Phase shift measurement method based on Moire profilometry

Abstract

The invention discloses a phase shift measurement method based on Moire profilometry, and the method comprises the steps: enabling a camera to synchronously collect deformation fringes containing the deformation information of an object during the projection of coding fringes; establishing a digital twinborn model of a measured object, and generating a digital reference stripe with prior contour information according to the digital twinborn model; performing digital multiplicative superposition on the reference fringes and the deformed fringes to generate moire fringes for phase calculation, and extracting moire fringe information through Butterworth low-pass filtering; and finally, a real phase is obtained through phase unwrapping and unwrapping processing and is used for actual measurement and calibration. According to the method, the strategy of'digital twin reference fringes + multi-step phase shift 'is combined, intensity noise and nonlinear errors are effectively suppressed, and the measurement precision is remarkably improved. The method is suitable for industrial detection scenes such as satellite antenna thermal deformation and the like, and micron-scale precision deformation measurement can be realized under the condition of no microscopic optical path view field.

Description

Technical Field

[0001] This invention belongs to the field of non-wafer three-dimensional topography restoration technology, specifically involving a phase shift measurement method based on computational moiré profile. Background Technology

[0002] Fringe projection, a technique in structured light measurement, is an ideal solution for industrial inspection fields such as satellite antenna thermal deformation measurement due to its non-contact nature, high precision, and strong anti-interference capabilities. However, the measurement accuracy of this technique is usually limited by the field of view, making it difficult to simultaneously meet the requirements of a large field of view and high precision. Existing research has made many attempts to improve accuracy or expand the field of view, but certain limitations still exist. In the paper "Real-time microscopic 3D shape measurement based on optimized pulse-width-modulation binary fringeprojection," Hu Yan et al. introduced microscopic optical structures into fringe projection, achieving a depth measurement accuracy of approximately 4 μm within a measurement volume of 8 mm × 6 mm × 8 mm. Although this scheme has the advantage of micron-level accuracy in local areas, its field of view is limited to less than 10 mm due to its reliance on microscopic optical paths, making it difficult to apply to deformation monitoring of large objects. In the paper "High precision computer-generated moiré profilometry," Cao Yiping et al. used the computational moiré profilometry method to achieve a three-dimensional shape measurement accuracy of approximately 0.1 mm under conventional field of view conditions. Although this method has good practicality, it still cannot meet the requirements for detecting micron-level deformation in precision components such as satellite antennas during thermal deformation. Summary of the Invention

[0003] To overcome the shortcomings of the prior art, this invention provides a phase shift measurement method based on computational moiré profilometry. By introducing the principle of generating digital twin reference fringes from prior contour data through digital twin technology, and combining multi-step phase shift to suppress various errors such as intensity noise and nonlinear effects, a micrometer-level precision reconstruction of the three-dimensional morphology under the condition of no microscopic optical path field of view is achieved.

[0004] This invention is achieved using the following technical solution: a phase shift measurement method based on computational Moiré profiles, comprising the following steps:

[0005] S1, a series of coded stripes are projected onto the surface of the object being detected using a projector, and the camera simultaneously captures a deformed stripe pattern modulated with the object's surface height information, including two sets of 12-step phase-shift deformed stripe image data with complementary phases, and the two sets of 12-step phase-shift deformed stripe image data are stored in a computer.

[0006] S2, construct a digital twin model of the object under test, simulate the real measurement conditions, generate a reference fringe pattern that contains the prior initial contour modulation information of the object under test, including two phase complementary digital twin reference fringe image data, and store the above two digital twin reference fringe image data in the computer.

[0007] S3 performs differential DC removal processing on the deformed fringe pattern in S1, which has the modulation information of the object surface height, and the reference fringe pattern in S2, which contains the modulation information of the prior initial contour of the object under test, respectively, to obtain 12 deformed fringe patterns without DC components and 1 digital twin reference fringe pattern without DC components.

[0008] S4. The 12 deformed fringe patterns without DC components are superimposed with the digital twin reference fringe patterns without DC components by multiplication to generate moiré fringes, resulting in 12 multiplicative superimposed fringe patterns.

[0009] S5. Perform Butterworth low-pass filtering on the 12 multiplicative superposition fringe patterns to obtain 12 phase-shifted moiré fringe patterns.

[0010] S6. Perform 12-step phase deconstruction on the 12 phase-shifted moiré fringe patterns to obtain the wrapped phase.

[0011] S7, unwrap the wrapped phase to obtain the true phase.

[0012] S8. The system is calibrated using the inverse linear model in the phase height relationship model to obtain the calibration coefficients. The true phase obtained by demodulation during measurement is substituted into the calibrated inverse linear model to obtain the height deviation value. This value is added to the prior initial contour data of the object in S2 to finally obtain the deformed three-dimensional morphology data, that is, to restore the three-dimensional morphology of the object.

[0013] Compared with the prior art, the significant advantages of this invention are as follows: This invention uses digital twin fringes as the accuracy benchmark, utilizes spatial domain phase complementary fringes combined with low-pass filtering to suppress noise; then, it generates high-sensitivity moiré fringes by using a digital template and measured fringes to amplify surface deviations; finally, it introduces a multi-step phase shift strategy to complete the accurate phase solution, realizing micron-level precision measurement of continuous three-dimensional contours without a microscopic optical path. Attached Figure Description

[0014] Figure 1 This is a flowchart of a phase shift measurement method based on computational Moiré profile according to the present invention. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0016] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to specific embodiments. The embodiments described with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application.

[0017] Combination Figure 1 A phase shift measurement method based on computational Moiré profiles, comprising the following steps:

[0018] S1, a series of coded stripes are projected onto the surface of the object being detected using a projector, and the camera simultaneously captures a deformed stripe pattern modulated with the object's surface height information, including two sets of 12-step phase-shift deformed stripe image data with complementary phases, and the two sets of 12-step phase-shift deformed stripe image data are stored in a computer.

[0019] The camera captures a deformed fringe pattern, which is synchronized with the trigger signal emitted when the projector projects the coded fringe image. The projector projects two sets of 12-step phase-shift coded fringes with complementary phases. The camera captures the deformed fringe image modulated by the contour height information and transmits it to the computer for storage, awaiting further processing.

[0020] The innovation of this invention lies in its novel computational moiré profilometry framework, which combines multi-step phase-shifting projection with a single digital twin reference fringe. This represents a fundamental reversal of traditional methods: conventional computational moiré profilometry typically projects a single fringe pattern onto an object, then generates multiple reference fringes with different phase shifts in a computer for superposition analysis. This method is susceptible to noise and nonlinear errors inherent in single-frame projections. This invention, however, takes the opposite approach, performing a 12-step phase-shifting operation at the projection stage. By projecting multiple frames of coded fringes, it actively acquires a set of deformed fringes with extremely high signal-to-noise ratio and rich phase information. In the computation stage, only a single prior reference fringe generated by the digital twin model is needed.

[0021] The principle behind this design is to shift the core of error resistance from the "digital phase shift at the post-processing end" to the "physical phase shift at the data acquisition end," leveraging the inherent strong noise immunity of multi-step phase shift technology to ensure the quality of the acquired deformed fringes from the source. This fundamentally suppresses major error sources such as intensity noise and nonlinearity, laying the foundation for subsequent generation of high-quality moiré fringes and extraction of accurate phase, thereby improving measurement accuracy and stability.

[0022] S2, construct a digital twin model of the object under test, simulate the real measurement conditions, generate a reference fringe pattern that contains the prior initial contour modulation information of the object under test, including two phase complementary digital twin reference fringe image data, and store the above two digital twin reference fringe image data in the computer.

[0023] During numerical simulation, the three-dimensional prior initial contour data of the object under test is introduced. With the help of digital twin technology, two frames of phase-complementary deformable fringe image data are generated based on the technical parameters of the structured light projection system. These images are used as standard "template" stripes for the surface shape information of the object under test.

[0024] The core innovation of this invention lies in integrating digital twin technology into computational moiré profilometry. By constructing digital reference stripes containing the true prior contour information of the object being measured, a highly consistent comparison benchmark is established for phase measurement.

[0025] Unlike traditional methods that use idealized reference fringes with fixed, uniform initial phases, the digital twin reference fringes generated in this invention assign initial phase values ​​for each pixel based on prior 3D contour data of the object under test and actual measurement system parameters. This means that the phase distribution of the reference fringes is not an idealized uniform field, but rather a pre-simulated modulation effect of the real object contour on the fringes, thus achieving a high degree of matching with the deformed fringes actually acquired by the camera in terms of spatial frequency and phase distribution.

[0026] S3, differential DC removal processing is performed on the deformed fringe pattern with the object surface height information modulation in S1 and the reference fringe pattern with the prior initial contour modulation information of the measured object in S2, respectively, to obtain 12 deformed fringe patterns without DC components and 1 digital twin reference fringe pattern without DC components.

[0027] Differential DC-DC conversion is performed as follows:

[0028] The spatial domain algebraic subtraction of the two sets of phase-complementary 12-step phase-shift deformed fringe images, i.e., removing their DC components, yields 12 deformed fringe images without DC components; the spatial domain algebraic subtraction of the two generated phase-complementary deformed fringe images, i.e., removing their DC components, yields 1 digital twin reference fringe image without DC components.

[0029] S4. The 12 deformed fringe patterns without DC components are superimposed with the digital twin reference fringe patterns without DC components by multiplication to generate moiré fringes, resulting in 12 multiplicative superimposed fringe patterns.

[0030] Multiplicative superposition is the spatial domain multiplicative superposition of 12 deformed fringe patterns without DC components with digital twin reference fringe patterns without DC components, i.e., Hadamard product.

[0031] S5. Perform Butterworth low-pass filtering on the 12 multiplicative superimposed fringe patterns to obtain 12 phase-shifted moiré fringe patterns.

[0032] Low-pass filtering involves converting each superimposed fringe to the frequency domain, generating a Butterworth low-pass filter window, and extracting the moiré signal from each superimposed fringe.

[0033] S6, perform 12-step phase deconstruction on the 12 phase-shifted moiré fringe patterns to obtain the wrapped phase;

[0034] The moiré phase shift diagram is extracted using the multi-step phase shift method formula to obtain the moiré wrapped phase.

[0035] S7, unwrap the wrapped phase to obtain the true phase;

[0036] The Moiré wrapping phase is unwrapped using the spatial phase expansion method to obtain the true phase.

[0037] S8. The system is calibrated using the inverse linear model in the phase height relationship model to obtain the calibration coefficients. The true phase obtained by demodulation during measurement is substituted into the calibrated inverse linear model to obtain the height deviation value. This value is added to the prior initial contour data of the object in S2 to finally obtain the deformed three-dimensional morphology data, that is, to restore the three-dimensional morphology of the object.

[0038] Phase-height conversion is used to calibrate the system using a phase-height relationship model to obtain calibration parameters. The recovered true phase during measurement is then substituted into the calibrated inverse linear model to obtain the deformation. The deformation is added to the prior initial contour data of the object under test to finally obtain the deformed three-dimensional morphology data, thus restoring the three-dimensional morphology of the object under test.

[0039] Example 1:

[0040] The CMOS camera of this invention is equipped with a sensor with a resolution of 1024(H)×1280(V), a pixel size of 4.5μm×4.5μm, and an output data bit width of 8 bits; the DLP projector is equipped with a sensor with a resolution of 1080(H)×1920(V), a pixel size of 5.4μm×5.4μm, and a data bit width of 8 bits; the displacement calibration PZT is P-737.5SL, providing a movement range of 500µm; the data processing software used is MATLAB R2023b; the data processing equipment information is as follows: Windows 10 64-bit, 13th Gen Intel(R) Core(TM) i5-13600KF @ 3.50GHz, 32G RAM.

[0041] Two sets of 12-frame periodic sinusoidal fringe patterns are designed and generated in a computer. In each set, the later frame lags the previous frame by π / 6 in phase, and each frame in the second set lags the corresponding frame in the first set by π in phase. The two sets, totaling 24 frames, have the same DC, modulation depth, and fringe frequency. The mathematical expression for the first set of fringe patterns is... Mathematical expression for the second set of stripes They are respectively:

[0042] ,

[0043] ,

[0044] In the formula, a is the DC current, b is the modulation index, and f is the DC signal. p The fringe frequency is given by the phase shift step numbering i∈{0,1,2,…,11}. Represents the coordinates of a pixel.

[0045] The computer-generated stripe coding pattern is synchronously transmitted into a projector, which projects it onto the test surface according to a set time sequence. A camera sequentially captures two sets of 12 frames each of the deformed fringe patterns modulated by the sample contour height. The mathematical expression of the first set of deformed fringe patterns is obtained. Mathematical expression for the second set of deformed stripe patterns They are respectively:

[0046] ,

[0047] ,

[0048] In the formula, R(x,y) is the reflectivity distribution of the sample surface, A is the linearity of the test surface stripes, B is the modulation degree of the test surface stripes, f is the frequency of the test surface stripes, and φ(x,y) is the phase distribution of the height modulation of the test surface.

[0049] By constructing a digital twin model of the object under test, simulating real measurement conditions, two frames of sinusoidal reference fringe patterns are generated, each containing the nominal surface profile modulation information and phase difference π of the object under test. The mathematical expression for the first frame is... Second frame mathematical expression They are respectively:

[0050] ,

[0051] ,

[0052] In the formula, A0 is the direct current of the reference fringe, B0 is the modulation index of the reference fringe, f0 is the fringe frequency of the reference fringe, and φ0 is the reference phase that encodes the prior morphology.

[0053] By performing spatial algebraic subtraction on two computer-generated digital twin reference fringes with a phase difference of π, the DC component is removed while the AC component is retained, resulting in a digital twin reference fringes pattern without a DC component. Its mathematical expression is... for:

[0054] ,

[0055] By performing spatial algebraic subtraction on two sets of 12 deformed patterns captured by the camera, similar to DC removal, a deformed fringe pattern without DC components is obtained. Its mathematical expression is... for:

[0056] ,

[0057] The 12 deformed fringe patterns after removing the DC component are multiplied and superimposed with the digital twin reference fringe pattern after removing the DC component to generate moiré fringes, resulting in a multiplicative superimposed fringe pattern, the mathematical expression of which is... for:

[0058] ,

[0059] The superimposed fringe patterns are converted to the frequency domain and subjected to Butterworth low-pass filtering. The mathematical expression of the filter is as follows: for:

[0060] ,

[0061] In the formula, (u,v) are frequency domain coordinates, (u 2 +v 2 ) 1 / 2 It is the distance from the frequency point (u,v) to the frequency origin, and D0 is the normalized cutoff frequency.

[0062] Extracting low-frequency moiré fringe components yields the moiré phase-shift fringe pattern, whose mathematical expression is... for:

[0063] ,

[0064] In the formula, abs represents the modulo operation, IFFT is the inverse fast Fourier transform, FFT is the fast Fourier transform, and ⊙ is the Hadamard product (element-wise multiplication at corresponding positions).

[0065] The 12 moiré fringe patterns extracted by low-pass filtering were dephased using the multi-step phase-shifting method to obtain the wrapped phase. Unwrapping yields a continuous phase distribution.

[0066] ,

[0067] In the formula, N is the number of phase shift steps.

[0068] After obtaining the continuous phase distribution, the phase information is converted into a height deviation from the "template" contour. Before reconstructing the 3D shape of the object, mathematical modeling of the measurement system is required. Using the inverse linear model in the phase-height model, a mapping function relationship between phase and height is pre-established based on the known height; this can be called the phase-height relationship.

[0069] ,

[0070] In the formula, h(x,y) is the height distribution, k1(x,y) and k2(x,y) are the calibration model parameters, and ∆ϕ(x,y) is the phase deviation.

[0071] After calibrating the phase-height model with known k1(x,y) and k2(x,y), the phase deviation ∆ϕ(x,y) of the measured part can be obtained by using the phase shift measurement method based on computational Moiré profilometry proposed in this paper. This allows us to obtain the height deviation of the measured part from the "template" surface and ultimately achieve the restoration of the three-dimensional shape.

[0072] In summary, this application proposes a phase shift measurement method based on computational moiré profilometry, using digital twin fringes as the accuracy benchmark; utilizing spatial domain phase complementary fringes combined with low-pass filtering to suppress noise; further generating high-sensitivity moiré fringes through a digital template and measured fringes to amplify surface deviations; and finally introducing a multi-step phase shift strategy to complete accurate phase solution, achieving micron-level precision measurement of continuous three-dimensional profiles without a microscopic optical path.

[0073] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to the above embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0074] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A phase shift measurement method based on computational Moiré profile, characterized in that, Includes the following steps: S1, a series of coded stripes are projected onto the surface of the object being detected using a projector, and the camera simultaneously captures a deformed stripe pattern modulated with the object's surface height information, including two sets of 12-step phase-shift deformed stripe image data with complementary phases, and the two sets of 12-step phase-shift deformed stripe image data are stored in a computer. S2, construct a digital twin model of the object under test, simulate the real measurement conditions, generate a reference fringe pattern that contains the prior initial contour modulation information of the object under test, including two phase complementary digital twin reference fringe image data, and store the above two digital twin reference fringe image data in the computer. S3, differential DC removal processing is performed on the deformed fringe pattern with the object surface height information modulation in S1 and the reference fringe pattern with the prior initial contour modulation information of the measured object in S2, respectively, to obtain 12 deformed fringe patterns without DC components and 1 digital twin reference fringe pattern without DC components. S4. The 12 deformed fringe patterns without DC components are superimposed with the digital twin reference fringe patterns without DC components by multiplication to generate moiré fringes, resulting in 12 multiplicative superimposed fringe patterns. S5. Perform Butterworth low-pass filtering on the 12 multiplicative superimposed fringe patterns to obtain 12 phase-shifted moiré fringe patterns. S6, perform 12-step phase deconstruction on the 12 phase-shifted moiré fringe patterns to obtain the wrapped phase; S7, unwrap the wrapped phase to obtain the true phase; S8. The system is calibrated using the inverse linear model in the phase height relationship model to obtain the calibration coefficients. The true phase obtained by demodulation during measurement is substituted into the calibrated inverse linear model to obtain the height deviation value. This value is added to the prior initial contour data of the object in S2 to finally obtain the deformed three-dimensional morphology data, that is, to restore the three-dimensional morphology of the object.

2. The phase shift measurement method based on computational Moiré profile according to claim 1, characterized in that: In S1, the deformed fringe pattern captured by the camera is synchronized with the trigger signal emitted when the projector projects the coded fringe image; the projector projects two sets of 12-step phase-shift coded fringes with complementary phases respectively, and the camera acquires the deformed fringe image modulated by the contour height information and transmits it to the computer for storage in the computer for further processing.

3. The phase shift measurement method based on computational Moiré profile according to claim 2, characterized in that: In S2, during numerical simulation, the three-dimensional prior initial contour data of the object under test is introduced. With the help of digital twin technology, based on the technical parameters of the structured light projection system, two frames of phase-complementary deformable fringe image data are generated, which are used as the standard "template" fringe for the surface shape information of the object under test.

4. The phase shift measurement method based on computational Moiré profile according to claim 3, characterized in that, In S3, the differential DC-DC conversion process is as follows: The spatial domain algebraic subtraction of the two sets of phase-complementary 12-step phase-shift deformed fringe images, i.e., removing their DC components, yields 12 deformed fringe images without DC components; the spatial domain algebraic subtraction of the two generated phase-complementary deformed fringe images, i.e., removing their DC components, yields 1 digital twin reference fringe image without DC components.

5. The phase shift measurement method based on computational Moiré profile according to claim 4, characterized in that, In S4, multiplicative superposition involves performing spatial domain multiplicative superposition of 12 deformed fringe patterns without DC components with digital twin reference fringe patterns without DC components, i.e., Hadamard product.

6. The phase shift measurement method based on computational Moiré profile according to claim 5, characterized in that, In S5, low-pass filtering converts each superimposed fringe to the frequency domain, generates a Butterworth low-pass filter window, and extracts the moiré signal from each superimposed fringe.

7. The phase shift measurement method based on computational Moiré profile according to claim 6, characterized in that, In S6, the multi-step phase shift method is used to process and extract the moiré phase shift map to obtain the moiré wrapped phase.

8. The phase shift measurement method based on computational Moiré profile according to claim 7, characterized in that, In S7, the unwrapping method uses spatial phase expansion to expand the Moiré wrapping phase and obtain the true phase.

9. The phase shift measurement method based on computational Moiré profile according to claim 8, characterized in that, In S8, the phase height conversion uses the phase height relationship model to calibrate the system and obtain calibration parameters. The true phase recovered during measurement is then substituted into the inverse linear model after calibration to obtain the deformation.

10. The phase shift measurement method based on computational Moiré profile according to claim 1, characterized in that, In S8, the deformation amount is added to the prior initial contour data of the object under test, and finally the deformed three-dimensional shape data is obtained, that is, the three-dimensional shape of the object under test is restored.

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