Low noise speckle interferometry system and method based on a spatial light modulator

Abstract

The application provides a low-noise speckle interferometry system and method based on a spatial light modulator, relates to the technical field of speckle interferometry, and comprises a laser, a light splitting prism one and an imaging element; a laser beam emitted by the laser is split into transmitted light and reflected light by the light splitting prism one; part of the transmitted light is reflected by a light splitting prism three and then irradiated on the imaging element as reference light; part of the reflected light sequentially passes through a linear polarizer and a half-wave plate, is modulated by a spatial light modulator assembly, is irradiated on a light splitting prism four, is reflected to a measured object surface to occur diffuse reflection, and slow light is obtained; the speckle interferometry system modulates object light by using the spatial light modulator assembly, makes the emitted light modulated by the spatial light modulator assembly irradiate the measured object at multiple illumination angles, forms independent speckle fields on a target surface of the imaging element, and can effectively suppress speckle de-correlation noise after multiple measurement superposition, and then the accuracy of subsequent measurement results is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of speckle interferometry, and particularly relates to a low-noise speckle interferometry system and method based on a spatial light modulator. BACKGROUND

[0002] As a non-contact and high-sensitivity optical measurement method, speckle interferometry is widely used in the detection and analysis of small deformations of rough surfaces. However, in the actual application process, the phase fringe pattern obtained by speckle interferometry is inevitably affected by speckle decorrelation noise. This noise mainly comes from the misalignment of speckle patterns caused by object deformation, which significantly limits the measurement accuracy. In addition, with the increase of the coherence of the laser light source, this noise will further increase, seriously affecting the accuracy of the measurement results.

[0003] There have been a lot of researches on using image denoising algorithms and other image post-processing measures to suppress speckle decorrelation noise. Although speckle decorrelation noise is uniformly present at the statistical level, the noise at the edge of the fringe is in the phase jump itself, so it is very difficult to suppress the noise while protecting the edge. Filter algorithms mainly include spatial filter algorithms represented by sine and cosine transformation and frequency domain filter algorithms represented by windowed Fourier transform and wavelet transform. Filter algorithms have the conflict between time consumption and filtering effect. For example, the sine and cosine transformation has poor effect when dealing with high-density and high-noise fringes, while the windowed Fourier transform has the problems of needing to adjust a large number of parameters, long time consumption, and high threshold, etc. Therefore, simply using filter methods to suppress speckle decorrelation noise restricts the practicability of speckle interferometry.

[0004] In the prior art, a lot of researches have been conducted on speckle contrast suppression in the fields of holography and laser projection. For example, PICART et al. modeled the speckle noise decorrelation degree in dual-wavelength and multi-wavelength holography, and proposed a new correlation coefficient expression; YAMADA, TRINH-THI-KIM et al. weakened the temporal coherence of laser in laser projection by changing the illumination angle and wavelength; Lixin Xu et al. used a rotating spherical lens to reduce the temporal coherence of laser, so that the speckle coherence was reduced to a level that could not be detected by the human eye; Morozov et al. designed a passive speckle suppression device based on the combination of a prism and a Fresnel lens, which could suppress speckle coherence while ensuring illumination uniformity.

[0005] However, most of these researches are aimed at reducing the speckle contrast in intensity images, while speckle interferometry relies on high speckle contrast to improve fringe quality, so the noise suppression methods in holography cannot be directly applied to speckle interferometry.

[0006] Therefore, how to reduce the speckle decorrelation noise in the speckle interference technology is a technical problem to be solved by those skilled in the art. SUMMARY

[0007] (One) technical problem to be solved

[0008] In view of the deficiencies of the prior art, the present application provides a low-noise speckle interference system and method based on a spatial light modulator, which solves the problem of poor speckle decorrelation noise suppression effect in speckle interference technology.

[0009] (Two) technical solutions

[0010] To achieve the above object, the present application is realized by the following technical solutions:

[0011] In a first aspect, the present application provides a low-noise speckle interference system based on a spatial light modulator, comprising: a laser, a beam splitter prism one and an imaging element;

[0012] The laser beam emitted by the laser is divided by the beam splitter prism one into transmitted light and reflected light;

[0013] Part of the transmitted light is reflected by the beam splitter prism three and then irradiates on the imaging element as reference light;

[0014] Part of the reflected light passes through a linear polarizer and a half-wave plate in sequence, is modulated by a spatial light modulator assembly, irradiates on a beam splitter prism four, and is reflected to the measured object surface to occur diffuse reflection to obtain slow light; part of the diffuse light passes through the beam splitter prism four, a Fourier lens four, an aperture diaphragm two, a Fourier lens three and the beam splitter prism three in sequence, and then irradiates on the imaging element as object light;

[0015] Wherein, the Fourier lens three and the Fourier lens four constitute a 4f system, the measured object surface is located on the front focal plane of the Fourier lens four, the imaging element imaging surface is located on the back focal plane of the Fourier lens three, and the aperture diaphragm two is located on the frequency spectrum plane in the 4f system constituted by the Fourier lens three and the Fourier lens four.

[0016] Preferably, the speckle interference system further comprises a laser beam expander;

[0017] The laser beam expander is located between the laser and the beam splitter prism one, and is used to expand the diameter of the laser beam while maintaining the collimation of the laser beam during the irradiation to the beam splitter prism one.

[0018] Preferably, the spatial light modulator assembly comprises a spatial light modulator, a screen display, a Fourier lens one, a Fourier lens two, an aperture diaphragm one and a beam splitter prism two;

[0019] Part of the reflected light passes through the half-wave plate and then the beam splitter prism two, and then irradiates on the spatial light modulator, and then the spatial light modulator modulates the light to generate modulated light, and then the modulated light is reflected by the beam splitter prism two, and then passes through the Fourier lens one, the aperture diaphragm one and the Fourier lens two in sequence, and then is reflected by the beam splitter prism four to the measured object surface to generate diffuse reflection, and then the diffuse light is obtained.

[0020] In a second aspect, the present application provides a low-noise speckle interferometry method based on a spatial light modulator, which utilizes a speckle interferometry system to perform interference, and includes the following steps:

[0021] The laser beam emitted by the laser passes through the laser beam expander to expand the diameter of the laser beam and maintain the collimation of the emitted laser, and then is divided into transmitted light and reflected light by the beam splitter prism one.

[0022] Part of the transmitted light is reflected by the beam splitter prism three, and then irradiates on the imaging element as reference light.

[0023] Part of the reflected light passes through the linear polarizer and the half-wave plate in sequence, and then the reflected light passing through is completely converted into modulated light that can be modulated by the spatial light modulator assembly, and then the obtained modulated light is modulated by the spatial light modulator assembly, and then a group of stripe patterns with the same period and different directions are input to the spatial light modulator assembly, so that the spatial light modulator assembly causes the emitted light modulated by the modulated light to change in angle, and at the same time, the periodic phase change is introduced to the object light; the obtained emitted light irradiates on the beam splitter prism four, and then is reflected to the measured object surface to generate diffuse reflection, and then the diffuse light is obtained.

[0024] Part of the diffuse light passes through the beam splitter prism four, the Fourier lens four, the aperture diaphragm two, the Fourier lens three and the beam splitter prism three in sequence, and then irradiates on the imaging element as object light, and then interferes with the reference light on the target surface of the imaging element.

[0025] Preferably, a plurality of stripes with fixed rotational changes are input to the spatial light modulator through the screen display to form a group of stripe patterns as the input of the spatial light modulator, so that the emitted light of the spatial light modulator passes through the Fourier lens and converges at different positions of the aperture diaphragm one and presents uniform distribution, and each stripe with a fixed direction includes four stripe patterns with the same period but regular translation to generate a fixed phase difference.

[0026] Preferably, the reference light and the object light interfere on the target surface of the imaging element, and the light intensity expression of the speckle interference pattern obtained on the target surface of the imaging element is:

[0027]

[0028]

[0029] where (x, y) is the coordinate system, is the light intensity of the object light, is the reference light intensity, A o (x, y) is the object light amplitude, A r is the reference light amplitude, φ(x, y) is the object light phase;

[0030] φ SLM (x, y) is the phase introduced by the beam deflection generated by the spatial light modulator;

[0031] where d x and d y are the pixel sizes of the spatial light modulator, θ x and θ y are the beam deflection angles;

[0032] Let the reference light be a plane light, and the reference light keeps unchanged in the whole measurement process, and its own phase is ignored.

[0033] Preferably, the complex amplitude of the object light before deformation can be calculated by the following formula:

[0034]

[0035] Ae iφ is the complex amplitude expression of the light wave, where A is the amplitude, and φ is the phase, and here and below, the coordinate system (x, y) is omitted;

[0036] In the formula, i is the imaginary symbol, e iφ is the exponential term carrying the phase information of the object.

[0037] After deformation, the same speckle interference pattern acquisition step as above is taken, and the complex amplitude of the object light after deformation is obtained The conjugate multiplication of the two complex amplitudes is performed to obtain the phase amplitude vector:

[0038]

[0039] In the formula, is the amplitude of the phase amplitude vector, δφ = φ - φ' corresponds to the out-of-plane deformation of the object, and ε is the speckle decorrelation noise introduced by the deformation;

[0040] Due to the high precision repeatability of the spatial light modulator, the same direction of the stripe is modulated before and after the deformation of the object to obtain the same φ SLM , so that the phase is eliminated after subtraction, and the final phase amplitude vector calculation formula is:

[0041] Γ=OO ′* = aei(δφ) e iε ; (5)

[0042] When N independent phase-amplitude vectors Γ are superimposed, the expression of the phase-amplitude vector sum is as follows:

[0043]

[0044] where a n and ε n are the speckle decorrelation noise of N independent phase-amplitude vectors;

[0045] where the right side of the equation represents the phase-amplitude vector sum, whose phase is the superimposed speckle decorrelation noise;

[0046] In the analysis of the statistical distribution of speckle decorrelation noise, first, the inverse transformation of Euler's theorem is fitted by variable transformation, and the phase-amplitude vector is decomposed into real and imaginary parts represented by trigonometric functions. The phase-amplitude vector sum is decomposed into real and imaginary parts to obtain:

[0047]

[0048] Solving the average value of R and I, we get:

[0049]

[0050] where and can be expressed by the characteristic function of the random variable ε n , so that the average values of the real and imaginary parts are obtained:

[0051]

[0052] The variances of the real and imaginary parts can be obtained by a similar method:

[0053]

[0054] where C R,I is the covariance representing R and I:

[0055]

[0056] Since the speckle decorrelation noise ε n obeys the zero-mean Gaussian distribution, the mean, standard deviation and covariance of the real and imaginary parts are simplified as:

[0057]

[0058] C R,I = 0; (12)

[0059] According to the central limit theorem, the joint density function of R and I can be obtained as:

[0060]

[0061] Substitute formula 5 into formula 13 and integrate the amplitude, so as to obtain the probability density function of the accumulated noise phase ψ:

[0062]

[0063] Wherein the coefficients c1 and c2 mainly depend on the characteristic function M ε (ω) of the speckle decorrelation noise.

[0064] According to the central limit theorem, the distribution of the superposition of multiple independent and identically distributed variables tends to be normal distribution, so as to obtain the standard deviation of the superimposed speckle decorrelation noise according to the probability density function shown in formula 14, and combined with the result in formula 12, finally the standard deviation of the superimposed speckle decorrelation noise is:

[0065]

[0066] It can be obtained that the standard deviation of the speckle decorrelation noise theoretically presents The rule, and after superimposing multiple times, the speckle decorrelation noise can be effectively suppressed.

[0067] In a third aspect, the present application provides a computer readable storage medium storing a computer program for low-noise speckle interferometry based on a spatial light modulator, wherein the computer program causes a computer to execute the method for low-noise speckle interferometry based on a spatial light modulator.

[0068] In a fourth aspect, the present application provides an electronic device comprising:

[0069] One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the program comprises a program for executing the method for low-noise speckle interferometry based on a spatial light modulator.

[0070] (III) Beneficial effects

[0071] The present application provides a low-noise speckle interferometry system and method based on a spatial light modulator. Compared with the prior art, the following beneficial effects are achieved:

[0072] The speckle interferometry system proposed in this invention utilizes a spatial light modulator to modulate the object light, and inputs a fringe pattern consisting of multiple fringes into the spatial light modulator, causing the object light to illuminate the object at various illumination angles, forming independent speckle fields on the target surface of the imaging element. The mean, standard deviation, and covariance of the complex amplitude before and after object light deformation are processed. It can be seen that the standard deviation of speckle decorrelated noise theoretically exhibits... Therefore, when using speckle interferometry for measurement, multiple measurements can be superimposed to effectively suppress speckle decorrelation noise, thereby improving the accuracy of subsequent measurement results. Attached Figure Description

[0073] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0074] Figure 1 This is a schematic diagram of a low-noise speckle interferometer system based on a spatial light modulator in an embodiment of the present invention;

[0075] Figure 2 for Figure 1 A schematic diagram illustrating the principle and structure of a mid-space light modulator for modulating the angle of an illumination beam.

[0076] Figure labels: 1. Laser; 2. Laser beam expander; 3. Beam splitter 1; 4. Linear polarizer; 5. Half-wave plate; 6. Screen display; 7. Spatial light modulator; 8. Beam splitter 2; 9. Fourier lens 1; 10. Aperture stop 1; 11. Fourier lens 2; 12. Imaging element; 13. Beam splitter 3; 14. Fourier lens 3; 15. Aperture stop 2; 16. Fourier lens 4; 17. Beam splitter 4; 18. Object under test. Detailed Implementation

[0077] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0078] This application provides a low-noise speckle interferometry system and method based on a spatial light modulator, which solves the problem of poor speckle decorrelation noise suppression in speckle interferometry.

[0079] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0080] Example:

[0081] Firstly, such as Figures 1-2 As shown, a low-noise speckle interferometer system based on a spatial light modulator includes a laser 1, a beam splitter 3, and an imaging element 12.

[0082] The laser beam emitted from the laser 1 is split into transmitted light and reflected light by the beam splitter prism 3.

[0083] Part of the transmitted light is reflected by the beam splitter prism 13 and then used as reference light to illuminate the imaging element 12.

[0084] Part of the reflected light passes through the linear polarizer 4 and the half-wave plate 5 in sequence, and is modulated by the spatial light modulator assembly. It then illuminates the beam splitter 17 and is reflected onto the surface of the object 18 for diffuse reflection, thus obtaining slow-reflected light. Part of the diffused light passes through the beam splitter 17, the Fourier lens 16, the aperture stop 15, the Fourier lens 14, and the beam splitter 13 in sequence, and then illuminates the imaging element 12 as the object light.

[0085] Among them, Fourier lens 3 13 and Fourier lens 4 16 constitute a 4f system, and the surface of the object under test 18 is located on the front focal plane of Fourier lens 4 16, the imaging surface of imaging element 12 is located on the rear focal plane of Fourier lens 3 13, and aperture stop 2 15 is located on the spectral plane of the 4f system composed of Fourier lens 3 13 and Fourier lens 4 16.

[0086] Specifically, the object light is polarized by the linear polarizer 4, and then the polarization state of the object light is adjusted by the half-wave plate 5, so that it is completely converted into modulated light that can be modulated by the spatial light modulator, and then modulated by the spatial light modulator assembly.

[0087] Based on the spatial light modulator component, the light can be modulated by the spatial light modulator component and illuminated at different reverse illumination angles on the surface of the test object 18 to cause diffuse reflection, which can effectively avoid the influence of other diffraction order light spots that may be introduced by the spatial light modulator 7.

[0088] like Figure 1 As shown, a low-noise speckle interferometer system based on a spatial light modulator also includes a laser beam expander 2;

[0089] The laser beam expander 2 is located between the laser 1 and the beam splitter 1, and is used to expand the diameter of the laser beam while maintaining the collimation of the laser beam as it illuminates the beam splitter 3.

[0090] Specifically, the laser beam expander 2 is designed based on a Galileo telescope structure and is made of a set of negative lenses of high light transmission and a set of achromatic doublet positive lenses.

[0091] As shown in Figures 1-2 , the spatial light modulator assembly comprises a spatial light modulator 7, a screen display 6, a Fourier lens one 9, a Fourier lens two 11, an aperture diaphragm one 10 and a light splitting prism two 8;

[0092] Part of the reflected light passes through the light splitting prism two 8 to irradiate on the spatial light modulator 7 after being emitted from the half-wave plate 5, and the modulated light is generated after being modulated by the spatial light modulator 7. The modulated light is reflected by the light splitting prism two 8 in turn to pass through the Fourier lens one 9, the aperture diaphragm one 10 and the Fourier lens two 11, and then is reflected by the light splitting prism four 17 to the surface of the measured object 19 to occur diffuse reflection to obtain the diffuse light. The Fourier lens one 9 and the Fourier lens two 11 constitute another 4f system, wherein the exit of the spatial light modulator 7 is on the front focal plane of the Fourier lens one 9, the surface of the measured object 18 is on the back focal plane of the Fourier lens two 11, and the aperture diaphragm one 10 is on the frequency spectrum plane in the 4f system constituted by the Fourier lens one 9 and the Fourier lens two 11.

[0093] It should be noted that the spatial light modulator 7 is signal connected with the screen display 6;

[0094] The spatial light modulator 7 adjusts the received reflected light through the 4f imaging system, and the 4f imaging system can effectively avoid the influence of other diffraction order light spots that may be introduced by the spatial light modulator 7.

[0095] In addition, the 4f imaging system combined with the aperture diaphragm one 10 also maintains the collimation and spot size of the exit light beams of the spatial light modulator 7 and the measured object 18.

[0096] Specifically, a plurality of stripes with fixed rotational changes are input to the spatial light modulator 7 through the screen display 6 to form a stripe group as the input of the spatial light modulator 7, so that the exit light of the spatial light modulator 7 is concentrated at different positions of the aperture diaphragm one 10 and presents uniform distribution, as shown in Figure 2 When two transverse stripes with opposite directions are modulated, the exit light beams of the spatial light modulator 7 present symmetrical exit angles up and down, and the convergence points on the aperture diaphragm one 10 are also symmetrical relative to the zero point;

[0097] Meanwhile, each fixed direction stripe contains four stripe patterns with the same period but regular translation, as shown in Figure 2 to generate a fixed phase difference and meet the requirement of time phase shift. The data on a line in the center of each stripe pattern are selected to draw a curve, and it can be seen that the four curves have a fixed phase difference.

[0098] It should be noted that the plurality of fringes in the fringe group are of the same period but different directions;

[0099] The input fringe group is equivalent to a rotating grating, so that the output light after modulation by the spatial light modulator assembly has an angle change and is irradiated on the surface of the measured object 18 at different illumination angles to produce diffuse reflection.

[0100] In a second aspect, a low-noise speckle interferometry method based on a spatial light modulator includes the following steps:

[0101] The laser beam emitted by the laser 1 is expanded in diameter and kept collimated after passing through the laser beam expander 2, and is then split by the beam splitter prism 1 3 into transmitted light and reflected light;

[0102] Part of the transmitted light is reflected by the beam splitter prism 3 13 and irradiated on the imaging element 12 as reference light;

[0103] Part of the reflected light passes through the linear polarizer 4 and the half-wave plate 5 in sequence, so that the transmitted reflected light is completely converted into modulated light that can be modulated by the spatial light modulator assembly. The acquired modulated light is modulated by the spatial light modulator assembly, and a fringe group with the same period but different directions is input to the spatial light modulator assembly, so that the spatial light modulator assembly modulates the output light of the modulated light and introduces periodic phase changes to the object light; the acquired output light is irradiated on the beam splitter prism 4 17 and reflected to the surface of the measured object 18 to produce diffuse reflection, and the diffuse light is obtained;

[0104] Part of the diffuse light passes through the beam splitter prism 4 17, the Fourier lens 4 16, the aperture diaphragm 2 15, the Fourier lens 3 14, and the beam splitter prism 3 13 in sequence, and is irradiated on the imaging element 12 as object light, and interferes with the reference light on the target surface of the imaging element.

[0105] It should be noted that in the application process, the beam splitter prism 1 3, the beam splitter prism 2 8, the beam splitter prism 3 13, and the beam splitter prism 4 17 can be the same, the Fourier lens 1 9, the Fourier lens 2 11, the Fourier lens 3 14, and the Fourier lens 4 16 can be the same, and the aperture diaphragm 1 10 and the aperture diaphragm 2 15 can be the same.

[0106] The basic working principle of the 4f imaging system is a prior art, which will not be described here.

[0107] Specifically, the reference light and the object light interfere on the target surface of the imaging element 12, and the light intensity expression of the speckle interferogram obtained on the target surface of the imaging element 12 is:

[0108]

[0109] where (x, y) is the coordinate system It is the light intensity of the object. It is the intensity of the reference light, A o (x,y) represents the amplitude of the object light, A r The reference beam amplitude is φ(x,y), and the object beam phase is φ(x,y).

[0110]

[0111] φ SLM (x,y) represents the phase introduced by the beam deflection caused by the modulation of the spatial light modulator 7, where d x and d y Let θ be the pixel size of the spatial light modulator. x and θ y This represents the beam deflection angle.

[0112] Let the reference light be a plane light. Considering that the reference light remains unchanged throughout the measurement process, its phase is negligible.

[0113] It should be noted that in order to ensure that the speckle fields generated by the outgoing light from the grating diffracted in different directions after being modulated by the spatial light modulator 7 and illuminating the test object 18 are uncorrelated, the covariance of the speckle fields before and after deformation must be close to 0.

[0114] According to inferences in relevant literature, the intensity covariance of the speckle field is affected by the spot diameter, the standard deviation of the surface height of the measured object 18 (i.e., surface roughness), and the magnitude of the changes in the initial illumination angle and illumination angle.

[0115] The complex amplitude of the object before deformation can be calculated using the following formula:

[0116]

[0117] The complex amplitude expression for a light wave is Ae iφ Where A is the amplitude and φ is the phase, with the phase placed as a power of the natural logarithm e. This is a common expression in optics, and the following expressions are similar. To simplify the expression of the formula, the coordinate system (x,y) is omitted here and below.

[0118] In the formula, i is the imaginary number symbol, e iφ This is the exponential term that carries the phase information of the object.

[0119] After deformation, the same speckle interferogram acquisition steps as described above are followed to obtain the deformed object light complex amplitude. By multiplying the two complex amplitudes by their conjugates, we can obtain the phase amplitude vector:

[0120]

[0121] In the formula is the amplitude of the complex vector, δφ = φ - φ' is the deformation of the object surface, and ε is the speckle decorrelation noise introduced by the deformation;

[0122] Due to the high precision repeatability of the spatial light modulator 7, the same φ can be obtained by modulating the same direction of the fringe before and after the deformation of the object SLM Thus, the phase is eliminated after subtraction, and the final complex vector calculation formula is:

[0123] Γ = OO' * = ae i(δφ) e iε ; (5)

[0124] When there are N incoherent complex vectors Γ, the expression of the sum of the complex vectors is as follows:

[0125]

[0126] In the formula, a n and ε n are the speckle decorrelation noises of the N incoherent complex vectors;

[0127] In the formula, the on the right side of the equal sign represents the sum of the complex vectors, and the phase is the speckle decorrelation noise after superposition.

[0128] In the analysis of the statistical distribution of the speckle decorrelation noise, the complex vector is generally first decomposed into real and imaginary parts represented by trigonometric functions through variable transformation to fit the inverse transformation of Euler's theorem. The advantage of this is that some simplification can be made in the derivation process through the properties of trigonometric functions. The complex vector sum is decomposed into real and imaginary parts to obtain:

[0129]

[0130] Solving the average values of R and I, we obtain:

[0131]

[0132] Among them and can be expressed by the characteristic function of the random variable ε n , so that the average values of the real and imaginary parts are obtained:

[0133]

[0134] The variances of the real and imaginary parts can be obtained by a similar method:

[0135]

[0136] In the formula, C R,I is the covariance representing R and I:

[0137]

[0138] Since the speckle decorrelation noise ε n Since the speckle decorrelation noise ε

[0139]

[0140] C R,I =0; (12)

[0141] According to the central limit theorem, the joint density function of R and I can be obtained as follows:

[0142]

[0143] Substitute formula 5 into formula 13 and integrate the amplitude, so that the probability density function of the accumulated noise phase ψ is obtained as follows:

[0144]

[0145] Where the coefficients c1 and c2 mainly depend on the characteristic function M ε (ω) of the speckle decorrelation noise.

[0146] According to the central limit theorem, the distribution of the superposition of multiple independent and identically distributed variables tends to be normal distribution, so the standard deviation of the superimposed speckle decorrelation noise is obtained according to the probability density function shown in formula 14, and combined with the result in formula 12, the standard deviation of the superimposed speckle decorrelation noise is finally obtained as follows:

[0147]

[0148] It can be seen that the standard deviation of the speckle decorrelation noise theoretically presents Therefore, after superimposing multiple measurements, the speckle decorrelation noise can be effectively suppressed.

[0149] Compared with the prior art, the present application has the following beneficial effects:

[0150] The speckle interference system proposed in the present application modulates the object light by using a spatial light modulator, inputs a fringe pattern group composed of multiple fringes into the spatial light modulator, and processes the mean value, standard deviation and covariance of the complex amplitude of the object light before and after deformation, so that the standard deviation of the speckle decorrelation noise theoretically presents Therefore, when measuring by using the speckle interference technology, the speckle decorrelation noise can be effectively suppressed after superimposing multiple measurements, thereby improving the accuracy of the subsequent measurement results.

[0151] It is to be noted that, in the present text, relational terms such as first and second and the like can be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0152] The above examples are merely used to illustrate the technical solutions of the present application, but not to limit it; although the present application has been described in detail with reference to the foregoing examples, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A low-noise speckle interferometry system based on a spatial light modulator, characterized in that, The speckle interferometry system comprises a laser, a beam splitter prism one and an imaging element; The laser beam emitted by the laser is split into transmitted light and reflected light by the beam splitter prism one; Part of the transmitted light is reflected by the beam splitter prism three and then irradiated on the imaging element as reference light; Part of the reflected light passes through a linear polarizer and a half-wave plate in sequence, is modulated by the spatial light modulator assembly, is irradiated on the beam splitter prism four, is reflected to the measured object surface to be diffused, and obtains diffused light; part of the diffused light passes through the beam splitter prism four, a Fourier lens four, an aperture diaphragm two, a Fourier lens three and the beam splitter prism three in sequence, and is irradiated on the imaging element as object light; The Fourier lens three and the Fourier lens four constitute a 4f system, the measured object surface is located on the front focal plane of the Fourier lens four, the imaging element imaging surface is located on the rear focal plane of the Fourier lens three, and the aperture diaphragm two is located on the frequency spectrum plane in the 4f system constituted by the Fourier lens three and the Fourier lens four; The reference light and the object light interfere on the target surface of the imaging element, and the light intensity expression of the speckle interference pattern obtained on the target surface of the imaging element is: ；（1） （2） wherein is a coordinate system coordinate ， is the light intensity of the object light, is the light intensity of the reference light, is the amplitude of the object light, is the amplitude of the reference light, is the phase of the object light; introducing a phase for beam deflection resulting from modulation by the spatial light modulator; wherein and is the pixel size of the spatial light modulator, x and y is the beam deflection angle; The reference light is plane light, and the phase of the reference light is ignored in the whole measurement process; The complex amplitude of the object light before deformation can be calculated by the following formula: ；（3） is the complex amplitude representation of the light wave, where A is the amplitude, Here and in the following the coordinate system (x,y) is omitted; wherein is the imaginary unit, is the exponential term carrying the phase information of the object; After deformation, the complex amplitude of the object light is obtained Conjugate multiplication is performed on the two complex amplitudes to obtain a phase amplitude vector: ；（4） wherein is the magnitude of the complex amplitude vector, is the out-of-plane deformation of the object, is the speckle decorrelation noise introduced by the deformation; Due to the high precision repeatability of the spatial light modulator, the same direction of the fringe can be obtained by modulating before and after the object deformation Thus, the phase can be eliminated after subtraction, and the final phase amplitude vector calculation formula is obtained as follows: ； (5) When there are N non-coherent phase-amplitude vectors The superposition gives the expression for the sum of phase-amplitude vectors as follows: ；（6） wherein is speckle decorrelation noise of N independent phase vectors; The right side of the equation The sum of the phase amplitude vectors represents the superimposed speckle decorrelated noise. In the analysis of the statistical distribution of the speckle decorrelation noise, firstly, the inverse transformation of Euler's theorem is fitted through variable transformation, the phase amplitude vector is decomposed into real part and imaginary part represented by trigonometric function, and the phase amplitude vector is decomposed into real part and imaginary part to obtain: ；（7） solving and the average value of which is ；（8） where and The characteristic function of a random variable can be expressed as Re{} and Im{} are the real and imaginary parts of the complex number ；（9） The variances of the real part and the imaginary part can be obtained by a similar method: （10） In the formula to represent and covariance: ；（11） Due to speckle decorrelation noise Since the real and imaginary parts obey a zero-mean Gaussian distribution, let the mean, standard deviation and covariance of the real and imaginary parts be simplified as: According to the central limit theorem, the joint density function of and is ；（13） Substituting equation 5 into equation 13 and integrating over the amplitude, the probability density function of the accumulated noise phase is obtained p(φ) = 1 2π e -φ2 2 （14） where the coefficients and depend mainly on the characteristic function of the speckle decorrelation noise ; According to the central limit theorem, the distribution of the superposition of multiple independent and identically distributed variables tends to be a normal distribution, so the standard deviation of the superimposed speckle decorrelation noise is obtained according to the probability density function shown in formula 14, and combined with the result in formula 12, the standard deviation of the superimposed speckle decorrelation noise is finally obtained as: ；（15） It is found that the standard deviation of decorrelation noise of speckle presents a regularity in theory. the regularity.

2. A low-noise speckle interferometer system based on a spatial light modulator as claimed in claim 1, characterized in that, The speckle interferometry system further comprises a laser beam expander; The laser beam expander is located between the laser and the beam splitter prism one, and is used to expand the diameter of the laser beam while maintaining the collimation of the laser beam during irradiation to the beam splitter prism one.

3. A low noise speckle interferometer system based on a spatial light modulator as claimed in claim 2, wherein, The spatial light modulator assembly comprises a spatial light modulator, a screen display, a Fourier lens one, a Fourier lens two, an aperture diaphragm one and a beam splitter prism two; The spatial light modulator modulates the light, and the modulated light is reflected by the beam splitter prism two, passes through the Fourier lens one, the aperture diaphragm one and the Fourier lens two in sequence, is reflected by the beam splitter prism four, diffuses on the measured object surface, and obtains diffused light; the Fourier lens one and the Fourier lens two constitute another 4f system, wherein the spatial light modulator exit is located on the front focal plane of the Fourier lens one, the measured object surface is located on the rear focal plane of the Fourier lens two, and the aperture diaphragm one is located on the frequency spectrum plane in the 4f system constituted by the Fourier lens one and the Fourier lens two.

4. A low-noise speckle interferometry method based on a spatial light modulator, characterized by, The speckle interferometry system of claim 3 is used for interference, and specifically comprises the following steps: The laser beam emitted by the laser passes through a laser beam expander to enlarge the diameter of the laser beam and maintain the collimation of the emitted laser beam, and is then split by a beam splitter prism into transmitted light and reflected light; Part of the transmitted light is reflected by a beam splitter prism three and then irradiated on the imaging element as reference light; Part of the reflected light passes through a linear polarizer and a half-wave plate in sequence, and then the reflected light passing through is completely converted into modulated light that can be modulated by the spatial light modulator assembly. The modulated light is modulated by the spatial light modulator assembly, and a group of stripe patterns with the same period and different directions are input to the spatial light modulator assembly, so that the spatial light modulator assembly causes the emitted light modulated by the modulated light to change in angle, and at the same time introduces a periodic phase change to the object light; the obtained emitted light is irradiated on a beam splitter prism four and then reflected to the surface of the measured object to be diffusely reflected, and diffused light is obtained; Part of the diffused light passes through the beam splitter prism four, a Fourier lens four, an aperture diaphragm two, a Fourier lens three, and a beam splitter prism three in sequence, and then is irradiated on the imaging element as object light, and interferes with the reference light on the target surface of the imaging element.

5. A low-noise speckle interferometry method based on a spatial light modulator as claimed in claim 4, characterized in that, A plurality of stripes with fixed rotational changes are input to the spatial light modulator through the screen display to form a group of stripe patterns as the input of the spatial light modulator, so that the emitted light of the spatial light modulator is concentrated on different positions of the aperture diaphragm one by the Fourier lens one and is uniformly distributed, and each stripe with a fixed direction includes four stripe patterns with the same period but regular translation to generate a fixed phase difference.

6. A computer-readable storage medium, characterized in that, The computer program for low-noise speckle interferometry based on a spatial light modulator, wherein the computer program causes a computer to execute the low-noise speckle interferometry based on a spatial light modulator according to any one of claims 4-5.

7. An electronic device, comprising: Comprise: One or more processors, memories, and one or more programs, wherein the one or more programs are stored in the memories and configured to be executed by the one or more processors, and the programs comprise instructions for executing the low-noise speckle interferometry based on a spatial light modulator according to any one of claims 4-5.

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