example of FIGS. 1A and 1B, it will be possible to measure not only the distance of a luminous point Pi situated in an object plane of interest 11 substantially coincident with the reference plane P _REF, but also the distance of points luminous P ₂ and P ₃ located on either side of this reference plane, provided that they are in the measuring zone of length L _m defined according to the desired accuracy.

For the determination of the distance from a luminous point Pi to the reference plane P _REF , the telemetry device comprises a separator element 20 making it possible to form from a beam B 'emitted by the luminous point Pi and emerging from the luminaire system. 10, at least two beams coherent with one another (not shown in FIGS. 1A and 1B) and having a region of spatial superposition in which said coherent beams interfere with one another.

The separator element 20 will be described in more detail below and may comprise for example a network, advantageously a two-dimensional array, located near the detection plane P _DET (example of FIG. 1A) or the plane P ' _DET conjugate of P _DET detection plane (example of Figure 1B). The separator element 20 may also comprise a separator blade or a separator cube, as will be illustrated by way of examples in the following description.

The separating element is arranged in such a way that the detection plane or the conjugate plane of the detection plane is in the spatial superposition zone of the beams which are coherent with one another and come from the separating element. Thus, on the detection plane of the detector, is formed for each source point Pi an image which is the convolution of the response impulse of the imaging system (PSF) with an interference pattern resulting from the interference of beams from the separator element.

By the choice of the parameters of the separator element (for example the pitch of the grating in the case of a diffraction grating type separator element, or the optical index and the thickness of the separating plate in the case of a separator element. splitter separator element), it is possible to fix the interfrange of the interference pattern and to print within the image a modulation whose period is advantageously smaller than the diameter φ of the impulse response of the imaging system, given by:

φ = 2τ = 0.61-NA (2)

where r is the radius of the PSF, NA is the numerical aperture of the imaging system and its magnification. As will be detailed later, the period of the modulation (in other words the interfrange of the interference pattern) depends on the relative position of the source point with respect to the reference plane P _REF which is the conjugate plane of the plane of detection P _DET in the object space of the imaging system 10. The separator element thus described associated with the detector, therefore behaves as a sensor of the relative curvature of the wave emitted by each source point of the object, this which makes it possible to ultimately determine a relative elevation map of the object.

FIGS. 2A to 2D illustrate in greater detail the principle of the method implemented according to a particular example in which the separator element comprises a network 21.

The network 21 is advantageously a two-dimensional diffraction grating. Two independent axial positioning measurements (eg distance measurements relative to the reference plane) (one along each of the axes of the network) can thus be obtained for a single source point, which increases the axial location accuracy while making possible measurements on images presenting any distribution of sources (continuum of fluorophores, scene of the everyday life ...).

The network 21 is, in a variant, a transmission network adapted to transmit all of the incident light energy, ie a phase grating, when the arrangement is in transmission, or may alternatively be a reflection grating adapted to reflect the entirety of the light energy incident when the assembly is in reflection. One or the other of these variants makes it possible to maximize the signal-to-noise ratio of the 3D localization.

Advantageously, a transmission or reflection grating will be chosen which does not transmit, respectively does not reflect, the order 0. This makes it possible to make the interferences formed by the diffracted orders independent of the luminous wavelength. To eliminate the zero order can be obtained for example by adjusting to π [2π] the modulation of the phase shift introduced over a period, for example by etching the network substrate or local modification of the substrate index. Another possibility to suppress the order 0 is to remove the order 0 in the Fourier space of the network, but in this case, there is introduced a loss of photons and therefore a loss of signal to noise ratio.

The pitch p of the grating is advantageously chosen so as to form more than one fringe per

"Image point" of a source point of the object, the image point being confused with the impulse response of the imaging system, or PSF, in super resolution microscopy applications for example. Typically it will be possible to choose the pitch of the grating comprised between one third of the radius of the image point and three times the radius of the image point, in order to have sufficient lateral sampling of the fringes and to limit oversampling. Typically, it will be possible to choose a pitch p of the order of the diameter of the image point, to have 2 fringes per image point; and in the case of the application of super resolution microscopy, a pitch p between r / 3 and 3r, advantageously of the order of 2r, where r is the radius of the PSF given by equation (2) ci - above.

FIGS. 2A to 2D illustrate, by way of example and schematically, the wave propagation in the case of a measuring device comprising a diffraction grating 21 and the light intensity measured in a lateral direction in the plane of detection in the case of two source points positioned at two different axial positions.

To facilitate the theoretical demonstration, we assume in this example a one-dimensional network of pitch p and it is assumed that the network diffracts only the orders +1 and -1. Such a diffraction grating is, for example, a complex amplitude grating as described, for example, in J. Primot et al. ("Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard", Applied Optics, Vol 39, Issue 31, pp. 5715-5720 (2000)). In practice, however, we may prefer a network that diffracts all orders except the zero order, such a network being simpler to manufacture (phase network with a checkerboard pattern "chessboard phase" for example, as described in the quoted article by Primot et al.) and not to lose photons.

As can be seen in FIGS. 2B and 2D, there is a variation of Γ interfringe Λ as a function of the distance of the source point with respect to the reference plane (ie the conjugate plane of the detection plane in the object space of the system of imaging). The relationship between the interfrange (period of the modulation) and the distance from the source point considered to the reference plane can be determined theoretically from the parameters of the diffraction grating chosen, as is explained below according to an example. In the example shown in FIGS. 2A and 2C, the grating 21 is located at a distance d from the detection plane P _DET - In this example, the grating makes it possible to form two diffracted beams coherent with each other, denoted ΒΊ and B ' ₂ and corresponding respectively to the orders +1 and -1. The grating 21 diffracts the light according to the order +1 with an angle α with respect to the propagation of the direct light (ie order 0 of the grating, indicated in simple dotted lines in the figures). The lateral shift between the point of impact on the detection plane of the diffracted order 1 and the point of impact (theoretical) of the order 0 is noted in FIGS. 2A and 2C. The lateral offset corresponds to half lateral shift between the points of impact the two "replicas" formed by the two coherent beams entre between each other and B ' ₂ .

The wave vectors of the + and -1 diffracted orders corresponding to the bundles ΒΊ and B ' ₂ respectively are noted:

with sin (a) = - where A is the wavelength.

E is the scalar electromagnetic field from the image of the source point in the detection plane of the detector:

■ 27Γ,.

E {x) = A (x) e T ^{s (x)}

where A (x) is the amplitude of the field and S (x) is the spherical wave area associated with the curvature of the wavefront from the source point that can be approximated by S (x) = -, with z the distance of the image from the source point to the detection plane. The interferogram / (x) formed by the orders +1 and -1 on the detection plane located at a distance d from the network can be described by:

/ (x) = i ₀ (x) [1 + cos ^ - [S (x-ε) -S (x + ε) + 2x ^■ sin (a)] (3)

With i _Q (X) "A ² (x)

ε = d ^■ tan (a) ~ d ^■ -

By Taylor's development to order 1 of equation (3) we deduce:

= Î ₀ (X) [l + cos ^ - [x- It is therefore concluded that the measured intensity signal has a carrier ί ₀ () 0 ^a PSF of the imaging system), modulated by a signal of period Λ = p / (2 [l - ^ j) therefore dependent only on the distance z between the image of the source point and the detector (desired distance reported in the image space of the imaging system) and the distance d between the network and the detection plane (fixed and known).

In the case illustrated above, as appears in equation (5), the choice of a network in which the zero order is suppressed makes it possible in particular to eliminate the dependence of the intensity signal with the wavelength. and to overcome the effects of chromaticism.

The approximation used to determine equation (5) above both to give a step of Λ → ± ∞ when z → d. In a real case, we can consider the approach of a Gaussian beam; in this case S → 0 (and therefore Λ → p / 2) when z → d.

FIG. 3 illustrates the evolution of Λ as a function of z with the Gaussian approach in the case of two lateral offset values ε, respectively ει = ΙΟμιη (solid line curve) and ε ₂ = 4 μιη (dotted line curve) ) with a diffraction grating of the type of that described by means of FIGS. 2A to 2D having a pitch = 20 μτη. The values ει = ΙΟμιη and ε ₂ = 4 μιη respectively correspond to values of the distance d between the grating and the detection plane d = 200 μπι and d ₂ = 80 μπι. On this curve, the interfrange Λ measured is normalized by the half-period of the network and the normalized distance z as a function of the depth of field.

These two curves show first of all that it is possible from the value of the interfrange to determine the distance z between the image of a source point and the detector and thus to deduce it in the object space. of the imaging system, the distance between a source point of the object and the reference plane. The curves of FIG. 3 further illustrate the shape of the curve as a function of the value of the lateral half-shift ε between the replicas, the lateral half-offset being proportional to the distance d between the grating and the plane of detection. The curves show that by playing on ε one can enlarge the zone along the optical axis where the measurement is possible but one loses in precision of localization.

In all cases, the network will advantageously be placed at a distance sufficiently close to the detection plane so that the lateral shift introduced between the replicas is less than the diameter of the image point, for example the diameter of the PSF (φ, equation (2)) in the case of super resolution microscopy application. In other words, we will seek to have: ε≤φ

let d≤0.61 - g _y - - ^ (6)

Inequency (6) is expressed as a function of the choice of the microscope objective at a ratio dlp typically less than a value between 10 and 50 depending on the choice of the microscope objective; thus for spas networks typically between 10 and 30 μιη, the distance d will be chosen less than a value that may vary between ten microns and 1 mm depending on the choice of the microscope objective.

Although described in the case of a one-dimensional network having two diffraction orders, the principle illustrated by means of FIGS. 2A to 2D extends to other examples of diffraction gratings, and in particular a two-dimensional grating allowing two independent axial measurements. (one following each axis of the network) for each source point.

As illustrated by FIGS. 2A-2D and 3, the axial positioning of the object-forming source points can thus be obtained by measuring the period or local frequency of the interfering frequency formed on the detection plane.

Advantageously, the positioning of each source point is determined by comparing the measured value of the period / local frequency of the interfering gram formed on the detection plane with a calibration curve of the period / frequency as a function of the axial positioning of the source point. . The calibration curve can be obtained either theoretically (like the curve shown in FIG. 3 for example) or experimentally by frequency measurements obtained on images of source points whose axial positioning is known.

In practice, the measurement of the local period / frequency of interference generated on the detector can be obtained in several ways.

The measurement can be done in the direct space (ie directly on the image) by local adjustment (fitting) of the image by a function describing the interferogram (see equation (1) above for example) . This allows to go back to the local period of the interferogram.

The measurement can also be done by local Fourier transform to find the main peak in the Fourier space, that is to say the local frequency in the image area considered.

Alternatively, it is also possible to proceed with a wavelet transform (intermediate case of the two previous ones). Of course, a diffraction grating as described above may be replaced by any system making it possible to generate an equivalent phase and / or absorption function, for example a spatial light modulator (SLM) or a deformable mirror. With SLM, however, the need to work with polarized light results in detrimental photon loss, especially in microscopy applications. With a deformable mirror, the limit comes from the reduced number of actuators that results in too much period of the equivalent network.

Other types of separator elements may be integrated in the device according to the present description to form the curvature sensor thus described. It suffices that such a separating element makes it possible to separate the incident beam emitted by the luminous point into at least two mutually coherent beams having a region of spatial superposition in which the beams interfere.

FIGS. 4A and 4B thus illustrate two examples of measuring devices according to the present description. In the example of FIG. 4A, the separating element comprises a separating plate, for example a semi-reflecting plate, to form a Murty interferometer-type interferometer assembly and in the example of FIG. 4B, the separating element comprises a splitter cube to form a Mach-Zender type interferometric assembly.

The telemetry device 300 shown diagrammatically in FIG. 4A comprises, as in the example of FIG. 1B, a two-dimensional detector 30 with a detection plane P _D AND and an imaging system 10 adapted to form an image of a source point Pi an object plane of interest 1 1 in an image plane 1 1 'close to a plane P'DET conjugate PDET detection plane, the device further comprising a relay optics 40 to conjugate the plane P'DET with In the example of FIG. 4A, the telemetry device 300 furthermore comprises a semi-reflecting plate 22 of thickness e, for example a glass plate of index n, arranged to allow reflection. partially on each of the air-glass interfaces so as to form two coherent beams between them, referenced ΒΊ and B ' ₂ in Figure 4 A, which have a region of spatial superposition in which the beams can interfere. In the example of FIG. 4A, the semi-reflecting plate is arranged so as to form an angle of 45 ° with the optical axis of the imaging system, to form an interferometer known as the Murty interferometer. .

As in the theoretical description previously described on the basis of the use of a network, Γ intergram / gram / (x) formed on the detection plane by the image of a point source at a distance z from the image by the imaging relay system (40) of the semireflecting plate (here confused with the plane of the detector) can be described by:

/ (x) "i ₀ (x) [l + cos (y [S (x - ε) - S (x + ε)])] (7) / (x)" ί ₀ () [l + ^cos ( γ ^)] (Gaussian hypothesis)

In this example however, the parameter ε is written:

V2

ε «- e for n = 1.6

4

With n the index of glass constituting the glass slide and e the thickness of the blade. The telemetry device 400 shown diagrammatically in FIG. 4B comprises, as in the example of FIG. 1B, a two-dimensional detector 30 with a detection plane P _DET and an imaging system 10 adapted to form an image of a source point Pi d an object plane of interest 11 in an image plane 11 'close to a plane P' _DET conjugated to the detection plane P _DET , the device further comprising a relay optics enabling the plane P ' _DET to be combined with the plane of detection P _DET -

In this example, the relay optics comprises two optics 41, 42, between which is arranged the separating element formed here of a Mach-Zender interferometer 23. The interferometer comprises in this example a separating plate Si (or of a separator cube) making it possible to form, from the beam B 'coming from the source point Pi and emerging from the imaging system 10, two beams ΒΊ and B' ₂ coherent with one another. These beams propagate in two independent arms each containing a mirror with total reflection (M _ls M ₂ ). The beams are recombined thanks to the cube (or blade) separator S ₂ . The beams are symbolized for the sake of clarity in Figure 4B by their optical axis.

As in the previous example, a shift 2ε between the beams ΒΊ and B ' ₂ is generated. The offset can be obtained and adjusted either by a displacement of one of the separating plates (Si, S ₂ ) transversely to the optical axis or by a tilting of one of the mirrors (Mi, M ₂ ). We arrive at the same equation (7) as for the case of the Murty interferometer

Among the three examples of separator elements described, the diffraction grating makes it possible to obtain a greater measurement stability because the free space propagation lengths of the beams that are coherent with one another and intended to interfere are less important and, because of this, also the number of free parameters affecting the measurement are lower (notably the angle of the separating plate in the case of Murty's interferometer and angles of the mirrors and semi-reflective plates in the case of Mach Zender's interferometer). The diffraction grating also makes it possible to work with all the photons coming from the source point, which is not the case for the Mach Zender assembly, for example. It is therefore preferable to use the diffraction grating as a separating element. As explained above, the network can also allow, in case of suppression of the order 0, to form achromatic interferences unlike the other separator elements.

FIG. 5 shows a diagram illustrating an exemplary device according to the present description, applied to three-dimensional microscopic imaging, in particular for imaging biological specimens formed of molecular complexes. The molecular complexes, whose average sizes are typically from a few nanometers for small complexes to about 100 nanometers for the most imposing structures, are marked according to known techniques by a probe capable of emitting a light signal, for example a fluorescent probe. , thus forming emitting particles smaller than the diffraction limit of the optical system used to form an image thereof. The particles that one seeks to locate evolve in a support medium that can be liquid or solid, for example in the form of a gel, for example a biological medium. The support medium may be arranged directly on a sample holder, deposited on a plate or held between two plates, for example glass plates. O object (FIG. 5) is the support medium and the emitting particles evolving therein, as well as the holding plate (s), if appropriate.

The three-dimensional imaging device 500 comprises in the example of FIG. 5 an imaging system 10 able to form the emitting particle (ie the source point) an image on a detection plane P _DET of a detector 30, advantageously a matrix detector, for example a CCD camera, CMOS, an amplified camera EMCCD type (abbreviation of the English expression "Electron Multiplying Coupled Charge Display"), a camera sCMOS, a matrix of photomultipliers.

In this example, the imaging system 10 comprises a microscope objective 12, corrected for example for an optical configuration of focus-infinity work, associated with a lens 13, referred to as a tube lens, making it possible to form an image on an intermediate detection plane 11 '. The microscope objective assembly and tube lens forms a conventional optical microscope system.

The imaging device 500 further comprises relay objectives 40 making it possible to form a plane P ' _DET conjugate of the detection plane P _DET of the detector 30 in the image space of the imaging system 10, the image plane 11 'being located near the conjugate plane P' _DET . Because of the very small size of the emitting particles (less than the diffraction limit of the imaging system), the image, which is the convolution of the object with the impulse response of the imaging system or PSF, is here substantially confused with the impulse response. A motorized platform (not shown) may be present and allows the sample O to be moved in an XY plane perpendicular to the optical axis of the microscope objective. A mechanical axial focusing device (not shown) may be present and can adjust the axial position of the sample relative to the focal plane object of the microscope objective 12 and thus image the area of interest. The sample holder, the motorized platform, the axial focusing device, the microscope objective 12 and the tube lens 13 are arranged in a microscope body 60 of known type. The microscope body may furthermore comprise, in a conventional manner, an eyepiece, a source of illumination of the sample associated with a condenser.

In the example of FIG. 5, the microscope body is of inverted type (microscope objective positioned under the sample) but it could equally well be a right microscope (microscope objective above the microscope). 'sample).

The imaging device 500 also comprises a separator element 20, for example a two-dimensional network close to the conjugate plane P ' _DET for the formation of at least two coherent beams with a region of spatial superposition at the detector, for the implementing the method of determining the distance according to the present description.

As described above, the network is for example a phase grating for suppressing the order 0 and whose pitch is chosen to form on the detector interference of period less than the lateral resolution of the microscope. It is arranged perpendicular to the optical axis so that the coherent replicas between them overlap and can interfere with each other.

FIGS. 6A to 6C show images obtained at different stages of application of the method according to the present description, in a super-resolution microscopy application implemented with a device of the type of that of FIG. 5.

Object O is a biological sample of CHO ("Chinese Hamster Ovary") cells fixed with paraformaldehyde. The tubulin proteins of the cellular cytoskeleton were fluorescently labeled with specific antibodies. The fluorescent probes are of the Alexa 647 type and the sample is observed by means of a CMOS type matrix detector 30 by the dSTORM technique, in which flashing is achieved through the use of the Vectashield mounting product (Vectro Labs) and the use of a 635 nm laser.

Figure 6A shows a fluorescence image at the start of acquisition of dSTORM; the density of the fluorescent molecules is still significant, resulting in a spatial continuum of fluorescence emission. However, it is already possible to view the interference. Figure 6B shows a zoom on part of the image being acquired in which the density of emitters is lower; the response of a single fluorescent emitter (quantum dot) in which the modulation resulting from the interference of coherent replicas between them is distinguished. The periodicity of this modulation makes it possible to determine the axial positioning of the transmitter relative to the reference plane, as explained above. The lateral positioning is obtained by determining the centroid of the image (or image point) by barycentre or ideally by adjusting the image by a Gaussian describing the PSF of the imaging system 10, after suppression of the filtering modulation (pass low frequency) of the thumbnail. FIG. 6C shows the dSTORM 3D image reconstructed by 3D localization of each fluorescence emitter according to the present description (as in 6B) thanks to the stochastic flashing of the emitters, the gray scale representing the axial positioning of the emitters. These images illustrate the application of the present method even on fluorescence continuums on which standard methods of 3D imaging (for example the techniques based on the control of the shape of the PSF could not function).

FIGS. 7A, 7B, 7C show experimental measurements of the light distribution measured using a type 500 assembly in the presence of single fluorescent emitters (of the nanocrystal semiconductor type, or quantum dot) situated either in a conjugated plane the detector (7B) is before (7C) or after (7A) while remaining in the depth of field (ie no variation of the dimension of the image). It is clear that Γ interfringe Λ change depending on the axial positioning of the transmitter (i) although one is in the depth of field and (ii) without the size of the image of the transmitter is widened by compared to classical imagery (circle of confusion).

By way of comparison, FIGS. 8A and 8B represent experimental images of the same biological sample obtained by a standard epi-fluo (8 A) imaging and 3D STORM imaging technique with the technique proposed herein. description (8B) again on a CHO cell (Chinese Hamster Ovary) attached to paraformaldehyde. The gain in lateral resolution (8B) with respect to 8A is clearly observed and also the axial positioning allowing to follow the 3D spatial evolution of the cyto skeleton. In addition to applications in three-dimensional microscopy, the applicants have shown that the distance measurement method according to the present description can also be applied to "passive" telemetry, that is to say without measurement of flight time, for the measurement. of distances of objects in a scene.

FIG. 9 thus represents a scene with several objects O ₁ , O ₂ , situated at different distances from a distance measuring device 600. The objects are illuminated in natural light and retro diffuse the natural light so that each point of an object Oi forms a source point Pi.

The device 600 comprises, as previously, a detector 30 with a detection plane P _DET , an imaging system 10 adapted to form a scene in an image plane located near the detection plane P _DET , and a separator element 20. , for example a diffraction grating close to the detection plane P _DET , and making it possible to form, from a beam emitted by the light point and emerging from the imaging system, at least two mutually coherent beams ("replicas") presenting a region of spatial superposition in which the beams interfere. The imaging system 10 comprises for example a photo or video lens adapted to work at infinity

The reconstruction of the axial positioning of the source points can be done in a volume of a few times the depth of field (~ 10x) of the imaging system. Axial resolutions are of the order of depth of field and up to 1/100 of the latter. Depending on the photo or video lens used (aperture, focal length) the absolute values of the axial resolution and the depth of field change. It may be interesting to adjust the aperture given a focal length so that the dynamic measurement of axial positioning of the various points of the object encompasses all the objects of interest in a given scene; that is, the objects of interest are included in the depth of field a few times. Also, if the focal length and the aperture are fixed, the modification of the lateral offset ε (for example, in the case of use of a grating, by translating the latter with respect to the detection plane according to the optical axis) allows to adjust the axial positioning measurement dynamic with the technique described in order to obtain a reconstruction of all the objects of interest of the scene.

In this embodiment, the measurement of the variation of the interfringe from one point to another makes it possible to go back to the 3D profile of the constituents of the scene.

Although described through a certain number of exemplary embodiments, the optical telemetry method according to the invention and the device for implementing said method comprise different variants, modifications and improvements which will be obvious to those skilled in the art, it being understood that these various variants, modifications and improvements are within the scope of the invention as defined by the following claims.

Claims

1. Device (100, 200, 300, 400, 500) for measuring the distance, with respect to a reference plane (PREF), of a luminous point (Pi) of an object (O), comprising:

a two-dimensional detector (30) comprising a detection plane (PDET); an imaging system (10) adapted to form an image of a luminous point

(Pi) located on an object plane of interest (1 1) in an image plane (1 1 ') located near the detection plane (PDET) OR a plane (P'DET) conjugate of the detection plane;

a separating element (20) making it possible to form, from a beam emitted by a luminous point of the object plane of interest (1 1) and emerging from the imaging system (10), at least two coherent beams with one another, presenting a region of spatial superposition in which the beams interfere;

signal processing means (50) making it possible to determine, from the interference pattern formed on the detection plane and resulting from optical interferences between said coherent beams, the distance of the luminous point to a conjugate plane of the plane detection device in the object space of the imaging system (10), said conjugate plane of the detection plane forming the reference plane (PREF).

2. Device according to claim 1, wherein the period (Λ) of the fringes of the interference pattern thus formed is smaller than the resolution of the imaging system.

3. Device according to one of the preceding claims, wherein the separator element comprises a diffraction grating (21) close to the imaging plane (1 1 ').

4. Device according to claim 3, wherein the diffraction grating is a two-dimensional diffraction grating.

5. Device according to any one of claims 3 or 4, wherein the diffraction grating is a transmission network, respectively in reflection, which does not transmit, respectively does not reflect, the zero order.

6. Device according to any one of the preceding claims, further comprising a relay optics (40) for forming a conjugate plane of the detection plane in the image space of the imaging system.

The device of any one of the preceding claims applied to three-dimensional microscopic imaging, wherein the imaging system comprises a microscope objective (12).

8. Device according to any one of claims 1 to 6 applied to passive telemetry, wherein the imaging system comprises a photo or video lens adapted to work at infinity.

9. Method for measuring the distance, with respect to a reference plane (P _REF ), from a luminous point (Pi) of an object of interest (O), comprising:

the formation of an image of the luminous point (Pi) situated on an image plane (11 ') located near the detection plane (P _DET ) of a two-dimensional detector (30) or a plane (P' _DET) ) conjugate of the detection plan;

the formation, by means of a separating element (20), from a beam (Β ') emitted by the luminous point (Pi) and emerging from the imaging system (10) from at least two coherent beams between them (ΒΊ, B ' ₂ ) and having a region of spatial superposition in which the beams coherent with each other interfere;

the determination, from the interference pattern formed on the detection plane (P _DET ) and resulting from the optical interferences between said coherent beams, of the distance from the luminous point (Pi) to a conjugate plane of the plane of detection in the object space of the imaging system (10), said conjugate plane of the detection plane forming the reference plane (P _REF ).

10. The method of claim 9, wherein the distance from the luminous point (Pi) to the reference plane is obtained from the measurement of the period (Λ) of the fringes of the interference figure.