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

Introduction The present invention relates to a method and device for optical measurement. 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, Materials Science, Metrology, control, measurement and observation and to all processes of acquiring information from optical observations, in the macroscopic or microscopic field. Many definitions, used for the whole of this invention, are grouped in a later chapter: "Definitions and technical details". Microscopy An optical microscope is an instrument generally used to view, analyze, or measure objects too small to be seen with the naked eye. See Figure 1, which illustrates the microscopy paradigm. Optical microscopy consists of illuminating a biological or non-biological sample, 11, with a light source (not shown) using a microscope, 10, and measuring over time, using visual observation or a detection module, 12, the light emitted, re-emitted, scattered, reflected, or transmitted by the sample. In biology, the sample consists of one—or a plurality—of different biological entities, 13 and 14, positioned at different locations. Examples of such entities include, among others, a cell, a virus, a protein, or a fragment of DNA. In machine vision, the sample might be, for example, a semiconductor element. Microscopy is segmented into different modalities with different characteristics and purposes. Numerous 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 companies such as Zeiss, Leica, Nikon, or Olympus. Microscopy applications can be segmented in different ways: one of them is to distinguish microscopy modalities devoted to the visualization of tiny point sources from those devoted to the measurement of continuous objects. The case of minuscule point sources is, a priori, much simpler. The object consists of a small number of points of light; these can be described by a small number of parameters—the descriptors defined subsequently—greatly simplifying both the physical problem and the algorithmic complexity. The case of a continuous object, described by a spatial distribution—or spatiotemporal distribution, if we consider continuous dynamics—is different and is also described in this patent application. Fluorescence microscopy Fluorescence microscopy is a microscopy modality; in many applications, it has replaced other microscopy techniques. A fluorescence microscope is an optical microscope used to study the properties of objects, or organic or inorganic substances, using fluorescence phenomena instead of, or in addition to, other modalities such as reflection and absorption. We refer again to Figure 1, describing, this time, a fluorescence microscope used either in Biology or in Computer 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 fixed to specific and predetermined positions of the objects, 13 and 14; the light emitted by the point sources is observed instead of the light emitted by the objects, 13 and 14, themselves. The sample is illuminated by light of a specific wavelength, or wavelengths, which is absorbed by point sources, thus inducing the emission of light at different and higher wavelengths. During the collection of the emitted light, in fluorescence, the illumination light is separated from the weaker emitted fluorescence by the use of an emission spectral filter. Fluorescence microscopy studies the light emitted by tiny point sources called fluorophores. However, when the density of fluorophores is high, they are no longer analyzed individually but treated as a continuous object. It is important to note, even at 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 for visualizing biological objects. Biological activity and information, including details above the resolution limit of 200–250 nm, are routinely visualized and measured using fluorescence microscopy. This resolution limit is derived from the Rayleigh criterion, which, at best, 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, on 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 rotating disk configuration, and the wide-field imaging microscope. Confocal microscopy We now refer to Figure 2, which is a simplified representation of a prior art confocal fluorescence microscope 200. A confocal fluorescence microscope, Fig. 2, is an optical instrument. Its main hardware components are shown in Figure 2. They include: • A light source, 20, • an optomechanical frame not shown, • a cube of filters, 21, • a microscope objective 22, and, • a detector assembly, 23, • a processing unit, not shown. The light source, 20, which can be an arc lamp or a laser, creates the light energy needed for fluorescence. The optomechanical frame, not shown, supports all the optical elements and includes auxiliary optics and alignment capabilities. It also includes optical elements, not shown, capable of shaping the beam to allow its focusing to a point of minimal size by means of the microscope objective. It may also include, in a confocal scanning fluorescence microscope, a scanning mechanism, spatial or angular, not shown, to change the position of the point source relative to the object to be measured. The filter cube, 21, channels the different optical signals and prevents contamination of the fluorescence signal by the excitation light. The filter cube is composed of: excitation filter, 210, dichroic mirror, 211, and emission filter, 212. The microscope objective, 22, focuses the light created by the source into the focal plane of the objective, 24, into a small light distribution, the optimal light distribution being an Airy disk. The microscope objective, 22, also collects the fluorescent light emitted by the fluorophores. For a confocal scanning fluorescence microscope, the system can be descanned, meaning that the returning light can pass through the scanning mechanism to compensate for the 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 reimaged onto the image plane of the detector, 26. The detector assembly, 23, detects the overall fluorescence intensity in the illuminated volume and converts it into a digital signal. For a scanning confocal microscope, the detector assembly consists of a single-element detector, such as a PMT or SP AD. For a rotating disk confocal microscope, the detector assembly consists of an array of detection elements, such as a CCD, an EMCCD, a CMOS, or an SP AD array. The set of components mounted from the light source to the dichroic filter is the lighting 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: • Projecting 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 light analyzed by the confocal hole • Integration of light analyzed by a photoelectric detector • Visualization of the measured intensity as a pixel value in an image Fluorescence microscopes are available from several manufacturers, such as Nikon, Zeiss, Leica, and Olympus. Fluorescence microscopes can be either standard microscopes adapted for fluorescence or specialized 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 functions 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 scales smaller than 200 nm in biological samples. At this level of spatial resolution, important phenomena can be observed: intracellular biological processes, cellular information transfer, protein folding and unfolding, and modifications to DNA and RNA. Thus, for example, measuring this intracellular information will open new avenues for understanding biological activity and will lead to advances in knowledge and monitoring for research and medical diagnostics. However, the various existing microscopy methods and microscopes, lacking super-resolution capabilities, only allow microscopic observation below the limit of optical diffraction. This restricts their use to a limited set of applications. Superresolution New optical methods, known as superresolution methods, are capable of producing images with a resolution exceeding the diffraction limit. These methods are being developed by several companies, laboratories, and researchers, and some of the instruments using these methods, called superresolution microscopes, are commercially available. A review of superresolution techniques was published by the Swedish Academy of Sciences on the occasion of the 2014 Nobel Prizes in Chemistry

[38] . Several comparative analyses of superresolution methods have been published recently in the literature, such as the articles by Schermelleh et al. [1]. An updated bibliography on super-resolution can be found on the Zeiss company website, and on the Nikon company website. New superresolution techniques allow us to obtain information beyond the resolution limit. The main problem with all existing superresolution techniques is the performance envelope limit, expressed in terms of lateral and longitudinal resolution, speed, required light intensity, and phototoxicity in the biological sample, and therefore the ability to measure different biological samples. This point was also emphasized by Eric Betzig during his masterful presentation at the 2014 Nobel Prize in Chemistry ceremony. Furthermore, most existing superresolution methods and instruments can provide either good lateral resolution or good longitudinal resolution, but rarely both. Furthermore, all these instruments are complex and require a high level of technical skill from the operator. Furthermore, these instruments can generally only observe a small portion of biological specimens, due to significant operational limitations, such as, for some of them, a shallow depth of field or very high intensities that are harmful to cells. Another problem with existing superresolution methods and instruments is that most of them are able to recover the attributes of a single fluorophore in the illuminated volume, but fail to simultaneously recognize the presence of multiple fluorophores and measure their attributes. An additional problem with some existing superresolution methods and instruments is that they are presented to users and perceived as a general-purpose tool, capable of replacing 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 or diagnostic tools. Another problem with some existing superresolution methods and instruments is that most of these methods and instruments are built as standalone 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 they are based on an image acquisition paradigm in which the fundamental unit of information is one or more images, or one or more two- or three-dimensional Regions of Interest (ROIs). The algorithmic, systemic, and superresolution methods described later in the context of this invention will, by their inherent flexibility, enable the development of new acquisition strategies. These dynamic and selective acquisition procedures will be defined by optimized management of the acquisition sequence and interactive and deferred processing. They will allow for more advanced optimization of useful information, defined by criteria based on the shape, geometry, and dynamics of one or more fluorescent objects, individually or in relation to each other. Another problem with most existing fluorescence and superresolution microscopy methods and instruments is that they are designed to study samples on microscope slides. However, the confocal microscope is now used in many medical fields as an in-vivo diagnostic tool for internal and external examinations of the human body. This is achieved through the use of optical fibers to illuminate and visualize the fluorescence emitted by the tissues being diagnosed. Superresolution microscopy does not currently allow for such in-vivo diagnostics. The algorithmic, systemic, and superresolution methods described later in the context of this invention will enable the development of new in-vivo diagnostic methods that will reduce the need for biopsies and shorten patient waiting times. There is therefore still an urgent need to provide super-resolution methods and instruments and algorithmic methods capable of measuring a biological object or scene with high precision. SUMMARY OF THE INVENTION A first aspect of the invention relates to 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 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 a scanning module to optically scan the sample, a detection module to detect 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 scan points of the sample; an image acquisition module to acquire, 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, 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 can combine, thanks to Bayes' law, the probabilistic formulation of a noise model, as well as possible priors on a light distribution created in the sample by projection. In one embodiment, the algorithm module is configured for estimating the light distribution in the sample using point emitter clouds, which favors sparse solutions; and to estimate the average a posteriori, represent the results, based on the posterior average, either as an image or as numerical or graphical data According to one embodiment, the a posteriori mean estimation is performed using a Monte Carlo Markov Chain (MCMC) algorithm. Another aspect of the invention relates to 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 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, a scanning module for optically scanning the sample, integrated or not into the device, a detection module to detect 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; an image acquisition module to acquire, 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 for processing the data and reconstructing the sample, The representation of the results, based on the results of the MAP algorithm, is either in the form of an image or in the form of numerical or graphical data. According to one embodiment, the MAP algorithm also contains a frequency bandwidth limitation constraint. In one embodiment, the MAP algorithm uses a Nesterov-type accelerated numerical scheme According to one embodiment for a sequence of images, redundancy in frequency information is used, due to the different frequency characteristics of the different distributions projected onto the sample, to compensate for and greatly reduce the impact of missing points or scanning irregularities. According to one embodiment, 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. 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 non-local similarity tree being applied to the solution as a regularization. According to one embodiment, a mask of variable size is used in the detector plane 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 process 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, 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 scan points of the sample; image acquisition to acquire, 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, 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. An a posteriori law can combine, thanks to Bayes' law, the probabilistic formulation of a noise model, as well as possible priors on a light distribution created in the sample by projection. In one embodiment, the algorithm comprises Estimating the light distribution in the sample using point emitter clouds, which favors sparsity solutions; and the estimation of the posterior mean, represent the results, based on the posterior average, either as an image or as numerical or graphical data According to one embodiment, the a posteriori mean estimation is performed using a Monte Carlo Markov Chain (MCMC) algorithm. 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 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, 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 image sequence, 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, is either in the form of an image or in the form of numerical or graphical data. According to one embodiment, the MAP algorithm also contains a frequency bandwidth limitation constraint. In one embodiment, the MAP algorithm uses a Nesterov-type accelerated numerical scheme According to one embodiment for a sequence of images, redundancy in frequency information is used, due to the different frequency characteristics of the different distributions projected onto the sample, to compensate for and greatly reduce the impact of missing points or scanning irregularities. According to one embodiment, 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. 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 non-local similarity tree being applied to the solution as a regularization. According to one embodiment, a mask of variable size is used in the detector plane to obtain images having either different axial characteristics or different or optimized stray light rejection capacities, globally or locally BRIEF DESCRIPTION OF THE DRAWINGS The invention will now be described in relation to 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 provided by way of example and to illustrate the discussion of embodiments of the invention. They are presented solely to provide what can be considered the most useful and easily understood 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 greater detail than is necessary for a basic understanding of it. The description, taken with the drawings, makes it clear to those skilled in the art how the various forms of the invention can be implemented in practice. In the drawings: Fig. 1 is a simplified representation of a prior art confocal fluorescence microscope, also used as a support for the invention; Fig. 2 is a simplified pictorial representation of a super-resolution fluorescence microscopy system, according to one embodiment of the present invention; Fig. 3 is a simplified schematic illustration of a conical diffraction module, according to one embodiment of the present invention; Fig. 4a to 4f are simplified pictorial representations of the measurement and volumetric 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 super-resolution lateral module, according to one embodiment of the present invention; Fig. 6b is a simplified schematic illustration of another embodiment of a super-resolution lateral module, according to one embodiment of the present invention; Fig. 7a to 7c presents tables of light distributions of a conical diffraction modulus 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]; Figure 7d complements these distribution tables by showing the variation of the so-called shifted half-moon distributions as a function of axial position (z-axis). Fig.8 is a simplified schematic illustration of one of the implementation methods of dark tracking; Fig. 9 is a simplified schematic illustration of a fluorophore data superresolution algorithm method, according to an 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 the figures, similar reference numbers identify similar parts. Definitions and technical details We will use the term "biological" to describe any entity in the life sciences, regardless of its origin (human, animal, or plant) and the purpose of its observation (research, diagnosis, or therapy). This term includes the medical uses of the technique described. Microscopy, for example, is used in biology to observe, study, and measure biological entities (objects) and their dynamics. We will use, by extension, the term Artificial Vision to describe all 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 measure Semiconductors or to characterize materials. The usual definitions are used in the description for: phase and polarization, polarimetry, Jones vectors and matrices, Stokes parameters and techniques for measuring Jones and Stokes parameters. The usual definitions are used for: optical diffraction limit, Rayleigh number, Airy disk and its radius and diameter. In the context of the invention, we use the terms superresolution, super-resolved, superresolution imaging, and superresolution microscopy to describe the acquisition of optical data, in imaging, microscopy, or computer vision, at a resolution exceeding the optical diffraction limit. The usual definitions are used for fluorescence and for fluorophores. We will use the terms longitudinal and axial interchangeably to describe the dependence of light along the propagation axis, which we refer to as the z-axis or longitudinal axis. We will use the term lateral to describe the dependence of light along 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 TEMoo 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 that allows coupling 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 can contain local segments that oscillate faster than its fastest Fourier components.

[26] The center or centroid of a light distribution is the center of gravity of the 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. Two light distributions are co-localized 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, the definition of which is broadened to include all optical means that transmit, refract or reflect light; auxiliary optics - optical sub-module intended to interface and adjust either the geometric parameters or the phase and / or polarization parameters between two other sub-modules or optical modules -; polarizer; analyzer; retarder blade; beam splitter, polarizing and non-polarizing; beam combiner, polarizing and non-polarizing. In this patent application, the usual definitions are used for azimuthal and radial polarizers. We will extend, implicitly or explicitly, certain developments described later for azimuthal and radial polarizers to all spatially variable polarizing elements. 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), encompassing the following 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) encompassing the following 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 International Reflection Fluorescence Microscopy). In this patent application, common definitions are used for various microscopy techniques, standard resolution or super-resolution, fluorescent or non-fluorescent, such as the English terms "Computational Microscopy," "Correlative Microscopy," "Cross-platform microscopy," FCS - "Fluorescence Correlation Spectroscopy," FCCS - "Fluorescence 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), LSE (Least Squares Estimation), and ICE (Iterated Conditional Expectation) algorithms. We refer to the E-LSE (Emitter-Least Squares Error) algorithm, a new algorithm described in this patent application. We refer to a partial polarizer to describe an element or module whose absorption is different for both linear polarizations - linear dichroism - or for both circular polarizations - circular dichroism. We refer to dynamic polarization or phase elements to describe optical means whose polarization or phase properties vary over time in a controlled, discrete or continuous manner. These dynamic polarization or phase elements include, but are not limited to: rotating wave blades on their axis, light valves based on liquid crystal technologies, electro-optical devices, also known as Pockels cells, Kerr cells, for example using PLZT material components, 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 polarization state depends on the wavelength. The simplest of the polarization dispersive submodules is the multimode or thick waveplate. We will refer to the "centroid algorithm" to describe the usual procedure for measuring the centroid and possibly the width (FWHM - English acronym 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 array. We will use the following terms: o optical image, for the spatial distribution of light intensity, o electronic image, to describe the spatial distribution of charges for a CCD, current for a CMOS or 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. To simplify reading and understanding the text, we will also use the term image for the output of a single-pixel detector such as a PMT or SP AD, 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 simplified generic term image. For the images, we use the terminology employed for array detectors, such as CCDs, EMCCDs, and CMOS. For SP ADs and SP AD arrays, the result of a measurement is a time-ordered list of photon impacts, detailing, for each photon, the impact time and position. To simplify the presentation of this document, we will include this case in our definition of images. The detailed images in this document, in many cases, can be described as microimages, images of a size substantially equal to a small number of Airy disk diameters, typically less than 5 diameters, and / or with a small 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 polarization state of incident light. The polarization state 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 may or may not interact with each other, and may be projected sequentially or simultaneously. In most of these systems and devices, the two optical paths are physically separated. This physical separation creates a set of constraints at the system engineering level, which, although solvable, significantly increase the system's complexity and cost. We refer to common-path systems to designate a set of devices in which the two different beams propagate along the same physical path, with only minor variations. In this invention, we will refer, by extension, to quasi-common-path systems, to refer to 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 optical path in the optical element being negligible compared to the total optical path. This definition allows us 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 alter the functionality and advantages of a common-path system. In the remainder of this invention, for the sake of simplicity, 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, 6} In Optics, it is common to decompose the components of the field, namely its amplitude, phase and polarization, into orthogonal, Cartesian or polar modes. Many decompositions into polar orthogonal modes, such as Gaussian, Hermite-Gaussian, HGG and "Elegant" and Laguerre-Gaussian modes, are known to the Man of the Art. In this document, we will primarily use the decomposition of the field amplitude. Singular waves This research theme in Optics, initiated by the seminal article by JF Nye and M. Berry in 1974 [4], is now known as "singular optics". Examples of regular and singular waves are presented below. We use the English term beam shaping to describe the transformation of a wave of a given shape and topology into a wave of another shape or topology, and in particular the transformation of a regular wave into a singular one and vice versa. Compact light topology and distributions A point-based light distribution will be considered compact if it fulfills one of the compactness conditions defined below, by two alternative and non-exclusive conditions: • that is, more than 75% of the energy is contained within a circle with a radius less than 1.75 times the Airy radius, • either a luminous domain, containing more than 65% of the energy, is delimited by a line of zero intensity contained within a circle of radius less than twice the Airy radius, We distinguish different families of point light distributions, with different topologies: Regular distributions, in their usual definition in Optics, The distributions or singular waves, also called optical vortices, of topological charge (azimuthal order) £, in which the phase varies from 0 to 2n £, around the direction of propagation, £ being an integer. Amplitude distributions with azimuthal variation of order Σ, also called Laguerre-Gauss distributions, The azimuthal-variant polarization and optionally phase distributions of order ^ also called radially polarized Laguerre-Gauss modes. Two compact light distributions will be considered to belong to different topological families if they fulfill at least one, and any one, of the following conditions: One is regular and the other is singular. One is a point and the other is an annular. The azimuthal orders Σ of the amplitude of the two light distributions differ, The azimuthal orders £ of the polarization or phase of the two light distributions differ. 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 in opposite directions. Light nano-emitters A light nanoemitter is a small secondary emitter attached to an object; its size is significantly smaller than a fraction of the wavelength, typically but not limited to less than one-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 may 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 secondary point 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" [5], for example using RESOLFT techniques, photoactivation and photodepletion phenomena, two- or more-photon fluorescence, elastic or inelastic 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. We will extend our definition of nanoemitters, including diffusing, absorbing and reflecting particles attached to a biological or organic entity; the action of a diffusing, reflecting or absorbing particle on the electromagnetic field can indeed 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. In this patent application, we will refer to the descriptors of a nanoemitter to denote the set of information describing a nanoemitter as a point source at a given instant. Since the nanoemitter is considered a point source, the information representing it contains a limited number of parameters, namely: its position in space, its intensity, and the spectral, intensity, coherence, phase, and polarization characteristics of the light emitted by the fluorophore, as a function of the incident light. In this patent application, we will refer to the descriptors of a structured object. For example, for a uniform line, the set of information representing it contains a limited number of parameters, namely: its orientation in space, its intensity, the spectral, intensity, coherence, phase and polarization characteristics of the light emitted by the object, as a function of the incident light. For a continuous distribution, the object is represented, as is usual in image processing, by an intensity matrix. However, in most cases, and in the description of the invention, we refer, by the designation of descriptors, to a subset of the descriptors of a nanoemitter or 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 scope of the invention, which will include within its field of application all the descriptors of light nanoemitters. To simplify understanding of the context of the invention, the following description refers only to the simplest case, in which the nanoemitter is a fluorophore and the physical interaction is one-photon fluorescence. However, this description should be understood as a simplified illustration of a general description of the methods and concepts applicable to all previously mentioned or known nanoemitters, regardless of the underlying physical phenomenon. It is noteworthy that the nanoemitter samples the incident field or intensity at a precise three-dimensional position, unaffected by the overall spatial distribution of the incident intensity. We will refer to this remarkable property in this patent application as the sampling capability of the light nanoemitter. However, the described embodiment of the invention also allows for the measurement of structured objects and continuous distributions that do not possess the sampling capacity of the light nanoemitter. We refer again to Figure 1, which represents an array 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. Alternatively, the emitted light may consist of a continuous distribution, not shown in Figure 1, or any combination of nanoemitters, structured objects, or continuous distributions. The array of nanoemitters, structured objects, or continuous distributions is referred to as an array of "luminous 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, for the sake of simplicity, to refer to the luminous biological object as the biological object itself, when no ambiguity can arise.The luminous biological object contains a great deal of relevant information related to the biological object, primarily spatiotemporal information, the object's position and orientation over time, and morphological information, for example in the case of a cell dividing in two. The measurement system according to at least one embodiment of the invention will allow the calculation of the measured map and the evaluation of the descriptors of any combination of nanoemitters, structured objects, or 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 further elaborated at different levels of abstraction. This first level of abstraction, which describes the direct results of the measurement, does not, a priori, contain any biological information but rather the results of a physical measurement described by nanoemitters, structured objects, or continuous distributions, which could, moreover, represent any labeled entity. The second level, the level of geometric abstraction, structures nanoemitters, whether 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, orientation, or morphology. At this level, the information is still physical and geometric, describing a set of objects. The geometric information uses the measured map and auxiliary information, potentially external to the system, about the relationship between the luminous points and the objects. The level of biological abstraction allows for a certain understanding of biological reality through a constitutive relationship between measured objects and corresponding biological entities. It contains a set of information about the biological object, primarily its position and dynamics, its shape, and its morphology. Biological information uses the map measured and geometric information, and auxiliary information, potentially external to the system, on the relationship of light points and objects to biological entities. A number of conclusions about the biological functionality of the sample can be obtained at this level. The functional level of abstraction allows for an understanding of biological reality. It consists of functional information, uncorrelated with geometric information, and answers questions in biological terms and jargon, such as: "Did the virus penetrate the cell?". An additional level of information can be defined that includes the control and instrumentation process; indeed, a more advanced control and instrumentation process can be defined, allowing access to more structured biological information through automation of the data acquisition process. An example of such a process is described by Steven Finkbeiner under the name "Robotic Microscopy Systems." This description of the levels of abstraction, defined in this application, was written, for simplicity, for Biology. It is applicable, mutatis mutandis, to all areas of Vision, biological and medical, artificial and industrial. Conical diffraction Conical diffraction or refraction, is an optical phenomenon predicted by Hamilton, [6] in 1832, and experimentally confirmed two months later by Lloyd, [7]. 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 0°, depending on the three indices of J -2 _ —2 refraction according to the law, tan (¾ = . V«2 ~«3 Hamilton predicted that light emerges in the form of a hollow cone of rays. Conical refraction is an important milestone in the history of science and played a role in demonstrating the theory of electromagnetic waves. A renewed interest in cone diffraction occurred in the latter years of the 20th century; it culminated in a comprehensive theory by Berry et al. [2], experimentally validated in 2009, [8]. Here, we follow Berry's theory, terminology, and definitions, including the change in nomenclature of the physical effect, from this point onward, using the more rigorous term cone diffraction. However, it is important to note that the term "conical diffraction" is also used for two other techniques unrelated to the technique we are describing: • Diffraction at oblique incidence 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. Conical diffraction has attracted considerable theoretical and experimental interest, but, "no practical application seems to have been found", [9]. Historically, cone diffraction has been observed in biaxial crystals. We use the term "cone crystal" to describe any inorganic or organic biaxial crystal exhibiting this phenomenon. 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, creating either intrinsically weaker conic diffraction or weaker conic diffraction along a shorter optical path. However, these effects can be used within 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

[10] ; liquid crystals include, but are not limited to, the thermotropic biaxial nematic phase

[11] ; externally induced birefringence effects 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 intrinsically achromatic. Additional chromatic effects include optical axis dispersion and the dependence of various parameters in the conical diffraction equations on wavelength. Chromatic dispersion of the optical axis creates an angle between the optical axis of the crystal, dependent on the wavelength, and the optical axis of the system. In most cases, this is due to the dispersion of refractive indices. Refractive indices depend on wavelength, according to Sellmeier's equations. The angle of the optical axis therefore varies with wavelength, creating a chromatic inclination angle of the optical axis in the plane created by the crystallographic x and z axes. It depends strongly on the type of crystal. In an MDT crystal, the least dispersive crystal in the visible spectrum, 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 telecommunications infrared, the angle varies by 0.05 degrees between 1,350 nm and 2,100 nm, and by less than 0.02 degrees over the telecommunications window—1450 nm to 1650 nm. On the other hand, the optical axis angle can vary significantly with wavelength in certain organic crystals such as DAST. Chromatic dispersion compensation along the optical axis can be achieved using geometric optics. Chromatic dispersion in the direction of the optical axis can be compensated 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 commercially available optical software programs by defining appropriate 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 different parameters present in the conical diffraction equations on the wavelength modifies the efficiency parameters of the conical diffraction effects. For linear conical crystals, defined later, the fundamental transfer function is identical to unity and thus trivially independent of wavelength. In contrast, the vortex transfer function depends on wavelength and can be represented by a chromatic factor equal to t(X). For sinusoidal conical crystals, defined later, the behavior differs from that of linear conical crystals: the fundamental wave depends on the wavelength, while the vortex wave is almost independent of it. Indeed, simulations show that the shape of the vortex wave is only slightly modified by a variation in the parameter, θ, from 0.5 to 0.75. In contrast, the shape of the fundamental wave depends on the wavelength, and this effect must be taken into account in the design of systems using both the fundamental and vortex waves. We now refer to Figure 3, which is a simplified schematic illustration of a configuration of a conical diffraction module, 300, according to an embodiment of the present invention. The incident light, 30, is assumed to be collimated, although other conditions can be adapted using simple optical means. The assembly itself comprises 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 conical effect through the conical ray, 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, may also be added. However, in some 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 can be an external microscope objective, or can 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 light distribution in the image plane. The influence of vector effects will be discussed below. The scale ratio or magnification is determined by the microscope objective. Let R be the spatial variable in the conical imaging plane, and U the wave vector, represented in cylindrical coordinates by R, 0r and U, 0u. Let X be the wavelength of the 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 conical radius depends on the material and the thickness of the crystal. We introduce normalized parameters that allow the description below of the light distribution to be valid both at the conical imaging plane and at the focal point of the microscope objective, within the limits of the scalar theory of diffraction. An example of the introduction of normalized parameters is described in reference [2]. The normalized radial position, p, the normalized wave vector, u, represented in cylindrical coordinates by p, 0r and u, 0u, and the normalized conical radius, po, are given by: P = 2^U0, u =-y-; p0 = 2^y0 (EQ.2) A Uq A Uo being the digital opening of the system. Different regimes exist for all low-interaction volumetric optical diffraction effects. Low-interaction volumetric diffraction effects have the following properties: • A modification of the incident light is created by a perturbation of Maxwell's equations, • the scale of the interaction much larger than the wavelength, typically more than 10 pm. The fact that these different regimes create entirely different optical effects has been studied primarily for acousto-optic interactions, but is present in all optical effects, including cone diffraction. We will use terminology adapted from Raman's work on acousto-optics and differentiate the following cases: po« 1, linear Raman Nath regime, referenced previously,

[37] , “linear thin conical crystal”, in which a simple surface approximation of the effect can be used, p0 < 1 and >0.5, sinusoidal Raman Nath regime, referenced previously,

[37] , "sinusoidal thin conical crystal", in which a surface approximation of the effect can be used, p0 < 3 and > 1, intermediate regime, referenced previously,

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

[37] under the name "thick crystal," similar to the Bragg regime in acousto-optics, in which the effects described by Hamilton and Lloyd are present. Only crystals of the Hamilton-Lloyd regime, or thick conical crystals, po>3, can be described by Hamilton's theory. 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, already noted this condition on the amplitude of the effect of biaxial crystals as early as 1832, [6], necessary for the validity of his description of conical refraction, by showing the necessity of "sufficient biaxial energy" “29 New consequences of Fresnel 's principles. It follows from those principles, that crystals of sufficient biaxal energy ought to exhibit two kinds of conical refraction, an external and an internal: a cusp-ray giving an external cone of rays, and a normal of circular contact being connected with an internal cone. » The emerging wave of the thin conical crystal, E(p, 0r), expressed in normalized coordinates for a circularly polarized wave, is constituted by the superposition of two waves, referenced here as fundamental, Ef (p), a regular wave, and vortex fundamental, Ev (p,9R), a singular wave; these two waves are coherent with each other, co-localized, circularly polarized and of inverse chirality: E(p, 0R) = EM + Ev(p, eR) = EM + ?M exp(-^R) (J) (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) = f duu cos(p0,u)J0(puf, Fv(p) = 2tcf du usin(pou) / x(pu).(EQ. 4) For a thin linear conical crystal, the fundamental basis can be approximated by an Airy disk and the vortex basis can be approximated by a linear vortex, represented by: Fv (p) = 2np0 f du u2 f (puf (EQ. 5) Assuming that the partial polarizer fraction, 29, is the scaling of the vortex wave by a, the Stokes parameters can be deduced from the previous equations, P being the angle of the linear polarization: So = (EMÎ + (a2FMÎ Sr = 2aEp(p)Fv(p') sin 0R; S2 = 2aEF(p')Fv(p') cos 0R; (EQ. 6) S3 = (EM)2 ~ (a2Fv(p))2 P = eR, As described previously, the emergent ground of the conical crystal, for a circularly polarized wave, consists of the superposition of two waves: the fundamental ground, a regular wave, and the vortex ground, a singular wave. All incident beams with homogeneous polarization can be decomposed onto the orthogonal basis composed of right-handed and left-handed circular polarizations. The incident beam is therefore the coherent superposition of two beams, one polarized with right-handed circular polarization and the other with left-handed circular polarization. The beam Emergence is the coherent superposition of four beams: two fundamental waves, the first created by the right-hand circularly polarized beam and the second by the left-hand circularly polarized beam, and two vortex waves created by the right- and left-hand circularly polarized beams. However, while the two fundamental waves have the same spatial distribution and can interfere while maintaining their topology, the two vortices have opposite chirality and create complex distributions. Different combinations of these waves can be achieved by choosing the input and output polarizations, thus yielding PSFs of various shapes. parsimonious object We will use the term "sparse object" to describe either a set of sparse, or sparse, point emitters of light, or a set of sparse objects. Sparseness is defined in references [41-43] and is not limited to point objects but includes, for example, filaments. For sparse emitters, the chosen limit is a number less than twelve, positioned within a volume whose size, in each dimension, is less than three wavelengths from the emission or reflection wavelength of the emitters. The volume smaller than three wavelengths, which contains the sparse object, will be referred to as a reduced-size analysis volume. We will use the term "continuous object" to describe a set of point or continuous light emitters that do not meet the conditions described earlier in the definition of a sparse object. The transition between these two regimes is not clear-cut, and many experimental cases will be intermediate between these two types of object. We now refer to figures 4a to 4c which are a simplified representation of the concept of volume confinement of the confocal microscope. The function of volumetric confinement is to limit, in three spatial dimensions, the observed region of the sample to the smallest possible volume, the analysis volume. Volumetric confinement limits the analysis volume by combining two effects: the confinement of projected light onto a small surface, ideally the size of the Airy disk, 50, and the elimination of defocused light through the confocal hole, 28 in Figure 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. Consider a sparse or continuous object, 51, consisting of an array of nanoemitters, 53 to 59. The nanoemitters 53 to 55 positioned within the analysis volume 60, and only them, are both excited by the light source and the photons emitted by them reach the detector module. The nanoemitters not located within the illumination cone, 56 and 57, are not illuminated by the incident light. The light emitted by the nanoemitters 58 and 59 does not located in 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 reference frame "i": The axes referenced "i" represent a Cartesian coordinate system centered on the center of the analysis volume, 61. The reference frame "a": The axes referenced "a" represent a Cartesian coordinate system centered, for each light nano-emitter, on the light nano-emitter considered as a discrete point, 62, When, using an embodiment of the invention which will be described later, 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 technique. However, alternative implementations, replacing the conical diffraction-based modules with modules based on other optical concepts, are capable of providing the same functionalities. They are an intrinsic part of the scope of this invention. Alternative optical concepts include, but are not limited to, uniaxial crystals, subwavelength gratings, structured laser modes, holographic components, and other techniques known to those skilled in the art. The optical and optoelectronic concepts, techniques and devices which can be used in embodiments of the invention are described for example in the book written by D. Goldstein, "Polarized light",

[12] , the "Handbook of Confocal Microscopy",

[13] , the "Handbook of Optics",

[14] . 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 incident light to different channels or detectors based on a property of the light. The simplest case is a dichroic plate that separates the light into two channels according to the wavelength. In this embodiment of the invention, we use the English term "Position Dependent Optical Semaphore" (PDOS) to describe an optical semaphore that channels light according to the position of the emitting point. The PDOS is determined by a series of transfer functions, Ti(x,y,z), which depend, for each channel or detector i, on the position of the emitter (x,y,z) within a reference volume. The order of the PDOS corresponds to the number of channels or detectors. The PDOS is lossless within an analysis volume if the sum of the transfer functions, Ti(x,y,z), is equal to one within the analysis volume. The confocal hole, described by Minsky,

[15] , could be considered in this embodiment of the invention as a degenerate PDOS of order 1. In most cases, the PDOS dependence is a complex function of the lateral and longitudinal positions. However, in embodiments of the invention, we use the English term "Longitudinal Position Dependent Optical Semaphore" (LPDOS) to describe an optical semaphore that channels light according to the longitudinal position of the emitting point. The LPDOS will be determined by a series of transfer functions, Ti(z), which, for each channel or detector i, depend on the longitudinal position of the emitter (z) within 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 via optical fibers A primary use of optical fibers is the exclusive transmission of the TEMoo mode. However, certain optical fiber configurations, such as FMFs or vortex fibers, mainly but not exclusively based on so-called "Photonic Crystal Fiber" (PCF) and so-called "vortex fiber," allow the simultaneous or non-simultaneous transmission of more complex modes, including vortex modes, with a vorticity equal to or less than 2. It would therefore be possible to relocate the optical distributions created by conical diffraction using optical fibers, allowing for a major simplification of the optical system. The possibility of offsetting the optical distributions created by conical refraction using optical fibers allows the application of embodiments of the invention to many additional applications, for example but not limited to gastric or gastroenterological observation, and to the observation of the colon and urinary tract. Moreover, some fibers, the "dual-core photonic crystal fibers", in English,

[16] , allow an interaction between two modes, one of which can be a vortex, and provide an additional physical mechanism to create diverse transfer functions. Measurements at multiple wavelengths In some embodiments of the invention, the object can be illuminated with monochromatic light using, for example, a conventional laser or a monochromatic lamp. Furthermore, in certain configurations, a broad-spectrum laser—also known as a "white laser"—can be used. This configuration is simple because one of the main parameters of the system is fixed and well-defined. However, in other embodiments of the invention, the object can also be illuminated at multiple wavelengths, either discretely, for example, using several lasers, or continuously, for example, using a lamp or laser with a broader spectrum. Many existing superresolution systems measure simultaneously or sequentially at multiple wavelengths. Indeed, it is possible to label similar or different elements with fluorophores having different spectral responses, allowing them to be identified and separated. 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 or similar wavelengths, 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 measurements of one wavelength with respect to the second is intrinsically non-existent because the super-resolution position information is derived from the projection of the light, which is perfectly identical for the different wavelengths. This allows relative calibration of the position of fluorophores at two different wavelengths, with accuracy limited only by the experimental calibration system, eliminating the major problem of registration between two images of different wavelengths. The ability to achromatize optical systems based on conical diffraction makes it a tool of choice for the implementation of optical systems, a common path, in many 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 degree of practical complexity. Other existing fluorescence systems use light with a broader spectral content to reduce artifacts, primarily speckle effects. As a corollary, the spectral properties of fluorescent proteins allow the potential of intracellular molecular interactions to be measured using the Förster-Förster (Fluorescence) Resonance Energy Transfer (FRET) technique. In some PSIT system implementations, the light from one or more incident laser beams is split into two beams using a beam splitter: the main beam, which performs the PSIT system's function, and a secondary, low-intensity beam used to measure the laser beam's position with a camera or position detector. This device allows for real-time measurement of the laser's position, independent of any wobble or other mechanical errors, with very high accuracy. Preliminary information and additional information 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 accuracy of the information collected from the sample for any of the levels of abstraction mentioned: the map, the geometric abstraction level, the biological abstraction level and the functional abstraction level. More generally, spectral diversity, information obtained at multiple wavelengths, polarization diversity, and information obtained by projecting different polarization states, extends the range of available information. The fact that the absence of energy, for example in the case of the vortex zero, is relevant information, opens up additional possibilities for acquiring 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 autofluorescence. One of the modalities described for certain embodiments of the invention will be referenced under the name of dark tracking. We introduce the concept of integral optical information, the information that could be retrieved from optical or electromagnetic wave measurements of a target by an observer from a given viewpoint. This information contains numerous parameters of the object, related to its position, the materials it is made of, its temperature, and its orientation. Optical integral information, however, does not contain information about regions of the object that do not have an optical path to the observer, for example an element positioned in an opaque box, or physical information that does not have an optical transcription. Super-resolved measurements and diffraction limit It was long believed that optics inherently limited the resolution of any optical system through the diffraction limit. The emergence of superresolution techniques—in various fields and under different names—has shown that it is possible to overcome this diffraction limit through various 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. Use of nonlinear interactions in superresolution and the RESOLFT and STED family of 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 for a super-resolution system. Many different techniques have stemmed from Hell's work, 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 effects, blinking and photoactivation on which the RESOLFT technology family and the localization microscopy technology family are based. 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 by Willig et al.

[19] , In the STED technique described in Hell's initial article [5], two beams are projected sequentially onto the object: a standard excitation beam, modeled in most cases by a light distribution described by an Airy function, and a depletion beam—having a doughnut or vortex shape. The effect of the depletion is to prevent fluorescence of fluorophores located at the surface of the depletion light distribution, while leaving the emission of fluorophores positioned at the center of the light distribution outside the depletion light distribution unaffected. This allows for the creation of an equivalent emission light distribution smaller than the initial excitation light distribution. This technique has made it possible to obtain very small equivalent emission light distributions, although it requires very high light depletion energies. Several variants of STED have been developed: CW STED

[20] , gated STED

[21] , and modulated STED

[22] . In CW STED, the pulsed laser used in the first version of STED is replaced by a simpler continuous-wave laser. In gated STED, emitted photons are discriminated according to their emission time to eliminate photons emitted from fluorophores that have not received sufficient time from the depletion beam. Modulated STED uses an intensity-modulated excitation beam in combination with synchronous detection dependent on the modulation frequency. This allows discrimination of 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 doughnut—or vortex—was created in the first version of STED using a spatially varying phase plate. This implementation requires the use of The system uses two separate optical paths for the two beams: the excitation beam and the depletion beam. This optical setup is complex, highly dependent on any mechanical drift, and creates intricate optical alignments. The developed system requires advanced technical expertise, and its cost is significant. Furthermore, this implementation is chromatic, as the phase plate adapted to one wavelength will no longer be suitable for another wavelength. Since the optical system is not achromatic, using a STED with two depletion wavelengths necessitates an even more complex optical system. To simplify the implementation of STED, several authors have proposed solutions allowing the realization of an STED in which the two beams, the excitation beam and the depletion beam, would propagate along the same optical path: Wildanger et al. 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 Abberior Instruments.

[28] . - Bokhor et al.

[24] propose the use of chromatic ring separation of pre-aligned beams; however, this solution blocks part of the depletion light. Hoefftnan

[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 alignment. - Menon et al;

[26] , propose diffractive lenses that allow the creation of amplitude zeros without phase singularities, Reuss et al.

[27] introduced a beamforming device placed directly in front of the objective lens. This device is based on the use of birefringent crystals, mounted as a segmented waveplate consisting of four segments. By choosing the thickness parameter of the waveplate, it is possible to create an element consisting of a phase plate for depletion and a neutral plate for excitation. Gould et al.

[45] use a single-layer matrix (SLM) to create either the lateral and / or axial depletion distributions separately. This solution allows the parameters to be varied dynamically to adapt to different wavelengths. Other studies integrate the lateral and axial distributions onto a single SLM. However, the previously described solutions are all highly chromatic and designed for a single excitation and depletion wavelength. Yet, biological applications often require a system with two or more excitation wavelengths. Indeed, it is common practice to label different biological objects with fluorescent markers differentiated by their excitation or emission wavelength. The most advanced fluorescence systems can use four to six different markers. The availability of only one super-resolution pathway severely limits the use of systems. Two-wavelength STED systems are also commercially available. It is clear that for an achromatic or 3D STED multi-wavelength 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 proposed solutions for STED, the initial laser beams are in the form of a regular distribution, and in most cases, a Gaussian distribution. These initial laser beams are subsequently transformed into an excitation beam, a regular wave, and a depletion beam, a singular wave, by a suitable optical system, as 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 and singular wave is much more complex. Co-locating these upstream beams can be commercially achieved using laser bench systems with optical fiber-based techniques.It is therefore relatively easy, as is the case in all confocal microscopes, to create a set of laser outputs at different wavelengths from the same optical fiber and thus co-located very precisely. The solution proposed in embodiments of the present invention allows for the use of this upstream co-localization, greatly simplifying the system and enabling the implementation of a multi-wavelength STED inherently. For this, it is preferable to use an optical system that combines the properties of a common optical path, achromaticity, and beam shaping. It is preferable to implement different beam shaping for the different beams: a regular wave for the excitation beam and a singular wave for the depletion beam, at any wavelength in the visible or infrared spectrum. The ability to perform achromatic beam shaping, allowing for a regular wave for one polarization and a singular wave for another, across the entire visible or infrared spectrum, differing for the various polarizations, is novel.The PSIT module enables the implementation of such an optical system, combining the properties of a common optical path, achromaticity, and beam shaping. To our knowledge, no such common-path, achromatic system with different beam shaping capabilities exists in the literature. Such a system certainly improves the simplicity of design and operation of the STED. 3D STED Numerous systems have been proposed to extend the STED concept to the third dimension. The solution adopted for all 3D STEDs is the "depletion ring" proposed by Stefan Hell's team, reference 36. The "depletion ring" creates a "black sphere," a distribution in which the intensity is zero at the center of the focusing field, and increases relatively rapidly with defocusing. An implementation of the "black sphere" has been described by Zhang,

[29] , 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 In this patent application, we will use the acronym SRCD, "Super Resolution using Conical Diffraction", to name the platform, modules and systems specific to the implementation of this invention. In this patent application, we will use the acronym PSIT, a method for projecting a sequence of topologically differing light intensities, or in English: "Projected Sequence(s) of Intensifies with varions Topologies"; the PSIT method can also be used to project sequences of topologically differing light intensities, at two or more wavelengths, sequentially or simultaneously. In this patent application, we will use the acronym PDOS, which stands for "Position Dependent Optical Semaphore". The SRCDP platform, "Super Resolution using Conical Diffraction Platform", is a Microscopy platform using optical modules based on conical diffraction. In this patent application, we will use the acronym LatSRCS to name the optical module implementing the PSIT method in the implementation of this invention. In this patent application, we will use the acronym LongSRCS to name the optical module implementing the PDOS method. The SRCDP platform, described in detail below, consists primarily of two hardware modules: two new and complementary optical modules, the LatSRCS and LongSRCS, mounted on a microscope, and an algorithmic module, SRCDA, "Super Resolution using Conical Diffraction Algorithm," which reconstructs the super-resolved information of the sample. In addition, the SRCDP platform includes an enhanced detection module, a system control module, and computer and software support. Furthermore, certain embodiments of the invention relate to a significant number of implementation variants of the PSIT and PDOS methods, the SRCD platform, the LatSRCS and LongSRCS optical modules and the SRCDA algorithm. 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 with a normalized conical parameter π of 0.388, calculated using a scalar approximation, for different input and output polarization states, including either a circular or linear polarizer or a radial or azimuthal polarizer at the input and / or output. These light distributions were calculated in an intermediate imaging plane and not at the focal point of the objective lens to separate conical refraction from vector effects. The polarization states—input and output—are characterized by their angle for linear polarizations and by their chiralities for circular polarizations. Referring to Figure 7b, this figure represents the light distributions, created through a conical crystal with a normalized conical parameter π of 0.818, calculated by a scalar approximation, for different input and output polarization states, including either a circular or linear polarizer or a radial or azimuthal polarizer at the input or output. These light distributions were calculated in an intermediate imaging plane and not at the focal point of the objective lens to separate conical refraction from vector effects. The input and output polarization states are characterized by their angle for linear polarizations and by their chiralities for circular polarizations. In these figures, we present a large number of different transfer functions, including cases involving circular, linear, azimuthal, or radial polarizers at the input or output. This description should be expanded to include, in addition to the circular, linear, azimuthal, and radial polarizers described in the figures, the cases of elliptical, dichroic, or partially dichroic polarizers, and spatially varying polarizers. Furthermore, as illustrated in Figures 7a and 7b, these transfer functions vary significantly depending on the normalized conical parameter po. Moreover, the introduction of two conical crystals, or of a conical crystal and a uniaxial or biaxial crystal (in which light propagates in a direction different from that of conical diffraction) in cascade, allows for an even greater number of transfer functions, as illustrated for two conical crystals in Figure 7c. In summary, in this patent application, we will refer to the term conical diffraction transfer function as the set of transfer functions that can be obtained using a small (<6) number of cascaded crystals and static or dynamic polarization elements, uniform or spatially varying. We will primarily note the following light distributions: • The fundamental: Figure 7aoo and 7an, obtained between parallel circular polarizers, which is a distribution close to the Airy distribution • The vortex: Figure 7aoi and 7aio obtained between crossed circular polarizers • The distribution we have called the "crescent moon" or Stokes distribution, subfigures 7ao,2-5, 7ai,2-5,7a2-5,0 and 7a2-s,i, and figure 7c describing the axial variation of the "crescent moon" or Stokes distributions. These distributions are obtained between a circular polarizer and a linear polarizer of variable angle; this distribution is antisymmetric 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 7as3 is obtained between two crossed polarizers; this distribution is symmetrical. • The distribution that we have called the "offset half-moon" distribution, Figure 7d, representing the "offset half-moon" distribution at different axial positions, is obtained between two elliptic 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 - cascading conical crystals, (not shown) with or without static or dynamic polarization elements between the crystals. The different light distributions are generated 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 previously defined. There are several polarization elements with different polarizations at different wavelengths. Using one of these elements allows the creation of two compact waves, either regular or singular at two wavelengths, or a regular wave at one wavelength and a singular wave at another. Such a device allows for a much simpler implementation of emission-depletion concepts, which are sometimes limited by tolerances or vibrations in 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 a depletion beam. However, cone diffraction can be used for beam shaping, as for example in the LongSRCS module, described later. A new variant of this module shapes the PSF to exhibit lateral and primarily axial variations. This modification of the emission beam's PSF, referred to as the "PSF," has numerous applications in various disciplines. For example, a cone diffraction-based module that modifies the PSF to create an axial dependence can enable the measurement of the longitudinal and lateral position of one or more nanoemitters, as described later. 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 out some of the random phase errors that are inevitably present in many biological object measurement processes. New light distributions can also be obtained as mathematical combinations of elementary light distributions. The "pseudo-vortex" 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 the theory of geometric imaging, a reduced image of the distribution of light in the image plane. However, as extensively described in the literature, for a lens with a high numerical aperture, the theory of geometric imaging 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 can be advantageous to keep the final analyzer fixed and add an additional element, either fixed or variable, the output polarization matching submodule, 74, to control the output polarization. We have found that circular symmetry in the output polarization significantly reduces vector effects and allows it to adapt to the direction of the fluorescent dipole. Such polarization can be circular, radial, azimuthal, or position-dependent. For circular polarization, the output polarization matching submodule 74 is simply a delay plate of a four-wavelength waveform.In this case, the longitudinal polarization elements have vortex symmetry and blend harmoniously into the system with only a small modification of the shape of the Stokes parameters, even for microscope objectives with a very high numerical aperture. Alternatively, the output polarization adaptation submodule, 74, can be variable and / or controllable and adapt to the topology and symmetry of each of the compact light distributions. *Modified Wollaston Prism Recall that a Wollaston prism can be used to split an incident beam into two emergent beams separated by an angle. By using several prisms in cascade, an incident beam can be split into a large number of emergent beams. The same effect can be achieved by modifying the Wollaston prism to create a compound Wollaston prism, by adding pieces of uniaxial crystal whose refractive index and birefringence orientation are chosen. A prism made from a single block of uniaxial crystal can thus be constructed that can split an incident beam into 2n emergent beams (for example, eight or sixteen) contained in a plane and separated by equal angles. Once focused onto the sample, 2n points are obtained that are aligned and equally separated. If the incident beam has passed through a LatSRC module, these 2n points are not 2n Airy disks, but rather the distributions created by the module, and are all identical.The advantage of using this beamsplitter is that it scans the sample more quickly since there are 2n 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 function of the confocal microscope is to limit, in three spatial dimensions, the observed region of the sample to a volume of the smallest possible size, the analysis volume. Consequently, in a confocal fluorescence microscope, the acquired information is a single intensity value for the entire analysis volume, conceived as a single entity. More precisely, detailed information about the position of the nanoemitters within 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 for further discrimination within the illuminated volume. Reference is now made to Figure 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 confocal fluorescence microscope, schematically represented in Figure 4a. In Figure 4d, an analysis volume, 60, is created at the focal plane of the microscope objective, 22; it contains a sparse object, 51, consisting of several nanoemitters, 53 to 59; the output of the system is a reconstructed sparse object, 63, and a list of the nanoemitters and a list of their attributes, 64. We now refer to Figure 4e, which is a simplified conceptual representation of another measurement paradigm, based on STED concepts, according to at least one embodiment of the invention. This measurement paradigm limits, in two (STED 2D) or three spatial dimensions (STED 3D), the observed region of the sample to the smallest possible volume, the analysis volume. In Figure 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 analysis volume to a smaller volume represented by 2001. In this paradigm, as in 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. We now refer to Figure 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 Figure 4f, an analysis volume, 60, is created at the focal plane of the microscope objective; it contains a sparse object, 51, comprising several nanoemitters, 53 to 59. One or more depletion waves, 2000, reduce the analysis volume to a smaller volume represented by 2001. As in Figure 4d, this volume contains a sparse 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 parsimonious 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 could perfectly well have represented a continuous object, mutatis mutandis. MEASUREMENT METHODS PSIT measurement method A PSIT measurement method according to an 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 from different topological families onto a sample; and o For each compact lighting distribution system: • light emission by the sample's nanoemitters, • creation, using the optics of the microscope, of an optical image, • Acquisition of the optical image by a photoelectric detector and creation of a digital image. In more detail, it should be noted that: The emission sequence consists of at least two point light distributions of different topological families. The emission sequence is projected onto a biological sample labeled with nanoemitters. The light emission emerging from each nanoemitter is dependent, for each nanoemitter, on the intensity, in the incoherent case, or of the electromagnetic field in the coherent case, incident to the spatial, three-dimensional position of the aforementioned luminous nanoemitter, sampling property of the luminous nanoemitter discussed previously. For each light distribution of the emission sequence projected onto the sample, an optical image is created. The set of images corresponding to all the light distributions of the emission sequence is referenced as the image sequence. The PSIT method according to this embodiment allows the acquisition of 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 a variation of the 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 initially designed to enable lateral superresolution; however, it can also be used to determine the longitudinal position of a nanoemitter. Indeed, some elementary light distributions are relatively insensitive—within reasonable limits—to variations in the nanoemitter's longitudinal position, while others are highly sensitive. A sequence of compact light distributions, some independent and some dependent on longitudinal position, would allow the longitudinal position of the nanoemitters to be determined. Furthermore, for light distributions that are highly dependent on the longitudinal position of the nanoemitter, a series of elementary light distributions slightly offset longitudinally from each other can be projected onto the sample, allowing a set of images containing longitudinal information. Original PDOS Method The PDOS method involves the distribution, via an "optical semaphore," of 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 different regions of the analysis volume onto different detectors. In practice, the optical semaphore creates, for each detector, a light transfer function emitted by a light nanoemitter, dependent on the spatial position of the light nanoemitter and different for each detector. 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. The PDOS method allows for the acquisition of essentially longitudinal information, that is, the longitudinal position of each nanoemitter. Mathematically, the process, according to embodiments of the invention, performs a transfer function that transforms the spatial distribution of the nanoemitters into raw information consisting of a set of images. The algorithm then performs the inverse operation: it reconstructs the spatial distribution of the nanoemitters from the set of images that make up the raw information. Modified PDOS Method We also present the modified PDOS method, an optical beam-shaping method 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 lobes of the distribution for a two-lobe (or more) axially varying distribution. This method has some similarity to the original PDOS method, described by one of the inventors in

[37] , but differs in that the variation of the topology of the created distribution 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 PALM, STORM or GSDIM modalities or similar. PDOS method and lateral measurements The PDOS method was initially designed to enable longitudinal superresolution; however, it can also be used to determine the lateral position of a nanoemitter. This is because elementary light distributions are also sensitive to variations in the nanoemitter's lateral position. For a planar sample, where light projection is not feasible, the PDOS method can replace the PSIT method for performing super-resolution measurements. All these variants are deemed to be part of the invention. However, in one of the implementations, the inventor chose 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. 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 Aop(m,n), representing, for the light distribution o, the image from the detection channel p. As with a confocal microscope, the measurement process analyzes a small volume within a much larger object. It will therefore require the addition of supplementary modules, similar to those of a confocal microscope, including a scanning process, and a software module for integrating, analyzing, and visualizing point data into surfaces and / or three-dimensional objects. In mathematical terms, the algorithm solves an inverse problem or a parameter estimation problem. The model equations are known, and a priori model, parametric or nonparametric, of the nanoemitter configuration is available. The most natural model assumes a small number of nanoemitters (a sparse object), but continuous models can also be used, assuming the presence of one-dimensional structures (lines, curves) or specific patterns. The set of mathematical procedures known to a person skilled in the art for solving inverse problems or estimating parameters can then be used. We describe later an example of an algorithm specifically adapted for measurement according to one embodiment of the invention. Furthermore, we present, for its symbolic value, a new solution to the problem of discriminating between two points positioned close to each other. This problem, studied by Lord Rayleigh, forms the basis of the resolution criterion in many areas of optics. The characteristics of the embodiments of the invention have thus been described in fairly broad terms so that its detailed description may be better understood, and so that the present contribution to the art may 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 an embodiment of the invention, either by combining the two methods PSIT and PDOS, original or modified, described above, or by using STED techniques, or by combining STED techniques with the methods PSIT or PDOS, original or modified. In one embodiment, the SRCDP platform observes, Figure 5, a biological sample, 11, incorporating an array of nanoemitters. The result of the observation of The biological sample by the SRCDP platform is the acquisition of super-resolution information, representative of the observed sample. The SRCDP platform, 500, Figure 5, mainly comprises: In its physical aspect: • A 200 confocal microscope, 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 implementing a STED or RELSOFT technique, according to another embodiment of the invention. The LongSRCS, original or modified, 800 optical module implements the steps for distributing the emerging light intensity in a plurality of images of the PDOS method or implements the variation of the emerging PSF as a function of 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 super-resolution information of the biological sample. • Other auxiliary elements, such as computer 66 and software 67, may be necessary for the realization of the platform, Detection module In confocal scanning microscopy, the detector is a single-element detector such as a PMT or SPAD. The detector acquisition time is determined by the scanning mechanism. An improved detector module, 65, can be implemented using small, low-pixel-count detectors. Such a module would not have been feasible ten or twenty years ago due to the lack of suitable technologies. Today, small, low-pixel-count detectors with high frame rates and low noise characteristics are available based on several technologies. SPAD arrays with a low pixel count, 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 CCD, EMCCD, or CMOS sensors. CCD, CMOS, or EMCCD sensors with a low pixel count already exist or can be specifically designed. Furthermore, CCD, CMOS, and EMCCD detectors can can be used by utilizing features such as region of interest, sub-windowing or "binning", "crop" or "fast kinetics" modes, available for some detectors. The spatiotemporal information referenced here is the position and time of impact of each fluorescent photon. In real-world systems, spatiotemporal information is corrupted by detector noise, which creates erroneous photons, and by detection inefficiency, which results in undetected photons, thus reducing performance. In SP AD arrays, for each photon, the pixel that detected it and the impact time are received; that is, complete spatiotemporal information is available. For CCD, CMOS, or EMCCD detectors, the acquisition of multiple frames is necessary to approximate the spatiotemporal information. In several implementations we will refer to separate detectors; in many cases the detectors may be either physically separated or consisting of different areas 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, using the system control procedure, 1101, controls and modifies the optical parameters of the SRCDP platform, 500, the electronic parameters of the enhanced detection assembly, 65, and the mathematical parameters of the SRCDA algorithmic procedures, 900, to optimize the emerging information, according to criteria defined by the system or by the user. Control is achieved 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 external information, 1105, relayed by the computer, if available. Note: 1105 is not shown in Figure 11. It is understood that the invention is not limited in its application to the details stated in the description contained herein or illustrated in the drawings. The invention is capable of other embodiments and of being carried out and performed in various ways. Those skilled in the art will readily 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 Algorithms The reconstruction algorithm we will detail applies not only to a given field analyzed using PSIT and PDOS methods, but also to cases where the measurements obtained by PSIT and PDOS are supplemented 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. In confocal microscopy, the direct model is enhanced by the fact that overlap between the different positions of the projected signals allows for the inclusion of more measurements at a given point. However, accounting for shifted projected signals does not introduce any additional complexity, since these shifted signals are simply added to the list of projected signals. We now refer to Figure 9, which is a simplified schematic illustration 900 of a fluorophore data superresolution algorithm method, according to an embodiment of the present invention. An algorithm procedure, shown in Figure 9, quantifies the number of fluorophores, retrieves the attributes of each fluorophore, and quantifies the accuracy of each output parameter. The preprocessing procedure, 111, reorganizes the spatiotemporal information, 110, into sets of super-resolution 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 x 16 pixels. Since the preprocessing procedure is applied to a small number of spatiotemporal elements, on the order of a few thousand, it can be performed in real time using existing computer hardware. The descriptor procedure, 113, the main calculation step, creates from each image a set of descriptors, 114, and their statistical relevance. The descriptors include, but are not limited to: the intensity of each image, the presence, in the image, of a light distribution and its characterization as a regular distribution or a vortex, its center of gravity, and its moments of order one and higher. The third step is a filtering operation, 115, in which only the descriptors, which are statistically relevant, are retained. The classification operation, 116, is the last step of the algorithm. The algorithm is able to recognize, on the basis of the set of descriptors, 114, and a knowledge base, 117, the different measurement cases such as a single fluorophore, two fluorophores separated longitudinally or laterally and three or more fluorophores. The SRCDA algorithm can use classical inverse problem techniques. However, three novel algorithmic approaches—the modified MAP algorithm, the E-LSE algorithm, and the ICE algorithm—are described in this patent application and are deemed to be part of this invention. Optical modules LatSRCS optical module implementing the PSIT method With reference to Figure 6a, we describe an optical module according to an embodiment of the invention, the LatSRCS, 700 optical module, and its specific function in microscopy. The optical module, LatSRCS, 700, according to this embodiment, is an optical module that projects onto a plurality of nanoemitters in a sample a sequence of compact light distributions of different topologies. Each nanoemitter fluoresces with a sequence of fluorescent light intensities that depend on the intensity incident on the nanoemitter and characterize the lateral position of the nanoemitter. In most embodiments, the compact light distributions of different topologies are created by 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 illumination path of the confocal microscope 200; it projects a sequence of compact light distributions of different topologies onto the sample 11 using the objective of the confocal microscope 200. In an embodiment using conical diffraction, the intensity incident at a specific position on the sample 11 will be proportional, for each light distribution, to a specific combination of Stokes parameters. The LatSRCS optical module, 700, utilizes an inherent feature, described previously, specific to the nanoemitter, which samples the incident light intensity at its precise position (the nanoemitter's position) and re-emits fluorescent light dependent on the incident light. Remarkably, the measured information is directly related to the nanoemitter's position within the compact light distribution. This information is captured by the nanoemitter's functionality—its property of absorbing and re-emitting 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 65-meter detection array. If the incident light varies over time according to a sequence of compact light distributions with different topologies, the intensity of the re-emitted fluorescent light varies proportionally. The sequence of the re-emitted fluorescent light will be proportional to the sequence of compact light distributions with different topologies. From this information, it is possible to determine 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 onto a microscope, the interaction with the sparse or continuous object, the collection of the light re-emitted by the microscope objective, 22, the detection of the light, fluorescent or non-fluorescent, by the enhanced detection array 65, and the analysis of the information by a suitable algorithm. In some embodiments, the enhanced detection array 65 consists of a single detector and recovers only the overall intensity as a function of time, while in other embodiments, the enhanced detection array consists of a small area of ​​pixels and also recovers the spatial distribution of the fluorescent light. The array of retrieved information, consisting of a plurality of images, referred to as super-resolution side images. In one embodiment, the contribution of a nanoemitter positioned in the illuminated volume to a specific super-resolution 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. Reference is now made to Figure 6a, which is a simplified schematic illustration of a LatSRCS, 700 optical module, according to an embodiment of the present invention. Figure 6a shows an optical module, LatSRCS, 700. It includes all the components of the conical diffraction module of Figure 3, which are implemented in the same way as in the conical diffraction module 300. The optics of the scanning confocal microscope's light source are assumed to be achromatic and in infinite conjugation, although other conditions can be adapted 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 lens 32, or a subset achromatically realizing the functionality of a conical crystal as explained previously, and a second lens 33; a partial polarizer, 29, described above, can also be added.The first two lenses, 31 and 33, are preferably configured as a 1:1 Keplerian telescope; the conical imaging plane, 35, is placed at the common focal plane of 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 for injection into the microscope. It further includes a polarization control submodule, 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. The 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 module for beam shaping We also present the modified LongSRCS module, an optical 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 lobes of the distribution for a two-lobe (or more) axially varying distribution. This module has some similarities to the original LongSRCS module. described by one of the inventors in

[37] , but differs in that the variation in the topology of the created distribution is used to measure axial or lateral parameters 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 a complementary module to the LatSRCS module, but also for the axial localization of nanoemitters, for example for localization modalities such as PALM, STORM, or GSDIM, or similar. The case where the input and output polarizations are elliptical, with the major axes of each ellipse oriented at a 90° angle to each other, is discussed in more detail. Among the distributions generated under these conditions, some exhibit significant axial variations, and these variations can be exploited to measure the position of a transmitter with high axial accuracy. We separate these distributions into two groups: those with a single lobe and those with two lobes. Single-lobe distributions exhibit a rotational effect in the plane dependent on the Z-axis, a spiral effect. Thus, Stokes distributions, generated from linear polarization (ellipticity = 0°) and circular polarization (ellipticity = 45°), show variations as shown in the table below. Using a suitable algorithm, the distribution's orientation can be detected and the emitter's position deduced with high axial accuracy (Figure 7c). Distributions with two or more lobes exhibit a shift effect of the two lobes along the Z-axis. Thus, so-called shifted half-moon distributions, created from two elliptical polarizations oriented at 90° but with the same ellipticity, show variations as shown in the table below. Using a suitable algorithm, the emitter position can be deduced with high axial accuracy by measuring the intensity ratio between the lobes; this variation is illustrated in Figure 7d. Furthermore, some more complex elementary light distributions, consisting of more complex wave superpositions, exist with a strong longitudinal dependence; for example, the "three-dimensional dark spots" described by Zhang,

[29] , create a black spot surrounded in three dimensions by a luminous sphere. These "three-dimensional dark 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 be part of the invention. However, in certain implementations, the inventor has chosen 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. SRCDA Algorithm Multi-image system and reconstruction algorithms We will refer to the set of optical and optoelectronic systems as a multi-image system, in which a set of different and differentiated images, originating from the same two-dimensional or three-dimensional spatial region of the object, are recorded and analyzed using a suitable algorithm to analyze the spatial and / or spectral distribution of the emitting spatial region. This differentiation can be due to the projection of spatially different illuminations, as described previously; it can also be due to a variation in the spectral content of the illumination; or it can be due to natural or externally imposed movement of the objects.Finally, it can be due to a stochastic variation in 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 stochastic detection-based superresolution, including the PALM and STORM processes and their countless variants, each bearing a different acronym. Other means of differentiating images from the same emitting spatial region are known to those skilled in the art and are considered to be an integral part of this invention. We will refer to a multi-image system using the E-LSE reconstruction algorithm as a multi-image system including the E-LSE reconstruction algorithm described below. Modified MAP reconstruction algorithm This algorithm differs from existing algorithms in the literature known to those skilled in the art, by presenting the following mathematical characteristics whose combination is novel and differs from traditional MAP approaches: • Bayesian formulation • no prior assumptions about the reconstruction, except for positivity (unlike traditional MAP approaches, which generally incorporate a prior assumption of regularity on the reconstruction, such as total variation) • Modeling Poisson noise leads to a data attachment term that can be written in the form of a Csiszar divergence (a well-known result) • the posterior law is exploited by a MAP, that is to say that we seek the reconstruction of maximum probability (we must therefore solve numerically 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 (oversampling factor of the reconstruction relative to the resolution of the acquired images) • imposition of a "good sampling" constraint for reconstruction (the highest frequencies of the reconstruction spectrum are forced to 0) • introduction of a "pinhole" factor (digital confocal) E-LSE Reconstruction Algorithm The proposed algorithm allows, from the images recorded by the camera(s) following the excitation of the sample by the set of chosen illuminations, the reconstruction of a high-resolution, two-dimensional or three-dimensional image of the sample. This algorithm is based on the combination of several principles: the formulation of the reconstruction as an inverse Bayesian 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 may be superimposed the modeling of other noise sources, notably the camera read noise), as well as possible a priori assumptions (positivity, regularity, etc.) about the distribution of light in the sample; - The E-LSE algorithm uses the same Bayesian formulation as the modified MAP algorithm, described previously, but exploits the posterior distribution differently (more completely): indeed, it calculates the mean of the posterior distribution 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 total variation type prior [31,32]; the use of point clouds or simple geometry emitters, which allows us to favor sparsim solutions (samples with a limited number of emitters, or whose emitters are concentrated on small dimension structures such as curves, or surfaces in the three-dimensional case (we therefore calculate in fact the average of the a posteriori law with a sparsim prior on the solution); Using the mean of the posterior law (and not its maximum value point) allows for a low dependence on the number of emitters used: therefore, it is 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 mean using 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 prior of parsimony by using a restricted 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]. Fish noise In the standard embodiment, where only Poisson noise is modeled, the posterior probability distribution density function is written in the form p(x,Â) =|eE^ (EQ. 9) where Z is a normalization constant - and not the axis of light propagation - which does not appear in the algorithm, and \ ' li(EQ-io) "h(y)logl B + \ k E (x, 2) = XkUi (xkl y) - i,y The emitter cloud is represented here by the vector x=(xi,X2,...xn) (n discrete positions in the domain of the high-resolution image to be reconstructed) and the vector ^=(^1,^2,--^n) which encodes the intensities of the emitters located at points xi,X2,...xn. Each quantity of type ut(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 an illumination of index i (z therefore encodes here both the position of the illumination signal and its shape). The positive real number B corresponds to the intensity of the continuous background, which generally results from both the sample (diffuse fluorescence, for example) and the sensor. Finally, the quantities mt(y) simply correspond to the measurements (images recorded by the camera): nii(y) is the intensity measured at pixel y of the image with index i, that is, the image recorded after illumination with index z). The proposed algorithm consists of evolving the emitters represented by the vectors x and 2 according to the law given by the density p(x,X). The algorithm is iterative: at each iteration, one of the emitters is perturbed (in position or intensity), and this perturbation is accepted or rejected according to the principle of the Metropolis-Hastings algorithm [3]. The reconstructed image is obtained by averaging, with equal weight for each iteration, the emitters thus constructed. If Xj and 2j correspond respectively to the position and intensity of the emitters at iteration j of the algorithm, then the image I reconstructed after N iterations is given by (EQ. 11) Several improvements can be made to this algorithm: the introduction of a burn-in step (the first iterations are not used in the reconstruction), the optimization of the initialization of the emitters, the optimization of the perturbations made at each iteration (proposition 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 as an image or as numerical or graphical data. The same reconstruction algorithm can be used in a second version including a set of additional parameters describing global spatial region parameters 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, from the same spatial region of the object, two-dimensional or three-dimensional - are recorded and analyzed. Dynamic E-LSE Algorithm Furthermore, in a variant of this algorithm, the dynamic E-LSE algorithm, the speed of the emitters can be taken into account. When observing dynamic samples, the velocity of observed objects can be easily incorporated into the E-LSE algorithm, either individually for each emitter or by defining populations of emitters with different velocities. In the case of time-lapse imaging (i.e., successive observations of the same sample over time), this can be achieved naturally by forcing the simultaneous reconstruction of successive images from moving emitters parameterized by their initial position and velocity. When acquiring a single image, it is also possible to account for the dynamic nature of the scene through its impact on the returning PSF (motion blur), the distortion of which is correlated with multiple observations of the same emitter.The overlap of the different micro-images obtained during the scan means that the same emitter is used during the acquisition of several micro-images (at different times, due to the temporal component of the scan). ICE Algorithm The ICE algorithm was recently introduced for image denoising in the case of total variation regularization

[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 expected value of the posterior distribution performed by LSE with the iteration of the explicit calculation of the mean of the posterior distribution of a pixel conditional on its neighbors. However, the application of the ICE algorithm to inverse problems for a single image or for a multi-image system remains to be demonstrated. ♦ Calibration In many cases, SRCDA algorithms use as input measurements taken on the sample, but also data inherent to the system that are based either on values theoretical values, or values ​​obtained after a calibration step. In this step, measurements are taken on a reference sample to precisely measure the illumination functions and the Back Transfer Function (BSF) of the optical system. Specifics and advantages of the different SRCDA algorithms The various SRCDA algorithms, described above, offer the following differences and advantages compared to the state of the art: MAP modified: • Production of naturally well-sampled images thanks to the introduction of resolution gain and the forcing of the highest frequencies to 0 (limits "night sky" type artifacts) • good compromise between controlled algorithmic complexity (which allows acceptable computation times to be maintained) and good reconstruction quality (solving the inverse problem by non-linear optimization, more interesting than the use of linear methods of the "reassignment" type

[40] for example) E-LSE: • introduction of the parsimony hypothesis in a flexible form (low sensitivity to the number of emitters) • very high-quality reconstructions, especially for sparse samples • The method's ability to adapt to the amount of local information, and good management of reconstruction uncertainties (averaging phenomenon in case of multiple possible interpretations) • possibility of modeling sparsity differently according to prior assumptions about the observed sample (use of emitters of type point, segment, curve, surface, etc., exclusively or in combination) Compound Optical Process Algorithm The optical process composed according to at least one embodiment of the invention is a logical complement to the SRCDA algorithm. Indeed, the reconstruction obtained by the SRCDA algorithm can lead to the conclusion that an additional image would improve the measurement performance. The SRCDP microscopy platform allows the acquisition of one—or more—complementary images chosen from a set of light distributions from the PSIT or PDOS methods. Resolution, parsimony, topology of illumination, and positivity The ability to exceed 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 one of the inventors in reference

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

[38] and

[41] . However, in the case of a sparse scene (actual sample support significantly smaller than the imaged area, for example, in scenes composed of filaments and / or point sources), and in the absence of a very large continuous background (so that a positivity constraint on the reconstructed image is effective), it is beginning to be recognized that this limit of 2 is no longer valid and can be exceeded [42–44]. A clear 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 accuracy 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, based on the acquisition of several images of different topologies used in this method, one of the inventors

[37] demonstrated the ability to extend this absence of an intrinsic resolution limit, replaced by a resolution limit related to the signal-to-noise ratio, to the case of detecting two nearby points (Rayleigh criterion) and measuring their position. This demonstration can be extended, with simple modifications, to the case of three points not positioned on a straight line. This demonstration is repeated in a later section. This demonstration is based on a new position measurement mechanism, described in the next section, which is different from and complementary to the centroid method used in classical systems. In the case of multiple point sources, with uniform illumination, the maximum superresolution factor depends primarily, besides the signal-to-noise ratio, on scene properties: the number of sources (relative to the number of measurements), the minimum distance between two sources, etc. [43-44]. In the PSIT method, the maximum superresolution factor will depend, in addition to the factors described above, on the chosen illuminations. Position measurement of a point using the PSIT method The PSIT method can be used as a technique to measure the position of a nanoemitter with high accuracy, using a measurement mechanism different 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 in the sequence, A vortex image consisting of the sum of 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 uniquely measured by measuring a parameter, pa, equal to the normalized arctangent, by a factor of 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, • The normalized intensity emitted by the nanoemitter illuminated by the vortex wave varies from 0 at the center to 1 at the maximum of the vortex, reaching 0 for a value slightly greater than the Airy radius. The arctangent of the ratio is a monotonic 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, Ih, and the total intensity emitted by the nanoemitter illuminated by the second half-moon distribution, Ive. The ratio between these two intensities follows a square tangent geometric law: = tan2i9 (EQ. 12) 'v The two measurements are redundant. This redundancy is a measure that allows us to classify the observed object as a unique point and to separate this case from other objects potentially present in the sample. A direct application of the PSIT method according to one embodiment of the invention for measuring the position of a nanoemitter with high precision is the integration of this measurement technique into a novel local stochastic optical reconstruction technique. One of the limitations of the applicability of stochastic techniques is the measurement process, which requires 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 far exceeding the Airy disk, at rates reaching micro or nanoseconds, allows the extension of stochastic techniques to numerous new applications. The images resulting from the use of the PSIT method can also be processed using the generalized Hough method, allowing the recognition of structured objects, lines, circles 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 preceding 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 half-moons contains a degeneracy between 0 and -0, will measure the value 0. As mentioned previously, if the value of the descriptor p is not zero, we know that the case under study is not one point but two or more. Furthermore, the descriptors p and 0 allow us to measure the characteristics of two points at a resolution far exceeding that defined by the Rayleigh criterion. Moreover, using a compound process, it is possible to separate this case from the vast majority of cases involving three or more points. An additional light distribution can be projected onto the sample, a half-moon inclined at an angle of 0°; the hypothesis of the presence of two points will be confirmed or refuted depending on the results of this image. Indeed, the measured energy will only be zero for two points, for a line, or for a series of points aligned in the direction of the angle 0°. 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 disregard practical limitations, the resolution limit is related to the number of photons detected. The resolution of a system using PSIT and / or PDOS techniques is therefore, in practice, dependent on the sample being observed. For a sparsely labeled sample (i.e., 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 a factor of 2 (locally or even globally). Dark Tracking Conical diffraction could enable the application of a whole family of superresolution or superlocalization techniques, the localization of a single molecule. We now refer to Figure 8, which schematically illustrates an original technique we have named "Dark Tracking". Referring to Figure 8, 80 represents the initialization phase, i.e., 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 emitter; 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 fluorescence that can be detected; 83 represents the repositioning of the emitter to 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 tracked element to a corrected position. The light distributions used by this technique are vortices generated by cone diffraction. However, this technique can also use other vortices or other distributions generated by cone diffraction. We assume that the molecule of interest has been labeled with one or more fluorophores that can be excited at X-rays. The molecule's position is first detected by a conventional X-ray confocal image. The scanner position is then adjusted to stimulate the sample such that the center of the vortex coincides exactly with the position of the emitter. The fluorescence signal is detected by a highly sensitive camera (e.g., EMCCD or sCMOS), or PMT, which allows detection of the emitter's low-amplitude signal thanks to high quantum efficiency. The localization process relies on the absence of a fluorescent signal when the emitter is located exactly at the center of the vortex.The fact that the intensity gradient is significant near the center of the vortex allows for precise localization 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 recenters the vortex on the emitter and stores the emitter's position. The feedback loop can be executed at the camera's frame rate (up to 1 kHz) or the detector's frame rate (several MHz), enabling real-time tracking of a molecule over a considerable period. Because we always try to minimize the fluorescence signal by minimizing the signal exciting the emitter, localization can be performed over long periods, as bleaching is less likely to occur with such small doses of light.The accuracy of the localization depends strongly on the signal-to-noise ratio of the image; therefore, background noise (camera noise and autofluorescence signal) must be taken into account. Now, suppose the sample is labeled with two different fluorophores that can be excited at two different wavelengths, XI and X2. We propagate two beams with different topologies that depend on their wavelengths. The first (XI) has a classic Gaussian shape and provides an overall confocal image of the sample. The second (X2) is a vortex beam used for dark tracking. By controlling the galvanometer mirror that scans the sample, dark tracking can be performed each time a line for the camera image is scanned, so the emitter's position 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, uses a single scanning system and delivers extremely low power to the tracked molecules. In practice, the use, alignment, and shaping of these two beams is not a trivial task when using conventional beam-shaping techniques, such as computer-generated holograms, spatial modulators, or spiral waveplates, primarily due to their inherent chromaticity. Conical diffraction can be used to simplify the setup. Using matched optics, a crystal can be matched to generate a vortex at one wavelength and a Gaussian beam at another wavelength, both following the same optical path. This allows the use of a single optical path from a fiber, which solves many practical problems.Dark-tracking technology can be easily used to study many biological questions in which conventional techniques for tracking the position of a particle are penalized by particle bleaching. Dark tracking has been described above in the context of using a vortex. However, numerous variations, using one or more distributions—for example, but not limited to half-moons or Stokes vectors—any distribution possessing a zero intensity and a gradient—preferably the steepest possible—with respect to one of the spatial dimensions, can enable dark tracking and are considered part of this invention. The ability of conic diffraction to create many different light distributions makes it a tool of choice for dark tracking. Reference is now made to Figure 6b, which is a simplified schematic illustration of a modified LatSRCS optical module, achromatic or not, 700, according to an 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 upstream of the module: lasers, 79a, 79b and 79c, optionally at different wavelengths, optical fibers, 78a, 78b and 78c, originating from lasers 79a, 79b and 79c, Optionally, polarization control submodules, 77a, 77b, and 77c, can be used to statically or dynamically modify the polarization of the lasers, 79a, 79b, and 79c. These submodules can be positioned before or after the fiber. However, in some implementations, for example, using PM (polarization maintaining) fibers, the polarization control submodules 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" (in English), 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, enabling the transformation of the light from the fiber into collimated light that can be used by the rest of the LatSRCS module, 700, in a manner similar to that described previously. Numerous variations of this device, known to those skilled in the art, can be added to this scheme 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 output parameters of the common fiber are adequate. Similarly, the common fiber, 76b, may not be necessary for certain implementations. Furthermore, the introduction, through a common optical fiber or directly via light propagating through space, of two or more wavelengths with different polarizations makes it possible to create a method and / or device capable of performing 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 completely 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 entrance of the system to transform these polarizations into orthogonal circular polarizations 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, resulting in an incoherent superposition of the two orthogonal polarizations. Another solution is the use of a polarization submodule (not shown), consisting, for example, of a thick uniaxial crystal with strong birefringence. Furthermore, in the same-polarization integrative method, a polarization submodule (not shown) for intensity ratio control can be used. This intensity ratio control submodule is different from the previous polarization submodule but can potentially be integrated with it. It can also potentially be integrated into the laser combiner, 76a, positioned between the laser and the optical fiber.This current ratio control polarization submodule can be used to control the current 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). We now refer again to Figure 6b. The polarization control submodules, 77a, 77b, and 77c, can be actuated to simultaneously create identical or different sequences of light distributions for the excitation and depletion pathways. Furthermore, the intensity of the lasers can be modulated, creating a complex timing diagram of the intensity of each laser, the sequence of excitation light distributions, and the 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, the following is projected sequentially: • First, an Airy distribution or a fundamental frequency is excited simultaneously with a depletion vortex. The resulting emission image will be called the positive image, • In the second stage, an excitation vortex is created simultaneously with a depletion vortex. The resulting emission image will be called the negative image. In a variant of the first place, we project only an Airy distribution or an excitation fundamental. The difference image consists of the weighted subtraction of these two images. However, this difference image can be a more sophisticated digital processing than a simple arithmetic difference and can incorporate a set of mathematical processes known to those skilled in the art, allowing optimization of the resulting image based, for example, but not limited to, the frequency content of the two images. This difference image, if the right parameters are chosen, will have a smaller size—in terms of PSF—than a classic STED, while requiring only a lower depletion intensity. Indeed, the goal of vortex depletion will no longer be to reduce the size of an Airy disk, thus requiring significant energy, as in classic STED or RESOLFT, but to reduce the excess energy present in the excitation vortex relative to the Airy distribution or the fundamental frequency.Furthermore, the depletion of the Airy or fundamental spectrum will couple with the subtraction of the negative image created by the excitation vortex, 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. Furthermore, this implementation can, in some cases, eliminate the need to trigger excitation as required in "Gated STED." Indeed, photons arriving before the complete application of depletion can be accounted for by a suitable choice of parameters, without requiring the addition of a complex and restrictive system. Finally, the need to modulate the STED ("ModSTED") can also be avoided because the emitted photons from the depletion vortex are almost identical to those from 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 and a sequence of depletion beams are simultaneously projected. These two beam sequences can differ in their polarization, creating light distributions with different topologies. This setup allows for the creation of a sequence of light distributions smaller than those that would have been obtained without the depletion beam. The SRCDA algorithm will be used in this implementation to determine the spatial distribution or position of point emitters. This embodiment, combining depletion and the algorithm, should allow for a suitable 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, in the form of an Airy disk, and a depletion beam, in the form of a vortex, are simultaneously projected, the two beams differing in their polarization. This device allows, without dynamic elements, the realization of a completely achromatic STED device. Use of helical symmetry distribution for 3D STED The solution implemented in STED or STED-3D systems uses an optical distribution with zero intensity at the central point, and which remains zero along the axis for a certain distance. Here, we propose the use, for STED-3D, of a distribution with a zero-intensity position, this zero-intensity position exhibiting a helical spatial variation as a function of the axial parameter. The preferred implementation of this distribution is the use of conical diffraction employing the optical distributions we have referred to as the Stokes distribution. These distributions could be realized, in particular but not exclusively, using techniques based on the devices mentioned previously, including but not limited to SLMs (Spatial Light Modulators) and segmented mirrors, which allow the creation of phase and / or amplitude distributions in the pupil.The use of helical topology distributions to create a zero-intensity distribution with helical motion is deemed to be part of this invention. In particular, the implementation of these distributions using conic diffraction is a preferred implementation of this invention, but implementations of these distributions using an SLM or a segmented mirror to create phase or amplitude distributions in the pupil are also considered to be among the implementations described in this invention. In a new variant of this method, the dual-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 allows, with a single input beam, the independent creation of the two beams necessary for 3D STED, the vortex. and the black sphere. The ability to create both beams using a single input depletion beam significantly simplifies the optical system. Furthermore, since this system has a common path, it can be implemented easily. 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 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 submodule—has previously created, as described above, a path difference greater than the coherence length of the depletion laser for a CW laser, and / or the pulse time for a pulsed laser or for gated STED, creating an incoherent superposition of the two orthogonal polarizations. Under these conditions, the two distributions do not interfere; since the two distributions have orthogonal polarizations, they will create, on the same polarization, one a fundamental—which, by a choice of crystal and optical system parameters, 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 allows, with a single input beam before the fiber, the independent creation of the two beams necessary for 3D STED: the vortex and the black sphere. The ability to create both beams using a single input depletion beam greatly simplifies the optical system. Furthermore, since this system has a common path, it can be implemented simply. The difference between these two variants lies in the output polarization of the two distributions, the black sphere and the vortex, which are orthogonal in the dual-polarization integrative method and identical in the single-polarization integrative method, each variant having advantages for certain configurations. 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 (two-polarization and single-polarization), the conical diffraction element is replaced by a submodule consisting of two conical diffraction crystals with substantially equal conical diffraction parameter values, separated by a polarization submodule. The polarization submodule is chosen such that at the depletion wavelength, it has no effect, and the effects of the crystals are additive, creating the vortex and / or the black sphere. At the excitation wavelength, the polarization submodule creates a 90° or 180° rotation of the polarization, the effect of the two crystals is canceled out, and the transmitted beam is identical to the incident beam.This device avoids creating overly "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 parameter of . conical diffraction differs from that of the depletion beam. This variant can be implemented at various depletion and excitation wavelengths, utilizing 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 previously and potentially complementary to the two integrative methods (two-polarization and single-polarization), and also compatible with the previous implementation with reasonable modifications, the conical diffraction element is replaced by a cascade of crystals with different spectral properties, such as LBO and KTP (KTA), so as to allow the realization of black spheres at multiple depletion wavelengths. Indeed, the dispersion of the characteristic parameter of the conical diffraction effect, po, prevents the realization of certain multi-wavelength distributions, particularly the black sphere, whose shape is highly dependent on this parameter.Compensating for the dispersion of the characteristic parameter of the conical diffraction effect, po, thus enables the realization of a 3D common-path STED at two or more wavelengths. Furthermore, compensating for the dispersion of the characteristic parameter of the conical diffraction effect, po, can be achieved over a wide range of wavelengths either as described previously by a combination of crystals, or by spectrally correcting the optical system to the second order, 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 correct a dispersion compensation of the characteristic parameter of the conical diffraction effect, po, created by a combination of crystals described previously. In another embodiment, using a confocal microscope, an original or modified LatSRCS module, and a LongSRCS module, a sequence of excitation beams and a sequence of depletion beams are simultaneously projected. These two beam sequences can differ in their polarization, creating light distributions with different topologies. The LatSRCS module allows for the creation of a sequence of light distributions smaller than those that would have been obtained without the depletion beam. The LongSRCS module implements the PDOS method to separate, on different detectors, collimated light emerging from nanoemitters positioned at the focal plane of the objective, from uncollimated light emerging from nanoemitters located either within or beyond the focal plane.The PDOS method, in this implementation, allows the acquisition of essentially longitudinal information, that is, 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 position of point emitters. In another embodiment using one of the implementations described above and employing a biaxial crystal to create beam shaping, a dynamic polarizing element is used before or after the biaxial crystal to correct the dynamic pupil motion, which in some cases can be created during the optical scanning of the confocal microscope. This pupil motion effect is, in some implementations by STED technologists, one of the performance limitations, without requiring an additional scanning system.

[35] In another embodiment using a confocal microscope, two or more light distributions localized at different wavelengths are projected using an original or modified LatSRCS module.The first light distribution makes the scene sparse, meaning it isolates emitters using a physical effect that dilutes the density of emitters capable of fluorescence, creating regions where the sparseness hypothesis holds true—that is, the presence of a single emitter or a small number of emitters. The physical effects used to achieve this sparseness will be the same as, or derived from, those used to create sparseness in single-emitting microscopy techniques. These techniques include, for example, PALM STORM, DSTORM, FPALM, and others. The second light distribution, at a different wavelength, will create fluorescence with a time-varying intensity. This second light distribution will use one of the PSIT techniques, either a sequence of discrete distributions or a sequence of continuous distributions.In the case of discrete distributions, light will be detected either by a matrix detector or a single detector. In the case of a continuous distribution, although it is also possible to use a matrix detector, the most likely 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 from intensity ratios. One of the most interesting cases is that of time-harmonic distributions in which the electro-optical cells are driven by a sinusoidal voltage. In this case, the xy position can be determined by measuring the time harmonics of the signal measured by the detector, which may be a single detector, and which indirectly contain the lateral position information. Many other implementations of this general method will be clear to the person skilled in the art, for example: Some of the distributions created by the LatSRCS module, 700, are superoscillations. In Figure 7b, the cases shown in Figures 7boo and 7bn are superoscillations. They consist of a naturally small spot surrounded by a large, intense ring. By projecting a depletion ring onto this superoscillation, it is possible to prevent the fluorophores within the ring from emitting at a low energy cost, and the size of the spot will be that of the central spot of the superoscillation. The successive or simultaneous creation of two—or more—depleted light distributions can advantageously replace the depletion vortex in all RELSOFT or STED modalities. One possible effect is the improvement of the shape of the depleted light distribution by taking vector effects into account. It is also possible to create more than two so-called "half-moon" distributions to explore different polarization states. ALTERNATIVE IMPLEMENTATIONS The described embodiments of the invention can be integrated into a confocal fluorescence microscope. The super-resolution system according to these embodiments of the invention constitutes a new measurement method, either as a complement to or replacement for existing microscopy methods. However, the super-resolution system according to these embodiments of the invention can also be integrated into other microscopy platforms.These microscopy platforms, described for example, include but are not limited to: wide field microscopes, dark field microscopes, polarization microscopes, phase difference microscopes, contrast differential 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 instrument. In another embodiment, the microscope platform that 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 algorithm. 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 A more in-depth discussion of how to use and exploit the invention should be clear from the description above. Therefore, no discussion of the form of use and operation will be described here. In this regard, 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 construction details and component arrangement described below or illustrated in the drawing. The invention is capable of other embodiments and can be implemented and carried out in various ways. Furthermore, it is understood that the phraseology and terminology used in this document are for descriptive purposes only and should not be considered restrictive. The references cited herein teach many principles that are applicable to the present invention. Therefore, the entire content of these publications is incorporated herein by reference, where appropriate for additional or replacement details, features, and / or technical information. The advantageous use of optical fibers is the transmission of the fundamental mode, the TEMoo mode, and only that. However, certain optical fiber configurations, primarily but not exclusively based on so-called "Photonic Crystal Fibers," allow the simultaneous or separate transmission of more complex modes, including vortex modes. It would therefore be possible to relocate the optical distributions created by conic refraction using optical fibers, enabling a major simplification of the optical system. In addition, some fibers, the "dual-core photonic crystal fibers",

[16] , allow interaction between two modes, one of which may be a vortex, and provide an additional physical mechanism to create diverse transfer functions. Many superresolution techniques are based on measuring point sources smaller than a fraction of a wavelength. Superresolution techniques, according to the described embodiments, allow the measurement of not only point sources but also structured objects, for example, and primarily, line segments, circles, or even continuous objects. In biology, this extension will enable the measurement of important biological entities, such as filaments, neurons, and certain microtubules. Although the descriptions of embodiments, for the sake of simplifying understanding of the invention, present applications in Microscopy, more specifically in Biology, and even more specifically in Fluorescence Biology, the applications can be extended to general applications of Microscopy and to the whole 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 with micron-level resolution, the resolution being between 1 and 10 pm. Furthermore, embodiments of the invention can be applied, as explained later, through an optical fiber. This enables numerous applications. additional, 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 stated in the description contained herein or illustrated in the drawings. The invention is capable of other embodiments and can be carried out and performed in various ways. 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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 to be measured, external to the device, 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 for each of the compact light distributions of different topology and for each of the scanning points of the sample; 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, 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 a Bayesian inverse problem and leads to the definition of a posterior distribution, 2. A device according to claim 1 in which an a posteriori law combining, thanks to Bayes' law, the probabilistic formulation of a noise model, as well as possible a priori assumptions 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 distribution of light in the sample by the use of clouds of point emitters which makes it possible to favor parsimonious solutions; estimate the posterior mean, and represent the results, based on the posterior 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, in which the estimation of the a posteriori average is carried out by means of a Monte-Carlo Markov Chain (MCMC) type algorithm. 5 (Unregulated MAP) An optical measuring device for determining the spatial distribution or location of re-emitting sources on a sample to be measured, external to the device, 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 for each of the compact light distributions 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, an unregularized MAP algorithm module with positivity constraint, the representation of the results, based on the results of the MAP algorithm, either as an image or as numerical or graphical data 6 An optical measuring device for determining the spatial distribution or location of re-emitting sources on a sample according to claim 5, wherein the MAP algorithm further contains a frequency band-limiting constraint. 7 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 and 6, wherein the MAP algorithm uses an accelerated digital scheme of the Nesterov type 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 the frequency information, due to the different frequency characteristics of the different distributions projected onto the sample, to compensate for and greatly 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 of 5 to 8, 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. 10 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 9, in which 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 masks numerical and the non-local similarity tree being applied to the solution as a regularization. 11 An optical measuring device for determining the spatial distribution or location of re-emitting sources on a sample according to any one of claims 1 to 8, using a mask of variable size in the plane of the detector to obtain images having either different axial characteristics or different or optimized stray light rejection capabilities, globally or locally 12. An optical measuring 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 topology, optical scanning of the sample, 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 topology and for each of the scanning points of the sample; 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 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 a posteriori distribution, 13. A method according to claim 12 in which an a posteriori law combines, thanks to Bayes' law, the probabilistic formulation of a noise model, as well as possible a priori on a distribution of light created in the sample by projection.

14. A method according to claim 12 or 13 in which the algorithm comprises estimating the distribution of light in the sample by the use of clouds of point emitters which makes it possible to favor parsimonious solutions; and estimating the a posteriori mean, represent the results, based on the posterior mean, either as an image or as numerical or graphical data 15. An optical measuring method according to any one of claims 12 to 14, in which the estimation of the posterior mean is carried out by means of a Monte-Carlo Markov Chain (MCMC) type algorithm.

16. An optical measuring 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 topology, optical scanning of the sample, 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 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 non-regularized MAP algorithm with positivity constraint, the representation of the results, based on the results of the MAP algorithm, either as an image or as numerical 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 band-limiting constraint.

18. An optical measuring 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 an accelerated Nesterov-type digital scheme.

19. An optical measuring 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, the redundancy in the frequency information, due to the different frequency characteristics of the different distributions projected onto the sample, to compensate for and greatly reduce the impact of missing points or scanning irregularities. The MAP algorithm is suitable for solving 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 measuring method for determining the spatial distribution or location of re-emitting sources on a sample according to any one of claims 12 to 21, using a mask of variable size in the plane of the detector to obtain images having either different axial characteristics or different or optimized stray light rejection capabilities, globally or locally.

23. Computer program comprising program code instructions recorded on a computer-readable medium for implementing the steps of the method according to one of claims 12 to 15 or of the method according to one of claims 16 to 22, when said program operates on a computer.

Images