Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
  • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
  • G01J9/0215—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods by shearing interferometric methods
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
  • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B5/00—Optical elements other than lenses
  • G02B5/18—Diffraction gratings
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
  • G01J2009/002—Wavefront phase distribution
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
  • G01J9/00—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength
  • G01J9/02—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods
  • G01J2009/0249—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods with modulation
  • G01J2009/0253—Measuring optical phase difference; Determining degree of coherence; Measuring optical wavelength by interferometric methods with modulation of wavelength

Definitions

• the present invention relates to a method for the analysis (typically the measurement of the complex field) of an electromagnetic wave in high definition. It also relates to a device implementing a method according to the invention.
• the invention enables a user to improve the performance in terms of resolution and definition of wavefront analyzers.
• the field of the invention is more particularly that of phase analyzers of an electromagnetic wave or a "wavefront".
• state-of-the-art wavefront analyzers are known, for example the SID4 reference range sold by the company Phasics, comprising a sensor-facing array and as used in FIG. the article "Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells "published in the journal OPTICS EXPRESS in 2009 (volume 17, number 15).
• These analyzers make it possible to characterize the incident wavefront by the technique known as quadrilateral shift interferometry. Since the recorded interferogram is almost sinusoidal, a small number of pixels, preferably 4x4, can be used to sample their deformation and to calculate the phase gradients of the incident wavefront and thus improve the resolution of the measurements with respect to Shack-Hartmann technology. It should be noted that the spatial resolution of the phase images remains less than the resolution of the sensor.
• Phase analysis methods are also known, such as that described in the article "Spatial carrier phase-shifting algorithm based on the main component analysis method” published in the journal OPTICS EXPRESS in 2012 (volume 20, number 15). .
• a single interferogram is recorded, then other spatially-shifted interferograms of a number of neighboring pixels are generated by computer, assuming that certain data, in particular the phase, are constant on this number of pixels.
• This method makes it possible to obtain phase images quickly.
• the resolution of the phase images obtained is also not that of the sensor used, since the constant phase is assumed over several pixels. The resolution of the phase measurement is thus reduced compared to that of the sensor.
• the purpose of this method according to the state of the art is not to obtain phase images with a high resolution but to quickly obtain a phase image with a slightly degraded resolution.
• the object of the present invention is to provide a method and / or device for analyzing a faster and / or more compact electromagnetic wave and / or with a better definition or resolution compared to the state of the art.
• This objective is achieved with a method for analyzing an electromagnetic wave, comprising: a reception of an incident electromagnetic wave by a diffractive element, and a transformation of this incident electromagnetic wave into an electromagnetic wave diffracted by the diffractive element, typically by transmission or reflection by the diffractive element
• a matrix sensor having a matrix of pixels aligned along one or two axis (s) of alignment of pixels
• the method comprising several acquisitions, by the matrix sensor, of a signal of the diffracted electromagnetic wave corresponding to several relative positions between the diffractive element and the matrix sensor
• the method comprising a calculation, from the several acquisitions corresponding to the several relative positions between the diffractive element and the matrix sensor, of a value of intensity and / or phase and / or phase gradient for different points of interest of the incident electromagnetic wave.
• the diffractive element and the sensor Preferably there is, between the diffractive element and the sensor, no optical mask and / or no other diffractive element. Preferably there is, between the diffractive element and the sensor, no optical element.
• the diffractive element can generate diffraction orders of the incident electromagnetic wave up to the sensor, preferably:
• the diffractive element is a periodic figure having a spatial periodicity along an axis of periodicity
• the diffractive element is a periodic figure having a spatial periodicity along two or more axes of periodicity.
• the interference pattern received by the matrix sensor can comprise at least nine harmonics or even at least thirteen harmonics, typically:
• the number of the several relative positions may be equal to the number of harmonics of the interference pattern received by the matrix sensor and taken into account by the processing means in the calculation of an intensity value and / or gradient of phase and / or phase.
• the method according to the invention may comprise a generation of diffraction orders of the electromagnetic wave incident by the diffractive element alone.
• the diffractive element is preferably a periodic figure having a spatial periodicity according to at least one or two periodicity axes (and / or preferably diffraction properties according to respectively at least one or two pairs of spatial directions of diffraction) .
• An angle between the periodicity axes of the periodic pattern and the pixel alignment axes may have a different value than another angle between the pixel alignment axes and the motion axes.
• the method according to the invention may comprise a calculation of an optimum value of the angle of inclination.
• the calculation of an optimum value of the angle of inclination may include a maximization of the determinant or conditioning of a matrix corresponding to a system of equations preferably comprising as many equations as the number of several relative positions between diffractive element and the matrix sensor.
• the method according to the invention may furthermore comprise an adjustment of this angle, preferably at its optimum value.
• the plurality of positions preferably correspond to several relative positions between the diffractive element and the matrix sensor for a fixed position of the incident electromagnetic wave.
• the plurality of positions preferably correspond to several positions of the diffractive element for a fixed position of the incident electromagnetic wave and for a fixed position of the matrix sensor.
• the several positions preferably correspond to several relative positions between the diffractive element and the matrix sensor along a displacement axis or two or more axes of displacement, preferably orthogonal to each other.
• Each axis of displacement or at least one of the axes of displacement may be orthogonal to a direction of propagation of the electromagnetic wave incident on the diffractive element.
• Each relative position between the diffractive element and the matrix sensor may differ from at least one of the other relative positions:
• this first pitch preferably being constant for all the relative positions, and / or
• this second pitch preferably being constant for all the relative positions.
• the method according to the invention may comprise a calculation of an optimum value of the first step and / or an optimum value of the second step (including when the step or steps are not constant).
• the calculation of an optimal value of the first step and / or an optimal value of the second step may comprise a maximization of the determinant or the conditioning of a matrix corresponding to a system of equations preferably comprising as many equations as the number of several relative positions between the diffractive element and the matrix sensor
• the multiple positions may correspond to at least three different positions.
• the multiple positions may correspond to at least nine different positions, or even at least thirteen different positions.
• the diffractive element preferably has a spatial periodicity according to at least two periodicity axes.
• the diffractive element may be a mobile diffractive element with respect to the matrix sensor.
• the diffractive element may comprise a Hartmann mask, a Hartmann Shack mask, a diffraction grating, and / or a combination of an intensity grating and a phase grating.
• the diffractive element may be carried or displayed by a fixed optical component relative to the matrix sensor, said optical component being arranged to move the diffractive element (or the display of this diffractive element) relative to the sensor.
• matrix said optical component preferably being a spatial light modulator for example liquid crystal.
• the calculation of a value of intensity and / or phase and / or phase gradient may comprise a resolution of a system of equations preferably comprising as many equations as the number of the several relative positions between the element diffractive and the matrix sensor.
• the system of equations can be solved by using a pseudo inverse matrix (preferably in real or direct space)
• All or part (preferably all but one) of the unknowns of the equation system are preferably expressed as a function of a gradient of the phase of the incident electromagnetic wave.
• a device for analyzing an electromagnetic wave comprising:
• a diffractive element arranged to receive an incident electromagnetic wave and to transform this incident electromagnetic wave into a diffracted electromagnetic wave, typically by transmission or reflection by the diffractive element
• a matrix sensor having a matrix of pixels aligned along one or two axis (s) of pixel alignment, said sensor being arranged to receive an interference pattern of the wave electromagnetic diffracted from the diffractive element,
• the device comprising displacement means arranged to modify the relative position between the diffractive element and the matrix sensor
• said device being arranged to make several acquisitions, by the matrix sensor, of a signal of the diffracted electromagnetic wave corresponding to several relative positions between the diffractive element and the matrix sensor
• the device comprising processing means arranged and / or programmed to calculate, from the several acquisitions corresponding to the several relative positions between the diffractive element and the matrix sensor, a value of intensity and / or phase gradient and / or phase for different points of interest of the incident electromagnetic wave.
• the diffractive element and the sensor Preferably there is, between the diffractive element and the sensor, no optical mask and / or no other diffractive element. Preferably there is, between the diffractive element and the sensor, no optical element.
• the diffractive element can be arranged to generate diffraction orders of the incident electromagnetic wave up to the sensor, preferably:
• the diffractive element is a periodic figure having a spatial periodicity along an axis of periodicity
• the diffractive element is a periodic figure having a spatial periodicity along two or more axes of periodicity.
• the processing means may be arranged and / or programmed to take into account, for the calculation of the intensity value and / or phase gradient and / or phase, at least nine harmonics or at least thirteen harmonics of the figure interference received by the matrix sensor, typically: - nine harmonics, for example in the case of four orders of diffraction of a perfect sinusoidal network on a regular Cartesian grid
• the processing means may be arranged and / or programmed to control the displacement means for a number of several relative positions equal to the number of harmonics of the interference figure taken into account by the processing means in the calculation of a Intensity value and / or phase and / or phase gradient.
• the diffractive element can be arranged to generate by itself diffraction orders of the incident electromagnetic wave.
• the diffractive element is preferably a periodic figure having a spatial periodicity according to at least one or two periodicity axes (and / or preferably diffraction properties according to respectively at least one or two pairs of spatial directions of diffraction) .
• the processing means are preferably arranged and / or programmed to calculate an optimum value of the angle of inclination. These processing means may be arranged and / or programmed to calculate the optimum value of the angle of inclination by a maximization of the determinant or the conditioning of a matrix corresponding to a system of equations preferably comprising as many equations as the number of several relative positions between the diffractive element and the matrix sensor.
• the device according to the invention may furthermore comprise means for adjusting this angle, preferably at its optimum value.
• the multiple positions may correspond to several relative positions between the diffractive element and the matrix sensor for a fixed position of the incident electromagnetic wave.
• the multiple positions may correspond to several positions of the diffractive element for a fixed position of the incident electromagnetic wave and for a fixed position of the matrix sensor, the displacement means being arranged to move the diffractive element for a fixed position of the electromagnetic wave. incident electromagnetic wave and for a fixed position of the matrix sensor.
• the plurality of positions may correspond to several relative positions between the diffractive element and the matrix sensor along a displacement axis or two or more axes of displacement, preferably orthogonal to each other.
• Each axis of displacement or at least one of the axes of displacement may be orthogonal to a direction of propagation according to which the diffractive element is arranged to receive the incident electromagnetic wave.
• the displacement means may be arranged such that each relative position between the diffractive element and the matrix sensor differs from at least one of the other relative positions:
• this first pitch preferably being constant for all the relative positions, and / or
• this second pitch preferably being constant for all the relative positions.
• the processing means are preferably arranged and / or programmed to calculate an optimum value of the first step and / or an optimal value of the second step (including when the step or steps are not constant). These processing means may be arranged and / or programmed to calculate an optimal value of the first step and / or an optimal value of the second step by a maximization of the determinant or the conditioning of a matrix corresponding to a system of equations preferably comprising as many equations as the number of several relative positions between the diffractive element and the matrix sensor. The multiple positions may correspond to at least three different positions.
• the multiple positions may correspond to at least nine different positions, or even at least thirteen different positions.
• the diffractive element preferably has a spatial periodicity according to at least two periodicity axes.
• the diffractive element may be a mobile diffractive element with respect to the matrix sensor.
• the diffractive element may comprise a Hartmann mask, a Hartmann Shack mask, a diffraction grating, and / or a combination of an intensity grating and a phase grating.
• the diffractive element may be carried or displayed by a fixed optical component relative to the matrix sensor, said optical component being arranged to move the diffractive element (or the display of this diffractive element) relative to the sensor.
• matrix said optical component preferably being a spatial light modulator for example liquid crystal.
• the processing means may be arranged and / or programmed to calculate an intensity value and / or phase gradient and / or phase by a resolution of a system of equations preferably comprising as many equations as the number several relative positions between the diffractive element and the matrix sensor.
• the processing means may be arranged and / or programmed to solve the system of equations by using a pseudo inverse matrix (preferably in real space).
• All or part (preferably all but one) of the unknowns of the equation system are preferably expressed as a function of a gradient of the phase of the incident electromagnetic wave.
• FIG. 1 is a schematic view of a preferred embodiment of a device according to the invention embodying a preferred embodiment of the method according to the invention, comprising a periodic figure 2 and a sensor 4,
• FIGS. 3 to 7 are equations explaining this method embodiment of the invention.
• FIG. 8 illustrates the Fourier transform of an interference pattern (or interferogram) of the diffracted wave 10.
• the device 1 comprises a diffractive element 2.
• the diffractive element 2 is a mobile diffractive element 2 because it is mounted on displacement means 3.
• the diffractive element 2 is a periodic figure having a spatial periodicity according to at least one or two periodicity axes (and / or preferably diffraction properties according to respectively at least one or two pair (s) of directions. spatial diffraction).
• This periodic figure 2 may be a periodic transmission figure (as illustrated) or reflection of the incident wave 9.
• the device 1 comprises a sensor 4, preferably a CCD, CMOS, sCMOS or microbolometric image sensor, for example the Bobcat IGV-B2020 camera.
• a sensor 4 preferably a CCD, CMOS, sCMOS or microbolometric image sensor, for example the Bobcat IGV-B2020 camera.
• the displacement means 3 are arranged to modify the relative position between the diffractive element 2 and the matrix sensor 4.
• the displacement means 3 are arranged to modify this relative position or to move the diffractive element 2 according to at least two axes of displacement 16, 17 located in the plane of the diffractive element 2 and preferably orthogonal to each other (and possibly in in addition, for adjustments, according to a third axis of displacement 18 orthogonal to the axes 16, 17).
• the displacement means 3 comprise a motorized stage (piezoelectric or electromagnetic stage) and have a typical displacement accuracy of 2/1000 of the pitch p of the periodic figure 2, typically 40 nm.
• the plate 3 is for example a reference Platinum Newport NPXY200SG platinum.
• the displacement means 3 are connected to means (preferably electronic and / or computer) control 5.
• the means 5 comprise for example an analog and / or digital electronic circuit, and / or a central unit of a computer, and / or a microprocessor, and / or software means.
• the sensor 4 comprises a two-dimensional matrix of pixels aligned along two axes 13, 14 of pixel alignment.
• the pixels are typically square in shape and are aligned along the two axes 13, 14 with a period for example equal to 7.4 .mu.m. In a variant, the period may vary between the two axes 13 and 14. In this embodiment, the two pixel alignment axes 13, 14 are orthogonal to one another.
• the sensor 4 is connected to means 6 (preferably electronic and / or computer) for receiving and processing the signals acquired by the sensor 4.
• the means 6 comprise for example an analog and / or digital electronic circuit, and / or a central unit of a computer, and / or a microprocessor, and / or software means.
• the means 6 are arranged and / or programmed to implement each of the calculation steps described below for the method embodiment of the invention.
• the diffractive element 2, the displacement means 3, the sensor 4, the control means 5, and the processing means 6 are placed inside a housing shown schematically by the reference 7 in FIG.
• the device 1 comprises one or more connectors 8 (for example of the USB type, micro USB, RS232, BNC, etc.).
• Each connector 8 is accessible from outside the casing 7, in particular in order to send to the outside of the device 1 the results of the processing, by the means 6, of the signals acquired by the sensor 4 and / or in order to send, from outside the device 1, instructions to the control means 5 and / or to the processing means 6.
• the diffractive element 2 is arranged to receive an incident electromagnetic wave 9 propagating in a direction of propagation 29.
• the diffractive element 2 is arranged to generate replicas of the incident beam 9 so that these replicas interfere with each other by propagation.
• the displacement means 3 are arranged to move the diffractive element 2 for a fixed position of the incident electromagnetic wave 9 and for a fixed position of the matrix sensor 4.
• the periodic figure 2 is flat.
• the periodic figure 2 has a spatial periodicity according to at least one or two axes of periodicity 11, 12 (the spatial periodicity may vary from one axis of periodicity 11 to another 12).
• the periodic figure 2 has diffraction properties according to respectively at least one or two couple (s) of spatial diffraction directions (32, 34) and / or (31, 33).
• the diffractive element 2 is thus arranged to transform this incident electromagnetic wave 9 into a diffracted electromagnetic wave 10.
• the diffractive element 2 and the sensor 4 are spaced apart by a non-zero distance (along the mean axis of propagation of the diffracted wave).
• the diffracted wave 10 comprises (and preferably consists of) different diffraction orders generated by the diffraction of the incident wave 9 by the periodic figure 2.
• the generated diffraction orders interfere at the level of the matrix sensor 4.
• An interference pattern is obtained which also includes periodicity axes.
• the Fourier transform of the signal obtained by the sensor 4 comprises different harmonics corresponding to the interferences between each pair of diffraction orders. Depending on the model used to describe the formation of this signal, the number of harmonics considered useful varies.
• the propagation direction 29 is perpendicular to the plane of the diffractive element 2 (plane in which the incident wave transformation 9 in the diffracted wave is carried out, and parallel to the axes 11, 12 and / or 16, 17) and / or in the plane of the sensor 4 (plane comprising the pixels of the sensor 4, and parallel to the axes 13, 14).
• the third axis of displacement 18 is perpendicular to the plane of the diffractive element 2 and / or to the plane of the sensor 4.
• the axes 11, 12 are orthogonal to each other.
• each two axes of displacement 16, 17 projected in the plane of the sensor 4, and more precisely in the present embodiment each two axes of displacement 16, 17, is parallel to one of the axes of alignment 13, 14.
• the diffractive element 2 is designed to, on its own, generate or select (that is to say, pass to the sensor 4) that some diffraction orders of the incident electromagnetic wave 9.
• the diffractive element 2 is arranged to perform this generation or selection without combination with another mask or grating or element having diffractive properties which would not be integral with the diffractive element 2.
• the present embodiment is "two-dimensional".
• the diffractive element 2 is arranged to generate at least three diffraction orders of the incident electromagnetic wave 9 up to the sensor 4.
• the diffractive element 2 is arranged to generate at least (or exactly) four diffraction orders of the incident electromagnetic wave 9 up to the sensor 4, and the processing means are arranged and / or or programmed to take into account, for the calculation of the intensity value and / or the phase gradient and / or phase, at least (or exactly) nine harmonics of the interference pattern received by the matrix sensor; even the diffractive element 2 is arranged to generate at least (or exactly) five diffraction orders of the incident electromagnetic wave 9 up to the sensor 4, and the processing means are arranged and / or programmed to take into account, for calculating the intensity value and / or phase and / or phase gradient, at least (or exactly) thirteen harmonics of the interference pattern received by the matrix sensor.
• the diffractive element 2 typically comprises any type of periodic optics.
• the diffractive element 2 comprises, for example, a Hartmann mask or a modified Hartmann mask (or "MHM” for Modified Hartmann Mask) as described for the reference GR of the patent application FR 2 795 175 A1 (typically silica network). with a step of 29.6pm) or a Hartmann Shack mask or a diffraction grating, or a combination of an intensity grating and a phase grating
• No projection of pixel alignment axis 13, 14 in the plane of the periodic figure 2 is preferably parallel to one or to one of the axis (s) 11, 12.
• the element 2 is mounted on adjustment means 20 or rotatable support 20 arranged to allow adjustment of the angular position 15 of the element 2 with respect to the sensor 4.
• the sensor 4 is arranged to receive an interference pattern of the diffracted electromagnetic wave 10.
• the device 1 is arranged to make several acquisitions, by the matrix sensor 4, of a signal of the diffracted electromagnetic wave corresponding to several relative positions (preferably at least three different positions, preferably at least nine different positions) between the diffractive element 2 and the matrix sensor 4.
• Each of these signals is therefore an electronic signal (analog and / or digital) generated by the sensor 4 in response to the reception of the diffracted electromagnetic wave 10 and comprising data for each pixels of the sensor 4.
• the displacement means 3 are arranged so that each relative position between the diffractive element 2 and the matrix sensor 4 differs from at least one of the other relative positions:
• this first pitch preferably being constant for all the relative positions, and / or
• this second pitch preferably being constant for all the relative positions.
• the two axes of displacement 16, 17 are orthogonal to each other.
• the two axes of displacement 16, 17 are orthogonal to the direction of propagation 29 in which the diffractive element 2 is arranged to receive the incident wave 9.
• the device 1 does not include any other element having diffraction properties (grating, etc.) that is not integral with the diffractive element 2.
• the device 1 does not comprise any other element having diffractive properties. (network, etc.) that does not move when the diffractive element 2 moves (under the action of the plate 3).
• This method comprises receiving the incident electromagnetic wave 9 by the diffractive element 2.
• This wave is for example a beam almost collimated white light coming out of a microscope.
• the incident electromagnetic wave 9 is not focused on the diffractive element 2.
• the incident electromagnetic wave 9 is focused on no point of the diffractive element 2.
• the wave 9 propagates in a direction of propagation 29 perpendicular to the plane of the diffractive element 2 and / or to the plane of the sensor 4.
• the wave 9 propagates in a direction of propagation 29 perpendicular to the axes 11 and 12.
• the method embodiment of the invention comprises a transformation of this incident electromagnetic wave 9 into the electromagnetic wave diffracted by the diffractive element 2.
• Wave 10 propagates in a medium direction of propagation
• each order propagating in its respective propagation direction 31, 32, 33 or 34 (in the case of 4 orders).
• the direction 30 is perpendicular to the plane of the diffractive element 2 and / or to the plane of the sensor 4.
• the propagation direction 30 is perpendicular to the axes 13 and
• the propagation directions 29 and 30 are identical.
• the diffractive element 2 generates or selects, alone (in particular without any combination with another mask or grating or element having diffraction properties not integral with the diffractive element 2), certain diffraction orders of the incident electromagnetic wave 9.
• the diffractive element 2 generates at least three diffraction orders, preferably:
• At least four diffraction orders (or exactly four diffraction orders, for example distributed around the optical axis 10, 30 with an angle of 90 ° separating each of them, these orders propagating in their respective directions; , 32, 33 and 34, as illustrated in FIG. 1) or - at least five diffraction orders (or exactly five diffraction orders, comprising the four orders previously described and, in addition, the zero order which propagates along the axis optical 10,30)
• FIG. 8 illustrates the Fourier transform of an interference pattern (or interferogram) in the case of a diffracted wave comprising four diffraction orders.
• the nine harmonics corresponding to the nine square areas delimited by dashed lines.
• the number of harmonics of the interference pattern received by the matrix sensor, and taken into account in the calculation of an intensity value and / or a phase gradient and / or phase may comprise at least nine harmonics or at least thirteen harmonics, typically:
• the method embodiment according to the invention comprises a reception of an interference pattern of the electromagnetic wave diffracted by the matrix sensor 4.
• the embodiment of the method according to the invention comprises several acquisitions, by the matrix sensor 4, of a signal of the diffracted electromagnetic wave corresponding to several relative positions between the diffractive element 2 and the matrix sensor 4.
• each acquisition, by the matrix sensor 4, of a signal of the diffracted electromagnetic wave 10 corresponds to:
• the several positions correspond to several relative positions between the diffractive element 2 and the matrix sensor 4 for a fixed position of the incident electromagnetic wave 9, plus exactly at several positions of the diffractive element 2 for a fixed position of the incident electromagnetic wave 9 and for a fixed position of the matrix sensor 4.
• the several positions correspond to several relative positions between the diffractive element 2 and the matrix sensor 4 along the two axes of displacement 16, 17.
• the axes of displacement 16, 17 are orthogonal to each other.
• each of the two displacement axes 16, 17, is orthogonal to the mean propagation direction 29 of the incident electromagnetic wave 9 on the diffractive element 2.
• the multiple positions correspond to at least three, preferably at least nine different positions.
• Each relative position between the diffractive element 2 and the matrix sensor 4 differs from at least one of the other relative positions:
• this pitch dy c being preferably constant for all the relative positions.
• sweep Any form of sweep can be used: grid, S, spiral, etc.
• the pitch dx c or dy c has a typical value of between 10 ⁇ m and 30 ⁇ m, with an accuracy of at least 0.04 ⁇ m (always in the case of a MHM).
• the diffraction element 2 is moved in order to shift in phase each of the harmonics composing the spectrum of the interferogram.
• the method embodiment according to the invention comprises a calculation (by the processing means 6), from the several acquisitions corresponding to the several relative positions between the diffractive element 2 and the matrix sensor 4, of a value of intensity and / or phase gradient and / or phase of the incident electromagnetic wave 9 at each of the points of the matrix sensor 4.
• This calculation comprises, for each of the points of interest of the incident electromagnetic wave 9, a resolution of a system of equations comprising as many equations as the number of several relative positions between the diffractive element 2 and the matrix sensor 4.
• the system of equations is solved for example by using a pseudo inverse matrix, in real space or in the Fourier space.
• the pseudo-inverse matrix is computed for example from the linear singular value decomposition algebra algorithm (SVD) which makes it possible to decompose the matrix into singular values. When the singular values are too low, these values are not taken into account when calculating the pseudo inverse matrix.
• the pseudo-inverse matrix makes it possible to find the solution to a system of linear equations in the least squares sense.
• N harmonic or exactly N harmonic (with N an integer, preferably greater than or equal to 2, preferably greater than or equal to 9)
• the diffractive element 2 comprises a combination of an intensity network and a phase grating as described for the reference GR of the patent application FR 2 795 175 A, and is arranged to select only 4 diffraction orders.
• the number of harmonics will be nine: 0 (crossing of the axes 11 and 12 projected on the plane of the sensor 4); +/- 1 along the axis 11 projected on the plane of the sensor 4; +/- 1 along the axis 12 projected on the plane of the sensor 4 and +/- 1 according to the two diagonals between these two axes 11 and 12 projected on the plane of the sensor 4.
• the diffractive element 2 considered in this example is the mask
• the approach used here is based on calculations in the Fourier space. They make it possible to manage the sinusoidal aspect of the fringes and thus to exploit the information contained in the pixels between the maxima, thanks to a sinusoidal fit.
• Io a constant corresponding to the intensity of the incident wave
• This distance z is typically less than 1 mm, to improve the sensitivity to phase variations;
• I 2 (x, y; dx, dy) a + be p + this p + of p +
• the resolution of the inverse pseudo matrix system therefore makes it possible to find the unknowns a, b, c, d, e, f, g, h, i.
• measurement resolution is understood to mean the smallest dimension of phase or intensity measurement or of phase gradients resolved by the sensor.
• sensor resolution is meant the smallest dimension detected by the sensor. This is typically the pixel size of this sensor.
• the intensity recorded by the sensor can be written as:
• the information sought to recover the amplitude of the electro ⁇ magnetic field is contained in the terms A m A n *.
• a m A n * At each point r of the detector, we have a measure I (r) and sixteen unknowns A m A n * (m, n are integers ranging from 1 to 4). If we make a Fourier transform of the signal I (r), because of symmetries, the information is in fact grouped around nine harmonics corresponding to the coefficients a, b, c, ...
• the windowing around the harmonics is no longer performed. Indeed, the displacement of the periodic figure 2 between each acquisition will make it possible to obtain the totality of the information contained by each harmonic.
• This optical component is preferably a spatial light modulator, such as a liquid crystal modulator, which displays the diffraction element 2 or the periodic figure 2 and moves the diffraction element 2 or the periodic figure 2 by modifying its display.
• a spatial light modulator such as a liquid crystal modulator
• Calculation of an optimum value of the pitch dx (or dx c ) and / or of an optimal value of the pitch dy (or dy c ) comprises a maximization of the determinant or the conditioning of a matrix corresponding to a system of equations comprising as many equations as the number of several relative positions between the periodic figure and the matrix sensor.
• the determinant or the conditioning of the matrix depends both on the displacements dx c and dy c of the plate 3 but also on the angle of inclination 15 of the grating 2.
• the optimum value of the inclination angle and / or the optimum value of the first step and / or the optimum value of the second step is arranged to minimize the calculation errors of the unknowns (coefficients a, b, c, d , e, f, g, h, i) of this system of equations.
• the determinant or conditioning for different triplets (dx c , dy c , 9) is calculated. Triplets for which the value of the determinant or the conditioning is high make it possible to determine the optimal points for the realization of "high-definition" phase images.
• This optimum pitch and / or angle value calculation may be performed by the device 1 before a measurement on the wave 9, or may be implemented during the construction or design or calibration of the device 1 .
• the sensor 4 is moved.
• the several relative positions correspond to several positions of the matrix sensor 4 for a fixed position of the incident electromagnetic wave 9 and for a fixed position of the periodic figure 2.
• this variant is less advantageous because it requires the interferograms to be readjusted. so that each of the pixels (x, y) of each interferogram correspond to the same points of the incident beam; and or
• the several relative positions correspond to several relative positions between the periodic figure 2 and the matrix sensor 4 according to a single axis of displacement 16 (this single axis of displacement 16 is then preferably orthogonal to the direction of propagation 29 of the electromagnetic wave incident 9 in the periodic figure 2). This can be the case:
• the periodic figure 2 comprises diffraction properties only along an axis of periodicity 11; or
• the periodic figure 2 has a spatial periodicity according to more than two periodicity axes (and thus generates more than five diffraction orders). This is for example the case of a diffractive element 2 comprising a grating with a hexagonal periodic pattern; and or
• steps dx or dx c , and / or dy or dy c are not necessarily constant between the different relative positions; and or
• optical elements between the periodic figure 2 and the sensor 4 in particular lenses for adapting the size of the wave 10 to the sensor 4 and / or mirrors for conveying the wave 10 to the sensor 4.
• this variant is less advantageous because it increases the volume and size of the device 1; and or
• the calculation method is not necessarily matrix. Any method for solving the system of P equations is compatible with the invention. and or
• the calculation method is not necessarily in real or Fourier space. We can actually use any function that has an inverse function to return to the starting space, since the calculations are based on linear combinations, and / or

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• Physics & Mathematics (AREA)
• Spectroscopy & Molecular Physics (AREA)
• General Physics & Mathematics (AREA)
• Optics & Photonics (AREA)
• Length Measuring Devices By Optical Means (AREA)
• Diffracting Gratings Or Hologram Optical Elements (AREA)
• Investigating, Analyzing Materials By Fluorescence Or Luminescence (AREA)

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• 2016
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