Low-noise speckle interference system and method based on spatial light modulator

Abstract

The invention provides a low-noise speckle interference system and method based on a spatial light modulator, and relates to the technical field of speckle interference, and the system comprises a laser, a first beam splitter prism and an imaging element. A laser beam emitted by the laser is divided into transmission light and reflected light by the beam splitter prism I; after being reflected by the third beam splitter prism, part of the transmission light is irradiated on an imaging element as reference light; part of the reflected light sequentially passes through a linear polaroid and a half-wave plate, is modulated by a spatial light modulator assembly, irradiates a fourth beam splitter prism, and is reflected to the surface of a measured object to generate diffuse reflection, so that slow-reflection light is obtained; according to the speckle interference system, object light is modulated by using a spatial light modulator assembly, so that emergent light modulated by the spatial light modulator assembly irradiates a measured object at various illumination angles, mutually independent speckle fields are formed on a target surface of an imaging element, speckle decorrelation noise can be effectively inhibited after multiple times of measurement and superposition, and the measurement accuracy is improved. And the accuracy of subsequent measurement results is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of speckle interferometry technology, and in particular to a low-noise speckle interferometry system and method based on a spatial light modulator. Background Art

[0002] As a non-contact, highly sensitive optical measurement method, speckle interferometry is widely used to detect and analyze minute deformations on rough surfaces. However, in practical applications, the phase fringe patterns obtained by speckle interferometry are inevitably affected by speckle decorrelation noise. This noise, primarily due to the misalignment of the speckle pattern caused by object deformation, significantly limits measurement accuracy. Furthermore, as the coherence of the laser light source increases, this noise is further enhanced, seriously affecting the accuracy of the measurement results.

[0003] There has been a lot of research on suppressing speckle de-correlation noise using image post-processing measures such as image denoising algorithms. Although speckle de-correlation noise is uniform at the statistical level, the noise at the edge of the stripes is in phase jumps, so it is very difficult to suppress the noise while protecting the edge. Filtering algorithms mainly include spatial filtering algorithms represented by sine and cosine transforms and frequency domain filtering algorithms represented by windowed Fourier transforms and wavelet transforms. There is a conflict between filtering algorithms’ time consumption and filtering effect. Algorithms with short time consumption, such as sine and cosine transforms, are not effective when dealing with high-density and high-noise stripes, while windowed Fourier transforms with excellent filtering effects have problems such as the need to adjust a large number of parameters, long time consumption, and high threshold. Therefore, the use of filtering methods alone to suppress speckle de-correlation noise restricts the practicality of speckle interferometry.

[0004] Extensive research on suppressing speckle contrast has been conducted in the fields of holography and laser projection. For example, Picart et al. modeled the degree of de-correlation of speckle noise in dual-wavelength and multi-wavelength holography and proposed a novel correlation coefficient expression. Yamada, Trinh-Thi-Kim et al. weakened the temporal coherence of laser light in laser projection by varying the illumination angle and wavelength. Lixin Xu et al. used a rotating spherical lens to reduce the temporal coherence of laser light, reducing the speckle coherence to a level that is geometrically imperceptible to the human eye. Morozov et al. designed a passive speckle suppression device based on a combination of a prism and a Fresnel lens, which can suppress speckle coherence while ensuring illumination uniformity.

[0005] However, most of these studies aim to reduce the speckle contrast in the intensity image, while speckle interferometry relies on high speckle contrast to improve fringe quality, so it is impossible to directly apply the noise suppression method in holography to speckle interferometry.

[0006] In view of this, how to reduce speckle decorrelation noise in speckle interferometry technology is a technical problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0007] (1) Technical problems solved

[0008] In view of the shortcomings of the existing technology, the present invention 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 technology.

[0009] (2) Technical solution

[0010] To achieve the above objectives, the present invention is implemented through the following technical solutions:

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

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

[0013] After three reflections by the beam splitter, part of the transmitted light is irradiated on the imaging element as reference light;

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

[0015] Among them, Fourier lens three and Fourier lens four constitute a 4f system, and the surface of the object to be measured is on the front focal plane of Fourier lens four, the imaging surface of the imaging element is on the back focal plane of Fourier lens three, and aperture stop two is on the spectrum plane in the 4f system constituted by Fourier lens three and Fourier lens four.

[0016] Preferably, the speckle interferometry system further includes a laser beam expander;

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

[0018] Preferably, the spatial light modulator assembly includes a spatial light modulator, a screen display, a first Fourier lens, a second Fourier lens, a first aperture stop, and a second beam splitter prism;

[0019] Among them, part of the reflected light is emitted through the half-wave plate and passes through the second beam splitter prism to illuminate the spatial light modulator. After being modulated by the spatial light modulator, modulated light is generated. After being reflected by the second beam splitter prism, the modulated light passes through the first Fourier lens, the first aperture stop, and the second Fourier lens in sequence, and is reflected by the fourth beam splitter prism to the surface of the object to be measured, where it is diffusely reflected to obtain diffuse light. The first and second Fourier lenses form another 4f system, in which the output port of the spatial light modulator is on the front focal plane of the first Fourier lens, the surface of the object to be measured is on the back focal plane of the second Fourier lens, and the first aperture stop is on the spectrum plane of the 4f system formed by the first and second Fourier lenses.

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

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

[0022] After three reflections by the beam splitter, part of the transmitted light is irradiated on the imaging element as reference light;

[0023] After partially reflecting light passes through a linear polarizer and a half-wave plate in sequence, the reflected light is completely converted into modulated light that can be modulated by a spatial light modulator assembly. The obtained modulated light is modulated by the spatial light modulator assembly, and a fringe pattern group with the same period but different directions is input to the spatial light modulator assembly, causing the spatial light modulator assembly to produce an angle change in the outgoing light modulated by the modulated light, while introducing a periodic phase change in the object light. The obtained outgoing light is irradiated on a fourth beam splitter prism and reflected to the surface of the object to be measured, causing diffuse reflection to obtain slow-emission light.

[0024] Part of the diffuse light passes through the fourth beam splitter prism, the fourth Fourier lens, the second aperture stop, the third Fourier lens and the third beam splitter prism in sequence, and then illuminates the imaging element as object light, and interferes with the reference light on the target surface of the imaging element.

[0025] Preferably, a plurality of stripes with fixed rotational direction changes are input into the spatial light modulator through a screen display to form a stripe pattern group as the input of the spatial light modulator, so that its outgoing light is converged at different positions of aperture diaphragm 1 through a Fourier lens and is uniformly distributed, and each stripe in a fixed direction contains four stripe patterns with the same period but regular translation to produce 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] Among them, (x,y) is the coordinate system coordinate, is the 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 caused by the spatial light modulator;

[0031] where d x and d y is the pixel size of the spatial light modulator, θ x and θ y is the beam deflection angle;

[0032] The reference light is assumed to be a plane light. The reference light remains unchanged during the entire measurement process and its own phase is negligible.

[0033] Preferably, the object-light complex amplitude 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. The coordinate system (x, y) is omitted here and below.

[0036] Where i is the imaginary number symbol, e iφ is the exponential term that carries the phase information of the object.

[0037] After deformation, the same speckle interferogram acquisition steps as above are performed to obtain the deformed object light complex amplitude. The conjugate multiplication of the two complex amplitudes gives 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 exact same φ can be obtained by modulating the stripes in the same direction before and after the object is deformed. SLM , thus eliminating the phase after subtraction, and the final phase-amplitude vector calculation formula is:

[0041] Γ=OO ′* =aei(δφ) e iε ; (5)

[0042] When N incoherent 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 is the speckle decorrelation noise of N incoherent phase-amplitude vectors;

[0045] The right side of the equal sign Represents the phase-amplitude vector sum, whose phase is the decorrelated noise of the superimposed speckle;

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

[0047]

[0048] Solving for the average values of R and I yields:

[0049]

[0050] in and We can use the random variable ε n The characteristic function of is expressed as follows, so as to obtain the average value of the real and imaginary parts:

[0051]

[0052] The variance of the real and imaginary parts can be obtained in a similar way:

[0053]

[0054] Where C R,I To express the covariance of R and I:

[0055]

[0056] Due to the decorrelation noise ε n Obeying the zero-mean Gaussian distribution, the mean, standard deviation and covariance of the real and imaginary parts are simplified to:

[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:

[0060]

[0061] Substituting Equation 5 into Equation 13 and integrating the amplitude yields the probability density function of the accumulated noise phase ψ:

[0062]

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

[0064] According to the central limit theorem, when multiple independent and identically distributed variables are superimposed, their distribution approaches the normal distribution. Therefore, the standard deviation of the speckle decorrelation noise after superposition is obtained according to the probability density function shown in formula 14. Combined with the result in formula 12, the standard deviation of the speckle decorrelation noise after superposition is finally obtained as:

[0065]

[0066] It can be obtained that the standard deviation of speckle decorrelation noise is theoretically The law of speckle decorrelation noise can be effectively suppressed after multiple measurement superposition.

[0067] In a third aspect, the present invention 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 enables a computer to execute a low-noise speckle interferometry method based on a spatial light modulator.

[0068] In a fourth aspect, the present invention 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, the programs including instructions for performing a low-noise speckle interferometry method based on a spatial light modulator.

[0070] (3) Beneficial effects

[0071] The present invention provides a low-noise speckle interferometry system and method based on a spatial light modulator. Compared with the existing technology, it has the following advantages:

[0072] The speckle interferometry system proposed in the present invention uses a spatial light modulator to modulate the object light, and inputs a fringe pattern group consisting of multiple fringes into the spatial light modulator, so that the object light illuminates the object under test at multiple illumination angles, forming mutually independent speckle fields on the target surface of the imaging element, and processing the mean, standard deviation and covariance of the complex amplitude before and after the deformation of the object light. It can be seen that the standard deviation of the speckle decorrelation noise is theoretically Therefore, when using speckle interferometry technology for measurement, the speckle decorrelation noise can be effectively suppressed by superimposing multiple measurements, thereby improving the accuracy of subsequent measurement results. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0074] Figure 1 Schematic diagram of the structure of a low-noise speckle interferometry system based on a spatial light modulator in an embodiment of the present invention;

[0075] Figure 2 for Figure 1 Schematic diagram of the principle structure of the spatial light modulator to modulate the angle of the illumination beam.

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

[0077] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0078] The embodiments of the present application provide a low-noise speckle interferometry system and method based on a spatial light modulator, thereby solving the problem of poor speckle decorrelation noise suppression in speckle interferometry technology.

[0079] In order to better understand the above technical solution, the above technical solution will be described in detail below with reference to the accompanying drawings and specific implementation methods.

[0080] Example:

[0081] First, as Figure 1-Figure 2 As shown, a low-noise speckle interferometry system based on a spatial light modulator includes a laser 1, a beam splitter prism 3 and an imaging element 12;

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

[0083] After being reflected by the dichroic prism 13, part of the transmitted light is irradiated on the imaging element 12 as reference light;

[0084] After partially passing through linear polarizer 4 and half-wave plate 5, the reflected light is modulated by the spatial light modulator assembly, impinges on beam splitter prism 17, and is reflected onto the surface of object 18 for diffuse reflection, obtaining slow-emission light. After partially passing through beam splitter prism 17, Fourier lens 16, aperture stop 15, Fourier lens 14, and beam splitter prism 13, the diffused light is impinged on imaging element 12 as object light.

[0085] Among them, Fourier lens three 13 and Fourier lens four 16 constitute a 4f system, and the surface of the object to be measured 18 is on the front focal plane of Fourier lens four 16, the imaging surface of the imaging element 12 is on the back focal plane of Fourier lens three 13, and aperture stop two 15 is on the spectrum plane in the 4f system constituted by Fourier lens three 13 and Fourier lens four 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 component.

[0087] Based on the spatial light modulator component, after modulation by the spatial light modulator component, the surface of the object under test 18 can be illuminated at different reverse illumination angles 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 interferometry 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 prism 1, and is used to expand the diameter of the laser beam while maintaining the collimation of the laser beam during the process of irradiating the beam to the beam splitter prism 3.

[0090] Specifically, the laser beam expander 2 is designed based on the structure of the Galilean telescope and is made of a group of negative lenses made of high-transmittance optical materials and a group of achromatic double-cemented positive lenses.

[0091] like Figure 1-Figure 2 As shown, the spatial light modulator assembly includes a spatial light modulator 7, a screen display 6, a Fourier lens 1 9, a Fourier lens 2 11, an aperture stop 10 and a beam splitter prism 2 8;

[0092] Among them, part of the reflected light is emitted through the half-wave plate 5, passes through the dichroic prism 2 8, and illuminates the spatial light modulator 7. After being modulated by the spatial light modulator 7, modulated light is generated. After being reflected by the dichroic prism 2 8, the modulated light passes through the Fourier lens 1 9, the aperture stop 10, and the Fourier lens 2 11 in sequence, and is reflected by the dichroic prism 4 17 to the surface of the object to be measured 19, where it is diffusely reflected to obtain diffuse light; the Fourier lens 1 9 and the Fourier lens 2 11 constitute another 4f system, wherein the exit port of the spatial light modulator 7 is on the front focal plane of the Fourier lens 1 9, the surface of the object to be measured 18 is on the back focal plane of the Fourier lens 2 11, and the aperture stop 10 is on the frequency spectrum plane of the 4f system constituted by the Fourier lens 1 9 and the Fourier lens 2 11.

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

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

[0095] In addition, the 4f imaging system combined with the aperture stop 10 also maintains the collimation and spot size of the light beam emitted by the spatial light modulator 7 and the object under test 18.

[0096] Specifically, a plurality of stripes with fixed rotation direction changes are input to the spatial light modulator 7 through the screen display 6 to form a stripe pattern group as the input of the spatial light modulator 7, so that the outgoing light can be converged at different positions of the aperture stop 10 through the Fourier lens 9 and present a uniform distribution, such as Figure 2 As shown, when two transverse stripes in opposite directions are modulated, the light beam emitted by the spatial light modulator 7 presents an emission angle that is symmetrical up and down, and the convergence point on the aperture stop 10 is also symmetrical relative to the zero point;

[0097] At the same time, each fixed-direction stripe contains Figure 2 The four fringe patterns shown have the same period but are regularly shifted to produce a fixed phase difference, meeting the requirements of time phase shift. The data on a line in the center of each fringe pattern is selected and plotted into a curve. It can be seen that the four curves have a fixed phase difference.

[0098] It should be noted that the multiple fringes in the fringe pattern group have the same period but different directions;

[0099] The input fringe pattern group can be equivalent to a rotating grating, so that the outgoing light modulated by the spatial light modulator component changes in angle and illuminates the surface of the object 18 at different illumination angles to cause diffuse reflection.

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

[0101] The laser beam emitted by laser 1 is expanded by laser beam expander 2 to maintain the collimation of the laser beam, and then is split into transmitted light and reflected light by beam splitter prism 3;

[0102] After being reflected by the dichroic prism 13, part of the transmitted light is irradiated on the imaging element 12 as reference light;

[0103] After partially reflecting light passes through the linear polarizer 4 and the half-wave plate 5 in sequence, the reflected light is completely converted into modulated light that can be modulated by the spatial light modulator assembly. The obtained modulated light is modulated by the spatial light modulator assembly, and a fringe pattern group with the same period but different directions is input to the spatial light modulator assembly, causing the spatial light modulator assembly to produce an angle change in the outgoing light modulated by the modulated light, while introducing a periodic phase change in the object light. The obtained outgoing light is irradiated on the beam splitter prism 17 and reflected to the surface of the object to be measured 18, where it is diffusely reflected to obtain slow-emission light.

[0104] After partially passing through the dichroic prism 17, the Fourier lens 16, the aperture stop 15, the Fourier lens 14 and the dichroic prism 13 in sequence, the part of the diffused light 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 specific applications, 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 stop 1 10 and the aperture stop 2 15 can be the same.

[0106] The basic working principle of the 4f imaging system is existing technology and will not be described in detail 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 interference pattern obtained on the target surface of the imaging element 12 is:

[0108]

[0109] Among them, (x, y) is the coordinate system is the 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;

[0110]

[0111] φ SLM (x, y) is the phase introduced by the deflection of the light beam modulated by the spatial light modulator 7, where d x and d y is the pixel size of the spatial light modulator, θ x and θ y is the beam deflection angle.

[0112] The reference light is assumed to be plane light. Considering that the reference light remains unchanged during the entire measurement process, the phase of the reference light itself can be ignored.

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

[0114] According to the inference in the relevant literature, the intensity covariance of the speckle field is affected by the spot diameter, the standard deviation of the surface height of the object 18 (ie, the surface roughness), the initial illumination angle, and the illumination angle variation.

[0115] The object-light complex amplitude before deformation can be calculated by the following formula:

[0116]

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

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

[0119] After deformation, the same speckle interferogram acquisition steps as above are performed to obtain the deformed object light complex amplitude. By conjugate multiplying the two complex amplitudes, we can get the phase-amplitude vector:

[0120]

[0121] 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;

[0122] Due to the high precision repeatability of the spatial light modulator 7, the same φ can be obtained by modulating the stripes in the same direction before and after the object is deformed. SLM , thus eliminating the phase after subtraction, and the final phase-amplitude vector calculation formula is:

[0123] Γ=OO′*=ae i(δφ) e iε ; (5)

[0124] When N incoherent phase-amplitude vectors Γ are superimposed, the expression of the phase-amplitude vector sum is as follows:

[0125]

[0126] Where a n and ε n is the speckle decorrelation noise of N incoherent phase-amplitude vectors;

[0127] The right side of the equal sign represents the phase-amplitude vector sum, whose phase is the superimposed speckle decorrelation noise.

[0128] When analyzing the statistical distribution of speckle decorrelation noise, we usually first fit the inverse transform of Euler's theorem through variable transformation to decompose the phase-amplitude vector into real and imaginary parts represented by trigonometric functions. The advantage of this is that the properties of trigonometric functions can be used to simplify some derivation processes. The phase-amplitude vector sum is decomposed into real and imaginary parts to obtain:

[0129]

[0130] Solving for the average values of R and I yields:

[0131]

[0132] in and We can use the random variable ε n The characteristic function of is expressed as follows, so as to obtain the average value of the real and imaginary parts:

[0133]

[0134] The variance of the real and imaginary parts can be obtained in a similar way:

[0135]

[0136] Where C R,I To express the covariance of R and I:

[0137]

[0138] Due to the decorrelation noise ε n It obeys a zero-mean Gaussian distribution, so the mean, standard deviation, and covariance of the real and imaginary parts can be further simplified as:

[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:

[0142]

[0143] Substituting Equation 5 into Equation 13 and integrating the amplitude yields the probability density function of the accumulated noise phase ψ:

[0144]

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

[0146] According to the central limit theorem, when multiple independent and identically distributed variables are superimposed, their distribution approaches the normal distribution. Therefore, the standard deviation of the speckle decorrelation noise after superposition is obtained according to the probability density function shown in formula 14. Combined with the result in formula 12, the standard deviation of the speckle decorrelation noise after superposition is finally obtained as:

[0147]

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

[0149] In summary, compared with the existing technology, the present invention has the following beneficial effects:

[0150] The speckle interferometry system proposed in the present invention uses a spatial light modulator to modulate the object light, and inputs a fringe pattern group consisting of multiple fringes into the spatial light modulator, and processes the mean, standard deviation and covariance of the complex amplitude before and after the deformation of the object light. It can be seen that the standard deviation of the speckle decorrelation noise is theoretically Therefore, when using speckle interferometry technology for measurement, the speckle decorrelation noise can be effectively suppressed by superimposing multiple measurements, thereby improving the accuracy of subsequent measurement results.

[0151] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or device comprising the element.

[0152] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A low-noise speckle interferometry system based on a spatial light modulator, characterized in that: include: Laser, beam splitter and imaging element; The laser beam emitted by the laser is split into transmitted light and reflected light by a beam splitter prism; After three reflections by the beam splitter, part of the transmitted light is irradiated on the imaging element as reference light; Part of the reflected light passes through the linear polarizer and half-wave plate in sequence, is modulated by the spatial light modulator assembly, illuminates the beam splitter prism four, and is reflected to the surface of the object to be measured, causing diffuse reflection to obtain slow-emission light; part of the diffuse light passes through the beam splitter prism four, Fourier lens four, aperture stop two, Fourier lens three, and beam splitter prism three in sequence, and then illuminates the imaging element as object light; Among them, Fourier lens three and Fourier lens four constitute a 4f system, and the surface of the object to be measured is on the front focal plane of Fourier lens four, the imaging surface of the imaging element is on the back focal plane of Fourier lens three, and aperture stop two is on the spectrum plane in the 4f system constituted by Fourier lens three and Fourier lens four.

2. The low-noise speckle interferometry system based on a spatial light modulator according to claim 1, wherein: The speckle interferometry system also includes a laser beam expander; The laser beam expander is located between the laser and the first beam splitter prism, and is used to expand the diameter of the laser beam while maintaining the collimation of the laser beam during the process of irradiating the path to the first beam splitter prism.

3. The low-noise speckle interferometry system based on a spatial light modulator according to claim 2, wherein: The spatial light modulator assembly includes a spatial light modulator, a screen display, a first Fourier lens, a second Fourier lens, a first aperture stop, and a second beam splitter prism; Among them, part of the reflected light is emitted through the half-wave plate and passes through the second beam splitter prism to illuminate the spatial light modulator. After being modulated by the spatial light modulator, modulated light is generated. After being reflected by the second beam splitter prism, the modulated light passes through the first Fourier lens, the first aperture stop, and the second Fourier lens in sequence, and is reflected by the fourth beam splitter prism to the surface of the object to be measured, where it is diffusely reflected to obtain diffuse light. The first and second Fourier lenses form another 4f system, in which the output port of the spatial light modulator is on the front focal plane of the first Fourier lens, the surface of the object to be measured is on the back focal plane of the second Fourier lens, and the first aperture stop is on the spectrum plane of the 4f system formed by the first and second Fourier lenses.

4. A low-noise speckle interferometry method based on a spatial light modulator, using the speckle interferometry system of claim 3 for interference, characterized in that: The following steps are involved: The laser beam emitted by the laser passes through the laser beam expander to expand the laser beam diameter and maintain the collimation of the output, and is then split into transmitted light and reflected light by the beam splitter prism; After three reflections by the beam splitter, part of the transmitted light is irradiated on the imaging element as reference light; After partially reflecting light passes through a linear polarizer and a half-wave plate in sequence, the reflected light is completely converted into modulated light that can be modulated by a spatial light modulator assembly. The obtained modulated light is modulated by the spatial light modulator assembly, and a fringe pattern group with the same period but different directions is input to the spatial light modulator assembly, causing the spatial light modulator assembly to produce an angle change in the outgoing light modulated by the modulated light, while introducing a periodic phase change in the object light. The obtained outgoing light is irradiated on a fourth beam splitter prism and reflected to the surface of the object to be measured, causing diffuse reflection to obtain slow-emission light. Part of the diffuse light passes through the fourth beam splitter prism, the fourth Fourier lens, the second aperture stop, the third Fourier lens and the third beam splitter prism in sequence, and then illuminates the imaging element as object light, and interferes with the reference light on the target surface of the imaging element.

5. The low-noise speckle interferometry method based on a spatial light modulator according to claim 4, characterized in that: Multiple stripes with fixed rotational directions are input into the spatial light modulator through a screen display to form a fringe pattern group as the input of the spatial light modulator, so that its outgoing light is converged at different positions of aperture 1 through a Fourier lens and is evenly distributed. Each stripe with a fixed direction contains four fringe patterns with the same period but regular translation to produce a fixed phase difference.

6. The low-noise speckle interferometry method based on a spatial light modulator according to claim 4, wherein: 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: Among them, (x,y) is the coordinate system coordinate, is the 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; φ SLM (x, y) is the phase introduced by the beam deflection caused by the spatial light modulator; where d x and d y is the pixel size of the spatial light modulator, θ x and θ y is the beam deflection angle; The reference light is assumed to be a plane light. The reference light remains unchanged during the entire measurement process and its own phase is negligible.

7. The low-noise speckle interferometry method based on a spatial light modulator according to claim 6, characterized in that: The object-light complex amplitude before deformation can be calculated by the following formula: Ae iφ is the complex amplitude expression of the light wave, where A is the amplitude and φ is the phase. The coordinate system (x, y) is omitted here and below. Where i is the imaginary number symbol, e iφ is the exponential term that carries the phase information of the object; After deformation, the same speckle interferogram acquisition steps as above are performed to obtain the deformed object light complex amplitude. The conjugate multiplication of the two complex amplitudes gives the phase-amplitude vector: 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; Due to the high precision repeatability of the spatial light modulator, the exact same φ can be obtained by modulating the stripes in the same direction before and after the object is deformed. SLM , thus eliminating the phase after subtraction, and the final phase-amplitude vector calculation formula is: When N incoherent phase-amplitude vectors Γ are superimposed, the expression of the phase-amplitude vector sum is as follows: Where a n and ε n is the speckle decorrelation noise of N incoherent phase-amplitude vectors; The right side of the equal sign Represents the phase-amplitude vector sum, whose phase is the decorrelated noise of the superimposed speckle; When analyzing the statistical distribution of speckle decorrelation noise, we first fit the inverse transformation of Euler's theorem through variable transformation to decompose the phase-amplitude vector into real and imaginary parts represented by trigonometric functions. The phase-amplitude vector sum is then decomposed into real and imaginary parts to obtain: Solving for the average values of R and I yields: in and We can use the random variable ε n The characteristic function of is expressed as follows, so as to obtain the average value of the real and imaginary parts: The variance of the real and imaginary parts can be obtained in a similar way: Where C R,I To express the covariance of R and I: Due to the decorrelation noise ε n Obeying the zero-mean Gaussian distribution, the mean, standard deviation and covariance of the real and imaginary parts are simplified to: According to the central limit theorem, the joint density function of R and I can be obtained: Substituting Equation 5 into Equation 13 and integrating the amplitude yields the probability density function of the accumulated noise phase ψ: The coefficients c1 and c2 mainly depend on the characteristic function M of the speckle decorrelation noise. ε (ω); According to the central limit theorem, when multiple independent and identically distributed variables are superimposed, their distribution approaches the normal distribution. Therefore, the standard deviation of the speckle decorrelation noise after superposition is obtained according to the probability density function shown in formula 14. Combined with the result in formula 12, the standard deviation of the speckle decorrelation noise after superposition is finally obtained as: It can be obtained that the standard deviation of speckle decorrelation noise is theoretically The law of.

8. A computer-readable storage medium, characterized in that The computer program based on low-noise speckle interferometry of a spatial light modulator is stored, wherein the computer program enables a computer to execute the low-noise speckle interferometry method based on a spatial light modulator according to any one of claims 4 to 7.

9. An electronic device, characterized in that: include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and the programs include instructions for executing the low-noise speckle interferometry method based on a spatial light modulator according to any one of claims 4 to 7.

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