Compact calibrated interferometric characterisation system

EP4584573A1Pending Publication Date: 2025-07-16ARYBALLE TECH +3
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Patent Information

Application Number
EP2023762527
Authority / Receiving Office
EP · EP
Patent Type
Applications
Current Assignee / Owner
Priority Date
2022-09-05
Filing Date
2023-09-01
Publication Date
2025-07-16

AI Technical Summary

Technical Problem

Existing interferometric systems for characterizing analytes in fluid media, such as volatile organic compounds, face challenges in determining the phase shift and its direction due to significant bulk on the photonic chip, requiring multiple photodetectors and diffraction gratings, which increases the system's size and complexity.

Method used

A characterization system with a reduced size is developed, utilizing a matrix of N Mach-Zehnder interferometers, each with a multimode output coupler having only two useful outputs phase shifted by π/2, coupled to 2×N photodetectors, and a processing unit that determines phase shift using calibration parameters to characterize analytes based on measured optical powers, reducing the bulk and complexity.

Benefits of technology

The system effectively determines the phase shift and its direction with reduced footprint on the photonic chip, enabling efficient characterization of analytes while maintaining accuracy, and allows for a more compact and cost-effective design.

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Abstract

The invention relates to an interferometry system for characterising analytes present in a fluid medium, the system comprising: at least one light source (11) suitable for emitting an optical signal having predefined power; an array of photodetectors (16); an array of N Mach-Zehnder interferometers (12(n)) each comprising an input divider (13) coupled to the light source, two waveguides forming a sensitive arm (14s) and a reference arm (14r), and a multimode output coupler (15) having a plurality of outputs, including two outputs, referred to as useful outputs (15u), phase shifted by π / 2, are coupled to the photodetectors; and a processing unit comprising, for each of the Mach-Zehnder interferometers (12(n)), predetermined calibration parameter values which are formed of: the input power Pjn(n) of the optical signal incident on an input divider (13) according to the predefined power of the optical signal emitted by the light source (11); and optical power offsets O1(n), O2(n) associated with each useful output (15u) and defined when the light source (11) is inactive.
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Description

CALIBRATED INTERFEROMETRIC CHARACTERIZATION SYSTEM WITH REDUCED FOOTPRINT TECHNICAL DOMAIN

[0001] The field of the invention is that of the characterization, by an interferometric system, of analytes present in a gaseous or liquid medium. STATE OF THE PRIOR ART

[0002] The ability to analyze and characterize analytes present in a fluid medium, such as for example odorous molecules or volatile organic compounds, or even compounds present in solution or in suspension in a liquid medium, is an increasingly important issue, particularly in the fields of health, the food industry, the perfume industry (fragrances), or even olfactory comfort in confined public or private places (automobile, hotels, shared places, etc.), etc. The characterization of such analytes present can be carried out by a characterization system.

[0003] Different characterization approaches exist, which are distinguished from each other in particular by the need or not to have to "mark" the analytes or receptors beforehand with a revealing agent. Unlike, for example, fluorescence detection which requires the use of such markers, detection using surface plasmon resonance imaging (SPRi) and that using an interferometric principle, for example of the Mach-Zehnder type (MZI), are so-called label-free techniques.

[0004] In such a characterization system, the analytes present in a fluid medium interact by adsorption / desorption with receptors located in one or more sensitive sites of a functionalized surface. The aim is to detect in real time an optical signal associated with each of the sensitive sites, representative of the temporal variation of the local refractive index due to the adsorption / desorption interactions of the analytes with the receptors. The intensity or power of each optical signal detected by an optical sensor is directly correlated to the adsorption / desorption interactions of the analytes with the receptors.

[0005] Figure 1A illustrates an example of a Mach-Zehnder interferometer 12 of a characterization system, described in document EP3754326A1. This characterization system comprises a functionalized surface where the receivers are located, a measuring device formed of a light source (a diffraction grating here ensures the coupling between the light source and the interferometer 12), a matrix of Mach-Zehnder interferometers 12 produced in a circuit integrated photonic circuit (PIC) of a photonic chip, and photodetectors (a diffraction grating here ensures coupling with a remote photodetector), and finally comprises a processing unit (also not shown). Each interferometer 12 comprises two waveguides, one of which forms a reference arm 14r, and the other a sensitive arm 14s on the surface of which the receptors are located. The presence of analytes adsorbed on the surface of the sensitive arm 14s modifies the properties of the optical signal traveling through it, and more precisely causes a modification of the phase of the optical signal, while the phase of the optical signal traveling through the reference arm 14r is not modified. The phase difference Φ(t) between these optical signals leads to constructive or destructive interference which modulates the power of the output optical signal detected by the photodetector.

[0006] Figure 1B illustrates an example of a signal (or sensorgram) obtained by a characterization system during an analyte characterization process. A sensorgram is here a signal corresponding to the temporal evolution of the phase shift Φ(t), during a reference phase Phref where the analytes are not present, followed by a characterization phase Phcarac where the analytes are present and interact with the receptors. The analytes can then be characterized from the values ​​Φ i and Φ f of the phase shift Φ(t) associated respectively with the reference phase Ph ref and to the Ph characterization phase carac .

[0007] However, since the power of the optical signal received by the photodetector is a sinusoidal function of the phase shift Φ(t), it may be necessary to be able to determine the direction of variation of the phase shift Φ(t). For this, according to one approach, the Mach-Zehnder interferometer has a 2×3 multimode output coupler (MMI for Multi Mode Interferometer). The multimode coupler therefore has three outputs phase-shifted by 2π / 3, which are called useful outputs since they are each coupled to a photodetector. Figure 1C illustrates an example of such a Mach-Zehnder interferometer 12, described in Halir et al., Direct and Sensitive Phase Readout for Integrated Waveguide Sensors, IEEE Photonics J., Vol.5, No.4, 6800906, August 2013, comprising a multimode coupler 15 coupled to three photodetectors 16.Also, for a matrix of N Mach-Zehnder interferometers 12, it is necessary to provide a matrix of 3×N photodetectors 16, which results in a significant footprint on the surface of the photonic chip. This footprint can be linked to the presence on the photonic chip of a matrix of 3×N diffraction gratings ensuring the coupling with a remote matrix photodetector (camera), or to the presence of the matrix of 3×N photodetectors when they are integrated into the photonic chip.

[0008] Mach-Zehnder interferometer characterization systems are described in particular in the article by Laplatine et al. entitled Silicon photonic olfactory sensor based on an array of 64 biofunctionalized Mach-Zehnder interferometers, Optics Express, Vol. 30, No. 19, pp.33955-33968, 2022, in the article by Milvich et al. entitled Integrated phase-sensitive photonic sensors: a system design tutorial, Advances in Optics and Photonics, Vol. 13, No. 3, p. 584-642, 2021, and in the article by Schweikert et al. entitled Improved Phase Detection in On-Chip Refractometers, 2021 International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), pp.113-114, 2021. PRESENTATION OF THE INVENTION

[0009] The invention aims to remedy at least in part the drawbacks of the prior art, and more particularly to propose a characterization system, of the interferometric type, having a reduced size, while being able to determine the phase shift Φ(t) and its direction of variation.

[0010] For this, the subject of the invention is a characterization system suitable for characterizing analytes present in a fluid medium, comprising a measuring device which comprises: - at least one light source, suitable for emitting an optical signal of predefined power; - a matrix of N Mach-Zehnder interferometers, with N>1, each comprising: an input divider coupled to the light source; two waveguides, forming a sensitive arm on the surface of which are located receptors with which the analytes are capable of interacting by adsorption / desorption, and a reference arm; and an output multimode coupler, coupled to the two waveguides; - a matrix of photodetectors, suitable for measuring the powers of the optical signals transmitted by the multimode couplers.

[0011] The characterization system also includes a processing unit, adapted to determine, for each Mach-Zehnder interferometer of index n ranging from 1 to N: a phase shift Φ(n)(t) between the optical signals circulating in the waveguides, from the measured powers; values ​​Φi(n) and Φf(n), from the phase shift Φ(n)(t), associated respectively with a reference phase where the analytes are not present and with a characterization phase where the analytes are present and interact with the receptors; then to characterize the analytes, from the values ​​Φ i(n) and Φ f(n) .

[0012] According to the invention, each of the multimode couplers has several outputs, of which only two, called useful outputs, phase shifted by π / 2, are coupled to the photodetectors. In addition, the photodetectors form a matrix of 2×N photodetectors, and each measure the powers P 1(n) (t) and P 2(n)(t) optical signals transmitted by the useful outputs of each Mach-Zehnder interferometer.

[0013] In addition, the processing unit includes, for each of the Mach-Zehnder interferometers, predetermined values ​​of calibration parameters formed: from an input power Pin(n) of the incident optical signal to the input divider, which is a function of the power predefined optical signal emitted by the light source; and offsets o 1(n) , o 2(n) optical power associated with each useful output and defined when the light source is inactive. In addition, it is suitable for determining the phase shift Φ(n)(t) from the optical powers P1(n)(t) and P2(n)(t) measured and associated with the useful outputs, and the predetermined values ​​of the calibration parameters Pin(n), o1(n) and o2(n).

[0014] Some preferred but non-limiting aspects of this characterization system are as follows.

[0015] Each output coupler may have outputs not coupled to the photodetector matrix, called non-useful, having pointed ends.

[0016] The characterization system may comprise a photonic chip containing: on the one hand the matrix of N Mach-Zehnder interferometers; and on the other hand a matrix of 2×N optical detection elements coupled to the N interferometers by integrated waveguides, the optical detection elements being either said photodetectors or diffraction gratings coupled to a matrix photodetector.

[0017] The measuring device may comprise a matrix of at least 4 Mach-Zehnder interferometers.

[0018] Each multimode coupler can be a 2×4 coupler.

[0019] The characterization system may include a calibration device adapted to determine, with the processing unit, the values ​​of the calibration parameters Pin(n), o1(n) and o2(n).

[0020] The calibration device may comprise a reservoir of so-called calibration analytes, fluidically connected to the measuring device to allow the calibration analytes to interact with the receptors, having a predefined concentration of calibration analytes to induce, when they interact with the receptors, a predefined minimum variation ΔΦmin of the phase shift Φ(n)(t) of each of the Mach-Zehnder interferometers.

[0021] The calibration device may comprise a Mach-Zehnder interferometer, called a calibration interferometer, coupled to at least one calibration photodetector.

[0022] The calibration interferometer may have a reference arm and a discontinuous arm.

[0023] The invention also relates to a method for calibrating a characterization system according to an embodiment where the calibration device comprises a reservoir of calibration analytes. The method then comprises the following steps: - activating the light source so that it emits the optical signal at the predefined power; - bringing the calibration analytes into contact with the receivers; - measuring by the photodetectors a power P1(n)(t), P2(n)(t) of the optical signals transmitted by each Mach-Zehnder interferometer, while the calibration analytes interact with the receivers and induce a variation of the phase shift Φ (n) (t) at least equal to the predefined minimum value ΔΦ min; - determine by the processing unit the values ​​of the calibration parameters Pin(n), o1(n) and o2(n) from the measured powers P1(n)(t), P2(n)(t), and store in the processing unit the determined values ​​of the calibration parameters Pin(n), o1(n) and o2(n).

[0024] The calibration parameters P in(n) , o 1(n) and o 2(n) can be determined from the minimum and maximum values ​​of the powers P 1(n) (t), P 2(n) (t) measured.

[0025] The invention also relates to a method for calibrating a characterization system according to an embodiment where the calibration device comprises a calibration interferometer and at least one calibration photodetector. The method then comprises the following steps: - measuring, by the calibration photodetector, a power of the optical signal transmitted by the calibration interferometer, while the light source is activated; - determining a value of the input power Pin,calib of the incident optical signal at an input divider of the calibration interferometer; then - determining the input value P in(n) for each of the interferometers of the measuring device, from the value P in,calib determined.

[0026] The method may comprise the following steps: measuring a power P1(n)(t), P2(n)(t) of the optical signals transmitted by each interferometer of the measuring device, by the photodetectors of the measuring device, while the light source is inactive; then determining the values ​​of the offsets o 1(n) and o 2(n) from the powers P 1(n) (t), P 2(n) (t) measured.

[0027] The invention also relates to a method for characterizing analytes by a characterization system according to any one of the preceding characteristics, comprising the following steps: - measuring, by the photodetectors of the measuring device, a power P1(n)(t), P2(n)(t) of the optical signals transmitted by each Mach-Zehnder interferometer, during a reference phase where the analytes are not present, and during a characterization phase where the analytes are present and interact with the receivers; - determining by the processing unit, for each Mach-Zehnder interferometer, the phase shift Φ(n)(t) between the optical signals circulating in the arms, from the powers P 1(n) (t), P 2(n) (t) measured and predetermined values ​​of the calibration parameters P in(n) , o 1(n) and o 2(n); - determine the values ​​Φi(n) and Φf(n) from the phase shift Φ(n)(t), associated respectively with the reference phase and the characterization phase; - characterize the analytes from the values ​​Φi(n) and Φf(n).

[0028] The step of determining the phase shift Φ (n) (t) can consist of determining: a phase shift φ (n) (t), called extracted phase shift, whose values ​​are between 0 and 2π, from the measured powers P1(n)(t), P2(n)(t) and the predetermined values ​​of the calibration parameters Pin(n), o1(n) and o2(n); then the phase shift Φ(n)(t), called unfolded phase shift, by unfolding the extracted phase shift φ(n)(t) by adding to it a positive or negative integer multiple of 2π. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Other aspects, aims, advantages and characteristics of the invention will appear better on reading the following detailed description of preferred embodiments thereof, given by way of non-limiting example, and made with reference to the appended drawings in which: Figure 1A, already described, is a schematic and partial perspective view of a Mach-Zehnder interferometer of a characterization system according to an example of the prior art; Figure 1B, already described, illustrates an example of the temporal evolution of a phase shift Φ(t) between the optical signals circulating in the two waveguides of a Mach-Zehnder interferometer, during a reference phase Phref then a characterization phase Phcarac; Figure 1C, already described, is a schematic and partial view of a Mach-Zehnder interferometer of a characterization system according to another example of the prior art, which comprises a 2×3 multimode output coupler;Figure 2A is a schematic and partial view of a calibrated and compact characterization system, according to one embodiment; Figure 2B is a schematic and partial view of another example of a Mach-Zehnder interferometer of the measuring device of the calibrated characterization system according to one embodiment; Figure 3A illustrates an example of the temporal evolutions of the extracted phase shift; and the unfolded phase shift Φ(t) associated with the optical signals circulating in the arms of a Mach-Zehnder interferometer of Fig. 2A or Fig. 2B, highlighting the unfolding of the phase; Fig. 3B illustrates a flowchart of a calibration method and a method for characterizing analytes according to one embodiment; Fig. 4A is a schematic and partial view of a compact characterization system, to be calibrated, according to one embodiment where the calibration device comprises a reservoir of calibration analytes; Figure 4B is a schematic and partial view of the characterization system to be calibrated in Fig. 4A, which illustrates the fluid connection conduits between the calibration analyte reservoir and the measuring device of the characterization system; Figure 5A illustrates an example of the temporal evolution of the power P1(n)(t) and P2(n)(t) of optical signals transmitted by the multimode coupler of a Mach-Zehnder interferometer of a characterization system according to one embodiment, with a view to determining the calibration parameters P in(n) , o 1(n) , and o 2(n); Figure 5B illustrates another example of temporal evolution of the extracted phase shift φ(n)(t), here in the form of an ellipse in a complex plane (x, y), also with a view to determining the calibration parameters Pin(n), o1(n), and o2(n); Figure 6A is a schematic and partial view of a compact characterization system, to be calibrated, according to another embodiment where the calibration device comprises a Mach-Zehnder calibration interferometer coupled to a calibration photodetector; Figure 6B is a schematic and partial view of another example of a Mach-Zehnder calibration interferometer. DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS

[0030] In the figures and in the remainder of the description, the same references represent identical or similar elements. In addition, the different elements are not shown to scale so as to enhance the clarity of the figures. Furthermore, the different embodiments and variants are not mutually exclusive and may be combined with each other. Unless otherwise indicated, the terms "substantially", "approximately", "of the order of" mean to within 10%, and preferably to within 5%. Furthermore, the terms "between ... and ..." and equivalents mean that the limits are included, unless otherwise indicated.

[0031] The invention relates generally to the characterization of analytes present in a fluid medium (gaseous or liquid). Generally speaking, characterization means obtaining information representative of the interactions of the analytes contained in the fluid medium with the receptors of sensitive sites of a functionalized surface of the characterization system. The interactions in question here are events of adsorption and / or desorption of the analytes with the receptors. This information thus forms an interaction pattern, in other words a “signature” of the analytes, this pattern being able to be represented for example in the form of a histogram or a radar diagram. More precisely, in the case where the system of characterization includes N distinct sensitive sites, the interaction pattern is formed by the N scalar or vector representative information.

[0032] The invention relates more specifically to a calibrated characterization system, i.e. one whose processing unit contains predetermined values ​​of calibration parameters, for each of the Mach-Zehnder interferometers of a measuring device, these values ​​thus enabling it to be able to determine the phase shift Φ (n) (t) between the optical signals circulating in the arms of each Mach-Zehnder interferometer as well as its direction of variation. The invention also relates to a characterization system to be calibrated, and comprising for this purpose a calibration device making it possible to determine, with the processing unit, these values ​​of the calibration parameters. Finally, it relates to a method for calibrating such a characterization system (to be calibrated), and to a method for characterizing analytes by means of such a calibrated characterization system.

[0033] Let us note here that the calibration parameters are formed, for each of the Mach-Zehnder interferometers of index n ranging from 1 to N, with N>1: of an input power Pin(n) of the incident optical signal at the input divider, which is a function of the predefined power of the optical signal emitted by the light source of the characterization system; and of offsets o 1(n) , o 2(n) optical power associated with each useful output and defined when the light source is inactive (and therefore the input power of the incident optical signal at the input splitter is zero). The term "offset" is synonymous with bias, offset, offset error, zero error, etc.

[0034] The characterization of the analytes is carried out by means of an interferometric type characterization system comprising at least: o a measuring device comprising: ^ at least one light source adapted to emit an optical signal of predefined power; ^ a matrix of N Mach-Zehnder interferometers, with N>1, each comprising: an input divider coupled to the light source; two waveguides which form a sensitive arm and a reference arm; and an output coupler of the MMI type (multimode coupler) having several outputs, including only two useful outputs phase-shifted by π / 2; ^ a matrix of 2×N photodetectors coupled to the useful outputs, either directly (the photodetectors then being arranged on or in the photonic chip) or indirectly (by means of a matrix of 2×N diffraction gratings produced on or in the photonic chip);o a processing unit: ^ comprising for each of the Mach-Zehnder interferometers of the measuring device, predetermined values ​​of the calibration parameters; ^ adapted to determine, for each of said interferometers, a phase shift Φ(n)(t) between the optical signals circulating in the arms, from the optical powers P; 1(n) (t) and P 2(n) (t) measured and associated with the useful outputs, and predetermined values ​​of the calibration parameters (input power P in(n) and o1 offsets (n) , o2 (n) ; then ^ adapted to characterize the analytes from values ​​Φi(n) and Φf(n) of the phase shift Φ(n)(t) associated respectively with a reference step Ph ref where the interferometers are not exposed to the analytes, and to a Ph characterization step carac where they are exposed to analytes.

[0035] According to the invention, the output coupler of each Mach-Zehnder interferometer is a multimode coupler having two inputs coupled to the arms and several outputs (preferably four outputs). Among these outputs, only two, phase shifted by π / 2, are coupled to the photodetectors and are therefore said to be useful. The other outputs are not used to characterize the analytes (no coupling to the photodetectors of the measuring device). This configuration therefore makes it possible to significantly reduce the size on the photonic chip, since only 2×N photodetectors are necessary, and no longer 3×N as in the Halir et al 2013 document mentioned previously. The size related to the waveguides connecting the output couplers to the photodetectors (when they are integrated into the photonic chip) or to the diffraction gratings (when the photodetectors are remote) is also significantly reduced.In addition, the predetermined values ​​of the calibration parameters make it possible to determine the phase shift Φ(n)(t) while being able to know its direction of variation.

[0036] As detailed below, the characterization system may further comprise a calibration device adapted to determine, with the processing unit, during a calibration process, the values ​​in question of the calibration parameters.

[0037] Figure 2A is a schematic and partial view of a calibrated characterization system 1, according to one embodiment. Figure 2B illustrates in more detail another example of an interferometer 12 (n) Mach-Zehnder of characterization system 1 of Fig.2A.

[0038] Generally speaking, the characterization system 1 comprises a measuring device 10, and a processing unit 3 containing predetermined values ​​of calibration parameters Param calib. The characterization system 1 is then said to be calibrated. The interferometers 12 (n) Mach-Zehnder of the measuring device 10 are integrated into a photonic chip, which may be of the silicon photonic type.

[0039] Analytes are elements present in the fluid medium (gaseous or liquid) to be analyzed, and are intended to be detected and characterized by the characterization system 1. They can be, for example, bacteria, viruses, proteins, lipids, volatile organic molecules, inorganic compounds, among others. Furthermore, receptors 2 (ligands, in English) are elements that cover one of the waveguides of the Mach-Zehnder interferometer 12 (sensitive arm 14s) and exhibit the ability to interact with analytes, although the chemical and / or physical affinities between analytes and receptors 2 are not necessarily known. The receptors 2 of the different sensitive surfaces preferably exhibit different physicochemical properties, which impact their ability to interact with analytes. Examples include amino acids, peptides, nucleotides, polypeptides, proteins, organic polymers, oligo- or polysaccharides, among others.

[0040] The 12 interferometers (n)Mach-Zehnder devices are made in a photonic chip containing an integrated photonic circuit, made for example from silicon. The light source 11 and the photodetectors 16 can be located on or in the photonic chip, or can be remote and coupled to it by optical couplers (diffraction gratings 17, etc.) as illustrated in fig. 2B. Similarly, the processing unit 3 can be located in or on the photonic chip, or be remote.

[0041] The measuring device 10 comprises at least one light source 11, a matrix of N Mach-Zehnder interferometers 12(n), and a matrix of 2×N photodetectors 16.

[0042] The light source 11 is preferably an optical source of coherent or non-coherent light, of a continuous or pulsed signal, and monochromatic, of reduced spectral width (for example less than 30nm, or even 15nm, or even 2nm or even 1nm) and of predefined central wavelength for example located in the near infrared. It can be a vertical cavity surface emitting laser source (VCSEL for Vertical Cavity Surface Emitting Laser in English), a hybrid laser source of type III-V / Si, a laser diode, or any other type of laser source. It can also be a light-emitting diode.

[0043] The measuring device 10 of the characterization system 1 comprises a matrix of N Mach-Zehnder interferometers 12(n), with N>1, preferably at least equal to 4, for example 64 or even more, referenced by the index n ranging from 1 to N. The interferometers 12(n) each comprise an input divider 13 (for example of the MMI type), two waveguides 14r, 14s coupled to the input divider 13, one of which forms a sensitive arm 14s to the quantity of analytes adsorbed to the receptors 2, and the other of which forms a reference arm 14r not sensitive to the analytes present, so that the optical signals circulating in the two arms 14r, 14s have an effective phase shift, noted Φ(t). The two waveguides 14r, 14s are then coupled to a multimode coupler 15 having several outputs phase-shifted by π / 2 (here four outputs), of which only two outputs phase-shifted by π / 2 are useful and coupled to the photodetectors 16.

[0044] In the example of Fig. 2A, the arms 14r, 14s extend in a spiral in the sense that they wrap around themselves between the input divider 13 and the multimode coupler 15. They can also extend in a serpentine fashion, or even extend in a rectilinear manner as illustrated in Fig. 2B. (possibly with a serpentine and / or spiral section). Other waveguide shapes are also possible.

[0045] The receptors 2 thus form N sensitive sites of a so-called functionalized surface of the photonic chip, this functionalized surface being intended to be exposed to the fluid medium containing the analytes. In other words, the sensitive sites are areas containing the receptors 2 and located at the level of the sensitive arms 14s of the interferometers 12 (n)They may have 2 receptors that differ from one sensitive site to another in terms of physicochemical affinity with the analytes. Several sensitive sites may be identical, for example, to detect a possible measurement drift.

[0046] The interferometers 12(n) each comprise a sensitive arm 14s on the surface of which receptors 2 are arranged to form a sensitive site, the other arm not comprising receptors 2 and forming the reference arm 14r. The waveguide of the sensitive arm 14s (high refractive index material) is located at a depth of the receptors 2 such that the optical signal propagating there (guided mode) has an effective index which depends on the quantity of analytes bound to the receptors 2 of the sensitive site. A notch (see for example patent application FR2106153 filed on 06 / 10 / 2021) can thus be made in the sheath covering the sensitive arm 14s, so as to allow the guided mode to be influenced by the presence of the adsorbed analytes.

[0047] Recall that the effective index of a guided mode is defined as the product of the propagation constant β and λ / 2π, λ being the wavelength of the optical signal. The propagation constant β depends on the wavelength λ and the mode of the optical signal, as well as the properties of the waveguide (refractive indices and geometry). The effective index of the mode corresponds, in a certain way, to the refractive index of the waveguide 'seen' by the optical mode. It is usually between the index of the core and the index of the cladding of the waveguide. It is therefore understood that the quantity of analytes adsorbed on the sensitive site modifies the properties of the optical mode and / or the waveguide, in particular the phase of the guided mode.

[0048] It therefore follows that the presence of analytes adsorbed on the sensitive site of the sensitive arm 14s causes a modification of the phase of the guided mode, whereas the phase of the guided mode traveling through the reference arm 14r is not substantially modified. The phase shift Φ(t) between the optical signals traveling through the arms and then received by the multimode coupler 15 results in a modification of the power of the optical signal recombined and detected by the photodetectors 16, due to constructive or destructive interference between the optical signals circulating in the two arms.

[0049] The output coupler 15 is, in this example, a 2×4 multimode coupler (MMI), but the number of inputs can be different. Here it comprises at least two outputs 15u, called useful, phase shifted by π / 2, and each coupled to a photodetector 16. The other outputs 15nu are called not useful, insofar as they are not coupled to the photodetectors 16. The latter may each have a pointed end (taper in English), so as to cause the optical signal to leak into the substrate of the photonic chip and to greatly reduce the retroreflection in the direction of the multimode coupler 15.

[0050] The measuring device 10 comprises a matrix of 2×N photodetectors 16, where each photodetector 16 is coupled to a useful output 15u of a multimode coupler 15 of an interferometer 12 (n). The photodetectors 16 measure the value of the power (or the intensity, equivalently) of the optical signal transmitted by each useful output 15u, at each measurement instant, and transmit this information to the processing unit 3. The power of the optical signals at the useful outputs 15u is noted P1(n) and P2(n). On the photonic chip, the interferometer matrix 12 is coupled to a matrix of 2×N detection elements, which can be either diffraction gratings 17 when the photodetectors are remote from the photonic chip (in the form of a camera with 2×N sensitive detection zones, each sensitive zone being able to comprise at least one detection pixel), or the photodetectors 16 themselves when they are integrated into the photonic chip.

[0051] The processing unit 3 allows the implementation of the processing operations of the analyte characterization method. For this purpose, it is coupled to the photodetectors 16 of the measuring device 10. It comprises at least one microprocessor and at least one memory. It thus comprises a programmable processor capable of executing instructions recorded on an information recording medium. It further comprises at least one memory containing the instructions necessary for implementing the characterization method. The memory is also adapted to store the information calculated at each measurement time.

[0052] The processing unit 3 contains in particular the predetermined values ​​of the calibration parameters Paramcalib, for each of the interferometers 12(n) of the measuring device 10, namely more precisely the power Pin(n) as well as the offsets o1(n) and o2(n). The power Pin(n) is a function of the predefined power of the optical signal emitted by the light source 11: in fact, the value P in(n) depends on the greater or lesser power of the signal emitted by the light source 11. Furthermore, the shifts are associated with the interferometers 12(n) and / or the photodetectors of the measuring device 10, and may come from the residual light present in the characterization system 1, or may even be linked to the dark current of the photodetectors 16.

[0053] The processing unit 3 is adapted to determine a phase shift φ (n)(t) called “extract” representative of the phase shift between the optical signals circulating in the arms of each interferometer 12(n), from the optical powers P1(n)(t) and P2(n)(t) measured by the photodetectors 16 for each of the interferometers 12(n), and the predetermined values ​​of the calibration parameters Param calib . It is also suitable for "unfolding the phase" to obtain the phase shift Φ (n) (t) said “unfolded”, then to determine values ​​Φ i(n) and Φ f(n) associated respectively with the reference phase Ph ref (absence of analytes) and the Phcarac characterization phase (presence of analytes). These values ​​Φi(n) and Φf(n) make it possible to determine the signature of the analytes, such as, for example: S = { Φf(n) – Φi(n)}n=1 ;N.

[0054] As illustrated in Fig. 2A, the characterization system 1 has a reduced footprint on the photonic chip, since the detection matrix now only has 2×N detection elements (diffraction gratings 17 or photodetectors 16). The footprint related to the waveguides which ensure the coupling between the multimode couplers 15 and the detection matrix is ​​also reduced. In the case of a remote camera, it has a reduced number of sensitive detection surfaces 2×N, which makes it possible to use a less expensive camera. In addition, thanks to the determination of the calibration parameters Param calib via the calibration device 20, the processing unit 3 is able to determine the phase shift Φ (n)(t) while knowing the direction of its variation. Finally, it can be shown that the error in determining the phase shift Φ(n)(t) can be lower in the case of 12(n) Mach-Zehnder interferometers with two useful 15u outputs phase-shifted by π / 2 than in the case of three useful outputs phase-shifted by 2π / 3.

[0055] Figure 3A illustrates an example of temporal evolutions of the extracted phase shift φ (n) (t) and the unfolded phase shift Φ(n)(t).

[0056] As previously indicated, the power P1(t) and P2(t) of the optical signals at the output of a Mach-Zehnder interferometer 12 varies periodically, and more precisely sinusoidally, depending on the phase shift between the optical signals traveling through the arms of the interferometer 12. As the phase extraction methods generally use an inverse trigonometric function such as an arc-tangent, the calculated phase shift then has values ​​modulo 2π: this is then the extracted phase shift φ(t).

[0057] Thus, as the analytes bind to the receptors 2 of a sensitive arm 14s, the phase shift increases between the optical signals traveling through the two arms of the interferometer. Also, the extracted phase shift φ(t) increases by presenting discontinuities of the order of 2π each time it reaches one of the limits of an interval of width 2π, here ]-π ; +π]. Thus, it increases until it reaches +π, then presents a discontinuity of a value of -2π to fall back to the value of -π, and then resumes its growth. The unfolded phase shift Φ(t), which is representative of the effective phase shift between the optical signals traveling through the arms of the interferometer, increases continuously without remaining contained in the interval ]-π ; +π].

[0058] Figure 3B illustrates a flowchart of a method 200 for characterizing the analytes, using the calibrated characterization system 1 of Fig. 2A. The characterization method 200 follows a calibration method 100.

[0059] In the preliminary calibration process 100, which will be described in detail later, the values ​​of the calibration parameters Param calib , namely the input power P in(n) and the offsets o1(n) and o2(n), are determined for each of the Mach-Zehnder interferometers 12(n) of the measuring device 10, and are stored in the processing unit 3. This method 100 is detailed further in connection with two embodiments described subsequently.

[0060] The characterization method 200 comprises a measurement step 210, by the photodetectors 16, at each measurement instant t i successive, powers P 1(n) (t i ) and P 2(n) (t i) of the optical signals transmitted by each of the interferometers 12(n). The measured values ​​are transmitted to the processing unit 3. These powers P1(n)(ti) and P2(n)(ti) correspond to the optical signals transmitted by the two useful outputs 15u of each multimode coupler 15. This step is carried out during a reference phase Ph ref where the functionalized surface is not exposed to analytes, and during a Ph characterization phase carac where it is exposed to analytes.

[0061] In a step 220, the processing unit 3 determines the extracted phase shift φ(n)(ti), from the calibration parameters Paramcalib: Pin(n), o1(n) and o2(n), and the measured values ​​of the optical power P1(n)(ti) and P2(n)(ti). This step can be carried out at each measurement time ti, as illustrated here, or can be carried out once the temporal evolution of the powers P 1(n) (t i ) and P 2(n) (t i) has been fully acquired.

[0062] For this, knowing that the optical powers P1(n)(ti) and P2(n)(ti) can be expressed by the following relations: we deduce the extracted phase shift φ(n)(ti) from the relation: ϕ^^^^t^^ = arg^x^t^^ − i × y^t^^^with: x^t^^ = P^^^^^t^^ − P^^^^^⁄ 4 − o^^^^y^t^^ = P^^^^^t^^ − P^^^^^⁄ 4 − o^^^^where P1(n)(ti) and P2(n)(ti) are the values ​​measured by the photodetectors 16, and where Pin(n), o1(n) and o2(n) are the predetermined values ​​of the calibration parameters Param calib (which do not depend on t i ).

[0063] In a phase unfolding step 230, the time evolution of the extracted phase shift φ(n)(ti) is then corrected by adding a positive or negative integer multiple of the width 2π of the interval ]-π ;+π], denoted m(ti)×2π, where m(ti) is a positive or negative integer. The latter is an increment which varies by one unit +1 or -1 at each discontinuity of the extracted phase shift φ (n) (t i ). This step is usually called phase unfolding or phase unfolding (phase unwrapping, in English). It allows to obtain the unwrapped phase shift Φ (n) whose values ​​are no longer modulo 2π, and which is then effectively representative of the effective phase shift.

[0064] Different approaches are possible. In this example, we calculate (sub-step 231) an instantaneous variation Δφ(n)(ti) = φ(n)(ti) – φ(n)(ti-1) of the extracted phase shift φ(n) between two successive measurement instants, then we determine (sub-step 232) the increment m(ti). During this step, we compare the value of this instantaneous variation Δφ (n) (t i ) to a predefined threshold value S1, for example at approximately π, to add or not a positive or negative unit to the previous increment m(ti-1). Finally, we determine (sub-step 233) the unfolded phase shift Φ(n)(ti) by adding to the extracted phase shift φ(n)(ti) the multiple of 2π, i.e. m(ti)×2π.

[0065] Finally, during a characterization step 240, the processing unit 3 determines a stationary value Φ i(n) of the unfolded phase shift Φ (n) (t i ), representative of the reference phase Ph ref (absence of analytes), and a stationary value Φ f(n)representative of the Phcarac characterization phase (presence of analytes). The signature S of the analytes can then be determined, for example from the relation: S = { Φf(n) – Φi(n)}n=1 ;N.

[0066] Figures 4A and 4B are schematic and partial views of a characterization system 1 to be calibrated, according to an alternative embodiment, where the calibration device 20 comprises a reservoir of so-called calibration analytes 21, the concentration of which is adapted to cause a predefined minimum variation in the unfolded phase shift Φ(n)(t).

[0067] The characterization system 1 comprises a measuring device 10 and a processing unit 3 identical to those of the characterization system 1 of FIG. 2A. It further comprises a calibration device 20, making it possible to determine, with the processing unit 3, the values ​​of the calibration parameters (power Pin(n) and offsets o1(n) and o2(n)) associated with each Mach-Zehnder interferometer 12(n).

[0068] The characterization system 1 may comprise a reservoir 4 of a reference fluid, not comprising analytes, this fluid being intended to be brought into contact with the functionalized surface during the reference phase. It may be a reservoir or controlled access to an environment without analytes of the characterization system 1. It may also comprise a reservoir 5 of a fluid containing the analytes to be characterized, this fluid being intended to be brought into contact with the functionalized surface during the characterization phase. Here also, it may be a reservoir or controlled access to an environment with analytes of the characterization system 1. Finally, it comprises the reservoir 21 of a fluid containing calibration analytes.

[0069] Thus, during the preliminary calibration process 100, the calibration reservoir 21 is placed in fluid communication with the measuring device 10, and the fluid with the analytes is brought to the functionalized surface. The concentration of the analytes has been predefined so that it causes a variation of the unfolded phase shift Φ (n) (t) at least equal to a predefined minimum value ΔΦ min , which depends on the method used to determine the calibration parameters Pin(n), o1(n) and o2(n).

[0070] With reference to Figure 5A which illustrates an example of temporal evolutions of the powers P1(n) and P2(n), the “min max” method, described in patent application EP21172910.8 filed on May 8, 2021, can be used. In this case, the minimum value ΔΦ min is preferably at least equal to 2π.

[0071] During this step, the functionalized surface is therefore exposed to the calibration analytes, and the photodetectors 16 measure the power P1(n) and P2(n) of at least one interferometer (if it is assumed that the calibration parameters Pin(n), o1(n) and o2(n) are identical for all the interferometers 12), and preferably, as here, of each of the interferometers 12 (n) . The calibration analytes therefore caused a variation of at least 2π in the unfolded phase shift Φ (n) (t).

[0072] We then measure the minimum value min(P1(n)(t)) which is equal to P1(n)(φ=π) and therefore to o1(n), according to the definition of P1(n)(φ) indicated previously. In addition, we measure the maximum value max(P1(n)(t)) which is equal to P1(n)(φ=0) and therefore to 2×(Pin(n) / 4)+o1(n). We can therefore deduce Pin(n). The approach is then carried out on the temporal evolution of the optical power P 2(n) (t), which allows us to deduce o 2(n), and therefore to determine the values ​​of the Paramcalib calibration parameters, which are then stored in the processing unit 3. As can be seen, this method also makes it possible to determine Pin1(n) and Pin2(n) if these values ​​were not equal for the two useful outputs 15u of the multimode coupler 15.

[0073] Figure 5B illustrates an example of a time evolution of the extracted phase shift φ (n) (t i ) in the complex plane (x; y), where x and y are the parameters defined previously. This representation is used in the context of the ellipse method, described in particular in the document Halir et al 2013 mentioned previously. In this case, the minimum value ΔΦmin is advantageously equal to 2π, but it can be less than 2π if enough values ​​have been acquired to be able to reconstruct a total ellipse by curve fitting.

[0074] The Paramcalib calibration parameters can be deduced from the position and shape of the ellipse. Indeed, the half-length 'a' of the minor axis is equal to Pin1(n) and the half-length 'b' of the major axis is equal to Pin2(n). In addition, the coordinates (x0; y0) of the center of the ellipse allow the offset values ​​to be deduced by the following relations: x0= P in1(n) + o 1(n) ; y0= P in2(n) + o 2(n) .

[0075] Note that other methods for determining the calibration parameters can be used, such as for example methods for solving by optimization a matrix system of equations of type P = M × X, where the observation matrix P contains the powers measured optics P 1(n) and P 2(n) , the matrix M depends on the calibration parameters, and where the matrix X only depends on the phase shift Φ.

[0076] Also, this embodiment variant where the calibration device 20 comprises an analyte reservoir 21 makes it possible to keep a reduced footprint in the photonic chip, insofar as it does not comprise additional interferometer(s) and photodetectors. Indeed, once the values ​​of the calibration parameters Param calib have been defined and stored in the processing unit 3, the reservoir 21 of calibration analytes can be removed, and a calibrated characterization system 1 is thus obtained. Note that this reservoir 21 can be maintained in the calibrated characterization system 1, for example to be able to periodically carry out a recalibration of the characterization system 1. Finally, note that this method makes it possible to determine the calibration parameters Param calib with precision for each of the 12 interferometers (n) of Mach-Zehnder.

[0077] Figure 6A is a schematic and partial view of a characterization system 1 to be calibrated, according to another variant embodiment, where the calibration device 20 comprises a Mach-Zehnder interferometer 22, called calibration, associated with at least one calibration photodetector 26. Figure 6B illustrates in more detail another example of a calibration interferometer 22 of the characterization system 1 of FIG. 6A.

[0078] The characterization system 1 here comprises a measuring device 10 and a processing unit 3 identical to those of the characterization system 1 of fig. 2A. It further comprises a calibration device 20, making it possible to determine, with the processing unit 3, the values ​​of the calibration parameters (power P in(n) and offsets o 1(n) and o 2(n) ) associated with each 12(n) Mach-Zehnder interferometer.

[0079] The calibration interferometer 22 does not have a sensitive arm, so that it is not affected by the possible presence of analytes in the fluid medium. It preferably has a shape similar to that of the interferometers 12 of the measuring device 10. Thus, it can have two arms extending continuously between the input divider 13 and the multimode coupler 15 and optically independent of the external medium, or, as illustrated here, a continuous arm 24r and a discontinuous arm 24d.

[0080] In this example where the calibration interferometer 22 comprises a discontinuous arm 24d, the area of ​​the functionalized surface at this discontinuous arm 24d may have a notch similar to that of the interferometers 12 and intended to receive the analytes. In this area, the analytes may nevertheless have been deposited. Alternatively, they may not have been deposited, but the notch may allow a possible influence of the external environment on the guided mode. This is why the waveguide 24d is here discontinuous. In the case where the two arms are continuous, the sheath locally has sufficient thickness to avoid any influence of the external environment on the guided modes.

[0081] Furthermore, in this example, the outputs of the multimode coupler 25 each transmit an optical signal of power Pin,calib / 2 / 4, or Pin,calib / 8. The four outputs of the multimode coupler 25 can each be coupled to a calibration photodetector. In order to avoid information redundancy, only one output (useful output 25u) of the multimode coupler 25 is coupled to the calibration photodetector 26.

[0082] The processing unit 3 is then able to determine at least one calibration parameter Pin,calib associated with this calibration interferometer 22, and can then define those of the interferometers 12(n) of the measuring device 10.

[0083] Thus, during a first step of the calibration process 100, the offsets o are determined 1(n) and o 2(n) of each interferometer 12 (n)of the measuring device 10. For this, while the light source 11 does not emit an optical signal, the photodetectors 16 of the measuring device 10 can measure an optical power, which then corresponds to the offsets o1(n) and o2(n). Alternatively, it is possible to measure only the offset ocalib associated with the calibration photodetector 26 and to consider that the offsets o 1(n) , o 2(n) photodetectors 16 of the measuring device 10 will be identical to the value o calib measured.

[0084] Then, the light source 11 is activated so that it emits an optical signal. This second step of the calibration method 100 can be concomitant with the reference phase Phref of the measurement step 210. The calibration photodetector 26 then measures the optical power P in,calib / 8 transmitted by the useful output 25u of the calibration interferometer 22. The processing unit 3 then determines the value P in(n)of each interferometer 12 (n) of the measuring device 10 from the measured Pin,calib / 8 value.

[0085] Particular embodiments have just been described. Different variants and modifications will appear to those skilled in the art.

Claims

CLAIMS 1. Characterization system (1), suitable for characterizing analytes present in a fluid medium, o comprising a measuring device (10) formed of: ^ at least one light source (11), suitable for emitting an optical signal of predefined power; ^ a matrix of N interferometers (12 (n) ) of Mach-Zehnder, with N>1, each comprising: an input divider (13) coupled to the light source (11); two waveguides, forming a sensitive arm (14s) on the surface of which are located receptors with which the analytes are able to interact by adsorption / desorption, and a reference arm (14r); and an output multimode coupler (15), coupled to the two waveguides; ^ a matrix of photodetectors (16), adapted to measure the powers of the optical signals transmitted by the multimode couplers (15); o and a processing unit (3), adapted to determine, for each interferometer (12 (n)) of Mach-Zehnder of index n ranging from 1 to N: a phase shift Φ (n) (t) between the optical signals circulating in the waveguides, from the measured powers; from the values ​​Φi(n) and Φf(n), from the phase shift Φ(n)(t), associated respectively with a reference phase where the analytes are not present and with a characterization phase where the analytes are present and interact with the receptors; then to characterize the analytes, from the values ​​Φ i(n) and Φ f(n) ; o characterized in that: ^ each of the multimode couplers (15) has several outputs, of which only two, called useful outputs (15u), phase-shifted by π / 2, are coupled to the photodetectors (16); ^ the photodetectors (16) form a matrix of 2×N photodetectors, and each measure the powers P 1(n) (t) and P 2(n)(t) optical signals transmitted by the useful outputs (15u) of each Mach-Zehnder interferometer (12(n)); ^ the processing unit (3) comprises, for each of the interferometers (12 (n) ) of Mach-Zehnder, predetermined values ​​of calibration parameters formed: of an input power Pin(n) of the incident optical signal at the input divider (13), which is a function of the predefined power of the optical signal emitted by the light source (11); and of optical power shifts o1(n), o2(n) associated with each useful output (15u) and defined when the light source (11) is inactive; ^ the processing unit (3) is adapted to determine the phase shift Φ(n)(t) from the optical powers P1(n)(t) and P2(n)(t) measured and associated with the useful outputs (15u), and of the predetermined values ​​of the calibration parameters P in(n) , o 1(n) and o 2(n) .

2. Characterization system (1) according to claim 1, in which each output coupler (15) comprises outputs (15nu) not coupled to the matrix of photodetectors (16), called non-useful, comprising pointed ends.

3. Characterization system (1) according to claim 1 or 2, comprising a photonic chip containing: on the one hand the matrix of N Mach-Zehnder interferometers (12(n)); and on the other hand a matrix of 2×N optical detection elements (16; 17) coupled to the N interferometers (12 (n)) by integrated waveguides, the optical detection elements being either said photodetectors or diffraction gratings coupled to a matrix photodetector.

4. Characterization system (1) according to any one of claims 1 to 3, wherein the measuring device (10) comprises a matrix of at least 4 Mach-Zehnder interferometers (12(n)).

5. Characterization system (1) according to any one of claims 1 to 4, wherein each multimode coupler (15) is a 2×4 coupler.

6. Characterization system (1) according to any one of claims 1 to 5, comprising a calibration device (20) adapted to determine, with the processing unit (3), the values ​​of the calibration parameters P in(n) , o 1(n) and o 2(n)7. Characterization system (1) according to claim 6, wherein the calibration device (20) comprises a reservoir of so-called calibration analytes (21), fluidically connected to the measuring device (10) to allow the calibration analytes to interact with the receptors, with a predefined concentration of calibration analytes to induce, when they interact with the receptors, a predefined minimum variation ΔΦ min of the phase shift Φ (n) (t) of each of the interferometers (12 (n)) of Mach-Zehnder.

8. Characterization system (1) according to claim 6, wherein the calibration device (20) comprises a Mach-Zehnder interferometer (22), called calibration, coupled to at least one photodetector (26) called calibration.

9. Characterization system (1) according to claim 8, wherein the calibration interferometer (22) comprises a reference arm (24r) and a discontinuous arm (24d).

10. Method for calibrating a characterization system (1) according to claim 7, comprising the following steps: o activating the light source (11) so that it emits the optical signal at the predefined power; o bringing the calibration analytes into contact with the receptors; o measure by the photodetectors (16) a power P 1(n) (t), P 2(n) (t) optical signals transmitted by each interferometer (12 (n)) of Mach-Zehnder, while the calibration analytes interact with the receptors and induce a variation of the phase shift Φ(n)(t) at least equal to the predefined minimum value ΔΦmin; o determine by the processing unit (3) the values ​​of the calibration parameters Pin(n), o1(n) and o 2(n) from the powers P 1(n) (t), P 2(n) (t) measured, and store in the processing unit (3) the determined values ​​of the calibration parameters P in(n) , o 1(n) and o 2(n).

11. Calibration method according to claim 10, in which the calibration parameters Pin(n), o1(n) and o2(n) are determined from the minimum and maximum values ​​of the powers P1(n)(t), P2(n)(t) measured.

12. Method for calibrating a characterization system (1) according to claim 8, comprising the following step: o measuring, by the calibration photodetector (26), a power of the optical signal transmitted by the calibration interferometer (22), while the light source (11) is activated; o determining a value of the input power Pin,calib of the incident optical signal at an input divider (23) of the calibration interferometer (22); then o determining the input value P in(n) for each of the interferometers (12 (n)) of the measuring device (10), from the determined value Pin,calib.

13. Calibration method according to claim 12, comprising the following steps: o measuring a power P1(n)(t), P2(n)(t) of the optical signals transmitted by each interferometer (12 (n) ) of the measuring device (10), by the photodetectors (16) of the measuring device (10), while the light source (11) is inactive; then o determining the values ​​of the offsets o1(n) and o2(n) from the powers P1(n)(t), P2(n)(t) measured.

14. Method for characterizing analytes by a characterization system (1) according to any one of claims 1 to 9, comprising the following steps: o measuring, by the photodetectors (16) of the measuring device (10), a power P 1(n) (t), P 2(n) (t) optical signals transmitted by each interferometer (12 (n)) of Mach-Zehnder, during a reference phase where the analytes are not present, and during a characterization phase where the analytes are present and interact with the receptors; o determine by the processing unit (3), for each Mach-Zehnder interferometer (12(n)), the phase shift Φ (n) (t) between the optical signals circulating in the arms, from the powers P 1(n) (t), P 2(n) (t) measured and predetermined values ​​of the calibration parameters P in(n) , o 1(n) and o2(n); o determine Φ values i(n) and Φ f(n) from the phase shift Φ (n) (t), associated respectively with the reference phase and the characterization phase; o characterize the analytes from the values ​​Φi(n) and Φf(n).

15. Characterization method according to claim 14, in which the step of determining the phase shift Φ(n)(t) consists of determining: o a phase shift φ (n)(t), called extracted phase shift, whose values ​​are between 0 and 2π, from the powers P 1(n) (t), P 2(n) (t) measured and predetermined values ​​of the calibration parameters Pin(n), o1(n) and o2(n); then o the phase shift Φ(n)(t), called unfolded phase shift, by unfolding the extracted phase shift φ(n)(t) by adding to it a positive or negative integer multiple of 2π.