Method and system for characterizing microorganisms by digital holographic microscopy

Abstract

The invention relates to a method for characterizing microorganisms present in a biological sample, said method comprising acquiring a real-time holographic digital image of the sample, generating a focused image by using a digital model for reconstructing the focused image, and characterizing bacteria based on the focused image. According to the invention, a plurality of calibration objects are provided in the acquisition field of view prior to acquisition of the holographic image, these objects having pre-characterized dimensions and refractive indexes and selected shapes, such that the interference pattern of the objects can be calculated using an image forming model for integrating the optical aberrations of the acquisition device. The optical aberration is limited according to the interference pattern of the object and the calculated interference pattern before the computer generates the focused image, and a digital model used to reconstruct the focused image integrates the quantized optical aberration.

Description

Technical Field

[0001] The present invention relates to the field of in vitro diagnostics and more particularly to the characterization of microorganisms, in particular bacteria, yeast and fungi, by digital in-line holographic microscopy.

[0002] The invention is advantageously applicable for determining the Gram type of bacteria, for understanding their morphology or for understanding the metabolic state of microorganisms after application of antimicrobial agents. Background Art

[0003] Microorganisms in biological samples are usually observed by color optical microscopy using a focused Köhler-type incoherent light source.

[0004] However, several problems arise. For example, in the case of in vitro microbiological diagnostics, the objects to be imaged in the target surface are usually on the order of micrometers, which requires high magnification microscopic imaging and, again, a great deal of expertise to prepare the sample, acquire the image (select the target area, focus), and interpret the image (identify the object in the case of complex samples as described above).

[0005] Digital holographic microscopy or DHM is an imaging technique that allows to overcome the depth of field constraints of conventional optical microscopy by acquiring defocused images. Schematically, it consists in recording interference patterns, usually called "holograms", formed by the interference between the light waves diffracted by the observed object and a spatially coherent incident reference wave. DHM microscopy allows the computer reconstruction of the phase (does not allow focused microscopy), as well as the digital reconstruction of the image of the object observed in various planes parallel to the image sensor plane. Moreover, since the image acquisition is defocused, DHM microscopy does not require the use of precise and therefore expensive plates to move the optical system and / or the sample along the optical axis.

[0006] This technology is described in: a review article by Myung K. Kim entitled “Principles and techniques of digital holographic microscopy”, published in SPIE Reviews Vol. 1, N°1, January 2010; an article by N. Wu et al. entitled “Three-dimensional identification of microorganisms using a digital holographic microscope”, published in Computational and Mathematical Methods in Medicine, Vol. 2013, article N°ID 162105; an article by Ahmed El Mallahi entitled “Automated three-dimensional detection and classification of living organisms using digital holography microscopy with partial spatial coherent source: application to monitoring of drinking water resources”, published in Applied Optics, Vol. 52 N°1, January 2013; European patent application EP 3252455 and French patent application FR 3111998. Soulez,F.,Denis,L.,Fournier,C.,Thiebaut, and Goepfert, C., “Inverse-problem approach for particle digital holography: accurate location based on local optimization”, JOSA A24, 1164–1171 (2007) and Soulez, F., Denis, L., Thiébaut, Fournier, C. and Goepfert, C., entitled “Inverse problem approach in particle digital holography: out-of-field particle detection made possible”, JOSA A 24, 3708-3716 (2007), describe 3D reconstruction of observed objects resulting in interference patterns.

[0007] Although DHM microscopy simplifies the use of microscopes by acquiring defocused images of the microorganisms to be observed and the associated computational reconstruction capabilities, some issues still exist:

[0008] - Due to the nature of the samples being observed. In particular, biological samples from Gram staining spread on microscope slides observed using DHM are dense, heterogeneous, stained complex media containing microscopic objects (e.g., bacteria, yeast, fungi) that often have very low color contrast and need to be accurately detected and characterized for in vitro diagnostics;

[0009] - The images reconstructed by some standard digital methods (such as Rayleigh-Sommerfeld propagation) have artifacts, called twin images, which are the counterpart of the phase information gain. Other methods based on methods called inverse methods, as described in the aforementioned article by Soulez, F. et al., do not have these disadvantages, but require the ability to make assumptions about the structure of the imaged object, for example, its flatness or its regularity.

[0010] Regardless of which reconstruction method is considered, the reconstruction will also be degraded by the optical aberrations of the DHM imaging system, in particular geometric and chromatic aberrations. These aberrations add artifacts to the acquired image, which complicates the analysis and processing of an already complex acquired image. These artifacts also exist in the context of focused microscopy, but are particularly troublesome in the case of holographic microscopy, since it typically works out of focus, in regions where the objective is not always optimized and with variable defocus, aberrations can vary from one acquisition to another. Therefore, characterizing the aberrations a priori on a separate objective, as is often done in microscopy, runs the risk of being invalid for another image.

[0011] Correction of optical aberrations of DHM systems is proposed in Zheng, G., Ou, X., Horstmeyer, R., and Yang, C., “Characterization of spatially varying aberrations for wide field-of-view microscopy”, Opt. Express 21, 15131–15143 (2013). However, this correction is based on the assumption that there is a reference point in the image without aberrations, which is a strong and often wrong assumption, resulting in relative and non-absolute corrections (at the reference point). Summary of the invention

[0012] The object of the present invention is to propose a method and a system for characterizing microorganisms using DHM technology, correcting their aberrations.

[0013] To this end, the object of the present invention is a method for characterizing microorganisms present in a biological sample, comprising:

[0014] a. acquiring a digital holographic image by a defocused microscopic imaging acquisition device having a coherent light source or a partially coherent light source, the device being configured to form an interference pattern on a matrix image sensor between the light source and the light diffracted by the sample;

[0015] c. A computer generates a focused image by applying a digital model for reconstructing a focused image to the digital holographic image;

[0016] d. Characterizing the microorganism based on the focused image.

[0017] According to the present invention:

[0018] a. Acquiring the digital holographic image includes providing a plurality of calibration objects different from the microorganisms present in the biological sample in the field of view of the acquisition device corresponding to the image, wherein the objects

[0019] - previously characterized in terms of dimensionality and refractive index;

[0020] - having dimensions selected so as to produce an interference pattern on a matrix image sensor;

[0021] - having a shape selected so that the interference pattern can be calculated using an image formation model that incorporates the optical aberrations of the acquisition device;

[0022] b. Before the computer generates the focused image, the method comprises:

[0023] - identifying a calibration object in said digital holographic image;

[0024] - calculating the interference pattern of the calibration object by applying the image formation model;

[0025] - quantifying the optical aberration of the acquisition device based on the interference pattern of the calibration object in the holographic image and the calculated interference pattern;

[0026] c. The digital model used to reconstruct the focused image incorporates quantified optical aberrations.

[0027] The calculation of the aberrations is performed computationally using a reverse parametric approach using the solution of a problem according to the following relationship in order to obtain the aberration correction function p(x, y):

[0028]

[0029] in is the refocused image, is the distance z between the target surface (6) and the plane of the sensor (2) 6 The parametric propagator at is similar to the Lorenz-Mie model, and p(x, y) is the correction function of the aberration.

[0030] In other words, the present invention proposes a corrected propagation model or "propagation operator" for reconstructing a focused image of the aberrations of the system used to illuminate and acquire the image in the interference pattern. As is known, the propagation operators, such as the most famous Lorenz-Mie and Rayleigh-Sommerfeld propagation operators, are based on significantly simplifying assumptions, in particular the perfection of the light source (e.g. a perfectly coherent light source in the case of DHM), a defect-free acquisition system, or even a homogeneous wavefront propagation medium without any jumps in the refractive index. These assumptions are powerful ones, since they give rise to industrial applications such as DHM microscopy, due to the clear relationships arising therefrom, which can be handled computationally. However, their impact on the reconstruction of the focused image can be very significant in terms of the final performance. Instead of trying to work on assumptions in order to define new equations for the propagation operator itself, the present invention proposes, by means of adding calibration objects in the field of view of the DHM acquisition system, a computational correction function, which, when combined with the propagation operator, recreates to a certain extent the imperfect reality of the industrial application, with a significantly increased performance. These objects are used to characterize aberrations, particularly geometric aberrations. This characterization is achieved by adjusting the data of a "direct" image formation model on certain specific areas of the image, which integrates the features of the object (particularly position, size, refractive index and optionally shape) and the features of the optical system (particularly any geometric aberrations). Therefore, it is advantageous to use an object with a relatively simple available direct model, such as a sphere (bead) with a uniform refractive index with a Lorenz-Mie model. As will be described below, the use of a direct model allows the light scattering of the calibration object (e.g., Lorenz-Mie model), its interaction with the incident light beam, and aberrations to be combined in a single model. Once these aberrations are characterized, they are reintroduced into the model for forming the image of the observed microorganism, which ultimately allows the reconstruction of the image (including module and phase) in the corrected focus, and therefore allows the generation of a more refined reconstruction that is less affected by artifacts. Once the image is reconstructed in the corrected focus of the estimated aberration, it can be directly interpreted by a human operator, or interpreted by an automatic analysis method of the machine learning type.

[0031] Another object of the invention is a system for characterizing microorganisms present in a biological sample, the system being configured to implement the above method. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The invention will be better understood from a reading of the following description, which is given by way of example only, and from a reference to the accompanying drawings, in which:

[0033] - Figure 1is a schematic cross-sectional view of a digital holographic microscopy acquisition system;

[0034] - Figure 2 yes Figure 1 Schematic cross-sectional view of a Gram slide viewed in oil immersion configuration;

[0035] - Figure 3 is a flow chart of a method according to the present invention applied to detecting the Gram type of a microorganism present in a biological sample;

[0036] - Figure 4 The aberrations are shown Figure 1 the impact of the interference pattern produced by the system;

[0037] - Figure 5 Reconstructed amplitude (left column) and phase (right column) without aberration correction (upper row) and with aberration correction (bottom row) are shown;

[0038] - Figure 6 A focus reconstructed phase image without aberration correction (left image) and a focus reconstructed phase image with aberration correction (right image) are shown. DETAILED DESCRIPTION

[0039] Methods and systems according to the present invention for determining the Gram type of bacteria present in a biological sample collected from a patient will now be described.

[0040] Figure 1An imaging system is schematically shown, in this case a coaxial holographic imaging system for imaging a sample 1 by means of a digital image sensor 2, which is placed in the image plane of the holographic imaging system. The imaging system is called a holographic imaging system because it is capable of acquiring holographic images, but the same imaging system can also acquire non-holographic images. An optical axis 5, called the z-axis, connects the sample 1 and the image sensor 2. In this case, the optical axis 5 is shown as straight, but can be more complex, depending on the configuration. The light source 4 is configured to illuminate the sample 1 in the field of view of the holographic imaging system with the aid of an illumination beam that is sufficiently coherent to acquire a hologram, i.e. a coherent or partially coherent illumination beam. The illumination light has the conventional characteristics required for holographic imaging without particular additional constraints. Thus, the illumination light can be monochromatic (e.g., having a wavelength of approximately 637.2 nm), or can consist of a plurality of wavelengths, for example, used one after another. The imaging system can include a set of optical components 8 on the optical path between the sample 1 and the image sensor 2. In the example shown, the holographic imaging system is provided with a microscope objective 8a and a tube lens 8b, which are arranged between the sample 1 and the digital image sensor 2. However, optical components such as the microscope objective 8a are optional, and the present invention is not limited to a holographic microscope with a lens or a specific set of optical components. Of course, the arrangement described herein is a non-limiting example. Any holographic imaging system can be used, whether it is coaxial or not, with or without a microscope objective, etc. In fact, the method relies on the use of a holographic image collected by an imaging system. Therefore, as long as the imaging system is able to collect a holographic image in which an interference pattern appears, the imaging system is suitable for implementing the method. The imaging system also includes an automatic data processing system not shown, which includes at least one processor, a memory, and is configured to receive at least one holographic image from the image sensor 2 and process the holographic image according to the method of the present invention. It is worth noting that a computerized system, such as a personal computer, includes a permanent computer memory that stores a set of computer-readable instructions for implementing the calculation steps described below.

[0041] refer to Figure 2, the sample 1 comprises a target surface 6 to be imaged. In the simplest case, the target surface 6 can be flat, or it can be curved. The target surface 6 can extend in a plane perpendicular to the optical axis 5, or can even have an inclination (usually referred to as "tilt") relative to the plane perpendicular to the optical axis 5. The position of the target surface 6 represents the spatial arrangement of the target surface 6 in the imaging system, including its position and its possible tilt. The target surface 6 can be a part of the sample 1, in particular when the sample 1 is a three-dimensional object with a certain volume, which contains multiple surfaces or layers at multiple positions on the optical axis 5. More generally, the target surface 6 corresponds to the position of the part of the sample 1 to be imaged. Typically, the sample 1 is placed on a support 12, such as a microscope slide, and the target surface 6 can advantageously correspond to the interface 12a between the support 12 and the sample 1, or even to a surface parallel to the interface 12a, as in the example shown, or at least its position can be inferred from the position of the interface 12a between the support 12 and the sample 1. It should be noted that the choice of the target surface 6 may benefit from some prior knowledge about the sample 1 and what is to be observed therein, for example the size of the microorganisms 15, in particular bacteria 15', present in the sample 1 and possibly resting on the support 12. By convention, a (O, x, y, z) coordinate system is defined, where for the orthogonal axes (x, y) in said surface 6, the intersection of the optical axis 5 and the target surface 6 is the origin, and where the z-axis is equal to the optical axis 5 and is oriented towards the sensor 2.

[0042] The sample 1 comprises at least one calibration object 10, which is located at a position corresponding to the position of the target surface 6. The calibration object 10 assumes a known shape, which can be described by geometric parameters and a refractive index. Preferably, the sample 1 contains a plurality of calibration objects 10, at least 3 reference objects 10, and more preferably at least 5 calibration objects 10. If the sample 1 may contain a plurality of calibration objects 10, it is generally not necessary for more than 100 calibration objects 10 to appear in the acquired image. More specifically, the number of calibration objects depends on the spatial accuracy required for mapping the aberrations.

[0043] The characterization parameters associated with the calibration objects 10 include at least position parameters, typically position coordinates, for individually positioning each calibration object 10. "The position of the reference object 10" is understood to mean the spatial arrangement of the reference object 10 in the imaging system, including its position and its possible tilt. Preferably, the characterization parameters associated with the calibration object 10 also include geometric parameters describing the known shape of the calibration object 10. The geometric parameters correspond to the prior knowledge of the geometric shape of the calibration object 10. In this regard, the calibration object 10 has a simple geometric shape, and preferably, the calibration object 10 has a spherical, cylindrical or ellipsoidal shape so that a "parameterized" 3D reconstruction method can be used, as will be described below. In the case of a calibration object 10 with a spherical shape, the geometric parameters can be simply formed by the radius r of a sphere modeled on the calibration object 10, and the position coordinates correspond to the center position of the sphere. More generally, these parameters are the parameters considered by the light diffraction model to be used (e.g., Mie model, generalized Mie model, Thompson model or Rayleigh model). Therefore, for a calibration object 10 that is generally spherical, the Mie light diffraction model (or the Lorenz-Mie solution) requires only the radius of the sphere as a geometric parameter. In the case where the calibration object 10 is generally cylindrical, the radius and the length are the only geometric parameters needed to describe the shape. Therefore, it is not necessary to know all the geometric parameters of the calibration object 10, but only those that correspond to the approximate shape of the calibration object 10 and are used by the light diffraction model.

[0044] The size of the calibration object 10 can be chosen within a wide range and can, for example, have a diameter (largest dimension) ranging from 10 nm to 100 μm. The choice of the size of the calibration object 10 is more constrained by secondary aspects. On the one hand, the size of the calibration object 10 must allow sufficient contrast to be generated, taking into account the wavelength of the illumination light, the difference in refractive index with the medium surrounding the calibration object 10, or even the contrast generated by other objects in the holographic image. Therefore, the diameter of the calibration object 10 is preferably greater than 10 nm, and more preferably greater than 100 nm. On the other hand, the projection surface of the calibration object 10 on the image sensor 2 must not be too large, so as not to change the quality of the holographic image. Usually, a projection surface of less than 10% (more preferably less than 1%) will allow a good holographic image quality to be provided, in addition, if the rest of the sample 1 is not too dense. In addition, the calibration object 10 must not hide the rest of the sample 1, in particular the target surface 6. Therefore, the size of the calibration object 10 is chosen not to occupy too much space in the field of view of the image sensor 2. In this regard, the calibration objects 10 are preferably located far apart from one another and not adjacent to one another, and are preferably sparsely distributed over the entire field of view of the image sensor 2 .

[0045] Like any material, the calibration object 10 has a refractive index. As long as the calibration object 10 is different from the rest of the sample 1, its refractive index will differ from the medium surrounding it, even if only very slightly. Therefore, a difference of 0.01 between the refractive index of the calibration object 10 and the refractive index of the medium surrounding the calibration object 10 allows its influence on the light diffraction to be identified in the acquired images and therefore allows the method to be implemented. However, preferably, the refractive index of the reference object 10 differs from the refractive index of the part of the sample 1 immediately adjacent to the calibration object 10 by at least 0.05, more preferably by at least 0.1. The refractive index of the calibration object 10 is preferably known and is input into the light diffraction model. In particular, in the case where the calibration object 10 is opaque, i.e., the complex component of its refractive index can be considered to tend to infinity at the wavelength considered, the light diffraction model can be modified accordingly so as to limit the number of parameters to be adjusted, thereby reducing the calculation time and avoiding any over-adjustment. In the case of a transparent or partially transparent calibration object 10, the refractive index of the calibration object 10 may also be unknown or imprecisely known and may be estimated using a diffraction model in the same way as the geometrical or positional parameters associated with the calibration object 10, thereby forming part of the characterization parameters associated with the calibration object 10.

[0046] refer to Figure 2 When the acquisition system 8 comprises an immersion microscope, the sample 1 may comprise an immersion medium 14 , in particular glycerol, and the light diffraction pattern may be related to the refractive index of the immersion medium 14 .

[0047] Apart from the fact that the calibration object 10 must have a known shape described by the characterization parameters associated therewith, or even must be very small relative to the wavelength of the illumination light, there are limited constraints on the choice of the calibration object 10. The reference object 10 can be opaque or transparent and can be formed from various materials, such as silica, polystyrene or metals such as gold. In view of the above considerations, the calibration object 10 can be an artificial object added to the sample 1. The advantage of adding an artificial calibration object lies mainly in the precise knowledge of its geometrical parameters and refractive index, as well as the regularity of its shape. In the case where artificial calibration objects 10 are added to the sample 1, these objects are chosen to have simple and regular shapes, preferably cylindrical or ellipsoidal, more preferably spherical, so as to allow the best match between the actual shape of the calibration object 10 and its roughly estimated shape described by the characterization parameters taken into account by the diffraction model. For example, in Figure 2 In the case shown, the calibration object 10 is an opaque polystyrene bead with a diameter of 1 μm.

[0048] The calibration object 10 may also be present on a support 12 of the sample 1, forming part of the support 12 at its interface with the sample 1. For example, the surface 12a of the support 12 may be etched, for example by photolithography, so as to reveal a shape therein, preferably circular, which may meet the requirements of a calibration object (e.g. a circular rib).

[0049] As described above, the calibration objects 10 are located at positions that match the position of the target surface 6, i.e. there is a matching relationship between the position of the target surface 6 and the position of each calibration object 10. For example, the density of the objects 10 is chosen so that they are deposited on the support 12. When these objects are calibration beads, the target surface 6 to be imaged is defined by a plane passing through the center of the objects 10. It should be noted that the present invention can also be implemented for calibration objects suspended in the medium 14.

[0050] While some configurations do not cause any problems, such as when the target surface 6 coincides with the surface of the support 12 on which the calibration object 10 is formed, other configurations may sometimes require precautions to be taken in order to ensure a match between the position of the calibration object 10 and the target surface 6. When the target surface 6 coincides with the surface 12a of the support 12, or is connected to the surface 12a of the support 12, for example, by a parallel relationship, the calibration object 10 can be deposited directly on the surface 12a of the support 12 before the rest of the sample 1 is mounted on the support 12. Therefore, the fluid immersion medium 14 (e.g., water) containing the suspended calibration object 10 can be pre-deposited on the surface 12a of the support 12 before the rest of the sample 1 is mounted.

[0051] Once the sample 1 has been mounted, it is illuminated 17 and the image sensor 2 captures at least one two-dimensional holographic image. It may be a single image captured or a series of images, in particular a series of holographic images captured for different positions of the capture plane 2' relative to the sample 1 along the optical axis 5 and / or with different wavelengths of illumination light.

[0052] These different positions of the acquisition plane 2 ′ relative to the sample 1 may be obtained by different positions of the sample 1 relative to the image sensor 2 along the optical axis 5 , for example by moving the image sensor 2 , for example by means of a motorized track or a motorized plate.

[0053] In the same way as any type of holographic imaging system that can be used as described above, various holographic image acquisition techniques can be used, as long as the acquired image reveals the optical effects of the presence of the reference object 10 in the field of view of the digital image sensor 2, in particular the interference pattern generated by the interference between the illumination light and the light scattered by the reference object 10, which appears in the holographic image as the interference pattern caused by the reference object. However, it goes without saying that the image is acquired with the holographic imaging system in a configuration suitable for imaging the calibration objects 10 (or more precisely, the interference patterns caused by them), and therefore with appropriate adjustments (illumination, etc.) that are common to a person skilled in the art.

[0054] Now refer to Figure 3 An example of a method according to the invention for determining the Gram type of microorganisms, in particular bacteria, present in a biological sample is described.

[0055] The method for determining the Gram type of bacteria starts with sampling a biological sample suspected of containing microorganisms, in particular bacteria, yeast or fungi, at step 20. The sample can be any type of sample, such as a sample collected from a patient or an animal, a sample collected from cosmetics or food, or an environmental sample (water, soil, air, etc.).

[0056] Then, in step 21, beads are added to this sample in liquid form, said beads serving as calibration objects for correcting any geometrical aberrations affecting the formation of the interference pattern acquired by the DHM acquisition system 8. In order to properly perform this correction, said sample is advantageously a stable colloidal suspension to avoid aggregation of said beads before depositing the biological sample onto a microscope slide. Advantageously:

[0057] i. The size and refractive index of the beads are also selected to have limited variation, preferably less than 50%. As described below, this limitation allows efficient automatic identification of beads in acquired DHM images and therefore allows full automation of the method according to the invention.

[0058] ii. The beads must not be too similar to objects expected in the sample, to reduce the risk of confusing them with such objects. In particular, as often happens in microbiology, where there may be quasi-spherical biological objects (e.g., shells) of comparable size to the beads, the refractive index of the beads and that of the microorganisms differ greatly, which can be achieved, for example, by the choice of bead material (e.g., metal), or by staining of the microorganisms (complex component of non-zero refractive index in certain wavelengths).

[0059] iii. The bead is large enough to scatter the incident light sufficiently (according to Rayleigh's law, very small particles do not scatter much light, according to the 1 / r^4 law) so as to form a sufficiently contrasting interference pattern on the plane of the sensor 2. In addition, it must be small enough to allow scattering over a wide enough angle (according to Mie's law) and avoid occupying too much of the field of view. In practice, beads from tens of nanometers to tens of micrometers are suitable in this region, with beads from hundreds of nanometers to a few micrometers being preferred.

[0060] iv. The surface concentration of beads deposited on the microscope slide is derived from the deposition volume, the initial concentration of beads and their possible aggregation state, and is carefully chosen. If the surface concentration of beads after deposition is too low, there is a risk that there will not be any beads in the field of view or not enough to produce a correct map. On the contrary, if the surface concentration of beads is too high, they will scatter the incident light too much, reduce the signal-to-noise ratio of the object of interest, and introduce artifacts in the reconstruction. In practice, an average of 3 to 300 beads per field of view is the operating area, preferably 5 to 30 beads, as described below.

[0061] v. The shape of the calibration object must allow a straightforward implementation of the light scattering model. Since the beads are spherical, this involves a relatively simple case where the Lorenz-Mie model applies, but other scattering models exist for more complex objects if necessary, such as those described in Gouesbet, G. and Mees, L., "Generalized Lorenz–Mie theory for infinitely long elliptical cylinders", JOSA A 16, 1333–1341 (1999).

[0062] The method continues with making a Gram-stained slide in a manner known per se in step 22. Once the sample is dried, glycerol is added to a microscope slide, the microscope is immersed in the glycerol, and in step 23 one or more DHM images are acquired.

[0063] Then, in a step 24 , the acquired DHM image is advantageously cut into a plurality of sub-images or “blocks” in order to obtain a correction for the aberrations of the acquisition system 8 , which are variable in its field of view.

[0064] In step 25, the method continues by reconstructing a focused image of the beads 10 using a non-aberration-corrected propagation operator to approximately characterize the positions and geometrical features of the beads 10 in each block, as well as the refractive index. The main purpose of this optional step is to approximately characterize the search space described below, in particular to identify the region where the desired local optimum is located, in order to speed up the calculation time. Therefore, this step allows the method according to the invention to be implemented in a (quasi) real-time manner and / or using limited computing resources. If the method according to the invention uses a large amount of computing resources, such as a network architecture consisting of a sufficient number of computing nodes for the target computing time, a priori assumptions about the search space can be determined and step 25 can be omitted.

[0065] Step 25 is advantageously based on a parametric method for reconstructing the beads, which can be achieved by choosing the geometry of the calibration object. The reconstruction uses a Lorenz-Mie propagation operator, such as that described in the article by Slimani, Farid et al. entitled "Near-field Lorenz-Mie theory and its application to microholography", Applied Optics (1984). In a first iteration, an optimization problem is implemented according to the following relationship:

[0066]

[0067] In this relationship:

[0068] v=(xyzrn) characterizes the position (x, y, z) in a coordinate system whose origin is equal to the intersection between the optical axis 5 and the plane of the sensor 2, r is the radius of the beads and n is their refractive index;

[0069] -m Mie (v) is the Lorenz-Mie model applied to beads;

[0070] -d is the intensity image of the considered block;

[0071] -||.|| 2，W is the least squares norm weighted by the inverse of the noise covariance matrix. This noise can be characterized a priori to improve the performance of the detection (e.g., sensor noise, dead pixels, etc.). By default, the noise is considered to be uniform and equal to Gaussian white noise;

[0072] - D is a search domain advantageously restricted to the characteristics of the calibration beads. It is worth noting that the variables r and n of the search space are restricted to the space [r0-Δr; r0+Δr]×[n0-Δn; n0+Δn], where r0 and n0 are nominal values ​​of the radius and refractive index of the beads, respectively, and Δr and Δn are their scattering, respectively, these data being provided, for example, by the bead manufacturer. Preferably, the refractive index of the beads, and more generally of the calibration objects, is known with an uncertainty Δn of ±2%. In a first iteration, the spatial search space (x,y,z) is restricted to the field of view of the acquisition system corresponding to the block under consideration and to the approximate depth z corresponding to sample 1.

[0073] Since the model is translation invariant in (x, y), solving this problem involves finding the maximum correlation between the model and the data in the plane (x, y) for each subset of parameters (z, r, n). To solve the problem efficiently according to relation 1, the LINCOA algorithm described in J. Nocedal and S. Wright, "Numerical optimization", Springer Science & Business Media, 2006 is preferred.

[0074] At the completion of this first iteration, if the residual is below a predetermined threshold, for example, quantized by the least squares norm, then at position (x t y t z t ) Identify the feature v t The first bead has a radius of r t , the refractive index is n t . By selecting beads with a refractive index different from the expected objects in the biological sample, the optimization problem (1) allows the beads to be identified from other objects. At the completion of this first iteration, the interference pattern corresponding to the identified beads is subtracted from the block and then a new optimization problem is implemented according to the relationship (1) to eliminate the block from the interference pattern. This iterative process continues as long as new beads are detected. Once the process has stopped for the block, step 25 is performed for the next block until all blocks are covered. For the approximate detection of beads, see also Soulez, F., Denis, L., Fournier, C., Thiébaut, and Goepfert, C., “Inverse-problem approach for particle digital holography: accurate location based on local optimization”, JOSA A 24, 1164–1171 (2007).

[0075] After performing step 25, a rough estimate of their position, radius and refractive index parameters is thus obtained.

[0076] The method according to the invention continues for each block by calculating 26 the aberrations affecting the interference pattern of the beads.

[0077] As is well known, reconstructing a focused image of the target surface 6 involves finding the transmission function of that surface corresponding to the local minimum of the following optimization problem:

[0078]

[0079]

[0080] where * is the convolution, and is the distance z between the target surface 6 and the plane of the sensor 2 6 A propagation operator is selected according to the intended application. As mentioned above, the prior art propagation operator does not take into account aberrations of any nature that affect the interference pattern recorded by the sensor 2.

[0081] According to a preferred embodiment, the present invention proposes:

[0082] 1. Use the propagation operator according to the following relationship Modification of the propagation operator according to the prior art

[0083]

[0084] Where p(x, y) is a function that quantifies the geometric aberration of the interference pattern in the plane of the sensor 2, hereinafter referred to as the "aberration function".

[0085] 2. Describe the function p(x,y) in the frequency basis selected according to the DHM acquisition system, such that:

[0086]

[0087] in is the Fourier transform, K x and K y is the frequency coordinate in the Fourier domain, b={b i (K x , K y )} i is an element of the frequency basis, α={α i} i is a function Coordinates in basis b. Advantageously, as will be described below, basis b is a Zernike polynomial The basis of , which is particularly suitable for capturing the geometric aberrations of an invariant optical system in the frequency domain as a first approximation around the optical axis. Such a polynomial is described, for example, in Zheng, G., Ou, X., Horstmeyer, R. and Yang, C., “Characterization of spatially varying aberrations for wide field-of-view microscopy”, Opt. Express 21, 15131–15143 (2013). Other polynomials are also possible, such as Legendre polynomials.

[0088] 3. Using parameter propagation operator Calculation Function The coordinates of {α i} i and the vector v = (xyzrn) of the calibration beads, which has the main advantage of providing a search in the space of solutions that converges without having to regularize the optimization problem, e.g., Legendre polynomials or Lorenz-Mie propagation operators applied to the beads. It is worth noting that the holographic image formation model (e.g., Lorenz-Mie model) is adjusted with respect to the data of each bead, convolved with the aberration model p(x, y), and the parameters to be adjusted are the parameters (xyzrn) and {α i} i .

[0089] More specifically, step 26 implements an optimization problem for each block and each bead detected in the block according to the following relationship:

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] n∈N and m∈Z verify n≥|m| and n-|m|∈2N

[0096] In this relationship:

[0097] -⊙ is the Hadamard product

[0098] - is the Lorenz-Mie model applied to beads;

[0099] - NA is the numerical aperture of the acquisition system 8 and λ is the wavelength of the illumination;

[0100] - is the inverse Fourier transform;

[0101] - D is the search space of vectors v = (xyzrn) of the beads under consideration. This search space is advantageously determined by the result of step 25, for example, Δv t / v t v < 0,1 t ±Δv t Preferably, the refractive index of the bead, more generally the refractive index of the calibration object, is known with an uncertainty Δn of ±2%;

[0102] -C is a Zernike polynomial basis Central coordinates The inventors conducted research and found that for Figure 1 The DHM acquisition system shown, coefficient The range of is between -10 and 10, and C is preferably restricted to the corresponding hypercube.

[0103] The inventors have observed that the function P(K x ,K y ,α) is exactly determined by the first 15 Zernike polynomials, so the vector The coefficients can also be set to 0, since the model is phase shift invariant. In addition, the coefficient It can also be set to 0 in order to maintain the point spread function (or PSF), which describes the response of the optical system 8 to a laterally centered point source of light. Therefore, the following optimization problem contains 12 adjustable parameters for an aberration model that takes into account various geometric aberrations: oblique astigmatism, horizontal and vertical coma, spherical aberration and secondary oblique astigmatism. The 5 parameters of the bead scattering model (3 spatial parameters, radius and refractive index) are added to these 12 parameters. Preferably, according to the relationship (6-9), the problem is solved by the LINCOA algorithm or other optimization algorithms, such as the algorithm described by MJD Powell in "On fast trust region methods for quadritic models with linear constraints", Report of the Department of Applied Mathematics and Theoretical Physics, Cambridge University, DAMTP 2014 / NA02 (2014).

[0104] Thus, upon completion of step 26, an aberration function p(x,y) is obtained for each position of the interference pattern corresponding to the calibration bead. In a first variant, one function is retained per block, for example by averaging the functions p(x,y) in that block. In a second variant, an overall function p(x,y) for the entire field of view is determined by interpolating the functions p(x,y) calculated over all blocks.

[0105] The method continues by reconstructing, in step 27, a refocused image based on the DHM image acquired with the aid of a reconstruction model incorporating the modeled geometric aberrations. As far as determining the Gram type of the microorganisms is concerned, the microorganisms are unknown at this stage. Thus, they may assume different forms (e.g. shell-like or rod-like), different sizes, or may even form aggregates or catenaries. Furthermore, the sample may include various objects (e.g. red blood cells). Therefore, no assumptions are made about the content of the sample in order to use non-parametric propagation operators, such as the Rayleigh-Sommerfeld propagation operator The reconstruction of the destination surface 6 is obtained by solving the problem according to the following relationship:

[0106]

[0107]

[0108]

[0109]

[0110] In this relationship:

[0111] -μ is a predetermined scalar, or even the problem is solved for each of the predetermined scalars according to the above relationship

[0112] The values ​​are resolved;

[0113] - is a regularization term that ensures convergence of the optimization problem and is preferably chosen as a function of a priori information about the desired reconstructed image, e.g., in the case of a typically low-contrast Gram slide, the transmission function The norm L1 or total variation of the gradient, as described in the article entitled “Regularized reconstruction of absorbing and phase object from a single in-line hologram, application to fluid mechanics and micro-biology” by F. Jolivet et al., Opt. Express 26, 2018;

[0114] The distance z is set to the average of the distances z calculated for the beads in step 26 , or even a plurality of distances z is selected in order to obtain a stack of focused images and thus a plurality of surfaces of interest 6 .

[0115] Preferably, the problem is solved according to the relationship (10-13) by, for example, the LINCOA algorithm or the Powell algorithm.

[0116] The method continues, in step 28, by analyzing the one or more reconstructed focused images in order to identify the microorganisms they contain and their Gram type. This analysis is performed in a manner known per se, for example by analyzing a screen displaying the one or more reconstructed focused images by a laboratory technician specialized in Gram typing, or by using a machine learning automatic characterization computer tool. Determining the Gram type then allows the adaptation of the antibiological therapy in the case of a patient suspected of being infected with a pathogenic bacterium, or more generally, of the antimicrobial therapy. Determining the Gram type also allows the orientation of the microbiological analysis workflow, for example, the selection of a culture medium for the subsequent identification of the microorganisms present in the sample, the selection of a chart for the use of a 2 Platforms to create antimicrobial profiles, or even select media for use with the MS or The identification was performed using the MS PRIME platform.

[0117] Figure 4 Shown by Figure 1Figure 2. Effects of aberrations introduced by the system described in Figure 2. The left column shows a system with limited aberration levels and the right column shows a system with significant aberration levels. It can be seen that the interference pattern, in this case that associated with the calibration beads, is significantly affected both in the plane of the sensor and in their position along the optical axis. Figure 5 5(a) and 5(b) show the reconstructed amplitude and phase, respectively, of a portion of a Gram slide that has not been corrected for aberrations according to the present invention. Figure 5 (c) and 5(d) show the same portion of a Gram slide with aberration correction according to the present invention applied. Figure 6 shows no aberration correction ( Figure 6 (a)) and with aberration correction ( Figure 6 (b)) The focused overall reconstructed image.

[0118] Extension of the teaching of the detailed embodiment

[0119] Embodiments of the invention applied to determining the Gram type of a microorganism have been described. The invention is applicable to any type of characterization of a microorganism using digital on-axis holography, for example, determining the sensitivity of a microorganism to an antimicrobial agent, as described in application WO 2017 / 207184.

[0120] More generally, the invention is applicable to any type of characterization, whatever the nature of the sample and whether it is biological or not, as long as the aim is to correct for aberrations that affect the formation of the interference pattern acquired by the DHM system.

[0121] The use of beads for calibration has been described. Any type of object that can be parametrically reconstructed by the inverse method is suitable: cylinders, ellipsoids, etc.

[0122] A direct immersion microscope without a lamella and without a correction collar has been described. Samples covered with a microscope slide are suitable, wherein the microscope is equipped with a collar for correcting the thickness of the lamella.

[0123] Extension of the teachings of the detailed embodiments to multiple wavelengths

[0124] The use of a single wavelength has been described. Multiple wavelengths can also be used to characterize samples.

[0125] The simplest way to solve this problem is to repeat the method of correcting the aberration independently for each wavelength. Thus, for each wavelength λ in the set of wavelengths Δ that require aberration correction, a function p(x,y) that quantifies the aberration and a transmission function are obtained: For wavelength λ, these functions will be denoted below as p λ (x,y) and An effective correction of chromatic aberration is thus obtained.

[0126] In addition to this independent treatment, and advantageously, by benefiting from the physical point of view that some features of the object, in particular position and geometry, are invariant with respect to wavelength, chromatic aberration can be corrected over multiple wavelengths. This can be achieved in accordance with two methods of the invention, which can be used alone or in combination:

[0127] 1. First, set one of the wavelengths as the reference (hereinafter referred to as λ ref ), and execute steps 25 and 26 of the method. Thus, the function of quantizing the aberration is obtained and the characteristics of the calibration objects, in particular their position and their geometrical characteristics (e.g., the radius r of a spherical bead). Then, for each other wavelength, steps 25 to 26 are performed again, but (i) the position and geometrical parameters are no longer adjustable and are set equal to the value obtained by λ ref Those obtained, (ii) the Zernike coefficients and is now an adjustable parameter and does not have to be zero. Therefore, the facts to be taken into account are: (i) the calibration object is assumed to be immovable and geometrically invariant between the two wavelengths, and (ii) if the system has chromatic aberrations, their images can be shifted between one wavelength and another. Therefore, the chromatic aberrations of the system are characterized. Step 27 can then be performed independently for all wavelengths or according to another method as described above. Finally, it should be noted that, by a variant of the method, more than one wavelength can be set as a reference, which can allow a more precise adjustment of the position and geometric parameters of the calibration object (for example, by averaging between the parameters obtained at different reference wavelengths).

[0128] 2. It is expected that once the chromatic aberration is corrected (e.g., independently for each wavelength, or corrected according to the method described in 1), the position of the object in the transmission plane is invariant across wavelengths. Advantageously, by defining a regularization term shared across wavelengths This can be reflected in the various problems according to relations (10)-(13), thereby providing that the object has the same position in the transmission plane for all wavelengths used. A more accurate aberration correction is thus obtained. Advantageously, the regularization term common to the various corrections is a term that promotes the co-location of the edges of the transmission function for multiple wavelengths according to the following relation:

[0129]

[0130] In this relationship:

[0131] - Λ is the set of wavelengths used;

[0132] - x and y are the coordinates of the pixel in the transmission function;

[0133] - is the sign of the gradient;

[0134] - is the real part of the function;

[0135] - is the imaginary part of the function;

[0136] -ε is a positive scalar with a low value, the purpose of which is to make relation (14) differentiable and to avoid zero division in the calculation of the gradient derivative.

Claims

1. A method for characterizing microorganisms present in a biological sample, comprising: a. acquiring a digital holographic image by a defocused microscopic imaging acquisition device having a coherent light source or a partially coherent light source, the device being configured to form an interference pattern on a matrix image sensor between the light source and the light diffracted by the sample; c. computer-generating a focused image by applying a digital model for reconstructing a focused image to the digital holographic image; d. characterizing the microorganism according to the focused image, Features: a.

1. Acquiring the digital holographic image includes providing a plurality of calibration objects different from the microorganisms present in the biological sample in the field of view of the acquisition device corresponding to the image, wherein the objects - previously characterized in terms of dimensionality and refractive index; - having dimensions selected so as to produce an interference pattern on said matrix image sensor; - having a shape selected so that the interference pattern can be calculated using a wavefront propagation model that incorporates the optical aberrations of the acquisition device; b. Before the computer generates the focused image, the method comprises: - identifying a calibration object in said digital holographic image; - calculating the interference pattern of the calibration object by applying the wavefront propagation model and quantifying the optical aberration of the acquisition device based on the interference pattern of the calibration object and the calculated interference pattern in the holographic image; c.

1. The digital model used to reconstruct the focused image incorporates quantified optical aberrations, The calculation of the aberration is performed by calculation using an inverse parameterization method using a problem solution according to the following relationship, thereby obtaining the aberration correction function p(x,y): in t t is the refocused image, is the distance z between the target surface (6) and the plane of the sensor (2) 6 The parameter propagation operator at , such as the Lorenz-Mie model, and p(x,y) is the correction function of the aberration.

2. A method according to claim 1, wherein the calibration object is a sphere having a radius in the range of 0.01 to 100 μm and having a polydispersity as coefficient of variation of less than 50%, preferably less than 25%, even more preferably less than 10%, wherein the refractive index of the calibration object is advantageously known with an uncertainty of ±2%.

3. A method according to claim 1 or 2, wherein the digital model used to reconstruct the focused image uses a propagation operator modified by the aberration correction function.

4. The method according to any one of the preceding claims, wherein the aberration correction function is a function according to the following relationship: in is the Fourier transform, K x and K y is the frequency coordinate in the Fourier domain, b={b i (K x ,K y )} i are elements of the frequency basis, and α = {α i } i is a function Coordinates in basis b.

5. The method according to claim 4, wherein when quantifying the aberration, the coordinates {α i } i is calculated together with the parameter vector of the calibration object considered by the parameter propagation operator.

6. A method according to any one of claims 4 or 5, wherein the basis is a Zernike polynomial basis.

7. The method of claim 6, wherein the Zernike polynomial basis is limited to the first 15 Zernike polynomials.

8. A method according to any one of the preceding claims, comprising a preliminary step of locating and approximately characterising a calibration object using an uncorrected aberration model.

9. A method according to any one of the preceding claims, wherein quantifying the aberration is performed at a plurality of positions of the holographic image.

10. The method according to any of the preceding claims, wherein the holographic image is divided into a plurality of blocks, and wherein the sample is prepared with at least one calibration object per block, preferably with at least 3 calibration objects per block.

11. The method of claim 10, wherein a reconstruction model is implemented for each block, said model integrating the quantized aberrations of the block.

12. Method according to any of the preceding claims, wherein the reconstruction is performed by means of a regularization method using a non-parametric propagation model, in particular a Rayleigh-Sommerfeld model.

13. A method according to any one of the preceding claims, wherein the correction of the optical aberrations is performed for multiple wavelengths.

14. The method of claim 13, wherein the optical aberration model is calculated for each of a plurality of wavelengths by imposing constraints on the position and / or geometrical parameters of the calibration object.

15. The method of claim 13, wherein the model for reconstructing the digital image incorporating chromatic aberration is calculated for each of the plurality of wavelengths by imposing constraints on object position parameters common to all of the plurality of wavelengths.

16. A system for characterizing microorganisms present in a biological sample, comprising: - a device for acquiring digital holographic images by means of a defocused microscopic imaging acquisition device having a coherent light source or a partially coherent light source, the device being configured to form an interference pattern on a matrix image sensor between the light source and the light diffracted by the microorganism; - a computing unit, which is configured to: c. computer-generating a focused image by applying a digital model for reconstructing a focused image to the digital holographic image; d. characterizing bacteria according to the focused image, Features: a.

1. Acquiring the digital holographic image includes providing a plurality of calibration objects different from the microorganisms present in the biological sample in the field of view of the acquisition device corresponding to the image, wherein the objects - previously characterized in terms of dimensionality and refractive index; - having dimensions selected so as to produce an interference pattern on said matrix image sensor; - having a shape selected so that the interference pattern can be calculated using a wavefront propagation model that incorporates the optical aberrations of the acquisition device; b. Before the computer generates the focused image, the method comprises: - identifying a calibration object in said digital holographic image; - calculating the interference pattern of the calibration object by applying the wavefront propagation model and quantifying the optical aberration of the acquisition device based on the interference pattern of the calibration object and the calculated interference pattern in the holographic image; c.

1. The digital model used to reconstruct the focused image incorporates quantified optical aberrations, The calculation of the aberration is performed computationally using an inverse parameterization method using the solution of the problem according to the following relationship, thereby obtaining the aberration correction function p(x, y): in t t is the refocused image, is the distance z between the target surface (6) and the plane of the sensor (2) 6 The parameter propagation operator at , such as the Lorenz-Mie model, and p(x, y) is the correction function of the aberration.

17. The system according to claim 13, wherein the computing unit is configured to implement the method according to any one of claims 2 to 15.

18. A computer program product comprising a computer memory storing computer readable instructions for implementing steps c) and d) of the method according to any one of claims 1 to 15.

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