High-precision fringe phase extraction method based on 2D-Hamming self-convolution window
By using 2D-Hamming self-convolution window and fast Fourier transform in striped image processing, the impact of spectrum leakage on phase extraction accuracy is solved, and more efficient spectrum leakage suppression and phase extraction accuracy are achieved. It is suitable for High-precision measurement scenarios.
Patent Information
- Application Number
- CN202411428583.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-14
- Publication Date
- 2025-01-03
AI Technical Summary
The prior art is difficult to effectively suppress spectrum leakage in striped images in high-precision measurements, resulting in insufficient phase extraction accuracy, especially when the noise environment is complex or the fringes are irregular, which greatly increases, affecting the reliability of the measurement results.
Using the method based on 2D-Hamming self-convolution window, by constructing a two-dimensional Hamming window and performing self-convolution operations, combining fast Fourier transform and fast intensity transmission equation de-wrapping algorithm, weighting and frequency domain processing are performed to suppress the frequency spectrum. leakage.
Significantly improves spectrum leakage suppression ability, reduces phase error, improves phase extraction accuracy and stability, is suitable for high-precision measurement scenarios, and maintains high accuracy in irregular or noise interference, with wide applicability and high Computational efficiency.
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Figure CN119251203A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of optical measurement and image processing, and specifically relates to a spectrum leakage suppression method based on a 2D-Hamming self-convolution window, which is used to improve the phase extraction accuracy in fringe image processing and is suitable for any scenario requiring high-precision measurement through fringe images. Background Art
[0002] Fringe technology is widely used in various high-precision measurement scenarios, such as optical profilometry, interferometry, phase lithography alignment, etc. This type of technology usually relies on the phase information of the fringe image and performs precise measurement by extracting the phase of the fringe. However, factors such as discrete sampling, non-integer cycle truncation, and asynchronous sampling of the fringe image will lead to spectrum leakage, which in turn affects the accuracy of phase extraction. Especially when the noise environment is more complex or the fringe pattern is irregular, the error caused by spectrum leakage will increase significantly, affecting the reliability of the measurement results.
[0003] In order to reduce the negative impact of spectrum leakage on fringe pattern phase extraction, window functions are usually used in the prior art for weighted processing to suppress spectrum side lobes. However, the spectrum leakage suppression capability of commonly used window functions (such as Hamming window, Hanning window, etc.) is still limited, especially in high-precision measurement, the effects of these window functions are not enough to fully meet the requirements of high-precision phase extraction.
[0004] Therefore, how to effectively suppress spectral leakage in fringe patterns and improve phase extraction accuracy has become an important technical challenge in the current field of optical measurement and signal processing. Summary of the invention
[0005] The present invention aims to solve the deficiencies in the above-mentioned prior art and proposes a high-precision fringe phase extraction method based on a 2D-Hamming self-convolution window. It is hoped that by constructing a 2D-Hamming self-convolution window, the influence of spectrum leakage on the phase extraction accuracy can be more effectively suppressed, thereby overcoming the limitations of traditional window functions in suppressing spectrum leakage and improving the phase extraction accuracy in fringe image processing. The method is suitable for various scenarios requiring high-precision phase measurement.
[0006] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:
[0007] The high-precision fringe phase extraction method based on a 2D-Hamming self-convolution window of the present invention is characterized in that it comprises the following steps:
[0008] S1: Discretize the acquisition size using imaging equipment Stripe diagram , where x and y represent the pixel coordinates of the fringe pattern in the row and column directions respectively; and represent the length of the fringe pattern in the row and column directions, respectively, and , ;
[0009] S2: According to , , determine the one-dimensional Hamming window in the row direction Length , one-dimensional Hamming window in the column direction Length , thus constructing a two-dimensional Hamming window by equation (1) ,in, Represents the order of self-convolution:
[0010] (1)
[0011] In formula (1), Represents dot multiplication operation;
[0012] S3: Use formula (2) to construct a two-dimensional Hamming self-convolution window , used for self-convolution operation of two-dimensional Hamming window;
[0013] (2)
[0014] In formula (2), is the convolution operator;
[0015] S4: Using formula (3) to calculate the fringe pattern Perform weighted operation to obtain the windowed fringe image :
[0016] (3)
[0017] S5: Use formula (4) to calculate the windowed fringe image Perform 2D-FFT operation and get Spectrum :
[0018] (4)
[0019] In formula (4), represents the imaginary unit, is the natural exponential function, and are the frequency components in the row and column directions respectively, and Respectively for and The differential of
[0020] S6: Using formula (5) to obtain the positive first-order spectrum containing phase information :
[0021] (5)
[0022] In formula (5), represents a bandpass filter;
[0023] S7: Use equation (6) to align the primary spectrum Perform the inverse FT operation to obtain the time domain distribution of the positive first-order spectrum :
[0024] (6)
[0025] In formula (6), and For and The differential of
[0026] S8: Use equation (7) to obtain the fringe pattern The wrapping phase :
[0027] (7)
[0028] In formula (7), and Respectively The imaginary and real parts of Represents the inverse tangent operation;
[0029] S9: Using the fast intensity transfer equation unwrapping algorithm to unwrap the wrapped phase Processing to obtain the absolute phase .
[0030] The high-precision fringe phase extraction method based on the 2D-Hamming self-convolution window of the present invention is also characterized in that the 2D-Hamming self-convolution window The sidelobe attenuation performance varies with the order of self-convolution The sidelobe attenuation performance includes: peak sidelobe level and sidelobe attenuation rate, and the peak sidelobe level of the two-dimensional Hamming self-convolution window is obtained according to equation (3) and equation (4) respectively. and sidelobe decay rate :
[0031] (8)
[0032] (9)
[0033] In formulas (8) and (9), and They represent the peak sidelobe level and sidelobe attenuation rate of the two-dimensional Hamming window respectively.
[0034] An electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the high-precision fringe phase extraction method, and the processor is configured to execute the program stored in the memory.
[0035] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the high-precision fringe phase extraction method when executed by a processor.
[0036] Compared with the prior art, the present invention has the following beneficial effects:
[0037] 1. More effective spectrum leakage suppression: Compared with traditional window functions, the sidelobe attenuation performance of the 2D-Hamming self-convolution window is significantly enhanced as the self-convolution order increases, which can more effectively suppress spectrum leakage. This greatly reduces the phase error caused by discrete sampling, asynchronous sampling and non-integer cycle truncation, and improves the measurement accuracy and stability.
[0038] 2. Improvement of phase extraction accuracy: By weighting the fringe image and performing frequency domain processing, the present invention can achieve high-precision phase extraction in complex noise environments, and is suitable for measurement tasks with high precision requirements, such as interferometry, three-dimensional profile imaging, etc.
[0039] 3. Wide range of application scenarios: The present invention is not only suitable for traditional lithography alignment and optical measurement, but can also be extended to other fields that require precise measurement based on fringe images, such as biomedical imaging, mechanical precision detection, etc. It has wide applicability and scalability.
[0040] 4. Stability and robustness of the algorithm: Due to the characteristics of the 2D-Hamming self-convolution window, this method can still maintain a high phase extraction accuracy when processing irregular or noisy fringe images, and has good anti-interference ability and robustness.
[0041] 5. High computational efficiency: The present invention adopts fast Fourier transform (FFT) and fast intensity transfer equation unwrapping algorithm to improve computational efficiency while ensuring accuracy, and is suitable for application scenarios of real-time measurement or processing of large amounts of data. BRIEF DESCRIPTION OF THE DRAWINGS
[0042] Figure 1 This is a flow chart of the high-precision fringe phase extraction method based on the 2D-Hamming self-convolution window of the present invention, showing the relationship between the various steps;
[0043] Figure 2 is an example of a fringe pattern acquired by an imaging device, showing the original fringe image and its light intensity distribution for subsequent processing;
[0044] Figure 3 The time domain structure of the first, second and fourth order 2D-Hamming self-convolution windows and the amplitude-frequency response diagram of the first order 2D-Hamming self-convolution window are shown, which intuitively demonstrates the characteristics of window functions of different orders;
[0045] Figure 4 The figure is a numerical relationship diagram between the sidelobe attenuation performance of the 2D-Hamming self-convolution window and the self-convolution order, showing the trend that the sidelobe level decreases with the increase of the order;
[0046] Figure 5 It is the time domain structure diagram of the fringe pattern after weighting by the first, second and fourth order 2D-Hamming self-convolution windows, which reflects the influence of weighted processing on the edge smoothness of the fringe pattern;
[0047] Figure 6 Schematic diagram of the process of extracting fringe phase, where: (a) shows the spectrum of the windowed fringe pattern; (b) shows the wrapped phase of the windowed fringe pattern; (c) represents the absolute phase of the windowed fringe pattern. DETAILED DESCRIPTION
[0048] In order to better understand the functions and features of the present invention, the preferred embodiments of the present invention are described in detail in conjunction with the accompanying drawings. Specifically, the high-precision fringe phase extraction method of the present invention is as follows: Figure 1 As shown, the following steps are included:
[0049] S1: Collection of fringe patterns
[0050] The fringe pattern can be discretized and collected by imaging equipment (such as CMOS camera) for computer processing. ,like Figure 2 The intensity of the fringe pattern is shown in It can be expressed as:
[0051] (1)
[0052] In formula (1), x and y represent the pixel coordinates of the fringe pattern in the row and column directions, respectively. and represent the background intensity and amplitude modulation of the fringe pattern, is the frequency of the fringe pattern, is the initial phase of the fringe pattern, and the lengths of the fringe pattern in the row and column directions are and The discrete acquisition of fringe patterns is the first step to achieve accurate phase extraction, and the acquired fringe pattern data will be used in subsequent phase processing steps.
[0053] S2: Constructing a two-dimensional Hamming window
[0054] The construction of the two-dimensional Hamming self-convolution window is based on the expansion of the one-dimensional Hamming window. The discretization expression of the one-dimensional Hamming window is:
[0055] (2)
[0056] In formula (2), m represents the position of the discrete sampling point. Then, by using the lengths in the row and column directions respectively and Perform a dot multiplication operation on the one-dimensional Hamming window to obtain a two-dimensional Hamming window:
[0057] (3)
[0058] In formula (3), represents the dot multiplication operation, Represents the order of self-convolution.
[0059] S3: Constructing a 2D Hamming self-convolution window
[0060] By performing self-convolution on the two-dimensional Hamming window, a two-dimensional Hamming self-convolution window is constructed. :
[0061] (4)
[0062] In formula (4), is the convolution operator. The sizes of the two-dimensional Hamming self-convolution window in the row and column directions are and Usually, in order to ensure the consistency of the convolution results, it is necessary to perform p-1 zero padding on the two-dimensional Hamming window to meet and A p-order two-dimensional Hamming self-convolution window.
[0063] like Figure 3 As shown, Figure 3 (a) to Figure 3(c) in the figure shows the time domain structures of the first-order, second-order, and fourth-order two-dimensional Hamming self-convolution windows, respectively. It can be observed that the time domain edge of the first-order two-dimensional Hamming self-convolution window (i.e., the classic two-dimensional Hamming window) is not completely zero, which is mainly due to the mathematical design of its window function. According to the time domain expression (2) of the Hamming window, the value of the window function at both ends (i.e., m = 0 and m = M) is not 0, but about 0.08. Therefore, the first-order two-dimensional Hamming self-convolution window has poor edge smoothing ability and is difficult to effectively suppress the oscillation and discontinuity of the stripe edge. Therefore, through the self-convolution method, the edge smoothing ability of the window function is significantly improved, thereby reducing the oscillation and discontinuity problem of the stripe pattern edge. In addition, the two-dimensional Hamming self-convolution window is obtained by performing self-convolution after dot multiplication of the one-dimensional Hamming window in the row and column directions, and its time domain and amplitude-frequency response both show four-fold rotational symmetry. Therefore, in order to describe the time domain and frequency domain characteristics of the two-dimensional Hamming self-convolution window more clearly and intuitively, it can be analyzed from a one-dimensional perspective.
[0064] Peak sidelobe level of a two-dimensional Hamming autoconvolution window and sidelobe decay rate It is proportional to the convolution order, which means that its ability to suppress spectrum leakage increases with the increase of convolution order:
[0065] (5)
[0066] (6)
[0067] In formulas (5) and (6), and They represent the peak sidelobe level and sidelobe attenuation rate of the two-dimensional Hamming window respectively.
[0068] The frequency domain characteristics of the two-dimensional Hamming window are very good. About 99.96% of the energy is concentrated in the main lobe, the peak sidelobe level is -43 dB lower than the main lobe, and the sidelobe attenuation rate is 6 dB / oct. After performing self-convolution, its peak sidelobe level (PSLL) and sidelobe attenuation rate (SLAR) are proportional to the convolution order. and ,like Figure 4 As shown in Figure 2, with the increase of the convolution order, the sidelobe performance of the two-dimensional Hamming self-convolution window is effectively enhanced, and thus its spectrum leakage suppression capability is improved.
[0069] S4: Generation of windowed fringe images
[0070] Use the constructed 2D Hamming self-convolution window Stripe pattern Perform weighted operation to obtain the windowed fringe image :
[0071] (7)
[0072] The time domain structure after weighting the fringe pattern with first-order, second-order and fourth-order two-dimensional Hamming self-convolution windows is as follows: Figure 5 As shown in Figure 2, it can be seen that with the increase of the convolution order, the smoothness of the edge of the fringe image is significantly enhanced.
[0073] S5: Frequency Domain Conversion
[0074] In the process of fringe phase extraction, the use of 2D fast Fourier transform (2D-FFT) is a common and efficient method. Convert to frequency domain and get its spectrum distribution :
[0075] (8)
[0076] In formula (8), is an imaginary unit, is the natural exponential function, and Represent the frequency components in the row and column directions respectively, and Express and The differential of .
[0077] S6: Select the positive primary spectrum
[0078] By using a bandpass filter To filter out interference signals in the frequency domain, especially the zero-frequency component representing the background light intensity and other interference frequencies. :
[0079] (9)
[0080] like Figure 6 As shown in (a) in the figure, the filtered positive first-order spectrum will be used for subsequent phase extraction.
[0081] S7: Inverse Fourier Transform
[0082] Perform an inverse Fourier transform (IFT) on the positive first-order spectrum and convert it back to the time domain to obtain the time domain distribution of the positive first-order spectrum :
[0083] (10)
[0084] In formula (10), and For and This step restores the frequency domain information to the time domain distribution for subsequent phase calculation.
[0085] S8: Calculation of the wrapping phase
[0086] like Figure 6 As shown in (b) in the figure, the inverse tangent operation is performed. , obtain the wrapped phase of the fringe pattern :
[0087] (11)
[0088] In formula (11), and Respectively The imaginary and real parts of .
[0089] S9: Phase Unwrapping
[0090] The phase value obtained from formula (11) is in the range In order to obtain the absolute phase, phase unwrapping is required. The present invention compares a variety of phase unwrapping algorithms and finally selects the fast intensity transfer equation (FTIE) phase unwrapping algorithm with high accuracy and high speed. This algorithm does not need to use wave propagation technology, but directly calculates the axial intensity derivative of the wrapped phase to obtain the absolute phase diagram, thereby improving the calculation efficiency and accuracy. Processing to obtain high-precision absolute phase ,like Figure 6 As shown in (c) in .
[0091] The high-precision fringe phase extraction method based on the 2D-Hamming self-convolution window proposed in the embodiment of the present invention has significant advantages. Specifically, the sidelobe attenuation performance of the 2D-Hamming self-convolution window is significantly enhanced with the increase of the self-convolution order p. This characteristic not only improves the ability to suppress spectrum leakage, but also effectively reduces the errors caused by noise and interference in the process of fringe image acquisition and processing. With the improvement of the sidelobe attenuation performance, the phase extraction accuracy of the fringe pattern is also significantly improved. This high-precision phase extraction method can achieve more precise measurements in practical applications, especially in fields requiring high reliability and high precision (such as industrial detection, material characterization, and optical measurement, etc.), showing unparalleled advantages and providing strong support for the development of related technologies.
[0092] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.
[0093] In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.
[0094] Finally, it should be noted that the above is only a preferred embodiment of the present invention and does not constitute a limitation on the scope of protection of the present invention. Any technical solution based on the concept of the present invention should be deemed to be within the scope of protection of the present invention. For ordinary technicians in this field, any improvement, deformation or adjustment made without departing from the core idea of the present invention should also be deemed to be included in the scope of protection of the present invention.
Claims
1. A high-precision fringe phase extraction method based on 2D-Hamming self-convolution window, characterized in that: The following steps are involved: S1: Discretize the acquisition size using imaging equipment Stripe diagram , where x and y represent the pixel coordinates of the fringe pattern in the row and column directions respectively; and represent the length of the fringe pattern in the row and column directions, respectively, and , ; S2: According to , , determine the one-dimensional Hamming window in the row direction Length , one-dimensional Hamming window in the column direction Length , thus constructing a two-dimensional Hamming window by equation (1) ,in, Indicates the order of self-convolution: (1) In formula (1), Represents dot multiplication operation; S3: Use formula (2) to construct a two-dimensional Hamming self-convolution window , used for self-convolution operation of two-dimensional Hamming window; (2) In formula (2), is the convolution operator; S4: Using formula (3) to calculate the fringe pattern Perform weighted operation to obtain the windowed fringe image : (3) S5: Use formula (4) to calculate the windowed fringe image Perform 2D-FFT operation and get Spectrum : (4) In formula (4), represents the imaginary unit, is the natural exponential function, and are the frequency components in the row and column directions respectively, and Respectively for and The differential of S6: Using formula (5) to obtain the positive first-order spectrum containing phase information : (5) In formula (5), represents a bandpass filter; S7: Use equation (6) to align the primary spectrum Perform the inverse FT operation to obtain the time domain distribution of the positive first-order spectrum : (6) In formula (6), and For and The differential of S8: Use equation (7) to obtain the fringe pattern The wrapping phase : (7) In formula (7), and Respectively The imaginary and real parts of Represents the inverse tangent operation; S9: Using the fast intensity transfer equation unwrapping algorithm to unwrap the wrapped phase Processing to obtain the absolute phase .
2. The high-precision fringe phase extraction method based on 2D-Hamming self-convolution window according to claim 1 is characterized in that: The 2D-Hamming self-convolution window The sidelobe attenuation performance varies with the order of self-convolution The sidelobe attenuation performance includes: peak sidelobe level and sidelobe attenuation rate, and the peak sidelobe level of the two-dimensional Hamming self-convolution window is obtained according to equations (3) and (4) respectively. and sidelobe decay rate : (8) (9) In formulas (8) and (9), and They represent the peak sidelobe level and sidelobe attenuation rate of the two-dimensional Hamming window respectively.
3. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the high-precision fringe phase extraction method according to claim 1 or 2, and the processor is configured to execute the program stored in the memory.
4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the high-precision fringe phase extraction method according to claim 1 or 2 are executed.