Device and method for reconstructing a wavefront
Patent Information
- Application Number
- FR2023008770
- Authority / Receiving Office
- FR · FR
- Patent Type
- Patents
- Current Assignee / Owner
- Filing Date
- 2023-08-18
- Publication Date
- 2025-09-05
- Estimated Expiration
- 2043-08-18
Abstract
Description
Title of the invention: Device and method for reconstructing a wavefront
[0001] The present invention relates to a device for reconstructing a wavefront. The present invention also relates to an associated method for reconstructing a wavefront.
[0002] The invention falls within the scope of microwave test benches used to evaluate the performance of algorithmic processing (radar or other) carried out by sensors arranged within an anechoic chamber. In particular, the invention arose within the scope of pre-studies carried out for the design of future test benches, the objective being to size as accurately as possible the anechoic chambers which will equip these test benches.
[0003] The criterion commonly used by designers to size a chamber is the Fraunhofer criterion, which gives the minimum distance to be respected in order to operate in far-field conditions (quasi-plane wavefront) when the emission source is point-like. However, the strict application of this criterion can give pessimistic chamber dimensions depending on the working frequency and the antenna diameter of the equipment under test (MST) considered. In addition, if the emission source is composed of several point sources, the Fraunhofer criterion is no longer applicable. Under these conditions, we can no longer rely on simple models (spherical wavefront) to size the chamber optimally.
[0004] In the context of a study aimed at evaluating the impact of the flatness defect of a wave emitted by a point (or multi-point) source on the performance of the processing carried out by a material under test (MST), we simulated the profile of the wavefront present at the level of the MST antenna (as a reminder, the wavefront is a theoretical construction representing the three-dimensional isophase surface of a radio wave). Since the simulated profile comes from a theoretical model, we must ensure that it is related to physical reality.
[0005] However, the direct reconstruction of a real wavefront by measuring its phase using an appropriate probe at any point in the area of interest is a complex operation.
[0006] In particular, a known solution consists of measuring, using an appropriate probe, integral with a suitable mechanical positioning device, the amplitude and phase of the electric field at any point in the portion of the plane in which the MST antenna is located. If the measurement of the amplitude does not pose any particular problem, on the other hand, that of the phase is a delicate operation due to the short wavelengths (centimetric waves) characterizing the microwave domain: a defect in positioning the probe by a few millimeters can in fact induce a significant phase error.
[0007] There is therefore a need for a means for reliably determining the shape of a wavefront.
[0008] To this end, the invention relates to a device for reconstructing a wavefront from an emitting source, the device comprising:
[0009] - an anechoic box, one of the faces of which is a grid pierced with several or openings, the emitting source being positioned at a distance d from the grid so that the wavefront from the emitting source is diffracted by each opening of the grid and generates an interference pattern in the anechoic box,
[0010] - a measuring unit suitable for measuring the variations in intensity of the figure of interference generated,
[0011] - a processing unit suitable for:
[0012] • determine path differences for the incident wavefront on the grid in function of the measurements made by the measuring unit, and
[0013] • reconstruct the incident wavefront on the grid as a function of the differences in determined steps.
[0014] According to other advantageous aspects of the invention, the device comprises one or more of the following characteristics, taken individually or in all technically possible combinations:
[0015] - the measuring unit comprises a probe secured to an electromechanical unit suitable for performing a linear scan of the interference pattern;
[0016] - the measuring unit comprises a matrix of probes, preferably electro-optical, suitable for taking a snapshot of the interference pattern;
[0017] - the processing unit is capable of processing the measurements made so as to reduce the signal-to-noise ratio of the measurements, the determination of the path differences being carried out with the processed measurements;
[0018] - when the interference pattern is symmetrical, the interference pattern comprises several unit portions of identical shape, the union of which forms the interference pattern, the processing comprising the determination of denoised values for a unit portion, called the reference portion, by averaging the corresponding measurements of all the unit portions, and the duplication of the reference unit portion to form a denoised interference pattern, the intensity values of the denoised interference pattern forming the processed measurements, and / or
[0019] - when the interference pattern is not symmetrical, the processing comprises:
[0020] • applying a transformation to frame the interference pattern in a enclosing figure, the enclosing figure being a symmetrical figure comprising several unit portions of identical shape, the union of which forms the enclosing figure global,
[0021] • the determination of denoised values for a unit portion, called reference, of the encompassing figure by averaging the corresponding measurements of all the unit portions, and duplicating the reference unit portion to form a denoised encompassing figure, and
[0022] • applying an inverse transformation to the denoised encompassing figure for obtaining a denoised interference pattern, the intensity values of the denoised interference pattern forming the processed measurements;
[0023] - the walking differences are determined by the processing unit by mini implementation of a cost function according to the least squares criterion, the cost function evaluating the difference between the measurements made on the interference pattern, and the corresponding expected values from a theoretical model;
[0024] - the anechoic box is a volume with several internal walls covered of a material absorbing electromagnetic waves;
[0025] - the grid is a conductive plate whose openings are circular holes or hexagonal, the positions of the openings corresponding to the nodes of a periodic two-dimensional network generated by the repetition of an elementary mesh exhibiting rotational symmetry.
[0026] The invention also relates to a method for reconstructing a wavefront from an emitting source by a reconstruction device, in which the method comprises:
[0027] - the generation of a wavefront by the emitting source positioned at a distance d of the anechoic box grid,
[0028] - the diffraction of the wavefront by each opening of the grid and the generation of an interference pattern in the anechoic box,
[0029] - the measurement, by the measurement unit, of the variations in intensity of the figure of interference generated,
[0030] - the determination, by the processing unit, of the path differences for the front incident wave on the grid as a function of the measurements made by the measuring unit, and
[0031] - the reconstruction, by the processing unit, of the incident wavefront on the grid in function of the determined walking differences.
[0032] Optionally, the method comprises repeating the steps of the method for different distances d from the emitting source to the grid of the box, and determining a distance d from which the wavefront incident on the grid meets a flatness criterion.
[0033] The invention will appear more clearly on reading the description which follows, given solely by way of non-limiting example, and made with reference to the drawings in which:
[0034] [Fig.l] [Fig.l] is a schematic view of an example of a reconstruction device,
[0035] [Fig.2] [Fig.2] is a schematic view of an example of the diffraction of a wavefront from a point source by openings in a grid so as to form an interference pattern,
[0036] [Fig.3] [Fig.3] is a schematic view of an example of the unit portions of a symmetrical interference pattern,
[0037] [Fig.4] [Fig.4] is a schematic view of an example of an enclosing figure framing a non-symmetrical interference figure, the enclosing figure being divided into unit portions, and
[0038] [Fig.5] [Fig.5] is a schematic view of an example flowchart of a wavefront reconstruction method.
[0039] A device 10 for reconstructing a wavefront F! from an emitting source S is illustrated by [Fig.l].
[0040] The emitting source S is capable of emitting an electromagnetic wave having one or more wavelengths X. The electromagnetic wave propagates in the form of a wave front Fb
[0041] The emitting source S is, for example, a point source or a multi-point source (i.e. composed of several point sources).
[0042] The device 10 comprises an anechoic box 12, a measurement unit 14 and a processing unit 16. Preferably, as illustrated by [Fig.l], the anechoic box 12, the measurement unit 14 and the emitting source S are inside the same chamber 18 (anechoic or not).
[0043] The anechoic box 12 is a volume of which at least some of the internal faces absorb sound or electromagnetic waves so as to reproduce free field conditions.
[0044] One of the faces of the anechoic box 12 is a grid 20 pierced with several openings 22.
[0045] The emitting source S is positioned at a distance d from the grid 20 so that the wavefront Fb coming from the emitting source S and incident on the grid 20 is diffracted by each opening 22 of the grid 20 and generates an interference pattern F in the anechoic box 12. The interference pattern F is formed for example on the face of the anechoic box 12 opposite the grid 20. As a variant, the interference pattern F is formed on a projection screen positioned, for example, on the face of the anechoic box 12 opposite the grid 20.
[0046] [Fig.2] illustrates an example of diffraction of a point source S by a grid 20 comprising openings 22 arranged in a crown to form a figure of interference F at point M. Note that [Fig.2] is purely didactic. It represents in fact a particular case intended to illustrate the principle of the invention. In practice, a grid is formed not of one but of a plurality of concentric crowns or by the periodic repetition of an elementary mesh whose vertices coincide with the openings or possibly of a plurality of openings arranged on the plate according to a given distribution.
[0047] Preferably, all the walls of the anechoic box 12 are covered with a material absorbing electromagnetic waves at the wavelength of the wavefront F! incident on the grid 20, with the exception of the face formed by the grid 20 and the opposite face where the interference pattern F is formed. The material is, for example, a polymer foam or glass fibers. The polymer foam is, for example, impregnated with a material absorbing radio waves at the frequencies considered.
[0048] In addition or as a variant, the external face (directed towards the source S) of the metal plate in which the openings 22 forming the grid 20 are pierced is also covered with an absorbent material.
[0049] In one example, the anechoic box 12 is a volume having 6 faces, such as a rectangular parallelepiped or a truncated pyramid. Alternatively, the anechoic box 12 is formed by a surface of revolution.
[0050] Preferably, the shape of the anechoic box 12 is flared so as to resemble that of a gramophone horn (the mouthpiece being located on the side of the grid and its diameter being at least equal to that of the latter). This makes it possible to avoid multipaths likely to occur inside the anechoic box 12 and which contribute to the genesis of the interference pattern (even when they have been attenuated thanks to the absorbent coating with which the interior walls of the box are lined). Thus, the interference pattern appearing in the central zone of the projection plane opposite that of the grid would be produced only by the direct paths (this results in increased conformity with the theoretical model used during the minimization of the least squares criterion). In practice, the anechoic box 12 has the shape of a truncated pyramid or truncated cone (simpler to produce than a true flared shape).
[0051] Preferably, the grid 20 is a conductive plate whose openings 22 are circular or hexagonal holes. The positions of the openings 22 correspond to the nodes of a periodic two-dimensional network generated by the repetition of an elementary mesh having rotational symmetry. The following elementary meshes are preferred: equilateral triangular mesh, square mesh, or hexagonal mesh.
[0052] Preferably, the diameter of the holes is of the order of the wavelength of the front wavelength Fb ideally equal to the wavelength of the wavefront Fb
[0053] The measuring unit 14 is suitable for measuring the intensity, in particular the intensity variations (troughs and peaks), of the interference pattern F generated.
[0054] The measuring unit 14 comprises, for example, a probe secured to an electromechanical unit capable of performing a linear scan of the projection screen. The linear scan is typically in boustrophedon.
[0055] Alternatively, the measuring unit 14 comprises a matrix of probes suitable for taking a snapshot of the projection screen. The probes are preferably electro-optical probes due to their compactness and their ability to perform a very precise localized measurement of the electric field without inducing any disturbance. In particular, each probe of the matrix is suitable for transforming the electric field of the incident wave that it captures into an analog signal. The analog signals are then digitized by a digitizing unit to obtain an image of the interference pattern F.
[0056] The processing unit 16 is capable of reconstructing the wavefront F! incident on the grid 20 as a function of the measurements carried out by the measuring unit 14.
[0057] The processing unit 16 is, for example, a calculator.
[0058] In one example, the processing unit 16 interacts with a computer program product that includes an information medium. The information medium is a medium readable by the computing unit. The computer program product including program instructions is stored on the information medium. The computer program can be loaded onto the processing unit 16 and causes the steps of determining path differences and reconstructing the wavefront Fb to be implemented when the computer program is implemented on the processing unit 16.
[0059] Optionally, the processing unit 16 is capable of processing the measurements carried out so as to reduce the signal-to-noise ratio of the measurements, the reconstruction of the wavefront F being carried out with the processed measurements. In particular, the processing makes it possible to improve the signal-to-noise ratio of the luminance of the image obtained from the interference pattern F (i.e. of the signal which corresponds to the contrast values of an image, from the deepest black to the purest white).
[0060] In one example, when the interference pattern F is symmetrical, the interference pattern F comprises several unit portions PU of identical shape, the union of which forms the interference pattern F. For example, [Fig. 3] illustrates an interference pattern F of circular shape divided into 6 equal portions. The processing comprises the determination of denoised values for a unit portion, called reference, by averaging the corresponding measurements of all the unit portions PU (i.e. for each sampled point of the portion of reference, the values measured at this point for all the unit portions PU are averaged). The reference portion is then duplicated to form a denoised interference pattern F. The intensity values of the denoised interference pattern F form the processed measurements.
[0061] In another example, when the interference pattern F is not symmetrical, the processing comprises applying a transformation to frame the measured interference pattern F in an enclosing pattern FE. The enclosing pattern FE is a symmetrical pattern comprising several unit portions PU of identical shape, the union of which forms the enclosing pattern FE. The processing further comprises determining denoised values for a unit portion, called a reference portion, of the enclosing pattern FE by averaging the corresponding measurements of all the unit portions PU, and duplicating the reference unit portion to form a denoised enclosing pattern FE. The processing finally comprises applying an inverse transformation to the denoised enclosing pattern FE to obtain a denoised interference pattern F. The intensity values of the denoised interference pattern F form the processed measurements.
[0062] The processing unit 16 is capable of determining path differences for the wavefront F! incident on the grid 20 as a function of the measurements (possibly processed measurements) carried out by the measuring unit 14.
[0063] In an exemplary implementation, the walking differences are determined by the processing unit 16 by minimizing a cost function according to the least squares criterion. The cost function evaluates the difference between the measurements made on the interference pattern F, and corresponding expected values from a theoretical model.
[0064] An example of the algorithm used is given in the following, taking the example of a point emitting source S located on the axis () - at L meters from a grid 20 with center Q comprising C concentric rings of radius lc ( 1 < c < C) and a wave front whose geometric profile is of revolution (see figure 2). The interference pattern located in the Oxy plane (at D meters from the grid 20) is sampled uniformly along the Ox and Oy axes. The intensity measured at point M of the interference pattern with coordinates ( Y v ] is noted Ppq. (Xp, yg}
[0065] The interference phenomenon at this point is modeled as follows: [00661 y J =
[0067] Where: A denotes the amplitude of the incident wave, d, the path difference (or phase difference) between the circle passing through the centers of the holes in the crown of the grid 20 of index c and the backprojection of this circle onto the incident wavefront, N( c) the number of holes in the crown of index c, k the wave number, P (1 pi P) (l <q<Q) les indices dénombrant l’ensemble des échantillons de coordonnées *P ) dans 'C ^'an r<:J‘ 'a distance entre le centre du trou d’indice n de la couronne d’indice c.
[0068] The phase differences (P) characterizing the incident wavefront are estimated by minimizing according to the least squares criterion the following cost function:
[0069] T _yp yG / * _ \2 ^ / ^=1-^(7=1 \ ^P^Zp^ Pp-d )
[0070] The product Zp^Zp^ is simplified as follows:
[0071] * / * x Ve (z*z) = EX b ' pq ab (z^z) = A^S^-ZR^'X^ e^P^ypA 1 • ' Pd [ fy^ay^b^a ' a,b / ]
[0072] Where: R denotes the real part and ( • ) the complex conjugation.
[0073] With:
[0074] = =
[0075] Either: 100761
[0077] Where: I denotes the imaginary part.
[0078] The cost function is finally written:
[0079] L = -sin(5c-Ô^)l(y^) ) ] -pM)
[0080] The phase differences 5C ( 1 < C < C ) sought are obtained by writing:
[0081] ^-=0(l <c<C) dbc v
[0082] And by solving the obtained system.
[0083] The algorithm we have just presented takes advantage of the geometric properties of the grid 20 and the wavefront. If the distribution of holes on the plane O xv is arbitrary then the interference phenomenon at point M is modeled as follows: 100841 V ) = zpq = a£W £° =XT
[0085] Where: Jl (1 n < TV) and ° (1 o < O) designate the indices counting the set of holes with coordinates T^xn, y ) in the Oxy plane
[0086] The processing unit 16 is capable of reconstructing the wavefront F! incident on the grid 20 according to the determined path differences. Indeed, knowing the path difference for different points of the wavefront F makes it possible to reconstruct the shape of the wavefront Fb
[0087] A method of reconstructing a wavefront F! from an emitting source S by a reconstruction device 10 as described previously will now be described with reference to [Fig.5].
[0088] The reconstruction method comprises a step 100 of generating a wavefront F, by the emitting source S positioned at a distance d from the grid 20 of the anechoic box 12.
[0089] The reconstruction method comprises a step 110 of diffraction of the wavefront F, by each opening 22 of the grid 20 and the generation of an interference pattern F on the projection screen present in the anechoic box 12.
[0090] The reconstruction method comprises a step 120 of measuring, by the measuring unit 14, the variations in intensity of the generated interference pattern F.
[0091] The reconstruction method comprises a step 130 of determining, by the processing unit 16, the path differences for the wavefront F! incident on the grid 20 as a function of the measurements carried out by the measuring unit 14.
[0092] The reconstruction method comprises a step 140 of reconstruction, by the processing unit 16, of the wavefront F! incident on the grid 20 as a function of the determined path differences.
[0093] In a specific embodiment aimed for example at determining the most accurate dimensions of an anechoic chamber, the method comprises repeating the steps of the method for different distances d from the emitting source S to the grid 20 of the anechoic box 12, and determining a distance d from which the wavefront F, incident on the grid 20, meets a flatness criterion. Typically, the flatness criterion makes it possible to evaluate from what distance d the flatness of the wavefront F is considered acceptable for the desired application.
[0094] Thus, the present invention makes it possible, by acquiring measurements of the interference pattern generated by the grid and following digital processing, to reconstruct the three-dimensional surface of the incident wavefront. The invention thus makes it possible to determine the shape of a wavefront in a simple and reliable manner. It also provides, depending on the embodiments, the following advantages: - The wavefront is reconstructed by simply measuring the intensity variations corresponding to the fringes (or troughs and peaks) of an interference pattern. - The interference pattern obtained presents a rotational symmetry, the exploitation of which makes it possible to improve the signal-to-noise ratio of the luminance (intensity variations) of the image obtained after sampling. The sensitivity of the method to the distance separating the source from the grid is high, which allows the evolution of the curvature of the wavefront with distance to be accurately measured. It is possible to acquire a snapshot of the wavefront with probe arrays, which is not possible with a high-precision mechanical positioning system due to the measurement time. In a dynamic context (when the emitting source is in motion), we can consider cinematographing the temporal evolution of the wavefront.
[0095] The device and method described have been proposed in the context of an experiment whose object is the acquisition of real static wavefronts in order to validate the results of a theoretical simulation. This device and method are also compatible with the following applications: antenna design, anechoic chamber design, study of the temporal evolution of real wavefronts, or validation and qualification of test means.
[0096] Those skilled in the art will understand that the described embodiments can be combined provided that they are technically compatible.
Claims
Claims
1. Device (10) for reconstructing a wavefront (FO) from an emitting source (S), the device (10) comprising: - an anechoic box (12) one of the faces of which is a grid (20) pierced with several openings (22), the emitting source (S) being positioned at a distance d from the grid (20) so that the wavefront (FO) from the emitting source (S) is diffracted by each opening (22) of the grid (20) and generates an interference pattern (F) in the anechoic box (12), - a measuring unit (14) capable of measuring the variations in intensity of the interference pattern (F) generated, - a processing unit (16) capable of: • determining path differences for the wavefront (FO incident on the grid (20) as a function of the measurements carried out by the measuring unit (14), and • reconstructing the wavefront (FO incident on the grid (20) as a function of the determined path differences.
2. Device (10) according to claim 1, in which the measuring unit (14) comprises a probe secured to an electromechanical unit capable of carrying out a linear scan of the interference pattern (F).
3. Device (10) according to claim 1, in which the measuring unit (14) comprises a matrix of probes, preferably electro-optical, capable of taking a snapshot of the interference pattern (F).
4. Device (10) according to any one of claims 1 to 3, in which the processing unit (16) is capable of processing the measurements carried out so as to reduce the signal-to-noise ratio of the measurements, the determination of the path differences being carried out with the processed measurements.
5. Device (10) according to claim 4, in which: - when the interference pattern (F) is symmetrical, the interference pattern (F) comprises several unit portions (PU) of identical shape, the union of which forms the interference pattern (F), the processing comprising the determination of denoised values for a unit portion, called reference, by averaging the corresponding measurements of all the unit portions (PU), and duplicating the reference unit portion to form a denoised interference pattern (F), the intensity values of the denoised interference pattern (F) forming the processed measurements, and / or - when the interference pattern (F) is not symmetrical, the processing comprises: • applying a transformation to frame the interference pattern (F) in an enclosing pattern (FE), the enclosing pattern (FE) being a symmetrical pattern comprising several unit portions (PU) of identical shape, the union of which forms the enclosing pattern (FE), • determining denoised values for a unit portion, called the reference, of the enclosing pattern (FE) by averaging the corresponding measurements of all the unit portions (PU), and duplicating the reference unit portion to form a denoised enclosing pattern (FE),and • applying an inverse transformation to the denoised bounding figure (FE) to obtain a denoised interference figure (F), the intensity values of the denoised interference figure (F) forming the processed measurements.,
6. Device (10) according to any one of claims 1 to 5, in which the walking differences are determined by the processing unit (16) by minimizing a cost function according to the least squares criterion, the cost function evaluating the difference between the measurements carried out on the interference pattern (F), and corresponding expected values from a theoretical model.
7. Device (10) according to any one of claims 1 to 6, in which the anechoic box (12) is a volume of which several internal walls are covered with a material absorbing electromagnetic waves.
8. Device (10) according to any one of claims 1 to 7, in wherein the grid (20) is a conductive plate whose openings (22) are circular or hexagonal holes, the positions of the openings (22) corresponding to the nodes of a periodic two-dimensional network generated by the repetition of an elementary mesh having rotational symmetry.
9. Method for reconstructing a wavefront (FO) from an emitting source (S) by a reconstruction device (10) according to any one of claims 1 to 8, in which the method comprises: - the generation of a wavefront (FO) by the emitting source (S) positioned at a distance d from the grid (20) of the anechoic box (12), - the diffraction of the wavefront (FO) by each opening (22) of the grid (20) and the generation of an interference pattern (F) in the anechoic box (12), - the measurement, by the measuring unit (14), of the variations in intensity of the interference pattern (F) generated, - the determination, by the processing unit (16), of the path differences for the wavefront (FO incident on the grid (20) as a function of the measurements carried out by the measuring unit (14), and - the reconstruction, by the processing unit (16), of the wavefront (FO incident on the grid (20) as a function of the determined path differences.
10. A method according to claim 9, wherein the method comprises repeating the steps of the method for different distances d from the emitting source (S) to the grid (20) of the box, and determining a distance d from which the wavefront (FO incident on the grid (20) meets a flatness criterion.