OPTICAL MEASUREMENT METHOD AND DEVICE

Abstract

The invention proposes an optical measurement method and an achromatic optical apparatus for determining the spatial position of at least one light nano-emitter, a structured object, or a continuous distribution on a sample. The method comprises: the projection of a sequence of at least two compact light distributions of different topological families onto the sample; the detection of the light re-emitted by said at least one light nano-emitter, structured object, or continuous distribution of the sample; the generation of at least one optical image for each light distribution from the detected light; and an algorithm module in which the formulation of the reconstruction of the sample and its spatial and / or temporal and / or spectral properties is considered as an inverse Bayesian problem and leads to the definition of an a posteriori distribution, an a posteriori law combining, by means of Bayes' law,The probabilistic formulation of a noise model, as well as any prior assumptions about a light distribution created in the sample by projection. Furthermore, the invention proposes an optical measurement method and an achromatic optical apparatus in which the algorithm module is configured to estimate the light distribution in the sample using point emitter clouds, thus favoring sparse solutions and estimating the a posteriori mean, and finally representing the results, based on the a posteriori mean, either as an image or as numerical or graphical data. Moreover, the invention proposes an optical measurement method and an achromatic optical apparatus in which the algorithm module is configured so that the a posteriori mean estimation is performed using a Markov Chain Monte Carlo (MCMC) algorithm. Furthermore,The invention proposes an optical measurement method and an achromatic optical apparatus in which the algorithm module is configured to perform a non-regularized MAP algorithm with a positivity constraint, and optionally a frequency-bandwidth limitation constraint, and optionally use a Nesterov-type accelerated numerical scheme,

Description

1 OPTICAL MEASUREMENT METHOD AND DEVICE INTRODUCTION The present invention relates to an optical measurement method and device. It finds applications in all fields of imaging, in particular but not limited to the field of Microscopy, including but not limited to the fields of Biology, Medicine, Pharmacy, Semiconductors, the Study of materials, Metrology, control, measurement and observation and all the processes of acquiring information from optical observations, in the macroscopic or microscopic domain. Numerous definitions, used for the whole of this invention, are grouped together in a later chapter: "Definitions and technical additions". Microscopy An optical microscope is an instrument generally used to see, analyze or measure objects too small to be visualized with the naked eye. We refer to the figure. 1, which represents an illustration of the paradigm of Microscopy, 100. Optical Microscopy consists of the illumination, by a light source, not represented, using a Microscope, 10, of a biological or non-biological sample. biological, 11, and the measurement as a function of time, using visual observation or a detection module, 12, of the light emitted, re-emitted, scattered or reflected or transmitted by the sample. In Biology, the sample consists of one - or a plurality - of different biological object entities, 13 and 14, positioned at different positions. Examples of such objects are, inter alia, a cell, a virus, a protein or a DNA fragment. In artificial industrial vision the sample can be, for example, a semiconductor element. Microscopy is segmented into different modalities with different characteristics and purposes. Many descriptions of the different modalities, their characteristics and their advantages exist extensively in the literature and can be found for example on the websites of the companies Zeiss, Leica, Nikon, or Olympus. Microscopy applications can be segmented in different ways: one of them is to distinguish the Microscopy modalities devoted to the visualization of tiny point sources from those devoted to the measurement of continuous objects. The case of tiny point sources is a priori much simpler. The object consists of a small number of luminous points; these can be described by a small number of parameters – the descriptors defined later – greatly simplifying the physical problem and the algorithmic complexity. The case of a continuous object, described by a spatial distribution - or spatio-temporal, if the continuous dynamics are taken into account, is different and is also described in this patent application. 3042043 2 Fluorescence microscopy Fluorescence microscopy is one of the modalities of microscopy; it has replaced, in many applications, other microscopy techniques. A fluorescence microscope is an optical microscope used to study the properties of objects, or organic or inorganic substances using the phenomena of fluorescence instead of, or in addition to other modalities such as reflection and absorption. We refer again to the figure. 1, describing, this time, a fluorescence microscope used either in Biology or in Artificial Vision to characterize, for example, materials; in fluorescence microscopy, tiny point sources, 15 to 18, for example fluorophores based on the physical phenomenon of one-photon fluorescence, are attached to specific and predetermined positions of the objects, 13 and 14; the light emitted by the point sources is observed instead of observing the light emitted by the objects, 13 and 14, themselves. The sample is illuminated by light of specific wavelength, or wavelengths, which is absorbed by the point sources, thereby inducing the emission of light at different and higher wavelengths. When collecting the emitted light, in fluorescence, the illuminating light is separated from the emitted fluorescence, which is weaker, by the use of an emission spectral filter. Fluorescence microscopy studies the light emitted by small point sources, fluorophores.However, when the density of the fluorophores is high, the fluorophores are no longer analyzed individually but treated as a continuous object. It is important to note, from this stage, that the same system allows the observation of continuous objects, and is not limited to the observation of point sources. Fluorophores have become an important tool in the visualization of biological objects. Activity and biological information including details above the 200 - 250 nm resolution limit are routinely visualized and measured using fluorescence microscopy. This resolution limit is derived from the Rayleigh criterion, which in the best case reaches 200 - 250 nm in specially designed systems. For a long time, until the emergence of the superresolution techniques described below, it was recognized that optical techniques, including fluorescence microscopy, are incapable of visualizing details smaller than the Rayleigh criterion, from the order of 200 - 250 nm. The main implementations of fluorescence microscopy, described in detail in the literature, are the confocal microscope, often used in a scanning or spinning disk configuration, and the wide-field imaging microscope. 3042043 3 Confocal Microscopy Referring now to Figure 2, which is a simplified representation of a prior art fluorescence confocal microscope 200. A fluorescence confocal microscope, FIG. 2, is an optical instrument. Its major hardware components are shown in the figure. 2. They include: - A light source, 20, - an optomechanical frame (not shown), - a filter cube, 21, - a microscope objective 22, and, - a detector assembly, 23, - a processing unit, not shown. The light source, 20, which may be an arc lamp or a laser, generates light energy necessary for fluorescence. The optomechanical frame, not shown, is the support for all the optical elements and includes auxiliary optics and alignment capabilities. It also comprises optical elements, not shown, capable of shaping the beam, to allow its focusing of a point of minimum size, by means of the objective of the microscope. It may also comprise, in a confocal scanning fluorescence microscope, a spatial or angular scanning mechanism, not shown, for modifying the position of the point source with respect to the object to be measured. The cube of filters, 21, channels the various optical signals and avoids contamination of the fluorescence signal by the excitation light. The cube of filters breaks down into: excitation filter, 210, dichroic mirror, 211, and emission filter, 212. The microscope objective, 22, focuses the light created by the source in the focal plane of the objective, 24, into a light distribution of reduced size, the light distribution considered to be optimal consisting of an Airy disc. The microscope objective, 22, also makes it possible to collect in return the fluorescent light emitted by the fluorophores. For a confocal scanning fluorescence microscope the system can be de-scanned, i.e. the return light can pass through the scanning mechanism to compensate for translation due to scanning. A detector lens, 25, creates, at the image plane of the detector 26, a magnified image of the focal plane of the objective, 24. A confocal hole, 27, is theoretically placed in the image plane of the detector, 26. In most practical systems, the confocal hole, 27, is placed in an intermediate imaging plane, not shown, and re-imaged on the detector image plane, 26. 3042043 4 The detector assembly, 23, detects the overall fluorescent intensity in the illuminated volume, and transforms it into a digital signal. For a scanning confocal microscope, the detector assembly consists of a single element detector, such as a PMT or SPAD. For a spinning disk confocal microscope, the detector assembly consists of an array of sensing elements, such as a CCD, EMCCD, CMOS, or SPAD array. The set of components mounted from the light source to the dichroic filter is the illumination path, 201. The set of components mounted from the dichroic filter to the detector assembly is the detection path , 202.The elementary optical process of a standard confocal microscope can be segmented into six parts: - Projection of light onto the analysis volume - Emission of fluorescent light by fluorophores - Imaging of fluorophores on the focal plane - Limitation in the focal plane of the analyzed light by the confocal hole - Integration of the analyzed light by a photoelectric detector - Visualization of the measured intensity as a pixel value in an image Fluorescence microscopes are available from several manufacturers, e.g. , Nikon, Zeiss, Leica or Olympus. Fluorescence microscopes can be either standard microscopes adapted to fluorescence or specific microscopes optimized for fluorescence. Modern microscopes are versatile instruments capable of operating in many different modalities, including but not limited to fluorescence modalities, using the same optomechanical platform and most components. Most fluorescence microscopes are developed as an open platform, capable of performing several additional functionalities with minimal modifications. Other fluorescence microscopes are dedicated instruments, customized for a specific task, such as medical or pharmaceutical diagnostics. However, other fundamental biological activities also occur at size scales below 200 nm in biological samples. At this level of spatial resolution, important phenomena can be observed: biological processes at the intracellular level, the transfer of cellular information, the folding and unfolding of proteins or the modifications of DNA and RNA. Thus, for example, the measurement of this intracellular information will open new avenues for the understanding of biological activity, and will lead to progress in the knowledge and monitoring of research and medical diagnosis. However, the various existing microscopy methods and the existing microscopes, not incorporating superresolution, allow microscopic observation below the limit of optical diffraction. This reduces their field of use to a limited set of applications. 3042043 Superresolution New optical methods, superresolution methods, are capable of obtaining images at a resolution greater than the diffraction limit. These methods are developed by several companies, laboratories and researchers and some of the instruments using these methods, superresolution microscopes, are commercially available. A summary of superresolution techniques was published by the Swedish Academy of Sciences, on the occasion of the awarding of the 2014 Nobel Prize in Chemistry

[38] . Several comparative analyzes of superresolution methods have recently been published in the literature, such as the articles by Schermelleh et al. [1]. An updated bibliography on superresolution can be found on the Zeiss company website, and on the Nikon company website. The new superresolution techniques make it possible to obtain information beyond the resolution limit. The main problem of all existing superresolution techniques is the limit of the performance envelope, expressed in terms of resolution, lateral and longitudinal, speed, necessary light intensity and phototoxicity in the biological object, and therefore the ability to measure different biological objects. This point was also underlined by Eric Betzig, during his masterful presentation at the 2014 Nobel Prize in Chemistry reception ceremony. In addition, most existing superresolution methods and instruments can provide either good lateral resolution or good longitudinal resolution, but rarely both. In addition, all these instruments are complex and require high technical skill from the operator. Moreover, these instruments can generally observe only a small part of the biological specimens, due to strong operational limitations, such as for some of them a shallow depth of field or very high intensities harmful to the cells.Another problem with existing superresolution methods and instruments is that most of them are able to recover, in the illuminated volume, the attributes of a single fluorophore, but fail to simultaneously recognize the presence of several fluorophores and measure their attributes. An additional problem with some existing superresolution methods and instruments is that these existing methods and instruments are presented to users and perceived by them as a general tool, suitable to replace standard or confocal microscopes. However, existing superresolution methods and instruments lack simplicity, robustness, ease of use and are expensive compared to standard microscopes, which hinders their use as general research tools or as diagnostic tools. Another problem with some existing superresolution methods and instruments is that most of these methods and instruments are built as stand-alone instruments designed to replace standard microscopes. Such an approach requires the replacement of existing instruments as well as the renewal of all peripheral systems and all the knowledge and know-how, related to microscopy platforms and developed over many years. Another problem with most existing fluorescence and superresolution microscopy methods and instruments is that these methods and instruments are designed on an image acquisition paradigm, for which the basic entity of information is a - or several images, or one - or several - two- or three-dimensional ROI regions - Region Of Interest. The algorithmic, systemic and superresolution methods described later in the context of the invention will allow, by their inherent flexibility, the development of new acquisition strategies. These dynamic and selective acquisition procedures will be defined by optimized management of the acquisition sequence and of interactive and deferred processing. They will allow a more evolved optimization of the useful information, defined by criteria based on the shape, the geometry and the dynamics of one or several fluorescent objects, separately or one compared to the other. Another problem with most existing fluorescence and superresolution microscopy methods and instruments is that these methods and instruments are designed to study samples on microscope slides. However, the confocal microscope is today used in many medical fields as an in-vivo diagnostic instrument for internal and external examinations of the human body through optical fibers used to illuminate and to visualize the fluorescence emitted by the tissues at diagnose. Superresolution does not currently allow performing such in-vivo diagnoses. The algorithmic, systemic and super-resolution methods described later in the context of the invention will allow the development of new in-vivo diagnostic methods which will reduce the need for performing biopsies and shorten the patient's waiting time. There is therefore still an urgent need to provide superresolution methods and instruments and algorithmic methods capable of measuring with great precision an object or a biological scene.3042043 7 SUMMARY OF THE INVENTION A first aspect of the invention relates to an optical measurement device for determining the spatial distribution or location of re-emitting sources on a sample, the sample comprising at least one re-emitting source, excited by light and re-emitting light according to a law determined as a function of the light projected onto the sample, the device comprising an achromatic projection module, containing a laser, the wavelength of which is tuned to the excitation wavelength of said at least one re-emitting source, for creating either a compact light distribution or a sequence of compact light distributions of different topology a scanning module for optically scanning the sample, a detection module for detecting the light re-emitted by said at least one source re-emitting of the sample for the or for each of the compact light distributions of different topology and for each of the sample scan points; an image acquisition module for acquiring for each scanning point, either an image or a sequence of images, for the sequence of images, each image corresponding to one of the compact light distributions of different topologies, a module for algorithm in which the formulation of the reconstruction of the sample and its spatial and / or temporal and / or spectral properties is considered as a Bayesian inverse problem and leads to the definition of an a posteriori distribution. An a posteriori law can combine, thanks to Bayes' law, the probabilistic formulation of a noise model, as well as any a prioris on a distribution of light created in the sample by projection. In one embodiment, the algorithm module is configured to estimate the distribution of light in the sample by the use of clusters of point emitters which makes it possible to promote parsimonious solutions; and estimating the a posteriori mean, representing the results, based on the a posteriori mean, either in the form of an image or in the form of numerical or graphical data According to one embodiment, the estimation of the a posteriori mean is carried out by means of of a Monte-Carlo Markov Chain (MCMC) type algorithm Another aspect of the invention relates to an optical measurement device for determining the spatial distribution or the location of reemitting sources on a sample, the sample comprising at least one source re-emitting, excited by light and re-emitting light according to a law determined as a function of the light projected onto the sample, the device comprising an achromatic projection module, containing a laser, the wavelength of which is tuned to the excitation wavelength of said at least one re-emitting source, to create either a compact light distribution or a sequence of light distributions c compacts of different topology, a scanning module for optically scanning the sample, integrated or not in the device, a detection module for detecting the light re-emitted by said at least one re-emitting source of the sample for the or for each of the distributions compact lights of different topology and for each of the scanning points of the object; an image acquisition module for acquiring for each scanning point, either an image or a sequence of images, for the sequence of images, each image corresponding to one of the compact light distributions of different topologies, a module for unregularized MAP algorithm with positivity constraint to process the data and reconstruct the sample, the representation of the results, based on the results of the MAP algorithm, either as an image or as numerical or graphical data According to a embodiment the MAP algorithm also contains a band-frequency limitation constraint According to one embodiment the MAP algorithm uses an accelerated numerical scheme of the Nesterov type According to one embodiment for a sequence of images, the redundancy in the frequency information is used, due to the different frequency characteristics of the different distributions projected on the sample, to compensate and reduce strongly the impact of missing dots or scan irregularities.According to one embodiment, the MAP algorithm is adapted to solve an inverse problem relating to a sum of a small number of terms, such as a low-frequency component and a more parsimonious component. According to one embodiment, the MAP algorithm is adapted to impose a non-local redundancy constraint on the solution, for example by calculating weights on the images or on the different digital masks and the tree of non-local similarities being applied to the solution as a regularization. According to one embodiment, a mask of variable size is used in the plane of the detector to obtain images having either different axial characteristics, or different or optimized stray light rejection capacities, globally or locally Another aspect of the invention relates to an optical measurement method for determining the spatial distribution or location of re-emitting sources on a sample, the sample comprising at least one re-emitting source, excited by light and re-emitting light according to a law determined as a function of the light projected onto the sample, the method comprising the achromatic projection, by a laser, the wavelength of which is tuned to the excitation wavelength of the said at least one re-emitting source, to create either a compact light distribution given a sequence of compact light distributions of different topology, the optical scanning of the sample on, the detection of the light re-emitted by said at least one re-emitting source of the sample for the or for each of the compact light distributions of different topology and for each of the scanning points of the sample; image acquisition to acquire for each scan point, either an image or a sequence of images, for the sequence of images, each image corresponding to one of the compact light distributions of different topologies, applying a algorithm in which the formulation of the reconstruction of the sample and its spatial and / or temporal and / or spectral properties is considered as a Bayesian inverse problem and leads to the definition of an a posteriori distribution. An a posteriori law can combine, thanks to Bayes' law, the probabilistic formulation of a noise model, as well as any a prioris on a distribution of light created in the sample by projection.In one embodiment, the algorithm comprises the estimation of the distribution of light in the sample by the use of clouds of point emitters which makes it possible to promote parsimonious solutions; and the estimate of the a posteriori mean, representing the results, based on the a posteriori mean, either in the form of an image or in the form of numerical or graphical data. According to one embodiment, the estimation of the a posteriori mean is carried out by means of a Monte-Carlo Markov Chain (MCMC) type algorithm Another aspect of the invention relates to an optical measurement method for determining the spatial distribution or the location of reemitting sources on a sample, the sample comprising at at least one re-emitting source, excited by the light and re-emitting light according to a law determined as a function of the light projected onto the sample, the method comprising the achromatic projection, by a laser, the wavelength of which is tuned to the excitation wavelength of said at least one re-emitting source, to create either a 3042043 compact light distribution or a sequence of topo compact light distributions different logies, the optical scanning of the sample, the detection of the light re-emitted by said at least one re-emitting source of the sample for the or for each of the compact light distributions of different topology and for each of the scanning points of the object; image acquisition to acquire for each scanning point, either an image or a sequence of images, for the sequence of images, each image corresponding to one of the compact light distributions of different topologies, the application of algorithm MAP not regularized with positivity constraint, the representation of the results, based on the results of the MAP algorithm, either in the form of an image or in the form of numerical or graphical data According to one embodiment the MAP algorithm additionally contains a band-frequency limitation constraint According to one embodiment the MAP algorithm uses an accelerated numerical scheme of the Nesterov type According to one embodiment for a sequence of images, redundancy in the frequency information is used, due to the characteristics different frequencies of the different distributions projected on the sample, to compensate and strongly reduce the impact of missing points or irregularities of scan. According to one embodiment, the MAP algorithm is adapted to solve an inverse problem relating to a sum of a small number of terms, such as a low-frequency component and a more parsimonious component. According to one embodiment, the MAP algorithm is adapted to impose a non-local redundancy constraint on the solution, for example by calculating weights on the images or on the different digital masks and the tree of non-local similarities being applied to the solution as a regularization. According to one embodiment, a mask of variable size is used in the plane of the detector to obtain images having either different axial characteristics, or different or optimized stray light rejection capacities, globally or locally 3042043 11 BRIEF DESCRIPTION OF THE DRAWINGS L The invention will now be described in connection with certain embodiments with reference to the following illustrative figures so that it may be better understood. With specific reference to the figures, it is emphasized that the indications shown are presented by way of example, and for the purpose of illustrating the discussion of embodiments of the invention and are presented only for the purpose of providing what can be considered the most useful and easy to understand description of the principles and conceptual aspects of the invention. In this regard, no attempt is made to show structural details of the invention in more detail than is necessary for a basic understanding of the invention, the description taken together with the drawings making it apparent to the art how the various forms of the invention can be realized in practice. In the drawings: Fig. 1 is a simplified representation of a confocal fluorescence microscope of the prior art, also used as a support of the invention; Fig.2 is a simplified pictorial representation of a fluorescence microscopy superresolution system, in accordance with one embodiment of the present invention; Fig. 3 is a simplified schematic illustration of a conical diffraction module, in accordance with one embodiment of the present invention; Fig. 4a-4f are simplified pictorial representations of measurement and volume confinement paradigms according to embodiments of the invention and confocal microscopy; Fig. 5 is a simplified pictorial representation of a particular embodiment of the SRCDP microscopy platform; Fig. 6a is a simplified schematic illustration of a superresolution side module, in accordance with one embodiment of the present invention; Fig. 6b is a simplified schematic illustration of another embodiment of a superresolution side module, in accordance with one embodiment of the present invention; Fig. 7a to 7c present tables of light distributions of a conical diffraction module as a function of the polarization of the input and output polarizers for several values ​​of the conical diffraction parameter, po. These light distributions were calculated by simulation of the equations developed by Berry, [2]; FIG. 7d completes these distribution tables by presenting the variation of the so-called shifted half-moon distributions as a function of the axial position (axis z). Fig.8 is a simplified schematic illustration of one of the embodiments of dark tracking; 3042043 12 Figs. 9 is a simplified schematic illustration of a fluorophore data superresolution algorithm method, in accordance with one embodiment of the present invention. Fig. 10 is a simplified schematic illustration of the calculation of the descriptors; Fig. 11 is a simplified schematic illustration of the SRCDP platform control module. In all figures, like reference numerals identify like parts. 3042043 13 DEFINITIONS AND TECHNICAL ADDITIONAL We will use the term biological to describe any life science entity, regardless of its origin, human, animal or plant, and the purpose of its observation, research, diagnosis or therapy. This term includes medical uses of the described technique. Microscopy is used in the field of Biology, for example, to observe, study and measure biological entities (objects) and their dynamics. We will use, by extension, the term Artificial Vision to describe all the applications of measurement, metrology or observation of objects or elements produced or constructed or made by a human being or a machine, for example, to observe, study and to measure Semiconductors or to characterize materials. The usual definitions are used in the description for: phase and polarization, polarimetry, vectors and Jones matrices, Stokes parameters and techniques for measuring Jones and Stokes parameters. The usual definitions are used for: optical diffraction limit, Rayleigh criterion, Airy disk and its radius and diameter. We use in the context of the invention the terms superresolution, superresolved, superresolution imaging and superresolution microscopy to describe the acquisition of optical data, in imaging, in microscopy or in artificial vision, at a resolution greater than the optical diffraction limit. The usual definitions are used for fluorescence and for fluorophores. We will use the terms longitudinal and axial alternately to describe the dependence of light along the axis of propagation, which we refer to as the z axis or longitudinal axis. We will use the term lateral to describe the dependence of light in axes orthogonal to the optical axis of the system, which we refer to as the x and y axes. The usual definitions are used in the description for the TEM00 mode of a fiber and the English terms, "Photonic Crystal Fiber" - PCF -, "few modes fiber" - FMF, vortex Fiber and "dual core Photonic Crystal Fiber" for specific fibers.We will refer to a device making it possible to couple several lasers at different wavelengths or at the same wavelength, with the same polarization or with different polarizations, in one or more optical fibers, using the term laser bench. The definition of superoscillations is that of Yakir Aaronov and Sir Michael Berry. A superoscillation is a phenomenon in which a signal that is globally band-limited may contain local segments that oscillate faster than its fastest Fourier components. [261 The center or centroid of a distribution of light is the centroid of intensity. The diameter of a light distribution is the diameter of the first zero of intensity, for regular and singular waves, without taking into account the central zero of the singular wave. 3042043 14 Two light distributions are co-located if their centers coincide or are separated by a small spatial value compared to the dimension of the light distribution. In this patent application, we will use the emission wavelength as the basic metric of the system. In this patent application, the usual definitions are used for the following optical components: lens whose definition is extended to include all the optical means which transmit, refract or reflect light, auxiliary optics - optical sub-module aimed at interface and adjust either the geometric parameters or the phase and / or polarization parameters between two other sub-modules or optical modules -, polarizer, analyzer, delay plate, beam splitter "beamsplitter" in English, polarizing and non- polarizing, beam combiner, polarizing and non-polarizing. In this patent application, the usual definitions are used for the azimuthal and radial polarizers. We will extend, implicitly or explicitly, certain developments described later for the azimuthal and radial polarizers, to all the polarizing elements that vary in space. In this patent application, the usual definitions, [3] and

[38] , are used for the different superresolution techniques; these techniques can be grouped into families: - REversible Saturable Optical Fluorescence Transitions (RESOLFT), grouping the techniques: Stimulated Emission Depletion microscopy (STED), Ground State Depletion (GSD), Saturated Structured Illumination Microscopy (SSIM) and SPEM (Saturated Pattern Excitation Microscopy), Localization Microscopy, (localization microscopy, in English) combining the techniques Photo-Activated Localization Microscopy (PALM), FPALM (3D Localization in Fluorescence Photoactivation Localization Microscopy), Stochastic Optical Reconstruction Microscopy (STORM), dSTORM (direct STORM) , SPDM (Spectral Precision Distance Microscopy), stochastic blinking, Ground State Depletion (GSD), and similar techniques (regardless of the acronym used) - Structured Image Microscopy (SIM) - FRAP (Fluorescence Recovery After Photobleaching), - TIRF (Total Internal Reflection Fluorescence Microscopy). In this patent application, the usual definitions are used for various Microscopy techniques, standard resolution or superresolution, fluorescent or not, such as the English terms "Computational Microscopy", "Correlative Microscopy", "Crossplatform-microscopy", FCS - “Fluorescence Correlation Spectroscopy”, FCCS - “Fluorescence 3042043 Cross-Correlation Spectroscopy”, or PCH - Photon Counting Histogram, RICS “Raster Imaging Correlation Spectroscopy” or FRAP - “Fluorescence Recovery After Photobleaching analysis”. In this patent application, the usual definitions are used for the Hough transform, for the MAP - “Maximum A Posteriori estimation” algorithms, LSE “Least Squares Estimation”, ICE “Iterated Conditional Expectation”. We refer to the E-LSE algorithm, “emitter-Least Square Error” a new algorithm described in this patent application. We refer to a partial polarizer to describe an element or a module whose absorption is different for the two linear polarizations - linear dichroism - or for the two circular polarizations - circular dichroism.We refer to dynamic elements of polarization or phase, to describe the optical means whose properties of polarization or phase vary according to time in a controlled way, in a discrete or continuous way. These dynamic polarization or phase elements include, but are not limited to: waveplates rotating on their axis, light valves based on liquid crystal technologies, electro-optical devices, also known as Pockels cells, cells of Kerr, for example by using components of PLZT material, resonant electro-optical devices, magneto-optical devices, also known as Faraday cells, acousto- or elasto-optical devices or any combination of these means. We refer to polarization or phase dispersive elements to describe elements whose state of polarization is wavelength dependent. The simplest of the polarization dispersive sub-modules is the multimode or thick wave plate. We refer to the "centroid algorithm" to describe the usual procedure for measuring the centroid and possibly the width (FWHM - acronym in English for "Full Width Half Maximum") of a light distribution. In this document, the usual definitions are used for the following optoelectronic components: photoelectric detector, CCD, EMCCD, CMOS, SPAD Single Photon Avalanche Diode and SPAD matrix. We will use the terms: o optical image, for the spatial distribution of light intensity, o electronic image, to describe the spatial distribution of charges for a CCD, of current for a CMOS or of events for a SPAD, created by the optical image, at a given instant, in a detection plane, o digital image, to describe a matrix of numbers created by digitizing the electronic image. 3042043 16 To simplify the reading and understanding of the text we will also use the term image for the output of a single pixel detector such as a PMT or SPAD, considering it as an image consisting of a single pixel. When no ambiguity exists, or when the distinction between the three types of images is not necessary, we will use the generic simplified term of image. For images, we use the terminology used for array detectors, such as CCDs, EMCCDs and CMOS. For SPADs and SPAD matrices, the result of a measurement is a time-ordered list of photon impacts detailing, for each photon, the impact time and the position of the impact. To simplify the presentation of this document, we will include this case in our definition of images. The images detailed in this document, in many cases, can be qualified as microimages, images of size substantially equal to a small number of diameters of the Airy disk, typically less than 5 diameters, and / or with a low number of pixels , typically 4*4 to 32*32. In a digital image Aj, the indices m and n represent the indices of the pixels; the origin of the pixels will be chosen as the projection of the center of the analysis volume defined in a later paragraph. Polarimetry and Stokes Vectors Polarimetry refers to the measurement of the state of polarization of incident light. The state of polarization of incident light can be described by Stokes parameters, a set of values, introduced by George Gabriel Stokes in 1852, and used in optics. Copropagation of two optical beams Many optical systems and devices use two - or more - beams with different properties. The beams can interact with each other or not, be projected sequentially or simultaneously. In the majority of these systems and devices, the two optical paths are physically separated from each other. This physical separation creates, at the system engineering level, a set of constraints which, although resolvable, significantly increase the complexity of the system and its cost. We refer to common path systems, to refer to a set of devices in which the two differentiated beams propagate along the same physical path, with minor variations.In this invention, we will refer, by extension, to quasi-common path systems, to reference a set of devices in which the two differentiated beams propagate along the same physical path, but separate and recombine in an optical module, the path optic in the optical element being negligible compared to the total optical path. This definition makes it possible to introduce the case of an optical module, containing a polarization splitter followed at a very short distance by an element combining the two polarizations, or any similar element. The introduction of such a module does not significantly change the functionality and benefits of a common path system. In the rest of this invention, to simplify the reading, when we refer to a common path system, we will include the case of a quasi common path system. Electric field in polar coordinates and angular modes E(p, 0) = A(p, 0) x exp[i cp(p, 0)]u(p, 0) (EQ. 1) It is usual in optics to decompose the components of the field, namely its amplitude, its phase and its polarization, in orthogonal, Cartesian or polar modes. Numerous decompositions into polar orthogonal modes, such as the Gaussian, Hermite-Gaussian, HGG and “Elegant” and Laguerre-Gaussian modes are known to those skilled in the art. We will mainly use in this document, the decomposition of the amplitude of the field Singular waves This research theme in Optics, initiated by the major article by J.F Nye and M. Berry, in 1974, [4], is now known as the 'singular optics'. Examples of regular and singular waves are presented in the following. We use the English term beam shaping to describe the transformation of a wave of given shape and topology into a wave of another shape or topology, and in particular the transformation of a regular wave into a singular wave and vice versa. Topology and compact light distributions A light distribution, punctual, will be considered compact if it fulfills one of the compactness conditions defined below, by two alternative and non-exclusive conditions: - either, more than 75% of the energy is contained in a circle of radius less than 1.75 times the Airy radius, - i.e. a luminous domain, containing more than 65% of the energy is delimited by a line of zero intensity included in a circle of radius less than twice the radius d 'Airy, We distinguish different families of point light distributions, of different topologies: Regular distributions, in their usual definition in Optics, Singular distributions or waves, also called optical vortices, of topological charge (azimuthal order) t, in which the phase varies from 0 to 27( t, around the direction of propagation, t being an integer. The azimuthal variation amplitude distributions of order f, also called di stribution de Laguerre-Gauss, 3042043 18 Polarization and optionally phase distributions with azimuthal variation of order (also called radially polarized Laguerre-Gauss modes. Two compact light distributions will be deemed to be of different topological families if they satisfy at least one, and any, of the following conditions: One is regular and the other is singular, One is punctual and the other is annular, The azimuthal orders f of the amplitude of the two different light distributions, The azimuthal orders E of the polarization or the phase of the two different light distributions. Alternatively, two light distributions projected onto a given volume will be deemed to have different topologies if in a substantial part of the jointly illuminated surface, the gradients are of reversed direction. Luminous nanoemitters A luminous nanoemitter is a small secondary emitter, attached to an object; it is of size substantially less than a fraction of a wavelength, typically but not limited to a size of less than a fifth of the wavelength; a light nanoemitter absorbs incident energy and re-emits light at the same wavelength as the incident light or at different wavelengths; the light emitted by the nanoemitter can be coherent, partially coherent or incoherent with the absorbed light.The main examples of light nanoemitters are fluorophores and nanoparticles, but they also include a large number of other elements. The definition, in the context of the invention, of light nanoemitters is determined by the following two conditions: creation of a point secondary light emitter, and predetermined positioning of this emitter relative to an artificial, biological or organic entity. The physical mechanisms that can create a nanoemitter are numerous; they include but are not limited to absorption, scattering or reflection, fluorescence, "emission-depletion", [51, e.g. using RESOLFT techniques, photo-activation and photo-depletion phenomena, fluorescence two or more photons, elastic or non-elastic scattering, Raman scattering, or other physical mechanisms known to those skilled in the art. We will use the term light emission to describe the emission of electromagnetic waves by the light nanoemitter, whether the light is coherent, incoherent or partially coherent. 3042043 19 We will extend our definition of nanoemitters to include scattering, absorbing and reflecting particles attached to a biological or organic entity; the action of a scattering, reflecting or absorbing particle on the electromagnetic field can in fact be described as the creation with an inverse phase, following Babinet's principle, for an absorbing particle of an auxiliary secondary field, emerging from the particle , superimposed on the incident electromagnetic field. We will refer in this patent application to the descriptors of a nanoemitter to denote the set of information describing a nanoemitter as a point source, at a determined instant. Given that the nanoemitter is considered as a point source, all of the information representing it contains a limited number of parameters, ie; its position in space, its intensity, the spectral, intensity, coherence, phase and polarization characteristics of the light emitted by the fluorophore, as a function of the incident light. We will refer in this patent application to the descriptors of a structured object. For example, for a uniform line, all the information representing it contains a limited number of parameters, namely: its orientation in space, its intensity, the spectral characteristics, intensity, coherence, phase and polarization of the light emitted by the object, as a function of the incident light. For a continuous distribution, the object is represented, as usual in image processing, by an intensity matrix. However, in the majority of cases, and in the description of the invention, we refer, under the designation of descriptors, to a subset of the descriptors of a nanoemitter or of a simple geometric object, including its geometric position , its intensity, and the type of fluorophore, when several populations of light nanoemitters, differentiated for example by their emission spectrum, are present in the same sample. This simplification used in the description does not alter the field of the invention which will include in its field of application all the descriptors of the light nanoemitters. To simplify understanding of the context of the invention, the remainder of the description refers only to the simplest case, that in which the nanoemitter is a fluorophore and the physical interaction is one-photon fluorescence. However, this description must be understood as a simplified illustration of a general description of the methods and concepts applicable to all of the light nanoemitters mentioned beforehand or known to those skilled in the art, regardless of the underlying physical phenomenon. . It is significant that the nanoemitter samples the field or the incident intensity at a precise three-dimensional position, without influence of the whole spatial distribution of the incident intensity. We will refer to this remarkable property in this patent application as the sampling capacity of the light nanoemitter. However, the embodiment of the invention described also makes it possible to measure structured objects and continuous distributions that do not have the sampling capacity of the light nanoemitter.We refer again to the figure. 1; which represents a set of nanoemitters or structured objects, positioned on a given biological object, 15 and 16 on the one hand and 17 and 18 on the other hand. Alternatively, the emitted light may consist of a continuous distribution, not shown in Figure 1, or any combination of nanoemitters, structured objects or continuous distribution. The set of nanoemitters, structured objects, or continuous distributions is referred to as a set of "bright biological objects"; they represent a map of the biological object, in the sense defined by Alfred Korzybski in general semantics. However, it is common practice to simplify the description, to reference the luminous biological object as the biological object itself, when no ambiguity can arise. The luminous biological object contains a lot of relevant information related to the biological object, mainly the spatiotemporal information, the position of the object and its orientation as a function of time, and the morphological information, for example in the case of the dividing a cell into two. The measurement system according to at least one embodiment of the invention will make it possible to calculate the map measured, and to carry out an evaluation of the descriptors of any combination of nanoemitters, of structured objects or an evaluation of the spatial distribution of continuous distributions. This measured map differs from the original map, due to noise, measurement conditions, system limitations, or measurement uncertainty. This information from the measured map can be elaborated later in different levels of abstraction. This first level of abstraction, which describes the direct results of the measurement, contains, a priori, no biological information but the results of a physical measurement described by nanoemitters, by structured objects or by continuous distributions, which could besides representing any marked entity. The second level, the level of geometric abstraction, structures nanoemitters, structured objects or continuous distributions in the form of geometric objects. It consists of a description of luminous objects and their dynamic characteristics, such as their position or orientation, or their morphology. At this level, the information is still physical and geometric information describing a set of objects. The geometric information uses the measured map and ancillary information, potentially external to the system, on the relationship between the light points and objects. The level of biological abstraction allows a certain apprehension of biological reality thanks to a constitutive relationship between the measured objects and corresponding biological entities. It contains a set of information about the biological object, mainly the position and its dynamics, its shape and its morphology. The biological information uses the measured map and geometric information, and ancillary information, potentially external to the system, on the relationship of light spots and objects to biological entities. A number of conclusions on the biological functionality of the sample can be obtained at this level. The functional level of abstraction allows an apprehension of biological reality. It consists of functional information, uncorrelated from geometric information, and answering questions in biological terms and jargon, such as: “Has the virus penetrated the cell? ". An additional level of information can be defined including process control and instrumentation; indeed, a more advanced control and instrumentation process can be defined, making it possible to trace back to more structured biological information, through an automation of the data acquisition process. An example of such processes is described by Steven Finkbeiner, under the name “Robotic Microscopy systems”. This description of the levels of abstraction, defined in this request, was written, for simplicity, for Biology. It is applicable, mutatis mutandis, to all fields of Vision, biological and medical, artificial and industrial.Conical diffraction Conical diffraction or refraction is an optical phenomenon predicted by Hamilton, [61, in 1832, and confirmed experimentally two months later by Lloyd, [71. Conical diffraction describes the propagation of a beam of light in the direction of the optical axis of a biaxial crystal. Indeed, in a biaxial crystal, the optical axis is positioned in the plane created by the crystallographic axes x and z; the angle with respect to the z axis is 00, depending on the three indices of -2 - -2 refraction according to the law, tan 00 = ni n2 -2 -2 - n2 - n3 Hamilton predicted that light emerges under the shape of a hollow cone of rays. Conical refraction is a milestone in the history of science and was instrumental in demonstrating the theory of electromagnetic waves. A revival of interest in conical diffraction occurred in the later years of the twentieth century; it resulted in a complete theory by Berry et al.[21, experimentally validated in 2009, [81. We follow Berry's theory, terminology and definitions here, including the change in naming of the physical effect, from this point on, using the more stringent term conical diffraction. However, it is important to note that the term "conical diffraction" is also used for two other techniques that have no relation to the technique we are describing: - oblique incidence diffraction is also called conical diffraction - The English term, "conical diffraction mounting" refers to a diffraction grating mounting in which the grating is mounted on a curved surface. 3042043 22 Conical diffraction has aroused considerable interest at the theoretical and experimental level, but “no practical application seems to have been found”, [91. Historically, conical diffraction has been observed in biaxial crystals. We refer to a conical crystal to describe an inorganic or organic biaxial crystal, exhibiting the phenomenon of conical diffraction. Some non-limiting examples of biaxial crystals include, Aragonite, KTP, KTA, KBiW, LBO, KNbO3, MDT, YCOB, BIBO, DAST, POM, NPP, LAP, LiInS2 and LiInSe2. Other effects exist, either creating inherently weaker conical diffraction or creating weaker conical diffraction along a shorter optical path. However, these effects can be used within the framework of the devices described. These effects include polymers, liquid crystals, and externally induced birefringence effects. Polymers include but are not limited to stretched polymer sheets and cascade polymerization, [101; liquid crystals include but are not limited to the thermotropic biaxial nematic phase, [111; the external effects of induced birefringence include, but are not limited to the application of an electric field creating an electro-optical effect, on a non-centrosymmetric cubic crystal, and the photoelastic modulator. The phase in the vortex created by conical diffraction is a geometric phase and is therefore inherently achromatic. The additional chromatic effects are the dispersion of the optical axis and the dependence of the different parameters present in the conical diffraction equations as a function of the wavelength. The chromatic dispersion of the optical axis creates a wavelength-dependent angle of the optical axis of the crystal with respect to the optical axis of the system. It is due, in the majority of cases, to the dispersion of the refractive indices. Refractive indices are wavelength dependent, following Sellmeier's equations. The angle of the optical axis therefore varies according to the wavelength, it creates a chromatic tilt angle of the optical axis in the plane created by the crystallographic x and z axes. It strongly depends on the type of crystal. In an MDT crystal, the least dispersive crystal in the visible, the direction of the optical axis varies by less than 0.1 degrees between 540 nm and 700 nm. In a KTP crystal, the most achromatic crystal in the telecom IR, the angle varies by 0.05 degrees, between 1,350 nm and 2,100 nm, and less than 0.02 degrees over the telecom window - 1450 nm to 1650nm. On the other hand, the θ0 angle can vary greatly depending on the wavelength in some organic crystals like DAST.Compensation for optical axis chromatic dispersion can be performed using geometric optics. The chromatic dispersion of the direction of the optical axis can be compensated by using the natural dispersion of glass or other optical materials, or by using gratings or prisms. The achromatization procedure does not differ, in this case, from the standard procedure for correcting any chromatic aberration in geometric optics. This procedure can be designed and optimized using one of the commercial optical software available by defining adequate target functions. A different concept of achromatization, is based on the use of two different materials, having inverse conical diffraction effects, with high and low chromatic dispersions. The dependence of the various parameters present in the equations of conical diffraction as a function of the wavelength, modifies the parameters of efficiency of the effects of conical diffraction. For linear conical crystals, defined later, the fundamental transfer function is identical to unity and thus trivially independent of wavelength. On the other hand, the transfer function of the vortex depends on the wavelength and can be represented by a chromatic factor equal to i (2k). For sinusoidal conical crystals, defined later, the behavior is different from that of conical linear crystals: the fundamental wave depends on the wavelength and the vortex wave is almost independent of it. Indeed, the simulations show that the shape of the vortex wave is only slightly modified by a variation of the parameter, 00 from 0.5 to 0.75. On the other hand, the shape of the fundamental wave depends on the wavelength and this effect must be taken into account in the design of systems using the two waves, fundamental and vortex. Refer now to Figure 3, which is a simplified schematic illustration of a configuration of a conical diffraction module, 300, in accordance with one embodiment of the present invention. The incident light, 30, is assumed to be collimated, although other conditions can be accommodated using simple optical means. The setup itself includes a first lens, 31, a conical crystal, 32 and an optional lens 33. The first two lenses, 31 and 33, are preferably configured as a 1:1 Kepler telescope. The numerical aperture of the first lens, 31, in image space, represented below by Uo, determines the parameters of the taper effect through the taper radius, defined below. A conical imaging plane, 35, is placed at the focal plane of the first lens 31; a polarizer, or partial polarizer, 29, described above, can also be added. However, in certain optical systems where the incident light is already polarized, this element is not necessary. A focusing lens, 36, determines the final size of the light spot. It may be an external microscope objective, or may be fused with the second lens 33, as implemented in another embodiment of this invention. The distribution of light projected onto the sample is, to a first approximation, neglecting vector effects, a reduced image of the distribution of light in the image plane. The influence of vector effects will be discussed below. The scale ratio or magnification is determined by the microscope objective. 3042043 24 Let the spatial variable, R, at the conical imaging plane, and the wave vector, U, be represented in cylindrical coordinates by R, OR and U, Or. Let X be the wavelength of light. The behavior of the electric field emerging from the conical crystal 32 is entirely characterized by a single parameter, the conical radius, RO; the taper radius depends on the material and the thickness of the crystal. We introduce normalized parameters allowing the description below of the light distribution to be valid both at the conical imaging plane and at the focus of the microscope objective, within the limits of the scalar theory of diffraction.An example of introducing the normalized parameters is described in reference [2] The normalized radial position, p, the normalized wave vector, u, represented in cylindrical coordinates by p, OR and u, Ou, and the normalized conical radius , po, are given by: U p = 2 7 Uo, u = -uo; po = 2 U0 (EQ. 2) 110 being the numerical aperture of the system. Different regimes exist for the set of weakly interacting volumetric optical diffraction effects. Weak interaction volume diffraction effects have the following properties: - a modification of the incident light is created by a disturbance of Maxwell's equations, - the scale of the interaction much greater than the wavelength, typically more than 10 i_tm. The fact that these different regimes create totally different optical effects has been studied mainly for acousto-optical interactions, but is present in all optical effects, including conical diffraction. We will use a terminology adapted from Raman works on acousto-optics and will differentiate the following cases: po« 1, linear Raman Nath regime, previously referenced,

[37] , "linear thin conical crystal", in which a surface approximation of the effect can be used, po< 1 and >0.5, sinusoidal Nath Raman regime, previously referenced,

[37] , "sinusoidal thin conical crystal", in which a surface approximation of the effect can be used, po < 3 and >1, intermediate regime, previously referenced,

[37] , "mean conical crystal", in which complex effects, coupling the effects of Raman Nath regimes and the Hamilton-Lloyd regime described later, po > 3, regime which we will call the Hamilton-Lloyd regime previously referenced,

[37] , under the denomination of “thick crystal”, similar to the Bragg regime in acousto-optics, in which the effects described by Hamilton and Lloyd are present. Only the crystals of the Hamilton-Lloyd regime, or thick conical crystals, po>3, can be described by Hamilton's theory, 3042043 and have the particularity of propagating the rays inside the crystal in the form of a “dark cone”, or “conefringent”, diffracting in the form of a cone, a term used by some authors. Hamilton had moreover, as early as 1832, [61, already noted this condition on the amplitude of the effect of biaxial crystals, necessary the validity of his description of conical refraction, by showing the necessity, of "sufficient biaxal energy" "29 New consequences of Fresnel's principles. It follows from those principles, that crystals of sufficient biaxal energv ought to exhibit two kinds of conical refraction, an external and an internai: a cusp-ray giving an external cone of rays, and a normal of circular contact being connected with an internal cone." The wave emerging from the thin conical crystal, E(p, OR), expressed in normalized coordinates for a circularly polarized wave, is formed by the superposition of two waves, referred to here as the fundamental wave, EF (p), a regular wave, and the vortex wave, Ev (p,OR), a singular wave; these two waves are coherent with each other, co-localized, circularly polarized and of inverse chirality: E(p, OR) = EF(p) + Ev (p,OR) = EF(P) (2-i) + Fv(p)exp(-i0R) (3 (EQ. 3) In this equation, EF(p) is the fundamental scalar amplitude, Fv(p) is the reduced vortex scalar amplitude; they are given by: EF(p) = 2n- f du u cos(po, u)Jo(pu); Fv(p) = 2n- f du u sin(pQu)h(pu). (EQ. 4) For a linear thin conical crystal, the fundamental wave can be approximated by an Airy spot and the vortex wave can be approximated by a linear vortex, represented by: Fv(P) = 2n-po f of u2 (EQ. 5) Assuming that the action of the partial polarizer, 29, is wave scaling vortex by a, the Stokes parameters can be deduced from the previous equations, f3 being the angle of the linear polarization: So = (EF(0))2 + (a2Fv(P))2 = 2cOEF(P)Fv(P ) sin OR; S2 = 212EF(P)Fv(P) cos OR; (EQ.6) 53 = (EF(P))2 (122Fv(P))2 = OR; As described previously, the wave emerging from the conical crystal, for a circularly polarized wave, is constituted by the superposition of two waves, the fundamental wave, a regular wave, and the vortex wave, a singular wave All incident beams at homogeneous polarization can be decomposed on the orthogonal basis composed of right circular and left circular polarizations. The incident beam is therefore the coherent superposition of two beams, one polarized in right circular polarization and the second in left circular polarization. The emerging beam is the coherent superposition of four beams; two fundamental waves, the first created by the beam polarized in right circular polarization and the second by the beam polarized in left circular polarization and two vortex waves created by the beams polarized in right and left circular polarization. However, if the two fundamental waves have the same spatial distribution and can interfere keeping their topology, the two vortices are of opposite chirality and create complex distributions. Different combinations of these waves can be achieved by choosing the input and output polarizations, which makes it possible to obtain PSFs of different shapes. Sparse object We will use the terms of a sparse object in English, to describe either a set of sparse emitters, or sparse, point light emitters, or a set of sparse objects, the sparseness being defined in the references [41-43] and not being limited to point objects but including, for example, filaments. For parsimonious transmitters, the chosen limit is a number less than twelve, positioned in a volume whose size, in each of the dimensions, is less than 3 wavelengths, at the emission or reflection wavelength transmitters. The volume of size less than 3 wavelengths, which contains the parsimonious object, will be referenced as a reduced size analysis volume. We will use the term continuous object to describe a set of point or continuous light emitters, not fulfilling the conditions previously described in the definition of the parsimonious object. The transition between these two regimes is not straightforward and many experimental cases will be intermediate cases between these two types of object. Reference is now made to FIGS. 4a to 4c which are a simplified representation of the concept of volume confinement of the confocal microscope. The functionality of volume confinement is to limit, in the three spatial dimensions, the observed region of the sample to a volume of the smallest possible size, the analysis volume. The volume confinement feature limits the analysis volume by the combination of two effects: the confinement of projected light to a small area, ideally the size of the Airy spot, 50, and the elimination of defocused light by the confocal hole, 28 of FIG. 2. The superposition of these two effects creates a small volume, the analysis volume, 60. This volume determines the size of the elementary region detected by the system. Let us consider a parsimonious or continuous object, 51, consisting of a set of nanoemitters, 53 to 59. The nanoemitters 53 to 55 positioned in the analysis volume 60, and only them, are simultaneously excited by the light source and the photons emitted by them arrive at the detector module. The nanoemitters not in the cone of illumination, 56 and 57, are not illuminated by the incident light. The light emitted by the nanoemitters 58 and 59 ne 3042043 27 located at the conjugate plane of the confocal hole, 28 of Figure 2, is blocked, almost entirely, by the confocal hole, 28 of Figure 2. Two different Cartesian coordinate systems are defined in the system, Figure 4c: The "i" frame: The axes referenced "i" represent a Cartesian frame centered on the center of the analysis volume, 61.The “a” frame of reference: The axes referenced “a” represent a Cartesian frame centered, for each light nanoemitter, on the light nanoemitter considered as a discrete point, 62, When, using an embodiment of the invention which will be described subsequently, a vortex is projected onto the sample under analysis, the center of the vortex will generally be defined as the center of the analysis volume. At least one embodiment of the invention uses conical diffraction to realize the fundamental optical modules of the art. However, alternative implementations, replacing the modules based on conical diffraction, by modules based on other optical concepts, are able to provide the same functionalities. They are intrinsically part of the scope of this invention. Alternative optical concepts include but are not limited to uniaxial crystals, subwavelength gratings, subwavelength gratings, structured laser modes, holographic components, and other techniques known to the Skilled in the Art, The optical and optoelectronic concepts, techniques and devices which can be used in embodiments of the invention are described in, for example, the book written by D. Goldstein, "Polarized light", [121, the “Handbook of Confocal Microscopy”, [131, the “Handbook of Optics”, [141. Optical Semaphore In this embodiment of the invention, we use the term optical semaphore to describe an optical element, passive or active, capable of channeling the incident light towards different channels or detectors according to a property of the light. The simplest case is a dichroic plate which splits light into two channels based on wavelength. We use in this embodiment of the invention the term, in English, "Position dependent Optical Semaphore" - acronym PDOS - or optical semaphore depending on the position - to describe an optical semaphore which channels the light according to the position from the transmitting point. The PDOS will be determined by a series of transfer functions, Ti(x,y,z) depending, for each channel or detector i, on the position of the emitter (x,y,z), in a reference volume. The order of the PDOS will be the number of channels or detectors. The PDOS will be “lossless” in English, in an analysis volume, if the sum of the transfer functions, Ti(x,y,z) is equal to unity in the analysis volume. 3042043 28 The confocal hole, described by Minsky, [151, could be considered in this embodiment of the invention as a degenerate PDOS of order 1. In the majority of cases the dependence of the PDOS is a complex function of the lateral positions and longitudinal. However, we use in embodiments of the invention the term, in English, of "Longitudinal Position dependent Optical Semaphore" - acronym LPDOS - or optical semaphore dependent on the longitudinal position - to describe an optical semaphore which channels the light in function of the longitudinal position of the emitting point. The LPDOS will be determined by a series of transfer functions, Ti(z) depending, for each channel or detector i, on the longitudinal position of the emitter (z), in a reference volume. The order of the PDOS will be the number of channels or detectors. The LPDOS will often be coupled with a stop, limiting the lateral field of the system. Transmission by optical fibers A main use of optical fibers is the exclusive transmission of the TEM00 mode. However, certain fiber optic configurations, such as FMFs or vortex fibers, mainly but not exclusively based on so-called "Photonic Crystal Fiber" (PCF acronym) fibers and so-called "vortex fibers" allow the transmission simultaneous or not, of more complex modes, including vortex modes, having a vorticity equal to or less than 2. It would therefore be possible to deport the optical distributions created by the conical diffraction using optical fibers, allowing a simplification major of the optical system.The possibility of deporting the optical distributions created by the conical refraction using optical fibers allows the application of the embodiments of the invention to many additional applications, for example but not limited to gastric or gastroenterological observation, and observation of the colon and urinary tract. Moreover, certain fibers, the “dual-core photonic crystal fibers”, in English, [161, allow an interaction between two modes, one of them being able to be a vortex, and provide an additional physical mechanism to create functions diversified transfers. Measurements at several wavelengths In embodiments of the invention the object can be illuminated in monochromatic light and by using for example a conventional laser or a monochromatic lamp. In addition, in certain configurations, a broad spectrum laser - called "white laser" can be used. This configuration is simple, because one of the main parameters of the system is fixed and well determined. However, in other embodiments of the invention the object can also be illuminated at several wavelengths, either discretely, for example using several lasers, or continuously, using for example a lamp or a laser with a broader spectrum. 3042043 29 Many existing superresolution systems measure simultaneously or sequentially at several wavelengths. Indeed, it is possible to label similar or different elements with fluorophores having different spectral responses, making it possible to recognize and separate them. It is important to present two different cases: - The use of fluorescent markers, emitting at two different wavelengths, excited by the same wavelength - The use of fluorescent markers emitting at two different wavelengths or similar, excited by two different wavelengths It should be noted that in the case of the use of fluorescent markers, emitting at two different wavelengths, excited by the same wavelength, the problem of registration between the measurements of one wavelength relative to the second, are inherently non-existent because the superresolution position information is derived from the projection of light, which is perfectly identical for the different wavelengths. This allows a relative calibration of the position of fluorophores at two different wavelengths, with a precision limited only by the experimental calibration system, eliminating the major problem of registration between two images of different wavelengths. The possibility of achromatizing optical systems based on conical diffraction make it a tool of choice for the implementation of optical systems, with a common path, in numerous applications, and more particularly for embodiments of the invention described. Achromatization is also possible for optical systems based on uniaxial crystals, and for almost all alternative implementations of this invention, with, for each of them, a greater or lesser practical complexity. Other existing fluorescence systems use light with a broader spectral content, to reduce artifacts, and mainly speckle effects. As a corollary, the spectral properties of fluorescent proteins make it possible to measure the potential of intracellular molecular interactions using the energy transfer technique of Fiirster - Fiirster (Fluorescence) Resonance Energy Transfer (FRET). In some implementations of PSIT systems, the light from one or more incident laser beams is split using a light splitter into two beams, the main beam which will accomplish the functionality of the PSIT system, and an additional low beam. intensity used to measure the position of the laser beam using a camera or a position detector. This device makes it possible to measure in real time the position of the laser independently of any wobble error or other mechanical error with very high precision.A priori information and complementary information 3042043 Embodiments of the described invention allow the integration and fusion of additional information external to the described platform, optical or contextual, to obtain an improvement in the precision of the information collected from the sample for any of the cited levels of abstraction: the map, the geometrical level of abstraction, the biological level of abstraction and the functional level of abstraction. More generally, spectral diversity, information obtained at multiple wavelengths, polarization diversity, and information obtained by projecting different polarization states, extends the range of information available. The fact that the absence of energy, for example in the case of the zero of the vortex, is relevant information, opens up additional possibilities for the acquisition of information without a "cost" in terms of the number of photons. This situation is of great importance for the detection of weak fluorescence phenomena, such as for example autofluorescence. One of the methods described for certain embodiments of the invention will be referenced under the name of dark tracking. We introduce the concept of optical integral information, the information that could be retrieved from optical measurements or by electromagnetic waves, on a target, by an observer, from a given point of view. This information contains many parameters of the object, related to its position, the materials that compose it, its temperature, or its orientation. The optical integral information does not, on the other hand, contain information on regions of the object having no optical path towards the observer, for example an element positioned in an opaque box, or physical information which does not there is no optical transcription. Super-Resolved Measurements and the Diffraction Limit It has long been considered that optics intrinsically limit the resolution of any optical system, across the diffraction limit. The appearance of superresolution techniques in different fields and under different names has shown that it is possible to exceed this diffraction limit, by different means. Embodiments described in this invention, such as the detection of the presence of two points of the same intensity, by projection of a vortex at the center of gravity of the light distribution created by the fundamental wave, are not limited in resolution. a priori and could ideally - with an infinite number of photons - obtain any resolution, as we will describe later for a specific case. 3042043 31 Use of nonlinear interactions in superresolution and family of RESOLFT and STED techniques The use of nonlinear interactions in a material medium, between two beams of light, was proposed in 1994 by Hell, [5] and [17 ], as the basis of a super resolution system. Many different techniques have resulted from the work of Hell creating several families of techniques, such as RESOLFT and "localization microscopy". Several reviews of these techniques have been published ([1] or

[38] ). These nonlinear interactions include but are not limited to two-photon interaction phenomena, emission-depletion, blinking and photoactivation effects upon which the RESOLFT family of technologies and the family of localization microscopy technologies. The RESOLFT family of technologies is well known and is described in several references, such as the initial article by Hell [5] and the initial patent

[17] , or by Schermelleh et al. [1], or in recent publications, Vicidomini et al.

[18] , or Willig et al.

[19] .In the STED technique described in the initial article by Hell [5], two beams are projected, sequentially onto the object: a standard excitation beam, modeled in the majority of cases by a light distribution described by a function d 'airy, and a depletion beam - having a donut or vortex shape; the effect of depletion is to prevent fluorescence from fluorophores in the surface of the depletion light distribution, while not altering the emission of fluorophores positioned in the center of the light distribution outside the distribution depletion light; this makes it possible to create an equivalent emission light distribution smaller than the initial excitation light distribution. This technique has made it possible to achieve equivalent emission light distributions of very small size, while nevertheless requiring very large light depletion energies. Several variants of STED have been developed: the “CW STED”,

[20] , the “gated STED”,

[21] , and the “modulated STED”

[22] . In the CW STED the pulsed laser used in the first version of the STED is replaced by a continuous laser - simpler. In the “gated STED” the emitted photons are discriminated according to their emission time to rule out the photons emitted from fluorophores which have not received the depletion beam for sufficient time; modulated STED uses an intensity modulated excitation beam, in combination with synchronous detection depending on the modulation frequency. This makes it possible to discriminate the fluorescence signal created by the excitation beam from the residual fluorescence caused by the depletion beam. Another variant, proposed by Gould et al.

[45] , uses an SLM to create, either separately or jointly, the lateral and / or axial depletion distributions. The donut - or vortex - was created, in the first version of the STED, using a spatially varying phase plate, "flat phase" in English. This implementation requires the use of two separate optical paths for the two beams, the excitation beam and the depletion beam. This optical assembly is complex, highly dependent on any mechanical drift, and creates complex optical alignments. The system developed requires high technicality and the cost of the system is high. Moreover, this implementation is chromatic, since the phase plate adapted to one wavelength will no longer be so at another wavelength. Since the optical system is not achromatic, the use of a STED at two depletion wavelengths requires an even more complex optical system. To simplify the implementation of the STED, several authors have proposed solutions making it possible to produce a STED in which the two beams, the excitation beam and the depletion beam, would propagate along the same optical path: Wildanger et al. have proposed a common optical path STED microscope, insensitive to mechanical drift, based on the dispersion properties of different optical materials,

[23] , This technology is marketed under the name EASYDOnut by the company Abberior Instruments.

[28] . Bokhor et al.

[24] , proposes the use of a chromatic annular separation of the pre-aligned beams; however this solution blocks part of the depletion light, Hoeffman

[25] , proposes the use of a module containing the pre-aligned optical elements creating the vortex, in the optical path of the depletion laser, to simplify the alignment, Menon et al ;

[26] , proposes diffractive lenses allowing to create amplitude zeros without phase singularities, Reuss et al.

[27] introduces a beamformer placed directly in front of the objective lens. This device is based on the use of birefringent crystals, mounted in the form of a segmented wave plate, consisting of four segments. By a choice of the thickness parameter of the plate, it is possible to produce an element consisting of a phase plate for the depletion and a neutral plate for the excitation. Gould et al.

[45] , uses an SLM to create, either separately, the lateral and / or axial depletion distributions. This solution makes it possible to vary the parameters dynamically to adapt to different wavelengths.Other works integrate the lateral and axial distributions on a single SLM. However, the proposed solutions described earlier are all strongly chromatic and are designed for a single wavelength of excitation and depletion. However, biological applications in many cases require a system with two or more excitation wavelengths. Indeed, it is common practice to mark different biological objects with fluorescent markers differentiated by their excitation or emission wavelength. The most advanced fluorescence systems can use four to six differentiated markers. The presence of a single super resolution channel strongly limits the use of the systems. Two-wavelength STED systems are also commercially available. It is clear that for a multi-wavelength achromatic STED or 3D STED microscope, using the same optical path for two depletion beams at two different wavelengths will simplify super-resolution on different fluorophores. In the prior art, for all the solutions proposed for the STED, the initial laser beams are in the form of a regular distribution and in the majority of cases of a Gaussian distribution. These initial laser beams will subsequently be transformed into an excitation beam, a regular wave, and a depletion beam, a singular wave, by an appropriate optical system, described by the various inventors. Co-locating these beams upstream when they are still in the form of a Gaussian distribution is relatively simple. Co-locating these beams downstream when they have been transformed into a regular, singular wave is much more complex. Co-localizing these upstream beams can be achieved commercially by laser bench systems using fiber optic based techniques. It is therefore relatively easy, as is moreover done in all confocal microscopes, to create a set of laser outputs at different wavelengths from the same optical fiber and therefore co-located in a very precise manner. The solution proposed in embodiments of the present invention makes it possible to rely on this upstream co-localization, greatly simplifying the system and allowing the realization of a multi-wavelength STED, in an intrinsic way. For this, it is preferable to use an optical system which combines the properties of common optical path, achromaticity and “beam shaping”. It is preferable to achieve a different beam shaping for the different beams, i.e. a regular wave for the excitation beam and a singular wave for the depletion beam, and this at any wavelength in the visible spectrum or infrared. The ability to perform an achromatic beam shaping, making it possible to obtain a regular wave for one polarization and a singular wave for another polarization, over all the visible or infrared light, differing for the different polarizations, is new. The PSIT module allows the realization of such an optical system which combines the properties of common optical path, achromaticity and “beam shaping”. To our knowledge, there is indeed no common path system, achromatic and allowing a different beam shaping for the different beams, in the literature. Such a system certainly improves the simplicity of design and use of the STED. 3D STED Many systems have been proposed to extend the STED concept to the third dimension. The solution adopted for all STED-3Ds is the "depletion ring" proposed by Stefan Hell's team, reference 36. The "depletion ring" makes it possible to create a "black sphere", a distribution in which the intensity is zero at the center of the focused field, and increases relatively rapidly with defocusing. An implementation of the "dark sphere" has been described, by Zhang, [291, creating a black spot surrounded in three dimensions by a luminous sphere and by one of the authors of this patent in reference 37. Acronyms We will use in this patent application patents the acronym, SRCD, “Super Resolution using Conical Diffraction” to name the platform, modules and systems specific to the implementation of this invention.We will use in this patent application the acronym, PSIT, method of projection of a sequence of light intensities differing topologically, or in English: “Projected Sequence(s) of Intensifies with various Topologies”; the PSIT method can also be used to project sequences of light intensities differing topologically, at two or more wavelengths, sequentially or simultaneously. We will use in this patent application the acronym, PDOS, spatially dependent optical semaphore, or in English: “Position Dependent Optical Semaphore”. The SRCDP platform, “Super Resolution using Conical Diffraction Platform”, is a Microscopy platform using optical modules based on conical diffraction. We will use in this patent application the acronym, LatSRCS to name the optical module implementing the PSIT method for the implementation of this invention. We will use in this patent application the acronym, LongSRCS to name the optical module implementing the PDOS method. The SRCDP platform, described in detail later, consists mainly of two hardware modules, two new and complementary optical modules, the LatSRCS and LongSRCS optical modules, mounted on a microscope, and an algorithmic module, SRCDA, “Super Resolution using Conical Diffraction Algorithm”, allowing to reconstruct the super-resolved information of the sample. In addition, the SRCDP platform includes an improved detection module, a system control module, and computer and software support. Moreover, certain embodiments of the invention relate to a large number of variant implementations of the PSIT and PDOS methods, of the SRCD platform, of the LatSRCS and LongSRCS optical modules and of the algorithm, SRCDA. 3042043 DETAILED DESCRIPTION OF THE INVENTION LIGHT DISTRIBUTIONS Light distributions created by conical diffraction Referring to Figure 7a, this figure represents the light distributions, created through a conical crystal of normalized conical parameter po of 0.388, calculated by a scalar approximation, for different states of input and output polarization, including at the input and / or at the output either a circular or linear polarizer or a radial or azimuthal polarizer. These light distributions were calculated in an intermediate imaging plane and not at the lens focus to separate conical refraction from vector effects. The polarization states - input and output - are characterized by their angle for linear polarizations and by their chirality for circular polarizations. Referring to Figure 7b, this figure represents the light distributions, created through a conical crystal of normalized conical parameter po of 0.818, calculated by a scalar approximation, for different input and output polarization states, including input or at the output either a circular or linear polarizer or a radial or azimuthal polarizer. These light distributions were calculated in an intermediate imaging plane and not at the lens focus to separate conical refraction from vector effects. The input and output polarization states are characterized by their angle for linear polarizations and by their chirality for circular polarizations. We present in these figures a large number of different transfer functions, including cases including at the input or at the output circular, linear, azimuth or radial polarizers. It is necessary to complete this description by including therein in addition to the circular, linear, azimuthal or radial polarizers described in the figures, the cases of elliptical, dichroic or partially dichroic polarizers, and spatially varying polarizers. Moreover, as illustrated in Figures 7a and 7b, these transfer functions vary greatly as a function of the normalized conical parameter po. In addition, the introduction of two conical crystals, or a conical crystal and a uniaxial or biaxial crystal (in which the light propagates in a direction of propagation different from that of the conical diffraction) in cascade allows a number even larger transfer functions as shown for two conical crystals in Figure 7c.In summary we will refer, in this patent application, under the term conical diffraction transfer function, all the transfer functions that can be obtained using a small (<6) number of crystals in cascade, and polarization elements, static or dynamic, uniform or spatially varying We will mainly note the following light distributions: - The fundamental: Figure 7a00 and 7aii, obtained between parallel circular polarizers, which is a distribution close to the Airy distribution - The vortex: Figure 7a01 and 7aio obtained between circular, crossed polarizers 3042043 36 - The distribution that we have called the “crescent moon” or Stokes distribution, the subfigures 7a0.2_5, 7a1.2-5, 7a2_5.0 and 7a2_5.1, and figure 7c describing the axial variation of the “crescent moon” or Stokes distributions. These distributions are obtained between a circular polarizer and a variable angle linear polarizer; this distribution is antisymmetrical and the axis rotates with the axis of the linear polarizer, - The distribution that we have called the “half-moon” distribution, subfigures 7a42, 7a35, 7a24 and 7a53 is obtained between two crossed polarizers; this distribution is symmetric. - The distribution that we have called the “shifted half-moon” distribution, FIG. 7d, representing the “shifted half-moon” distribution at different axial positions, is obtained between two elliptical polarizers for certain values ​​of ellipticity. - The more complex light distributions, Figure 7b, for a crystal with a normalized conical parameter, po, greater than 0.5 - the realization of additional light distributions using two - or more conical crystals in cascade, (not represented) with or without static or dynamic polarizing elements between the crystals. The realization of the different light distributions is achieved by modifying the input or output polarization. The different light distributions follow the same optical path and the optical system creating these distributions is a common path optical system, as we defined it previously. There are a number of polarizing elements having different polarization at different wavelengths. The use of one of these elements makes it possible to create two compact waves, either regular or singular at two wavelengths or a regular wave at one wavelength and a singular wave at another wavelength. Such a device allows a much simpler implementation of the emission-depletion concepts limited in certain cases by the tolerances or by the vibrations of the optical system. The preceding description, although valid for any optical beam, mainly described, for the LatSRCS Optical Module, described later, the shaping of an excitation beam, or of a depletion beam. However, conical diffraction can be used for shaping the emission beam, as for example in the LongSRCS module, described later. A new variation of this module is to shape the PSF so that it has lateral and mainly axial variations. This modification of the transmit beam PSF, referred to as the "PSF" has many applications, in different disciplines. For example, a module based on conical diffraction, modifying the PSF to create an axial dependence can allow the longitudinal and lateral position measurement of one or more nanoemitters, as described later. 3042043 37 Redundancy and random phase variations The elementary light distributions described in Figure 7 can be obtained in several different ways. Moreover, some of them can be obtained as an incoherent superposition of other elementary light distributions; for example the vortex can be obtained by any sum of two orthogonal "half-moon" light distributions. This redundancy makes it possible to average part of the random phase errors present inexorably in many processes for measuring biological objects. New light distributions can also be obtained as mathematical combinations of elementary light distributions.The "pseudovortex" light distribution, calculated from arithmetic combinations of the four "crescent moon" distributions, has the particularity of having a very strong curvature at the origin. Vector Effects and Direction of the Fluorescent Dipole The theory developed so far describes the distribution of light in the imaging plane of the microscope, 35. The distribution of light projected onto the sample is, according to geometric imaging theory , a reduced image of the light distribution in the image plane. However, as described extensively in the literature, for a high numerical aperture objective, geometric imaging theory is not exact and vector effects must be taken into account. These effects essentially consist of the presence of a longitudinally polarized component. Referring again to Figure 6a, to mitigate vector effects it may be advantageous to keep the final analyzer fixed and add an additional element, fixed or variable, the output bias adaptation sub-module, 74, to control the output bias. We have found that having the output polarization have circular symmetry substantially reduces vector effects and allows for matching the direction of the fluorescent dipole. Such polarization can be circular, radial, azimuthal or position dependent. For circular polarization, the output polarization matching sub-module 74 is simply a four wave delay plate. In this case, the longitudinal polarizing elements have vortex symmetry and blend smoothly into the system with only a small change in the shape of the Stokes parameters, even for microscope objectives with very high numerical aperture. Alternatively, the output bias adaptation sub-module, 74, may be variable and / or controllable and adapt to the topology and symmetry of each of the compact light distributions. 3042043 38 *Modified Wollaston prism Remember that a Wollaston prism can be used to separate an incident beam into two emerging beams separated by an angle. By using several prisms in cascade, it is thus possible to separate an incident beam into a large number of emerging beams. The same effect can be obtained by modifying the Wollaston prism, to create the composite Wollaston prism, by adding to it pieces of uniaxial crystal whose index and orientation of the birefringence are chosen. One can thus construct a prism from a single block of uniaxial crystal which can separate an incident beam into T emerging beams (e.g. eight or sixteen) which are contained in a plane, and separated by equal angles. Once focused on the sample, we obtain T points aligned and also separated. If the incident beam passed through a LatSRC module, these r points are not r Airy spots, but the distributions created by the module and are all identical. The advantage of using this beamsplitter is to scan the sample more quickly since there are r light points instead of just one. The modified Wollaston prism can be coupled with STED methods to duplicate all light distributions without changing the relationships between them. MEASUREMENT PARADIGMS The functionality of the confocal microscope is to limit, in the three spatial dimensions, the observed region of the sample to a volume of the smallest possible size, the analysis volume. As a corollary, in a confocal fluorescence microscope, the information acquired is a single intensity value for the entire analysis volume, conceived as a single entity. More clearly, the detailed information of the position of the nanoemitters inside the analysis volume is not accessible, a priori, in a confocal microscope. It was generally accepted that no additional optical information could be created that would allow additional discrimination within the illuminated volume. Reference is now made to FIG. 4d, which is a simplified conceptual representation of a measurement paradigm according to at least one embodiment of the invention. The measurement paradigm is much more ambitious than that of the fluorescence confocal microscope, shown schematically in Figure 4a.In Figure 4d, an analysis volume, 60, is created at the focal plane of the microscope objective, 22; it contains a parsimonious object, 51, consisting of several nanoemitters, 53 to 59; the result of the system is a reconstructed sparse object, 63, and a list of nanoemitters and a list of their attributes, 64. Referring now to Figure 4e, which is a simplified conceptual representation of another measurement paradigm, based on the concepts of STED, according to at least one embodiment of the invention. This measurement paradigm limits, in two (2D STED) or in three spatial dimensions, (3D STED), the observed region of the sample to a volume of the smallest possible size, the analysis volume. In FIG. 4e, an analysis volume, 60, is created at the focal plane of the microscope objective, it contains a parsimonious object, 51, comprising several nanoemitters, 53 to 59; one or more depletion waves, 2000, reduce by a depletion effect, the volume of analysis to a smaller volume represented by 2001. In this paradigm, as in the confocal, the superposition of all the effects creates a small volume, the analysis volume, 60. This volume determines the size of the elementary region detected by the system. Reference is now made to FIG. 4f, which is a simplified conceptual representation of a third measurement paradigm, combining the two preceding paradigms and used according to at least one embodiment of the invention. In FIG. 4f, an analysis volume, 60, is created at the focal plane of the microscope objective, it contains a parsimonious object, 51, comprising several nanoemitters, 53 to 59; one or more depletion waves, 2000, reduce by a depletion effect, the analysis volume to a smaller volume represented by 2001. As in Figure 4d, this volume contains a parsimonious object, 51, consisting of several nanoemitters, 53 to 59; however, unlike Figure 4d, and similarly to Figure 4e, the elementary volume is reduced by one or more depletion waves. The result of the system is a reconstructed sparse object, 63, and a list of nanoemitters and a list of their attributes, 64. The use of a sparse object in Figures 4d-f is for illustrative purposes and this figure would have perfectly able to represent a continuous object, mutatis mutandis. MEASUREMENT METHODS PSIT Measurement Method A PSIT measurement method according to one embodiment of the invention, a sequence of light distributions of different topologies is projected onto the analysis volume. The PSIT measurement method performs the following functions: o Projection of a sequence, the emission sequence, of compact light distributions of different topological families onto a sample; and o For each compact light distribution: - emission of light by the nanoemitters of the sample, - creation, using the microscope optics, of an optical image, - acquisition of the optical image by a detector photoelectric and digital image creation. In more detail, it should be noted that: The emission sequence consists of at least two point light distributions, from different topological families The emission sequence is projected onto a biological sample marked with nanoemitters, The light emission emerging from each nanoemitter is dependent, for each nanoemitter, on the intensity, in the incoherent case, or on the electromagnetic field in the coherent case, incident to the spatial, three-dimensional position of the above-mentioned light nanoemitter Sampling property of the light nanoemitter previously discussed . 3042043 For each light distribution of the emission sequence projected onto the sample, an optical image is created. The set of images corresponding to the set of light distributions of the emission sequence is referred to as the sequence of images. The PSIT method according to this embodiment makes it possible to acquire essentially lateral information, that is to say the lateral position of each of the nanoemitters. In one embodiment, the PSIT method is implemented by projecting light distributions of different topologies created by conical diffraction and modified by varying input and output polarization states.In one embodiment, the PSIT method can also be used to project sequences of topologically differing light intensities, at two or more wavelengths, sequentially or simultaneously. PSIT method and axial superresolution The PSIT method was originally designed to allow lateral superresolution; however the PSIT method can also be used to obtain the longitudinal position of a nanoemitter. Indeed, certain elementary light distributions are relatively insensitive - within reasonable limits - to a variation in the longitudinal position of the nanoemitter, others are on the contrary very sensitive to it. A sequence of compact light distributions, some of them independent and some of them dependent on the longitudinal position, would make it possible to trace the longitudinal position of the nanoemitters. In addition, for light distributions strongly dependent on the longitudinal position of the nanoemitter, a series of elementary light distributions shifted slightly longitudinally relative to each other can be projected onto the sample, allowing a set of images containing a longitudinal information. Original PDOS method The PDOS method includes the distribution by an “optical semaphore” of the light re-emitted by the nanoemitters or by the continuous object between at least two detectors. It was described by one of the inventors,

[37] . Ideally, the function of the optical semaphore is to separate on different detectors different regions of the analysis volume. Practically, the optical semaphore creates, for each detector, a transfer function of the light emitted by a light nanoemitter, depending on the position in space of the light nanoemitter and different for the different detectors. In one embodiment, the PDOS method is implemented so as to separate on different detectors the collimated light, emerging from nanoemitters positioned at the focal plane of the objective, from the non-collimated light emerging from nanoemitters located below or beyond the focal plane. 3042043 41 The PDOS method makes it possible to acquire essentially longitudinal information, that is to say the longitudinal position of each of the nanoemitters. Mathematically, the method according to embodiments of the invention produces a transfer function transforming the spatial distribution in space of the nanoemitters into the raw information consisting of a set of images. The algorithm performs the opposite operation: it reconstructs the spatial distribution in space of the nanoemitters from the set of images making up the raw information. Modified PDOS method We also present the modified PDOS method, an optical method for shaping the emission beam, for the axial and / or lateral localization of nanoemitters. This method implements a single-channel PDOS method, in which the variation of one of the parameters describing the created distribution is used to measure the axial or lateral parameters. The parameters used can be either an angle parameter for a helical axially varying distribution, or the ratio between the distribution's lobes - for a two (or more) axially varying lobe distribution. This method has a certain similarity with the original PDOS method, described by one of the inventors in

[37] , but differs from it by the fact that the variation of the topology of the distribution created is used to measure the axial or lateral parameters and not by an intensity ratio between two detectors, as described in the original version of the PDOS method. This method, like the original method, has applications as a complementary method to the PSIT method, but also for the axial localization of nanoemitters, for example for localization modalities, such as for example, PALM, STORM or GSDIM modalities or similar. . PDOS method and lateral measurements The PDOS method was originally designed to allow longitudinal superresolution; however the PDOS method can also be used to obtain the lateral position of a nanoemitter. Indeed, the elementary light distributions are also sensitive to a variation of the lateral position of the nanoemitter.For a plane sample, in the case where the projection of light is not feasible, the PDOS method can replace the PSIT method to carry out super-resolved measurements. All these variants are deemed to form part of the invention. The inventor has nevertheless chosen, in one of the implementations, to separate the lateral measurements from the longitudinal measurements into two disjoint but complementary optical modules in order to reduce the complexity of each of the complementary modules. 3042043 42 Information in Certain Embodiments of the Invention In certain embodiments of the invention, the intermediate result, the raw information, is obtained at the end of the detection step. The raw information consists of a set of images Ac,p(m,n), representing for the light distribution o, the image coming from the detection channel p. As in a confocal microscope, the measurement process analyzes a small volume within a much larger object. It will therefore require the addition of additional modules, similar to those of a confocal microscope including a scanning process, a software module for integration, analysis and visualization of point data on surfaces and / or three-dimensional objects. In mathematical terms, algorithmic solves an inverse or parameter estimation problem. The equations of the model are known and we have an a priori model, parametric or not, on the configuration of the nanoemitters. The most natural model is to assume a low number of nanoemitters (parsimonious object), but one can also use continuous models, assuming the presence of one-dimensional structures (lines, curves) or specific patterns. It is then possible to use all the mathematical procedures known to those skilled in the art for solving inverse problems or estimating parameters. We subsequently describe an example of an algorithm adapted specifically to the measurement according to an embodiment of the invention. Moreover, we present, for its emblematic value, a new solution of the problem of the discrimination of two points positioned at a short distance from each other. This problem, studied by Lord Rayleigh, is the basis of the resolution criterion in many fields of Optics. It has thus been described, in a rather broad manner, the characteristics of the embodiments of the invention so that the detailed description thereof can be better understood, and so that the present contribution to the art can be better appreciated. Many additional features of the invention will be described below. SYSTEM Hardware and Algorithmic Platform One embodiment of the invention is a hardware and algorithmic platform, referenced as the SRCDP platform, 500, illustrated in Figure 5. The SRCDP platform, 500, implements the method according to one embodiment of the invention, either by combining the two methods PSIT and PDOS, original or modified, described above, or by using the STED techniques, or by combining the STED techniques with the PSIT or PDOS methods, original or modified. In one of the embodiments, the SRCDP platform observes, FIG. 5, a biological sample, 11, integrating a set of nanoemitters. The result of the observation of the biological sample by the SRCDP platform is the acquisition of superresolution information, representative of the observed sample. The SRCDP platform, 500, Figure 5, mainly comprises: In its hardware part: - A confocal microscope 200, adapted or optimized, similar to the confocal microscope, described previously, and comprising all the appropriate components, as described previously - Two new and complementary optical modules, mounted on a standard microscope. The two new optical modules are the LatSRCS, 700, and LongSRCS, 800 optical modules, described in detail later with reference to Figures 6 and 8, respectively. The LatSRCS 700 optical module implements the illumination steps necessary for implementing the PSIT method according to one embodiment of the invention. Alternatively, the LatSRCS 700 optical module implements the illumination steps necessary for the implementation of a STED or RELSOFT technique, according to another embodiment of the invention.The original or modified LongSRCS optical module 800 implements the emergent light intensity distribution steps in a plurality of images of the PDOS method or, implements the variation of the emergent PSF, depending on lateral or axial parameters, according to one embodiment of the invention and, - the SRCDA algorithmic module, 600, capable, from the images created by the SRCDP platform, of reconstructing the superresolution information of the biological sample. - Other auxiliary elements, such as the computer 66 and the software 67, may be necessary for the realization of the platform, Detection module In confocal scanning microscopy the detector is a detector consisting of a single element such as a PMT or a SPAD. The detector acquisition time is determined by the scanning mechanism. An improved detection module, 65, can be implemented using small size, low pixel count detectors. Such a module would not have been feasible ten or twenty years ago, due to the lack of adequate technologies. Today, small size, low pixel count, high frame rate detectors with low noise characteristics are available based on several technologies. SPAD arrays with a low number of pixels, such as 32*32, have recently been demonstrated with acquisition rates up to 1 MHz. The improved detector module, 65, can also be implemented using CCDs, EMCCDs or CMOS sensors. CCD, CMOS or EMCCD sensors with a low number of pixels exist or can be designed specifically. Furthermore, CCD, CMOS EMCCD detectors can be used using region of interest, sub-windowing or “binning” functionalities, “crop” or “fast kinetics” modes, available for certain detectors. The spatio-temporal information referenced here is the position and time of impact of each fluorescent photon. In real systems, spatiotemporal information is corrupted by detector noise, which creates erroneous photons, and by detection inefficiency, which creates photons that go undetected, reducing performance. In the SPAD matrices, for each photon, the pixel that detected it and the impact time are received, i.e. the complete spatio-temporal information is available. For CCD, CMOS or EMCCD detectors, the acquisition of several frames is necessary to approximate the spatio-temporal information. In several implementations we will refer to separate detectors; in very many cases the detectors may be either physically separate or consist of different zones on the same detector, or a combination of the two previous cases. Control Module With reference to Figure 11 and Figure 5, in a preferred embodiment of this invention, the various control elements integrated into the SRCDP platform, 500 will be described: The Control Module, 1100, at using the control systemic procedure, 1101, controls and modifies the optical parameters of the SRCDP platform, 500, the electronic parameters of the improved detection assembly, 65, and the mathematical parameters of the SRCDA algorithmic procedures, 900, to optimize the emergent information, according to criteria defined by the system or by the user. The control is carried out by varying the control systems 1102, 1103 and 1104, of the different elements of the platform, 600, 800 and 900. The control system, 1100, will also use, if available, external information, 1105, relayed by IT support. Note: 1105 is not present in Figure 11 It is understood that the invention is not limited in its application to the details set forth in the description contained herein or illustrated in the drawings. The invention is capable of other embodiments and of being practiced and carried out in various ways.Those skilled in the art will easily understand that various modifications and changes can be applied to the embodiments of the invention as described above without departing from the scope of this invention SRCDA algorithm The reconstruction algorithm that we are going to detail applies not only in the case of a given field analyzed using the PSIT and PDOS methods, but also in the case where the measurements obtained by the PSIT and PDOS methods are enriched with additional measurements, using other Microscopy modalities. For example, confocal or wide-field microscopy measurements, at the same lateral or axial positions, or at different positions can be performed to calibrate certain parameters of the scene model. 3042043 In the case of confocal microscopy, the direct model is enriched by the fact that an overlap between the different positions of the projected signals makes it possible to take into account, at a given point, more measurements. Taking into account shifted projected signals does not however add any additional complexity, since these shifted signals are only added to the list of projected signals. Refer now to Figure 9, which is a simplified schematic illustration 900 of a fluorophore data superresolution algorithm method, in accordance with one embodiment of the present invention. An algorithm procedure, shown in Fig. 9, quantifies the number of fluorophores, retrieves the attributes of each fluorophore, and quantifies the precision of each output parameter. The preprocessing procedure, 111, reorganizes the spatio-temporal information, 110, into sets of superresolution images, 112. This operation can be performed using a filter bank procedure. The intermediate dataset is then a small series of small images, typically 16*16 pixels. The preprocessing procedure, applies to a small number of spatio-temporal elements of the order of a few thousand, it can be carried out in real time and using existing computer equipment. The descriptor procedure, 113, the main step of the calculation, creates from each image, a set of descriptors, 114, and their statistical significance. Descriptors include, but are not limited to: the intensity of each image, the presence, in the image, of a distribution of light and its characterization as a regular distribution or a vortex, its center of gravity and moments of order one and more. The third step is a filtering operation, 115, in which only the descriptors, which are statistically relevant, are kept. The classification operation, 116, is the last step of the algorithm. The algorithm is able to recognize, based on the set of descriptors, 114, and a knowledge base, 117, the different measurement cases such as a single fluorophore, two longitudinally or laterally separated fluorophores and three or more fluorophores. The SRCDA algorithm can use the classical techniques of inverse problems. However, three new algorithmic approaches, the modified MAP algorithm, the ELSE algorithm and the ICE algorithm are described in this invention patent application and are deemed to form part of this invention. OPTICAL MODULES LatSRCS optical module implementing the PSIT method We describe, with reference to FIG. 6a, an optical module according to one embodiment of the invention, the LatSRCS optical module, 700, and its specific function in microscopy. The optical module, LatSRCS, 700 according to this embodiment, is an optical module, projecting onto a plurality of nanoemitters of a sample, a sequence of compact light distributions of different topology. Each nanoemitter fluoresces with a sequence of luminous fluorescent intensities depending on the intensity incident on the nanoemitter and characterizing the lateral position of the nanoemitter. In most embodiments, the compact light distributions of different topologies are created by the interference, with varying amplitudes and phases between a regular wave and a singular wave. In the preferred embodiment, the regular and singular waves are created by a thin conical crystal.The LatSRCS optical module, 700, is positioned in the lighting path of the confocal microscope 200; it projects a sequence of compact light distributions of different topologies onto sample 11 using the confocal microscope objective 200. In one embodiment using cone diffraction, the incident intensity at a specific position on sample 11 will be proportional, for each light distribution, to a specific combination of Stokes parameters. The LatSRCS optical module, 700, uses an inherent functionality, previously described, specific to the nanoemitter, which samples the incident light intensity at its precise position (of the nanoemitter) and re-emits fluorescent light dependent on the incident light. It is remarkable that the measured information is directly related to the position of the nanoemitter inside the compact light distribution. This information is frozen by the functionality of the nanoemitter, its property of absorbing and reemitting light, which breaks the optical chain. This information is carried by the fluorescent light, in the form of an emergent light distribution, recoverable by a detection assembly 65. If the incident light varies in time according to a sequence of compact light distributions of different topologies, the intensity of the re-emitted fluorescent light varies in the same proportions. The sequence of re-emitted fluorescent light will be proportional to the sequence of compact light distributions of different topologies. From this information, it is possible to retrieve the position of the nanoemitter, as explained below. The PSIT method according to embodiments of the invention refers to the projection of a sequence of compact light distributions of different topologies in a microscope, the interaction with the sparse object or the continuous object, the collection of the light re-emitted by the objective of the microscope, 22, the detection of the light, fluorescent or not, by the improved detection assembly 65, and the analysis of the information by an appropriate algorithm. In some embodiments, the enhanced detector assembly, 65, consists of a single detector, and only retrieves the overall intensity as a function of time, while in other embodiments, the Enhanced detection consists of a small area of ​​pixels and also recovers the spatial distribution of fluorescent light. The set of retrieved information, consisting of a plurality of images, referred to as the superresolution side images. In one embodiment, the contribution of a nanoemitter positioned in the illuminated volume to a specific superresolution lateral image is proportional to a combination of the Stokes parameters of the incident light at the position of the nanoemitter. This new information makes it possible to refine the position of the nanoemitters or the spatial distribution of the continuous object, to quantify the number of nanoemitters present in the illuminated volume and to differentiate several nanoemitters present in the same volume. Refer now to Figure 6a, which is a simplified schematic illustration of a LatSRCS optical module, 700, in accordance with one embodiment of the present invention. Fig. 6a shows an optical module, LatSRCS, 700, it includes all the components of the conical diffraction module, of Fig. 3, which are implemented in the same way as in the conical diffraction module 300. The optics of the light source of the confocal scanning microscope is assumed to be achromatic and in infinite conjugation, although other conditions can be accommodated using auxiliary optics. The incident light, entering from the light source is parallel, 30. The optical module 700 itself comprises a first lens, 31, an achromatic 32, or a subassembly achromatically performing the functionality of a conical crystal as explained above, and a second lens 33; a partial polarizer, 29, described above, may also be added. The first two lenses, 31 and 33, are preferably configured as a 1:1 ratio Kepler telescope; the conical imaging plane, 35, is placed at the common focal plane of the lenses 31 and 33.The numerical aperture of the first lens, 31, determines the parameters of the conical diffraction effect through the normalized conical ray, defined below. The second objective, 33, restores the parallelism of the light, to inject it into the microscope. It further comprises a polarization control sub-module, 71, comprising, for example, a rotating quarter-wave plate, a pair of liquid crystal light valves, a Pockels or Kerr cell, 72, and an analyzer 73. Stokes parameter information can be transformed into sequential information, through a sequence of spatially differentiated light distributions, and carrying sequential information, as described above. Modified LongSRCS optical emission beam-shaping module We also present the modified LongSRCS module, an optical emission beam-shaping module, for the axial and / or lateral localization of nanoemitters. This module implements a single-channel PDOS method, in which the variation of one of the parameters describing the created distribution is used to measure the axial or lateral parameters. The parameters used can be either an angle parameter for a helical axially varying distribution, or the ratio between the distribution's lobes - for a two (or more) axially varying lobe distribution. This module has a certain similarity with the original LongSRCS module, 3042043 48 described by one of the inventors in

[37] , but differs from it by the fact that the variation of the topology of the distribution created is used to measure the axial parameters or lateral and not by an intensity ratio between two detectors, as described in the original version of the LongSRCS module,

[37] . This module, like the original module, has applications as an add-on to the LatSRCS module, but also for the axial localization of nanoemitters, for example for localization modalities, such as for example, PALM, STORM or GSDIM modalities or similar. The case where the input polarization and the output polarization are elliptical with an orientation of the major axes of each ellipse having an angle of 90° between them is treated in more detail. Among the distributions generated under these conditions, some exhibit large axial variations, and these variations can be exploited to measure the position of an emitter with high axial precision. We separate these distributions into two groups, the distributions which present a single lobe and those presenting two lobes. The distributions with only one lobe present a rotation effect in the plane depending on the axis Z, spiral effect. Thus, the Stokes distributions, produced from a linear polarization (ellipticity = 0°) and a circular polarization (ellipticity = 45°) present variations which appear in the table below. By using an appropriate algorithm, the orientation of the distribution can be detected and the position of the emitter deduced with high axial accuracy. (Figure 7c). Distributions with two or more lobes present a shift effect of the two lobes along the Z axis. Thus, the so-called shifted half-moon distributions, produced from two elliptical polarizations oriented at 90° but with the same ellipticity, present variations that appear in the table below. Using an appropriate algorithm, the position of the emitter can be deduced with high axial accuracy by measuring the intensity ratio between the lobes, this variation being illustrated in Figure 7d. Moreover, certain more complex elementary light distributions, consisting of more complex superpositions of waves, exist with a strong longitudinal dependence; for example the “dark three-dimensional spots” described by Zhang,

[29] , create a black spot surrounded in three dimensions by a luminous sphere. These "dark three-dimensional spots" consist of a superposition of Laguerre-Gauss functions, which can be realized inside a laser cavity or using a hologram or phase plate, as suggested by Zhang or using conical or uniaxial crystals as suggested by the inventor in

[37] . All these variants are deemed to form part of the invention.The inventor has nevertheless chosen, in certain implementations, to separate the lateral measurements from the longitudinal measurements into two disjoint but complementary optical modules in order to reduce the complexity of each of the complementary modules. 3042043 49 SRCDA ALGORITHM Multi-image system and reconstruction algorithms We will refer under the name of multi-image system to the set of optical and optoelectronic systems, in which a set of different and differentiated images, originating from the same spatial region of the object, two-dimensional or three-dimensional - are recorded and analyzed through a suitable algorithm for analyzing the spatial - and / or spectral distribution of the emitting spatial region. This differentiation may be due to the projection of spatially different illumination, as previously described; it can also be due to a variation in the spectral content of the illumination; it can also be due to a natural or imposed movement from the outside of the objects. Finally, it can be due to a stochastic variation of the content of the spatial region of the object, two-dimensional or three-dimensional, through a natural or imposed stochastic effect, such as the systems used in superresolution based on stochastic detection, including the processes PALM and STORM and their countless variants, each bearing a different acronym. Other means of differentiating images of the same emitting spatial region are known to those skilled in the art and are deemed to form an integral part of this invention. We will refer to as a multi-image system including the E-LSE reconstruction algorithm a multi-image system using the E-LSE algorithm described below Modified MAP reconstruction algorithm This algorithm differs from the existing algorithms in the literature known to those skilled in the art, by presenting the following mathematical characteristics, the combination of which is new and differs from traditional MAP approaches: - Bayesian formulation - no a priori on the reconstruction, apart from positivity (contrary to MAP approaches traditional ones, which in general incorporate a prior of regularity on the reconstruction, of the total variation type for example) - the modeling of the Poisson noise leads to a term of attachment to the data which is written in the form of a divergence of Csiszar (well-known result) - the posterior law is exploited by a MAP, i.e. we seek the maximum probability reconstruction (so we have to solve numerically solve an energy minimization problem, which is done with an iterative approach of the gradient descent type) - introduction into the model of a resolution gain factor (factor of oversampling of the reconstruction with respect to the resolution of the acquired images) - imposition of a "good sampling" constraint for the reconstruction (the highest frequencies of the reconstruction spectrum are forced to 0) 3042043 - introduction of a "pinhole" factor (digital confocal) Reconstruction algorithm E-LSE The proposed algorithm allows, from the images recorded by the camera (or cameras) following the excitation of the sample by all the chosen illuminations, to reconstruct a high resolution, two-dimensional or three-dimensional image. , sample. This algorithm is based on the combination of several principles: the formulation of the reconstruction as a Bayesian inverse problem which leads to the definition of an a posteriori distribution. This a posteriori law combines, thanks to Bayes' law, the probabilistic formulation of the noise model (Poisson noise inherent in the quantum nature of photon emission, to which the modeling of other sources of noise is possibly superimposed, in particular the camera reading noise), as well as possible a priori (positivity, regularity, etc.) on the distribution of light in the sample; - The E-LSE algorithm uses the same Bayesian formulation as the modified MAP algorithm, described previously, but operates differently (in a more complete way) the posterior law: indeed, one calculates the average of the posterior law and not its maximum value point (which is known to be more suitable for high-dimensional problems).This approach, considered by Besag in 1984

[30] , has recently been implemented numerically in the case of image denoising with a prior of the total variation type [31,32]; the use of swarms of point emitters or emitters with simple geometry, which makes it possible to favor parsimonious solutions (samples with a limited number of emitters, or whose emitters are concentrated on structures of small dimension such as curves, or surfaces in the three-dimensional case (we therefore in fact calculate the average of the a posteriori law with a parsimonious a priori on the solution); The fact of using the average of the a posteriori law (and not its point of maximum value) makes it possible to obtain a low dependence on the number of emitters used: it is therefore not necessary for the number of emitters used to correspond to the number of fluorophores actually activated in the sample; the estimation of the a posteriori average by means of a Monte-Carlo Markov Chain (MCMC) type algorithm [33,34], as in the references [31,32] mentioned above According to one embodiment of the algorithm, the sparsity a priori by the use of a limited number of emitters is not used and the mean of the posterior distribution is calculated over the set of possible images as in [31,32]. 3042043 51 Poisson noise In the standard embodiment, where only Poisson noise is modeled, the density of the posterior probability distribution is written in the form p(x,i1) = e-E(x'Â-) (EQ. 9) where Z is a normalization constant - and not the light propagation axis - which does not intervene in the algorithm, and = kui(x k, y) - mi (y) log (B + 21kui(xk, y))i (EQ. 10) The swarm of emitters is here represented by the vectors x=(xi,x2,...xn) (n discrete positions in the domain of the high resolution image to be reconstructed) and the vector 2=(21,22,...2n) which encodes the intensities of the emitters located at the points xi,x2,...xn. Each quantity of type ui(x,y) is determined during the calibration step: it represents the intensity emitted at pixel y of the camera by an emitter located at pixel x of the high-resolution image, in response to a illumination of index i (i thus codes here both the position of the illumination signal, but also its shape). The positive real B corresponds to the intensity of the continuous background, which generally results both from the sample (diffuse fluorescence for example) but also from the sensor. Finally, the quantities mi(y) simply correspond to the measurements (images recorded by the camera): mi(y) is the intensity measured at pixel y of the image of index i, i.e. the image recorded after illumination of index i). The proposed algorithm consists in making the transmitters represented by the vectors x evolve and in accordance with the law given by the density p(x,2). The algorithm is iterative: at each iteration, one of the transmitters is disturbed (in position or in intensity) and this disturbance is accepted or not according to the principle of the Metropolis-Hastings algorithm [3]. The reconstructed image is obtained by averaging, with an equal weight for each iteration, the emitters thus constructed. If xi and 2j correspond respectively to the position and the intensity of the emitters at iteration j of the algorithm, then the image I reconstructed after N iterations is given by / (x) = N 2.jk (EQ. 11) j,k;xk Several improvements can be made to this algorithm: the establishment of a bure-in step (the first iterations are not used in the reconstruction), the optimization of the initialization of the transmitters, the optimization of the perturbations performed at each iteration (proposal law), the use of a post-filtering step (for example a slight Gaussian blur), etc. The results of the algorithm can be transmitted to the user either in the form of an image or in the form of numerical or graphical data. 3042043 52 The same reconstruction algorithm can be used in a second version including a set of additional parameters describing global parameters of the spatial region of the object either known a priori or determined a posteriori. This algorithm, in its two versions, can be used in all multi-image systems, in which a set of different and differentiated images, originating from the same spatial region of the object, two-dimensional or three-dimensional, are recorded and analyzed.Dynamic E-LSE algorithm In addition, in a variant of this algorithm, the dynamic E-LSE algorithm, the speed of the transmitters can be taken into account. When observing dynamic samples, it is possible to simply incorporate into the E-LSE algorithm the speed of the observed objects, either individually for each of the emitters, or by defining populations of emitters with different speeds. In the case of so-called “time lapse” imaging (i.e. successive observations over time of the same sample), this can be achieved naturally by forcing the simultaneous reconstruction of successive images from mobile transmitters parameterized by their initial position and their speed. In the case of the acquisition of a single image, it is also possible to take into account the dynamic nature of the scene through its impact on the return PSF (shake blur), whose deformation is correlated with the multiple observation of the same transmitter. The overlap, “overlap” of the different micro-images obtained during the scan means that the same transmitter is called upon during the acquisition of several micro-images (at different instants, due to the temporal component of the scan). ICE algorithm The ICE algorithm was recently introduced for denoising images in the case of a regularization by total variation

[39] . The ICE algorithm can also be used to solve more complex inverse problems (deblurring, interpolation). This fixed point type algorithm converges very quickly, and the solution obtained is extremely close to that associated with the LSE algorithm for this problem. The principle of the ICE algorithm is to replace the calculation of the expectation of the posterior law performed by LSE by iterating the explicit calculation of the mean of the posterior law of a pixel conditionally on its neighbors. However, the application of the ICE algorithm to inverse problems for an image or for a multi-image system must be demonstrated. Calibration The SRCDA algorithms use, in many cases, the measurements taken on the sample as input, but also data inherent to the system which are based either on theoretical values, or on values ​​obtained after a so-called calibration step. . In this step, measurements are performed on a reference sample in order to precisely measure the illumination functions and the return transfer function (PSF) of the optical system. Specificities and advantages of the various SRCDA algorithms The various SRCDA algorithms, described previously, present the following differentiations and advantages compared to the State of the Art: Modified MAP: - production of images naturally well sampled thanks to the introduction of the gain of resolution and forcing to 0 of the highest frequencies (limits "night sky" type artefacts) - good compromise between controlled algorithmic complexity (which makes it possible to maintain acceptable calculation times) and good reconstruction quality (resolution of the inverse problem by non-linear optimization, more interesting than the use of linear methods such as “reassignment”

[40] for example) E-LSE: - introduction of the parsimony hypothesis in a flexible form (low sensitivity to the number transmitters) - reconstructions of very good quality, in particular for parsimonious samples - ability of the method to adapt to the amount of local information ale, good management of reconstruction uncertainties (phenomenon of averaging in the event of possible multiple interpretation) - possibility of modeling parsimony differently according to a priori on the sample observed (use of emitters of the point, segment, curve, surface type , etc., exclusively or in combination) Algorithm of the compound optical process The compound optical process according to at least one embodiment of the invention is a logical complement of the SRCDA algorithm. Indeed, the reconstruction obtained by the SRCDA algorithm can lead to the conclusion that an additional image would improve the performance of the measurement. The SRCDP microscopy platform allows the acquisition of one - or several - complementary images chosen from a set of light distributions from the PSIT or PDOS methods.3042043 54 Resolution, parsimony, illumination topology and positivity The ability to overcome the resolution limit, for nanoemitters, using PSIT methods, based on the specific topologies of certain illuminations created by these methods had already been described by a of the inventors in reference

[37] and is described again in the next paragraph. More generally, a microscopy system not using a non-linear effect is limited, in the general case, to a superresolution factor of 2 compared to the limit imposed by optical diffraction

[38] and

[41] . But in the case of a sparse scene (actual support of the sample significantly smaller than the size of the imaged area, for example in the case of scenes composed of filaments and / or point sources), and in the absence of too large a continuous background (so that a positivity constraint on the reconstructed image is effective), it begins to be recognized that this limit of 2 is no longer valid and can be exceeded [42 - 44]. An obvious example is given by the case of observing a single point source, even using a single image: in this case, the achievable resolution for the reconstructed image (i.e. the precision with which the source can be located) is not limited by optical diffraction but by the quantity of photons (more precisely, by the signal-to-noise ratio of the measurement). In the PSIT method, on the basis of the acquisition of several images of different topologies used in this method, one of the inventors,

[37] , had shown the capacity to extend this absence of intrinsic limit of resolution, replaced by a limit of resolution linked to the Signal to Noise ratio, in the case of the detection of two close points (Rayleigh criterion) and the measurement of their position. This demonstration can be extended, by simple modifications, to the case of three points, not positioned on a straight line. This proof is repeated in the next paragraph. This demonstration is based on a new position measurement mechanism, described in the next paragraph, which is different and complementary to the centroid method used in classical systems. In the case of several point sources, in the case of uniform illuminations, the maximum superresolution factor depends essentially, in addition to the signal-to-noise ratio, on the properties of the scene: number of sources (compared to the number of measurements), distance minimum between two sources, etc. [43-44]. In the PSIT method, the maximum superresolution factor will depend, in addition to the factors described previously, on the chosen illuminations. Artifact corrections The MAP algorithm described above is based on an accelerated gradient descent formulation and achieves a Poisson noise reduction and an improvement in resolution under positivity and local resolution constraints. As often happens for this family of inverse problem algorithms, and more generally for all the algorithms used in the context of this invention, including but not limited to the algorithms described previously, unmodeled data, errors calibration, a poor signal-to-noise ratio can create reconstruction artifacts, in the form of distortions or so-called "honeycomb" shapes (for diffuse light and / or thick objects. To minimize these effects, we have developed The following algorithms, the use of which, within the framework of the systems described in this invention or other optical acquisition systems will be deemed part of this invention: Each pixel of the fluorescence camera can be seen as a diaphragm. , positioned in a given axial and lateral position, the diaphragm allows some of the photons to pass; the ratio of the number of photons transmitted to the number d he incident photons depend on the axial and lateral positions; for the central pixel, the ratio of the number of photons transmitted to the number of incident photons is maximum when the emitter is at the nominal position. The peripheral pixels contain information relating to remote emitters, either laterally or axially from the nominal position.The ratio of the number of photons transmitted, by the central pixels and by peripheral pixels is a measure of the ratio of the quantity of light coming from the focused emitters, these emitters being modeled in the algorithm, to the quantity of light coming from emitters not -focused, these emitters not being modeled by the algorithm (excluding model and defocused light). This ratio makes it possible to quantify the proportion of modeled photons and off-model photons and therefore to adapt the parameters of the algorithm, globally or locally, according to this ratio. Moreover, by masking a certain number of pixels, it is possible to improve the proportion of photons coming from the focal plane and in particular from the illuminated zone. This masking of the pixels can be carried out a posteriori, and is based on a local likelihood index of the model used in the algorithm. It is also possible to replace this masking by a filtering, which separates each micro-image into a component which better verifies the model, and an “out-of-model” component. This approach could improve the proportion of photons and therefore the quality of the final result. The proportion of the out-of-model intensity having been evaluated in a region of the object, it is possible either to limit the resolution in the aforesaid region during the reconstruction, or to apply a subsequent processing to the reconstructed image to smooth the zones which have a low ratio of focused photons. It is also possible to separate each micro-image into two components and apply the algorithms described previously by estimating only the focused part. In addition, it is possible to evaluate the dependence of the reconstruction on the measurements and the reliability of this reconstruction. In low light, the low signal-to-noise ratio is amplified by the algorithm and can give a result that strongly depends on the measurement, and of which one is entitled to wonder if it is true. This is a reconstruction operator variance problem, whereas the previous point, the out-of-model, is a reconstruction bias problem. There are several ways to stabilize an operator (regularization, calculation of the a posteriori variance, solution in the sense of the quadratic risk (LSE) rather than MAP...). One solution is to add noise to the measurements to see if the result is stable. It turns out that a good property of random variables having a Poisson law is to be able to decompose into two or more Poisson random variables with lower means and therefore a lower signal-to-noise ratio. These variables are independent of each other but not independent of the initial variable. Another solution is the so-called "Split Photon" method. It consists in decomposing all the pixels observed into two values, which gives two new measurements, and in applying the reconstruction operator to these measurements. Being independent, these measurements are very likely to give different results if the signal-to-noise ratio (SNR) is low. We therefore pass from a measurement with a given signal-to-noise ratio (the value of the signal-to-noise ratio being represented by SNRO) to 2 measurements of signal-to-noise ratio equal to SNRO / sqrt(2). The two reconstructions are compared and if they differ, the reconstruction with all the photons which will be located at best halfway between the latter two is not reliable. In this case, a reconstruction with less important reconstruction parameters will give a more reliable reconstruction. Position measurement of a point by the PSIT method The PSIT method can be used as a technique for measuring the position of a nanoemitter with high precision, using a measurement mechanism different from and complementary to the centroid method. Consider a nanoemitter positioned at position x,y in Cartesian coordinates and p,0 in polar coordinates. An illumination sequence consisting of a fundamental wave, and a pair of so-called “half-moon” distributions, aligned along orthogonal axes is projected onto the nanoemitter. The preprocessing procedure creates two images: A "top hat" image consisting of the sum of the three images of the sequence, A vortex image consisting of the sum of the two half-moon images. A first descriptor is the Cartesian position calculated using the centroid algorithm on the “top-hat” image.Referring to Figure 10, the radial position p can be measured univocally by measuring a parameter, pa, equal to the normalized arctangent by a factor n, of the intensity ratio between the normalized intensity emitted by the nanoemitter illuminated by the vortex wave, Iv, and the normalized intensity emitted by the nanoemitter illuminated by the fundamental wave, IF. Indeed: - the normalized intensity emitted by the nanoemitter illuminated by the fundamental wave varies from 1 at the center for the fundamental wave to 0 at the Airy radius, 3042043 57 - the normalized intensity emitted by the nanoemitter illuminated by the he vortex wave varies from 0 in the center to 1 at the maximum of the vortex to arrive at 0 for a value slightly greater than the radius of Airy. The arctangent of the ratio is a monotone function. The azimuthal position can be measured by measuring the intensity ratio between the total intensity emitted by the nanoemitter illuminated by the first half-moon distribution, Ix, and the total intensity emitted by the nanoemitter illuminated by the second half-moon distribution , IV. The ratio between these two intensities is a square tangent geometric law: IVE = tan2 i9 (EQ. 12) Iv The two measurements are redundant. This redundancy is a measure making it possible to qualify the observed object as being a single point and to separate this case from the other objects potentially present on the sample. A direct application of the use of the PSIT method according to one embodiment of the invention to measure the position of a nanoemitter with high precision is the integration of this measurement technique into a new technique of local stochastic optical reconstruction . One of the limitations of the applicability of stochastic techniques is the measurement process, requiring a large number of images and therefore a long measurement time and high phototoxicity. The use of the PSIT technique according to at least one embodiment of the invention, which makes it possible to measure the position of a light emitter, at a resolution much higher than the Airy disk, at rates which can reach micro or nanoseconds allows the extension of stochastic techniques to many new applications. The images resulting from the use of the PSIT method can also be processed using the generalized Hough method, making it possible to recognize structured objects, line, circle or others, in an image. Recognition and measurement of two points: a new resolution criterion Let us now consider two nanoemitters of the same intensity positioned symmetrically around the center at positions p, 0 and p, -0 in polar coordinates. We will use the system described in the previous paragraphs. The three descriptors will give the following results: - The centroid will measure the center of gravity of the light distribution, which will be the origin, - The descriptor p, will measure the common radial value of the two nanoemitters, - The descriptor 0, which in the case of the half-moons contains a degeneracy between 0 and -0, will measure the value O. As mentioned previously if the value of the descriptor p is not null we know that the studied case is not a point but two or more. Moreover, the descriptors p and 0 allow us to measure the characteristics of two points at a resolution much higher than that defined by the Rayleigh criterion. What's more, by using a compound process, it is possible to separate this case from the vast majority of 3+ point cases. An additional light distribution can be projected onto the sample, a half-moon inclined at an angle 0; the hypothesis of the presence of two points will be confirmed or invalidated according to the results of this image. Indeed, the energy measured will only be zero for two points, for a line or for a series of points aligned in the direction of the angle O. This measurement is not limited a priori. Of course, a practical resolution limit exists first, related to signal quality, fluctuations and various imperfections. If we neglect the practical limits, the resolution limit is related to the number of photons detected. The resolution of a system using the PSIT and / or PDOS techniques is therefore, in practice, dependent on the sample observed.For a sample marked sparingly (that is to say in such a way that the fluorescent markers are positioned on non-dense structures such as walls, membranes, filaments, point sources), the resolution obtained can significantly exceed the factor 2 (locally or even globally). Dark Tracking Conical diffraction could make it possible to apply a whole family of superresolution or super localization techniques, the localization of a single molecule. Reference is now made to FIG. 8, which schematically illustrates an original technique that we have named “Dark Tracking”. Referring to FIG. 8, 80 represents the initialization phase, that is to say the detection of the emitter using a confocal scanner or any other known optical method. 81 represents the positioning phase of the vortex beam on the transmitter; 82 represents the case where the emitter moves relative to the center of the vortex and is excited by a fraction of the beam creating a fluorescence which can be detected; 83 represents the repositioning of the emitter in the center of the vortex beam such that no fluorescence is created and detected (recorded position Xi,Yi) and 84 corresponds to a feedback loop in which an independent localization system repositions the element tracked to a corrected position. The light distributions used by this technique are vortices generated by conical diffraction. However, this technique can also use other vortices or other distributions generated by conical diffraction. We assume that the molecule of interest has been labeled by one or more fluorophores which can be excited at 2L The position of the molecule is first detected by a classic confocal image at 2L The position of the scanner is then adjusted to stimulate the sample so that the center of the vortex coincides exactly with the position of the emitter. The fluorescence signal is detected by a very sensitive camera (eg EMCCD or sCMOS), or PMT, allowing detection of the low amplitude signal from the emitter thanks to high quantum efficiency. The localization process relies on the absence of fluorescent signal when the emitter is located exactly in the center of the vortex. The fact that the intensity gradient is large near the center of the vortex allows precise location of the emitter. If the emitter moves slightly, the intensity it absorbs will no longer be zero, and it will emit a fluorescence signal whose position and intensity are deduced from the image. A feedback loop then makes it possible to refocus the vortex on the transmitter and to memorize the position of the transmitter. The feedback loop can be run at the running speed of the camera (up to 1kHz) or the detector (several MHz), allowing tracking of a molecule in real time and over a period of time substantial. As we always try to minimize the signal emitted in fluorescence by minimizing the signal exciting the emitter, localization can be conducted over a long period of time, bleaching being less likely to occur with such small doses of light. The localization accuracy strongly depends on the signal-to-noise ratio of the image, therefore the background noise (camera noise and auto-fluorescence signal) must be taken into account. Now suppose that the sample is labeled with two different fluorophores which can be excited at two different wavelengths, M and X2. We propagate together two beams with different topologies which depend on their wavelength. The first (M) has a classic Gaussian shape and makes it possible to obtain a global confocal image of the sample. The second (2.2) is a vortex beam used for Dark Tracking. By controlling the galvanometric mirror that scans the sample, Dark-Tracking can be performed each time a line for the camera image is scanned, so that the position of the emitter is tracked at a much higher frequency. than the number of frames per second. The main advantages of this technique, compared to other single molecule tracking techniques, are the use of a single scanning system and the power sent to the tracked molecules is extremely low.In practice, using, aligning, and shaping these two beams is not a trivial task using conventional beam-shaping techniques, such as computer-generated holograms, modulators spatial or spiral waveplates, primarily because of their inherent chromaticity. Conical diffraction can be used to simplify assembly. Using suitable optics, a crystal can be adapted to generate a vortex at one wavelength, and a Gaussian beam at another wavelength along the same optical path. This allows the use of a simple optical path from a fiber which solves many practical problems. Dark-tracking technology can be easily used to study a number of biological questions in which conventional techniques for tracking a particle's position are penalized by particle bleaching. Dark Tracking was described above in the case of using a vortex. However, many variants, using one or more distributions, for example but not limited to half-moons or Stokes vectors, i.e. any distribution having a zero intensity and a gradient - if possible the strongest possible - depending of one of the spatial dimensions can allow the realization of Dark Tracking and are deemed to be part of this invention. The ability of conical diffraction to create many different light distributions makes it a tool of choice for performing dark tracking. Refer now to Figure 6b, which is a simplified schematic illustration of a modified LatSRCS optical module, achromatic or not, 700, in accordance with one embodiment of the present invention. This module differs from the implementation of a LatSRCS optical module, 700, described previously and shown in Figure 6a, by the addition of several elements before the module: lasers, 79a, 79b and 79c, optionally at lengths d different waves, optical fibers, 78a, 78b and 78c, from the lasers 79a, 79b and 79c, optionally, polarization control sub-modules, 77a, 77b and 77c, to statically or dynamically modify the polarization of the lasers, 79a, 79b and 79c, the polarization control sub-modules being able to be positioned before or after the fiber. However, in some implementations, for example using PM fibers, "polarization maintaining" in English, the polarization control sub-modules 77a, 77b and 77c may not be necessary and the polarization of the light from the fiber is determined by the relative position of the laser and the fiber, a "laser combiner", 76a, combining two or more laser sources optionally through optical fibers, 78a, 78b and 78c, into a common output fiber, 76b , - an optical element, 75, making it possible to transform the light coming from the fiber into collimated light capable of being used by the rest of the LatSRCS module, 700, in a manner similar to that described previously. Many variations of this device, known to those skilled in the art, can be added to this diagram and are claimed in this invention: for example, the two optical elements 31 and 75 can be integrated into a single element, or even removed if the common fiber output parameters are adequate. Also, the common fiber, 76b, may not be necessary for some implementations. Moreover, the introduction, through a common optical fiber, or directly into light propagating in space, of two or more wavelengths having different polarizations, makes it possible to create a method and / or a device able to perform the RESOLFT or STED techniques in all their different modalities. In this method and / or device, the excitation and depletion waves propagate along a common path and the LatSRCS module, 700, can be totally achromatic, or not in a simplified version, as described previously.In the simplest variant of this method, the excitation and depletion waves propagate along two orthogonal linear polarizations and a quarter-wave plate - optionally achromatic - is positioned at the input of the system to transform these polarizations into polarizations circular orthogonal in order to obtain, for one a fundamental wave and for the other a vortex. In a new variant of this method, the single-polarization integrative method, described in detail later, the fiber is a birefringent fiber and creates a path difference greater than the coherence length of the depletion laser, creating an incoherent superimposition of the two polarizations orthogonal. Another solution is the use of a polarization sub-module (not shown), consisting for example of a thick uniaxial crystal with strong birefringence. Additionally, in the integrative same-bias method, an intensity ratio control bias (not shown) sub-module may be used. This polarization, intensity ratio control sub-module is different from the previous polarization sub-module, but can potentially be integrated with it. It can potentially also be integrated into the laser combiner, 76a, positioned between the laser and the optical fiber. This intensity ratio control polarization sub-module, can be used to control the intensity ratio between the two polarizations, and therefore, as will be described later, the intensity ratio between the 2D depletion beam ( vortex) and the 3D depletion beam (black sphere). Reference is now made again to Figure 6b. The polarization control sub-modules, 77a, 77b and 77c, can be operated to create, simultaneously, sequences of identical or different light distributions for the excitation channel and the depletion channel. Additionally, the intensity of the lasers can be modulated, creating a complex timeline of each laser's intensity, sequence of excitation light distributions, and sequence of depletion light distributions. In an implementation of this method, using a confocal microscope and an original or modified LatSRCS module, achromatic or not, one projects sequentially: - First, an Airy distribution or a fundamental in excitation simultaneously with a depletion vortex. The resulting emission image will be called the positive image, - In the second stage, an excitation vortex, simultaneously with a depletion vortex. The resulting emission image will be called the negative image. In a variant of the first place, only an Airy distribution or a fundamental in excitation is projected 3042043 62 The difference image consists of the weighted subtraction of these two images. However, this difference image can be a more advanced digital processing than a simple arithmetic difference and can incorporate a set of mathematical processing known to those skilled in the art, making it possible to optimize the resulting image according, for example but unlimited, of the frequency content of the two images. This difference image, if the right parameters are chosen, will have a size - in terms of PSF - finer than a classic STED, while only requiring a lower depletion intensity. Indeed, the aim of the depletion of the vortex will no longer be to reduce the size of an Airy spot, thus requiring significant energy, as in the classic STED or RESOLFT, but to reduce the excess energy present in the excitation vortex with respect to the Airy distribution or the fundamental. Moreover, the depletion of the Airy or of the fundamental, will couple with the subtraction of the negative image, created by the vortex of excitation, which is equivalent to the mathematical subtraction of the two illuminations. The reduction in the size of the resulting PSF will be the combination of these two effects. Moreover, this embodiment can, in certain cases, dispense with the need to trigger the excitation as necessary in the “Gated STED”. Indeed, the photons arriving before the complete application of the depletion, can be taken into account by an adequate choice of parameters, without requiring the addition of a complex and constraining system.Finally, the need to modulate the STED, “ModSted” can also be avoided because the emission photons emitted by the depletion vortex hardly differ from those emitted by the excitation vortex and can also be compensated. In a second embodiment, using a confocal microscope and an original or modified LatSRCS module, a sequence of excitation beams, a sequence of depletion beams are simultaneously projected, the two sequences of beams possibly differing in their polarization, creating light distributions of different topologies. This device makes it possible to produce a sequence of light distributions of sizes smaller than those which would have been obtained without the depletion beam. The SRCDA algorithm will be used in this implementation to determine the spatial distribution or the position of point emitters. This embodiment, coupling the depletion and the algorithm, should allow an adequate compromise between the intensity of the projected depletion beam and the resolution gain. In another embodiment, using a confocal microscope and an original or modified LatSRCS module, an excitation beam is simultaneously projected, in the form of an Airy, and a depletion beam in the form of a vortex, the two beams differing in their polarization. This device makes it possible, without dynamic elements, to produce a completely achromatic STED device. Using Helical Symmetry Distribution for STED 3D 3042043 63 The solution implemented in STED or STED-3D systems uses an optical distribution of zero intensity at the center point, and remains zero along the axis, along a certain distance. We propose here, the use for the STED-3D, of a distribution having a position of null intensity, this position of null intensity having a helical space variation, according to the axial parameter. The preferred implementation of this distribution is the use of conical diffraction using the optical distributions which we have referred to as the Stokes distribution. These distributions could be carried out, in particular but not exclusively, by using the techniques based on the devices mentioned above, including but not exclusively the SLM (Spacial Light Modulator) and segmented mirrors which make it possible to create phase distributions and / or amplitude in the pupil. The use of helical topology distribution to create a zero intensity containing distribution having helical motion is deemed to be part of this invention. In particular the implementation of these distributions using conical diffraction is one of the preferred implementations of this invention but the implementations of these distributions using an SLM or a segmented mirror to create phase distributions or of amplitude in the pupil are also considered as one of the implementations described in this invention. In a new variant of this method, the two-polarization integrative method, the crystal parameters are chosen such that the fundamental wave creates a black sphere and the vortex wave creates a vortex. Under these conditions, the two orthogonally polarized distributions do not interfere and an incoherent superposition of the two beams makes it possible, with a single input beam, to independently create the two beams necessary for the 3D STED, the vortex and the dark sphere. The possibility of creating, using a single input depletion beam, the two beams, makes it possible to considerably simplify the optical system. Moreover, since this system has a common path, it can be implemented simply. A polarization sub-module (not shown), static or dynamic, positioned between the optical fiber and the crystal, can be used to control the intensity ratio between the two polarizations, and therefore, the intensity ratio between the beam 2D depletion beam (vortex) and the 3D depletion beam (black sphere).In a new variant of this method, the single-polarization integrative method, a birefringent fiber - or a polarization sub-module - previously created, as previously described, a path difference greater than the coherence length of the depletion laser, for a CW laser, and / or at the time of the pulse, for a pulsed laser or for the gated STED, creating an incoherent superposition of the two orthogonal polarizations. Under these conditions, the two distributions do not interfere; the two distributions being of orthogonal polarizations, will create, on the same polarization, one a fundamental - which by a choice of parameters of the crystal and the optical system, will be a black sphere, and the other a vortex. These two beams, derived from two incoherent distributions, as described previously, do not interfere; this device makes it possible, with a single input beam, before the fiber, to independently create the two beams necessary for STED 3D the vortex and the black sphere. The possibility of creating, using a single input depletion beam, the two beams, makes it possible to greatly simplify the optical system. Moreover, since this system has a common path, it can be implemented simply. The differentiation between these two variants is in the output polarization of the two distributions, the dark sphere and the vortex, which are orthogonal in the two-polarization integrative method and identical in the single-polarization integrative method, each of the two variants having advantages for some setups. In a new variant of this method, using conical diffraction, compatible with all the devices described previously, and potentially complementary to the two integrative methods, with two polarizations and with single polarization, the conical diffraction element is replaced by a sub -module consisting of two conical diffraction crystals, of substantially equal conical diffraction parameter value, separated by a polarization sub-module. The polarization sub-module is chosen such that at the depletion wavelength, the polarization sub-module has no effect, and the action of the crystals is added, creating the vortex and / or the black sphere. At the excitation length, the polarization sub-module creates a rotation of the polarization of 90° or 180°, the effect of the two crystals is subtracted, and the transmitted beam is identical to the incident beam. This device avoids creating too “exotic” distributions on the excitation beam. In some devices the crystals could have different values ​​of the conical diffraction parameter, to also create an effect on the excitation beam, but with a value of the conical diffraction parameter different from that of the depletion beam. This variant can be carried out at several depletion and excitation wavelengths, using the resources of polarization modules well known to those skilled in the art. In a new variant of this method, using conical diffraction, compatible with all the devices described above, and potentially complementary to the two integrative methods, with two polarizations and with single polarization, and also compatible with the previous implementation with modifications reasonable, the conical diffraction element is replaced by a cascade of crystals having different spectral properties, such as LBO and KTP (KTA) so as to allow the realization of dark sphere at several depletion wavelengths. Indeed, the dispersion of the characteristic parameter of the conical diffraction effect, po, does not allow certain distributions to be produced at several wavelengths, in particular the black sphere, the shape of which depends strongly on this parameter. Compensation for the dispersion of the characteristic parameter of the conical diffraction effect, po, therefore allows the realization of a 3D STED with a common optical path, at two or more wavelengths. Even more, dispersion compensation of the characteristic parameter of the conical diffraction effect, 3042043 in, can be achieved over a wide range of wavelengths either as previously described by a combination of crystals or by spectrally correcting the system second-order optics, i.e, by creating a wavelength-dependent numerical aperture to either compensate for the dispersion of the characteristic parameter of the conical diffraction effect, po, or to correct a compensation for the dispersion of the characteristic parameter of the conical diffraction effect, po, created by a combination of crystals previously described. In another embodiment, using a confocal microscope, an original or modified LatSRCS module, and a LongSRCS module, a sequence of excitation beams, a sequence of depletion beams are simultaneously projected, the two sequences of beams possibly differing by their polarization, creating light distributions of different topologies. The LatSRCS module makes it possible to produce a sequence of light distributions of sizes smaller than those which would have been obtained without the depletion beam. The LongSRCS module implements the PDOS method so as to separate on different detectors the collimated light, emerging from nanoemitters positioned at the focal plane of the objective, from the non-collimated light emerging from nanoemitters located below or beyond the focal plane. The PDOS method, in this implementation, makes it possible to acquire essentially longitudinal information, that is to say the longitudinal position of each of the nanoemitters, complementary to the lateral information obtained using the original or modified LatSRCS module. The SRCDA algorithm will be used in this implementation to determine the spatial distribution or the position of point emitters. In another embodiment using one of the implementations described previously and using a biaxial crystal to create the beam shaping, a dynamic polarization element before or after the biaxial crystal is used to correct the dynamic movement of the pupil, which in certain cases can be created during the optical scanning of the confocal microscope. This pupil movement effect being in certain implementations of the STED technologists one of the performance limits, without requiring an additional scanning system. [351 In another embodiment using a confocal microscope, two or more localized light distributions at different wavelengths are projected using an original or modified LatSRCS module. The first light distribution makes it possible to render the scene parsimonious, that is to say to isolate emitters using a physical effect, which dilutes the density of emitters capable of emitting fluorescence, so as to create regions in which the parsimony hypothesis is valid, that is to say the presence of an isolated emitter or of a small number of emitters. The physical effects that will achieve this parsimony will be the same or will be derivative effects of the effects used to create the parsimony for single emitter localization microscopy techniques. These techniques include, for example, the PALM STORM, DSTORM, FPALM and other techniques. The second light distribution at another wavelength will create fluorescence whose intensity will vary over time. This second light distribution will use one of the PSIT techniques, either a sequence of 3042043 66 discrete distributions, or a sequence of continuous distributions. In the case of discrete distributions, the light will be detected either by an array detector or by a single detector. In the case of continuous distribution, although it is also possible to use a matrix detector, the most probable implementation will be the use of a single detector; in this case the lateral position information xy and potentially the longitudinal distribution information z can be obtained by intensity ratios. One of the most interesting cases is the case of harmonic time distributions in which the electro-optical cells are driven by a sinusoidal voltage. In this case, the position xy can be found using a measurement of the temporal harmonics of the signal measured by the detector, which can be a single detector, which indirectly contain the lateral position information.Many other implementations of this general method will be apparent to those skilled in the art, for example: Some of the distributions created by the LatSRCS module, 700, are superoscillations. super oscillations. It consists of a naturally small spot, surrounded by a wide and intense ring. By projecting a depletion ring onto this superoscillation, it will be possible to prevent, at a low energy cost, the fluorophores contained in the ring from emitting and the size of the spot will be that of the central spot of the superoscillation The creation successively or of two - or more - light distributions in depletion simultaneously can advantageously replace the depletion vortex in all RELSOFT or STED modalities. One of the possible effects is to improve the shape of the depletion light distribution by taking vector effects into account. It is also possible to create a number greater than 2 of so-called "half-moon" distributions, to explore different states of polarization. ALTERNATIVE IMPLEMENTATIONS The embodiments of the invention described can be integrated on a confocal fluorescence microscope. The superresolution system according to embodiments of the invention consists of a new measurement modality, in addition to or replacing the existing microscopy modalities. However, the superresolution system according to embodiments of the invention can just as easily be integrated into other microscopy platforms. These microscopy platforms, described for example include but are not limited to: wide field microscopes, "Wide field microscope", dark field microscopes, "dark field microscope", polarization microscopes, phase difference microscopes , differential contrast interference microscopes, stereoscopic microscopes, Raman microscopes, microscopes dedicated to a specific task, such as "live cell imaging", "cell sorting", "cell motility" or any other optical microscopy. In another embodiment, the microscope platform which has been described is coupled to an electron microscopy system (CLEM-Correlative Light Electron Microscopy), or any other similar system such as TEM (Transmission Electron Microscopy), or EBM (Electron Beam Microscopy), or SEM (Scanning Electron Microscopy) In another embodiment of the invention, the microscope platform is a complete SRCDP platform, and includes a LongSRCS module, implementing the PDOS method and using the SRCDA algorithmic. In another embodiment of the invention, the microscope platform is a partial SRCDP platform, and uses the SRCDA algorithm. In another embodiment of the invention, the microscope platform is a partial SRCDP platform, and uses the control module. In another embodiment of the invention, the microscope platform further comprises a LongSRCS module, implementing the PDOS method. emerge from the above description. Therefore, no discussion of the form of use and operation will be described. In this respect, before explaining at least one embodiment of the invention in detail, it is understood that the invention is not limited in its application to the details of the construction and the scheme of the components set out in the following description or illustrated in the drawing. The invention is capable of other embodiments and can be practiced and carried out in various ways. Further, it is understood that the phraseology and terminology employed herein are for the purpose of description and should not be considered limiting. The references cited herein teach many principles which are applicable to the present invention. Accordingly, the entire contents of such publications are incorporated herein by reference, where appropriate for additional or replacement detail teachings, specifications and / or technical information. The advantageous use of optical fibers is the transmission of the fundamental mode, the TEM00 mode and only it.However, certain optical fiber configurations, mainly but not exclusively based on so-called “Photonic Crystal Fiber” fibers (in English) allow the simultaneous or non-simultaneous transmission of more complex modes, including vortex modes. It would therefore be possible to offset the optical distributions created by the conical refraction using optical fibers, allowing a major simplification of the optical system. 3042043 68 In addition, certain fibers, the “dual-core photonic crystal libers”, [161, allow an interaction between two modes, one of which can be a vortex, and provide an additional physical mechanism to create functions of diversified transfers. Many superresolution techniques are based on the measurement of point sources, of size less than a fraction of a wavelength. The superresolution techniques according to embodiments described allow the measurement of point sources, but also of structured objects, for example and mainly line segments, circles or even continuous objects. In Biology, this extension will allow the measurement of important biological entities, such as filaments, neurons and certain microtubules. Although the descriptions of the embodiments, to simplify the understanding of the invention, present the applications in Microscopy, more specifically in Biology, and even more specifically in Fluorescence Biology, the applications can be extended to the general applications of Microscopy and to the entire field of vision, including artificial vision. Embodiments of the invention can be applied, by choosing a different optical system, to numerous medical applications, for example but not limited to ophthalmological observation. This field of application corresponds to the measurement of biological or medical objects of micron resolution, the resolution being between 1 and 10 gm. Additionally, embodiments of the invention may be applied, as explained later, through an optical fiber. This allows many additional applications, for example but not limited to gastric or gastroenterological observation, and observation of the colon and urinary tract. It is understood that the invention is not limited in its application to the details set forth in the description contained herein or illustrated in the drawings. The invention is capable of other embodiments and of being practiced and carried out in various ways. Those skilled in the art will easily understand that various modifications and changes can be applied to the embodiments of the invention as described above without departing from its scope, defined in and by the appended claims. 3042043 69 References 1. L. Schermelleh, R. Heintzmann, and H. Leonhardt, "A guide to super-resolution fluorescence microscopy," The Journal of cell biology 190, 165-175 (2010). 2. M. V. Berry, "Conical diffraction asymptotics: fine structure of Poggendorff rings and axial spike," Journal of Optics A-Pure and Applied Optics 6, 289-300 (2004). 3. http: / / en.wikipedia.org / wiki / Superresolution 4. J. F. Nye and M. V. Berry, "Dislocations in Wave Trains," Proceedings of the Royal Society of London. 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Claims

CLAIMS 1. An optical measuring device for determining the spatial distribution or location of re-emitting sources on a sample, the sample comprising at least one re-emitting source, excited by light and re-emitting light according to a law determined as a function of the light projected onto the sample, the device comprising an achromatic projection module, containing a laser, the wavelength of which is tuned to the excitation wavelength of said at least one re-emitting source, to create either a compact light distribution or a sequence of compact light distributions of different topology, a scanning module for optically scanning the sample, a detection module for detecting the light re-emitted by said at least one re-emitting source of the sample for the or each of the compact light distributions of different topology and for each of the scanning points of the sample;an image acquisition module to acquire for each scan point, either an image or a sequence of images, for the sequence of images, each image corresponding to one of the compact light distributions of different topologies, an algorithm module in which the formulation of the reconstruction of the sample and its spatial and / or temporal and / or spectral properties is considered as an inverse Bayesian problem and leads to the definition of an a posteriori distribution,; 2. A device according to claim 1 wherein a posteriori law combining, by means of Bayes' law, the probabilistic formulation of a noise model, as well as possible priors on a light distribution created in the sample by projection 3. A device according to claim 1 or 2, wherein the algorithm module is configured to estimate the light distribution in the sample by using point emitter clouds, which favors sparse solutions; estimate the a posteriori mean; and represent the results, based on the a posteriori mean, either as an image or as numerical or graphical data. 4 (E-LSE - MCMC) The optical measuring device according to any one of the preceding claims, wherein the estimation of the a posteriori mean is performed by means of a Monte Carlo Markov Chain (MCMC) type algorithm (unregularized MAP). An optical measuring device for determining the spatial distribution or location of re-emitting sources on a sample, the sample comprising at least one re-emitting source.excited by light and re-emitting light according to a law determined as a function of the light projected onto the sample, the device comprising an achromatic projection module, containing a laser, the wavelength of which is tuned to the excitation wavelength of said at least one re-emitting source, to create either a compact light distribution or a sequence of compact light distributions of different topologies, a scanning module for optically scanning the sample, a detection module for detecting the light re-emitted by said at least one re-emitting source of the sample for the or for each of the compact light distributions of different topologies and for each of the scanning points of the object; an image acquisition module for acquiring, for each scanning point, either an image or a sequence of images, for the image sequence,each image corresponding to one of the compact light distributions of different topologies, a non-regularized MAP algorithm module with a positivity constraint, the representation of the results, based on the results of the MAP algorithm, either in the form of an image or in the form of numerical or graphical data 6 An optical measuring device for determining the spatial distribution or the location of re-emitting sources on a sample according to claim 5, wherein the MAP algorithm further contains a frequency-band limitation constraint 7 An optical measuring device for determining the spatial distribution or the location of re-emitting sources on a sample according to any one of claims 5 and 6,in which the MAP algorithm uses a Nesterov-type accelerated numerical scheme.

8. An optical measuring device for determining the spatial distribution or location of re-emitting sources on a sample according to any one of claims 5 to 7, using, for a sequence of images, the redundancy in frequency information, due to the different frequency characteristics of the different distributions projected onto the sample, to compensate for and significantly reduce the impact of missing points or scanning irregularities.

9. An optical measuring device for determining the spatial distribution or location of re-emitting sources on a sample according to any one of claims 5 to 8, in which the MAP algorithm is adapted to solve an inverse problem involving a sum of a small number of terms.as a low-frequency component and a more parsimonious component. An optical measuring device for determining the spatial distribution or localization of re-emitting sources on a sample according to any one of claims 5 to 9, wherein the MAP algorithm is adapted to impose a non-local redundancy constraint on the solution, for example by calculating weights on the images or on the different digital masks and the non-local similarity tree being applied to the solution as a regularization. An optical measuring device for determining the spatial distribution or localization of re-emitting sources on a sample according to any one of claims 1 to 8, using a variable-sized mask in the detector plane to obtain images having either different axial characteristics or different or optimized stray light rejection capabilities,12. An optical measurement method for determining the spatial distribution or location of re-emitting sources on a sample, the sample comprising at least one re-emitting source, excited by light and re-emitting light according to a law determined as a function of the light projected onto the sample, the method comprising achromatic projection, by a laser, the wavelength of which is tuned to the excitation wavelength of said at least one re-emitting source, to create either a compact light distribution or a sequence of compact light distributions of different topologies, optical scanning of the sample,the detection of the light re-emitted by said at least one re-emitting source of the sample for the or each of the compact light distributions of different topologies and for each of the scan points of the sample; image acquisition to acquire, for each scan point, either an image or a sequence of images, for the image sequence, each image corresponding to one of the compact light distributions of different topologies, the application of an algorithm in which the formulation of the reconstruction of the sample and its spatial and / or temporal and / or spectral properties is considered as an inverse Bayesian problem and leads to the definition of an a posteriori distribution, 13. A method according to claim 12 in which an a posteriori law combining, by means of Bayes' law, the probabilistic formulation of a noise model,as well as any prior assumptions about a light distribution created in the sample by projection.

14. A method according to claim 12 or 13, wherein the algorithm comprises estimating the light distribution in the sample by using point emitter clouds, which favors sparse solutions; and estimating the a posteriori mean, representing the results, based on the a posteriori mean, either in the form of an image or in the form of numerical or graphical data.

15. An optical measurement method according to any one of claims 12 to 14, wherein the a posteriori mean estimation is performed using a Monte Carlo Markov Chain (MCMC) algorithm.

16. An optical measurement method for determining the spatial distribution or location of re-emitting sources on a sample, the sample comprising at least one re-emitting source.excited by light and re-emitting light according to a law determined as a function of the light projected onto the sample, the method comprising achromatic projection, by a laser, whose wavelength is tuned to the excitation wavelength of said at least one re-emitting source, to create either a compact light distribution or a sequence of compact light distributions of different topologies, optical scanning of the sample, detection of the light re-emitted by said at least one re-emitting source of the sample for the or each of the compact light distributions of different topologies and for each of the scanning points of the object; image acquisition to acquire for each scanning point, either an image or a sequence of images, for the sequence of images, each image corresponding to one of the compact light distributions of different topologies,The application of an unregularized MAP algorithm with a positivity constraint, the representation of the results, based on the results of the MAP algorithm, either in the form of an image or in the form of digital or graphical data.

17. An optical measurement method for determining the spatial distribution or location of re-emitting sources on a sample according to claim 16, wherein the MAP algorithm further contains a frequency-bandwidth limitation constraint.

18. An optical measurement method for determining the spatial distribution or location of re-emitting sources on a sample according to any one of claims 16 and 17, wherein the MAP algorithm uses a Nesterov-type accelerated digital scheme.

19. An optical measurement method for determining the spatial distribution or location of re-emitting sources on a sample according to any one of claims 16 to 18, using, for a sequence of images,Redundancy in frequency information, due to the different frequency characteristics of the various distributions projected onto the sample, to compensate for and significantly reduce the impact of missing points or scanning irregularities.

20. An optical measurement method for determining the spatial distribution or location of re-emitting sources on a sample according to any one of claims 16 to 19, wherein the MAP algorithm is adapted to solve an inverse problem involving a sum of a small number of terms, such as a low-frequency component and a more sparse component.

21. An optical measurement method for determining the spatial distribution or location of re-emitting sources on a sample according to any one of claims 16 to 20, wherein the MAP algorithm is adapted to impose a non-local redundancy constraint on the solution.for example by calculating weights on the images or on the different digital masks and the non-local similarity tree being applied to the solution as a regularization.

22. An optical measurement method for determining the spatial distribution or the localization of re-emitting sources on a sample according to any one of claims 12 to 21, using a mask of variable size in the detector plane to obtain images having either different axial characteristics or different or optimized stray light rejection capacities, globally or locally.

23. A computer program configured to implement a method according to any one of claims 12 to 22.