A method for calculating the absolute phase of phase without phase shift in multi-frequency fringes for dynamic three-dimensional measurement.

Abstract

This invention relates to the field of dynamic three-dimensional measurement technology for irregular surfaces or contours, and provides a phase-shift-free multi-frequency fringe absolute phase calculation method for dynamic three-dimensional measurement. The method includes two processes: initial phase calculation and phase result optimization. The initial phase calculation process processes the acquired multi-frequency fringe pattern and calculates the absolute phase information of the corresponding pixels. The phase result optimization process uses the constraint of the absolute phase on the multi-frequency fringe pattern equation as a data fidelity term and the modulation degree of the fringe pattern as a smoothing constraint term. Through joint optimization of phase fidelity and modulation degree smoothness, the optimal absolute phase is solved. This invention introduces a multi-frequency fringe pattern combination that satisfies the uniqueness of the optimal phase. While maintaining high measurement efficiency, it comprehensively utilizes its information constraints to improve phase accuracy, thus contributing to high-efficiency and high-precision dynamic three-dimensional measurement.

Description

Technical Field

[0001] This invention relates to an algorithm for directly calculating the absolute phase distribution from a phase-shift-free multi-frequency fringe pattern for rapid dynamic measurement of three-dimensional surface topography or contour, belonging to the field of measurement technology for irregular surfaces or contours. Background Technology

[0002] Optical 3D topography measurement technology is widely used in various fields such as industrial manufacturing, surveying, medicine, and cultural heritage due to its advantages of being non-contact, highly accurate, and easy to operate. Structured light 3D measurement is an active, non-contact optical 3D topography measurement technology. With its high measurement accuracy and speed, as well as low cost, it has become one of the most widely used 3D measurement technologies. Fringe projection profilometry, a common structured light 3D measurement technique, typically projects several sinusoidal fringe patterns. By extracting the phase information of the fringe patterns, dynamic 3D measurement of moving objects can be achieved.

[0003] A classic fringe projection system consists of a camera and a projector. The projector projects a computer-generated standard sinusoidal fringe pattern onto the object's surface. After being modulated by the object's surface contour, the fringes deform, forming a deformed fringe pattern. The camera captures this deformed fringe pattern, and the absolute phase map is recovered through phase extraction and unfolding techniques. Finally, by combining the system calibration model and the absolute phase map, a three-dimensional reconstruction of the object's surface can be achieved.

[0004] As can be seen from the system composition and working principle of the fringe projection system, the accuracy of 3D measurement results, besides the accuracy of system model calibration, largely depends on the accuracy of the phase results. Obtaining the phase result of deformed fringe patterns typically involves two parts: phase extraction and phase unfolding. Commonly used phase extraction methods include the Fourier transform method and the phase-shifting method. The Fourier transform method has high measurement efficiency, requiring only the projection of a single frame of the fringe pattern to achieve phase extraction; therefore, it is often used for measurements in high-speed or dynamic scenes. However, the Fourier transform method requires windowing in the frequency domain to extract the fundamental frequency component, a process that results in the loss of high-frequency information from the fringes. Therefore, this method usually produces significant errors when measuring areas with abrupt changes in surface height or edges. The phase-shifting method requires the projection of multiple fringe patterns for phase extraction, resulting in lower time efficiency and making it unsuitable for dynamic scenes.

[0005] Due to the periodicity of phase in trigonometric functions, the phase range obtained by phase extraction is: In spatial geometry, there exist periodic jumps consistent with the fringe period, known as wrapping phase. Subsequent phase unwrapping is required to eliminate these periodic jumps and restore the continuous phase variation throughout space. Spatial phase unwrapping methods are commonly used to directly unwrap the phase from a single-frequency wrapping phase, but the results depend on the spatial continuity of the phase and the selection of the phase reference point, making it impossible to obtain an absolutely invariant unwrapped phase, resulting in poor stability in practical applications. Temporal phase unwrapping methods, by projecting fringes of different frequencies and extracting wrapping phases of different frequencies, can calculate globally unique absolute phase values ​​pixel-by-pixel, offering higher stability and accuracy. However, calculating wrapping phases at different frequencies requires phase shifting for each frequency, increasing the number of fringe patterns and reducing time efficiency. Summary of the Invention

[0006] This invention addresses the shortcomings of existing three-dimensional topography measurement techniques by proposing a phase-shift-free multi-frequency fringe absolute phase calculation method for dynamic three-dimensional measurement. This method balances phase extraction accuracy and time efficiency, improving phase accuracy while maintaining high measurement efficiency, thus achieving high-efficiency and high-precision dynamic three-dimensional measurement.

[0007] The present invention provides a method for calculating the absolute phase of multi-frequency fringes without phase shift for dynamic three-dimensional measurement, which adopts the following technical solution.

[0008] This method includes two processes: initial phase value calculation and phase result optimization.

[0009] (1) Initial phase value calculation process: This process processes the acquired multi-frequency stripe pattern and calculates the absolute initial phase value of the corresponding pixel;

[0010] (2) Phase result optimization process: The phase result is optimized by using the multi-frequency fringe diagram equation to constrain the phase result as the data fidelity term and the modulation information of the fringe diagram as the smoothing constraint term. The two together constitute the objective function. The phase result is optimized by jointly optimizing the phase fidelity and the modulation smoothness of the fringe diagram.

[0011] The two processes are explained in detail below.

[0012] The equation for the multi-frequency fringe pattern in the initial phase value calculation process of (1) is as follows:

[0013] ;

[0014] in , , , The light intensity distribution of the acquired image. This represents the absolute phase of the first frequency fringe pattern, which is the reference phase for the fringe pattern combination and also the target phase for subsequent optimization. , , , The spatial frequency of the fringe pattern. The background light intensity of the striped pattern. The modulation of the stripe pattern.

[0015] The initial phase value calculation process (1) specifically includes the following steps:

[0016] ① Filter the acquired images to reduce the impact of random noise;

[0017] ② Calculate the wrapping phase using the single-frame fringe pattern phase extraction method ;

[0018] ③ Calculate the absolute phase from the wrapped phase:

[0019] ;

[0020] in This indicates the absolute phase of each frequency fringe. This indicates the absolute phase order corresponding to each frequency fringe; fringe order. There are multiple combinations of orders, and the key to calculating the optimal absolute phase is to find the optimal order; , , , The spatial frequency of the fringe pattern;

[0021] Based on the selected multi-frequency fringe pattern combination, iterate through all possible fringe order combinations for each pixel and calculate the corresponding absolute phase value; select the absolute phase corresponding to the first frequency as the reference phase, and compare the difference between the absolute phase of other frequencies under each combination and the reference phase. The optimal order of a pixel is selected by choosing the stripe order combination with the smallest sum of differences, and phase unwrapping is performed based on this combination to generate the optimal absolute phase; simultaneously, this minimum difference is recorded. This forms a minimum difference map;

[0022] ④ Correct phase error by traversing each pair of pixels according to the difference map: Based on the distribution of the obtained difference map, calculate the sum of the two differences of each pair of adjacent pixels, compare the absolute phase of the two pixels in order of increasing difference sum, and group them according to pixel connectivity; take the group with the smallest difference as the reference group, merge and correct the phase according to the adjacency relationship between the other groups and the reference group, eliminate phase jump, and complete the preliminary correction of absolute phase.

[0023] The filtering in step ① involves using a smoothing filter to denoise the stripe pattern.

[0024] The single-frame fringe pattern phase extraction method in step ② includes, but is not limited to, Fourier transform, wavelet transform, and deep learning methods. Existing mature Fourier transform or wavelet transform methods can be used to extract the wrapped phase, or some phase extraction models based on deep learning methods can be used.

[0025] The multi-frequency fringe pattern in step ③ refers to a fringe pattern with no fewer than three frequencies.

[0026] In step ③, the multi-frequency fringe pattern combination refers to a sinusoidal fringe pattern projection sequence containing multiple spatial frequencies. The periods of the multiple frequency fringe patterns satisfy the least common multiple being greater than the horizontal width of the projection pattern, so that the absolute phase of each pixel satisfies the uniqueness.

[0027] In step ③, the multi-frequency fringe pattern combination refers to a sinusoidal fringe pattern projection sequence containing multiple spatial frequencies. The periods of the multiple frequency fringe patterns satisfy the least common multiple being greater than the horizontal width of the projection pattern, so that the absolute phase of each pixel satisfies the uniqueness.

[0028] The difference between the absolute phase of other frequencies and the reference phase for each combination in step ③. In a multi-frequency fringe pattern, the unfolded phase of the first frequency fringe is used as the reference phase, and the unfolded phases of the remaining frequency fringes are normalized to the reference phase. The sum of the differences between the normalized unfolded phases of each frequency fringe and the reference phase is calculated (each frequency has an error in its phase, and the smallest total error across multiple frequencies indicates the highest reliability). The smaller the sum of the differences, the closer the order combination is to the correct phase order combination, and the higher the reliability of the phase value. The phase with the highest reliability is selected as the unfolded result.

[0029] The difference between the absolute phase of other frequencies and the reference phase for each combination in step ③. The calculation formula is as follows:

[0030] ;

[0031] in, It is the frequency of the stripe pattern. and These represent the first frequency and the i-th frequency, respectively. It is the absolute phase of the first frequency fringe pattern, that is, the reference phase of the fringe pattern combination; Represents the absolute phase value corresponding to other different frequency stripe patterns; selects the difference between the absolute phase of other frequencies and the reference phase for each combination. The lowest order result is taken as the optimal solution, and the corresponding difference is also saved. .

[0032] The specific process of step ④, which involves traversing each pixel pair in the difference map to correct the phase error, is as follows:

[0033] First, perform a pixel-by-pixel traversal and grouping. The smaller the sum, the higher the traversal priority; determine the absolute phase difference between two pixels in a pixel pair, if the phase difference is less than... Pixel pairs are grouped based on neighborhood connectivity, with a phase difference greater than or equal to 1. The pixel pairs are grouped separately, resulting in several groups; the pixel pairs in each group are then searched. The value, in The smallest group is used as the reference group. Merging and phase correction are performed on the remaining groups based on their adjacency relationships with the reference group, ultimately yielding the corrected phase result. During phase correction, the highest-priority pixel pair between the reference group and the current group's adjacent edges must be extracted. One pixel in this pair belongs to the reference group, and its phase is... Another pixel belongs to the current group and its phase is The process of eliminating phase transitions is expressed as:

[0034] ;

[0035] in It is the corrected phase. It is an integer function.

[0036] The phase result optimization process described in (2) specifically includes the following steps:

[0037] ① Based on the frequency relationship between adjacent frame fringe patterns, the phase solution of adjacent frames is simplified to the phase solution of a single frame. With the initial phase value obtained, the phase search range is limited to the vicinity of the true value. Then, based on the constraints of the multi-frequency fringe pattern equation, the preliminary optimized phase result is obtained.

[0038] ② Combining the smoothness characteristics of natural images, the fringe modulation of neighboring pixels should also have a locally smooth distribution (the modulation changes within the pixel neighborhood are gradual). This characteristic is added as a penalty constraint to the objective function to obtain further optimized phase results.

[0039] In step ②, the objective function consists of a data fidelity term and a smoothing constraint term, and its expression is as follows:

[0040]

[0041] in, This is the absolute phase of the first frequency fringe pattern, which is the reference phase of the fringe pattern combination. and These represent the background light intensity and modulation of the striped pattern. The light intensity is represented by the fringe pattern. For the corresponding frequency, The first parameter is used to adjust the strength of the modulation constraint. The data fidelity term originates from the phase relationship constraints between multi-frequency fringe patterns, ensuring that the optimized phase satisfies the physical model; the second term... To smooth the constraint term, The penalty coefficient is... This is the standard deviation of the modulation scheme within the current pixel neighborhood. This term utilizes the spatial smoothing properties of the fringe modulation scheme to penalize unreasonable phase abrupt changes.

[0042] The above method utilizes the fringe pattern of specific frequency combinations to ensure that the optimal phase order combination satisfies the uniqueness constraint in space, finds the order combination with the smallest difference between the multi-frequency fringe phase and the reference phase as the phase expansion result, and combines the multi-frequency fringe pattern equation and the fringe pattern smoothness characteristic constraint to achieve phase error optimization.

[0043] This invention introduces a multi-frequency fringe pattern projection combination that satisfies the uniqueness of the optimal phase result. While maintaining high measurement efficiency, it comprehensively utilizes its information constraints to improve phase accuracy, thus achieving high-efficiency and high-precision dynamic three-dimensional measurement. It has the following characteristics:

[0044] (1) Compared with the traditional spatial phase unfolding method based on single-frame fringe pattern, it can avoid the constraints of phase reference point selection and has a wider measurement range;

[0045] (2) The unfolding of the wrapped phase is based on the actual selected combination of multi-frequency stripes. The number and frequency combination of multi-frequency stripes can be selected according to the horizontal width of the actual projection pattern, making the phase unfolding process more flexible.

[0046] (3) The present invention is based on multi-frequency stripe patterns distributed in multiple frames of images. The stripe pattern sequence corresponds to the image frame sequence. Constraints are established by determining the proportional relationship between stripe periods, thereby optimizing the phase results and improving accuracy.

[0047] (4) The smoothing characteristics of the fringe pattern modulation are combined with phase optimization. By optimizing the smooth distribution constraint of the modulation, more accurate phase information is obtained. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of three different frequency stripe patterns. Among them, (a) has a stripe pattern frequency of 1 / 14, (b) has a stripe pattern frequency of 1 / 16, and (c) has a stripe pattern frequency of 1 / 18.

[0049] Figure 2 yes Figure 1 A schematic diagram of the horizontal grayscale distribution of the stripes for the three frequencies.

[0050] Figure 3 This is the overall flowchart of phase calculation in this invention.

[0051] Figure 4 This invention relates to the frequency relationships of the actual multi-frequency fringe patterns and their corresponding absolute phase diagrams.

[0052] Figure 5 This is the optimal absolute phase distribution map calculated by the method of this invention. Detailed Implementation

[0053] This invention proposes a phase-shift-free multi-frequency fringe absolute phase calculation method for dynamic three-dimensional measurement. It utilizes a combination of multi-frequency fringe patterns, with the specific fringe frequencies flexibly selected according to actual requirements. The core principles are as described above. Regarding the number of frequencies, at least three frequencies are typically required; too few frequencies make it difficult to meet the requirement of unique optimal fringe order within the projected field of view. The frequency magnitude should be relatively moderate; too high a frequency will result in excessively fine fringes and loss of phase details, while too low a frequency will lead to increased nonlinear effects on the phase. A typical three-frequency fringe pattern combination and its lateral grayscale variation are shown below. Figure 1 and Figure 2 As shown, Figure 1 It contains a stripe pattern with three frequencies, namely 1 / 14, 1 / 16 and 1 / 18. The least common multiple of the periods of the three stripe patterns is 1008 pixels, which is greater than the horizontal resolution of the projector used, which is 912 pixels.

[0054] In a fringe projection dynamic 3D measurement system, multi-frequency fringe patterns are combined to serve absolute phase calculation. Initial phase extraction can employ established methods such as Fourier transform or deep learning-based approaches. The initial absolute phase value obtained from phase expansion is then optimized by incorporating the equations of the multi-frequency fringes. Based on these considerations, the overall flow of the phase-shift-free multi-frequency fringe pattern absolute phase calculation method proposed in this invention is as follows: Figure 3 As shown, it includes:

[0055] (1) Each time the phase is extracted, a single-frame projection-related phase extraction method (including but not limited to Fourier transform, wavelet transform, deep learning, etc.) is used to solve the wrapped phase;

[0056] (2) Calculate the unfolded phase value corresponding to all possible levels for a set of multi-frequency wrapped phases, select the optimal result according to the difference between the multi-frequency unfolded phase and the reference unfolded phase, and perform phase correction by grouping and merging the pixels based on the difference map;

[0057] (3) The optimized absolute phase information is obtained by iterative calculation with the multi-frequency fringe diagram equation plus neighborhood modulation smoothing constraint as the objective function.

[0058] The multi-frequency fringe pattern must satisfy the condition that the least common multiple of the fringe periods is greater than the horizontal width of the projected pattern. The difference between the multi-frequency phase and the reference phase refers to the process in the multi-frequency fringe pattern where the unfolded phase of the first frequency fringe is used as the reference phase, and the unfolded phases of the remaining frequency fringes are normalized to the reference phase. The difference between the normalized unfolded phase of each frequency fringe and the reference unfolded phase is calculated; the smaller the difference, the closer the phase order combination is to the correct phase order combination, and the higher the reliability of the phase value. The phase with the highest reliability is selected as the unfolded result. The traversal order based on the difference refers to the traversal order for correcting the phase results; the smaller the difference, the more reliable the phase value, and the higher the traversal priority. The absolute phase sizes of two neighboring pixels are compared, and pixel connectivity is considered for grouping. The group with the smallest difference is used as the reference group, and the remaining groups are merged and phase corrected according to their adjacency relationships with the reference group to eliminate phase jumps and complete the initial correction of the absolute phase.

[0059] The multi-frequency fringe diagram equation plus neighborhood modulation smoothing constraint refers to the objective function constructed based on the projected fringe diagram equation and fringe diagram characteristics, which is used to optimize the phase of the initial solution. The fringe diagram equation corresponds to the projected fringe diagram. If the phase information is reliable, it must satisfy the equation. By using the fringe diagram modulation smoothing characteristics, it is used as a penalty term of the function to constrain possible error points after iterative solution, and finally the optimized phase is obtained.

[0060] The following is a detailed description of the implementation process of the method of the present invention.

[0061] First, select a suitable fringe pattern frequency combination based on the actual projection requirements. Then, perform filtering, noise reduction, and phase extraction on each frame of the fringe pattern. Next, perform phase unrolling. Based on the frequency relationships between the multi-frequency fringe patterns, search for possible order combinations and calculate all absolute phase values. Compare the phase of different combinations with the reference phase at the corresponding position, and find the combination with the smallest difference as the optimal result. Commonly used multi-frequency fringe patterns and their corresponding absolute phase distributions are shown below. Figure 4 As shown, the multi-frequency fringe pattern that satisfies the uniqueness of the optimal phase order has a frequency ratio that ensures the optimal order combination can be found. For the phase correction problem, the difference between the two pixels in each pair of pixels is calculated, and the pixels are grouped according to the difference sum as the traversal order. Then, the phase of each group is merged and corrected according to the reference group, so as to obtain the most accurate result possible.

[0062] Since the initial phase expansion result is still affected by noise and error propagation, it needs to be optimized. Therefore, an iterative solution is constructed with the objective of minimizing the residual. The objective function includes a data fidelity term mainly based on the multi-frequency fringe pattern equation and a constraint term mainly based on smoothing the neighborhood modulation of the fringe pattern. The optimization variable is the absolute phase. And the influence of the adjustment system and The modulation of the stripe pattern is theoretically constant, and in the neighborhood of pixels in actual images, it basically conforms to the theoretical law. By cross-validation or based on prior knowledge, an appropriate penalty parameter is selected, and then the objective function is solved to obtain the optimized final phase information.

[0063] The core idea of ​​this invention is to comprehensively utilize the information of multi-frequency fringe patterns, ignore the small changes between adjacent image frames under the motion of objects, combine the concept of number theory phase expansion to complete phase expansion, and correct the phase results by traversing and grouping according to the reliability of each phase result. Based on the equation constraints of the multi-frequency fringe pattern itself, the fringe pattern modulation smoothing constraints are superimposed to jointly optimize the phase results to obtain the final absolute phase information.

[0064] The peaks function is applied as phase modulation to a standard sinusoidal fringe pattern, and Gaussian noise is added to simulate a real captured image. The phase calculation process described above is then performed based on the simulated fringe pattern. The first step is smoothing filtering, which can be done using Gaussian filtering, bilateral filtering, etc., with a window size of 5×5. The value is 1; then, the wrapping phase is extracted. Here, the commonly used Fourier transform method is used to perform 2D FFT (Fast Fourier Transform) on the filtered image data to obtain the frequency domain information of the image. The main frequency position is selected, and filtering is performed with the main frequency as the center. The Hanning window is selected as the filtering window function to reduce the influence of spectral leakage. Then, 2D IFFT (Inverse Fast Fourier Transform) is performed on the filtered frequency domain information to extract the phase angle and obtain the wrapping phase.

[0065] After obtaining the wrapped phase, all possible order combinations (151 types) are first determined based on the fringe pattern period (14 / 16 / 18) and lateral resolution (912), and the corresponding unfolded phase values ​​are calculated. The multi-frequency fringe unfolded phase results are normalized using the phase of the first frequency as the reference phase, and the difference between the normalized phase and the reference phase is calculated. The formula for calculating the difference is as follows:

[0066] ;

[0067] in, It is the frequency of the baseline fringe pattern. It is the frequency of the other stripes. The absolute phase representing the first frequency, also known as the reference phase. The phase values ​​representing the unfolded fringe patterns corresponding to different periods. The value representing the difference between the multi-frequency fringe phase and the reference phase is selected. The smallest order combination is taken as the optimal solution, and the corresponding difference is also saved. To correct the calculation errors in the phase, consider the results obtained above. Based on this, calculate the sum of differences between each pair of pixels, group the pixels into groups using this as the traversal order, and determine the absolute phase difference between the two pixels in a pixel pair. If the phase difference is less than... Pixel pairs are grouped based on neighborhood connectivity, with a phase difference greater than or equal to 1. The pixel pairs are grouped separately, resulting in several groups; the pixel pairs in each group are then searched. The value, in The smallest group is used as the reference group. The remaining groups are merged and phase corrected according to their adjacency relationship with the reference group to obtain the corrected phase result.

[0068] After obtaining the initial value of the phase expansion, the phase is optimized using the constructed objective function. The objective function is iteratively optimized based on the known intensity and frequency values ​​at each point of the fringe pattern, the initial modulation index, and the initial phase value. Classical optimization algorithms such as the Levenberg-Marquardt algorithm can be used. The phase solution range can be pre-defined to reduce optimization time. The initial modulation index is calculated using a matrix formed by the fringe pattern equations.

[0069] The optimal phase distribution can be obtained through the above process, such as... Figure 5 As shown.

Claims

1. A method for calculating the absolute phase of phase-shift-free multi-frequency fringes for dynamic three-dimensional measurement, characterized in that: It includes two processes: initial phase value calculation and phase result optimization. (1) Initial phase value calculation process: This process processes the acquired multi-frequency stripe pattern and calculates the absolute initial phase value of the corresponding pixel; (2) Phase result optimization process: The phase result is optimized by using the multi-frequency fringe diagram equation to constrain the phase result as the data fidelity term and the modulation information of the fringe diagram as the smoothing constraint term. The two together constitute the objective function. The phase result is optimized by jointly optimizing the phase fidelity and the modulation smoothness of the fringe diagram.

2. The method for calculating the absolute phase of phase-shift-free multi-frequency fringes for dynamic three-dimensional measurement according to claim 1, characterized in that: The equation for the multi-frequency fringe pattern in the initial phase value calculation process of (1) is as follows: ； in , , , The light intensity distribution of the acquired image. This represents the absolute phase of the first frequency fringe pattern, which is the reference phase for the fringe pattern combination and also the target phase for subsequent optimization. , , , The spatial frequency of the fringe pattern. The background light intensity of the striped pattern. The modulation of the stripe pattern.

3. The method for calculating the absolute phase of phase-shift-free multi-frequency fringes for dynamic three-dimensional measurement according to claim 1, characterized in that: The initial phase value calculation process (1) specifically includes the following steps: ① Filter the acquired images to reduce the impact of random noise; ② Calculate the wrapping phase using the single-frame fringe pattern phase extraction method ; ③ Calculate the absolute phase from the wrapped phase: ； in This indicates the absolute phase of each frequency fringe. This indicates the absolute phase order corresponding to each frequency fringe; fringe order. There are multiple combinations of orders, and the key to calculating the optimal absolute phase is to find the optimal order; , , , The spatial frequency of the fringe pattern; Based on the selected multi-frequency fringe pattern combination, iterate through all possible fringe order combinations for each pixel and calculate the corresponding absolute phase value; select the absolute phase corresponding to the first frequency as the reference phase, and compare the difference between the absolute phase of other frequencies under each combination and the reference phase. The optimal order of a pixel is selected by choosing the stripe order combination with the smallest sum of differences, and phase unwrapping is performed based on this combination to generate the optimal absolute phase; simultaneously, this minimum difference is recorded. This forms a minimum difference map; ④ Correct phase error by traversing each pair of pixels according to the difference map: Based on the distribution of the obtained difference map, calculate the sum of the two differences of each pair of adjacent pixels, compare the absolute phase of the two pixels in order of increasing difference sum, and group them according to pixel connectivity; take the group with the smallest difference as the reference group, merge and correct the phase according to the adjacency relationship between the other groups and the reference group, eliminate phase jump, and complete the preliminary correction of absolute phase.

4. The method for calculating the absolute phase of phase-shift-free multi-frequency fringes for dynamic three-dimensional measurement according to claim 3, characterized in that: The multi-frequency fringe pattern in step ③ refers to a fringe pattern with no fewer than three frequencies.

5. The method for calculating the absolute phase of phase-shift-free multi-frequency fringes for dynamic three-dimensional measurement according to claim 3, characterized in that: In step ③, the multi-frequency fringe pattern combination refers to a sinusoidal fringe pattern projection sequence containing multiple spatial frequencies. The periods of the multiple frequency fringe patterns satisfy the least common multiple being greater than the horizontal width of the projection pattern, so that the absolute phase of each pixel satisfies the uniqueness.

6. The method for calculating the absolute phase of phase-shift-free multi-frequency fringes for dynamic three-dimensional measurement according to claim 3, characterized in that: The difference between the absolute phase of other frequencies and the reference phase for each combination in step ③. This refers to the fact that in a multi-frequency fringe pattern, the unfolded phase of the first frequency fringe is used as the reference phase, and the unfolded phases of the remaining frequency fringes are normalized to the reference phase. Calculate the sum of the differences between the normalized expanded phase and the reference phase for each frequency fringe. The smaller the sum of the differences, the closer the order combination is to the correct phase order combination, and the higher the reliability of the phase value. Select the phase with the highest reliability as the expanded result.

7. The method for calculating the absolute phase of phase-shift-free multi-frequency fringes for dynamic three-dimensional measurement according to claim 3, characterized in that: The difference between the absolute phase of other frequencies and the reference phase for each combination in step ③. The calculation formula is as follows: ； in, It is the frequency of the stripe pattern. and These represent the first frequency and the i-th frequency, respectively. It is the absolute phase of the first frequency fringe pattern, that is, the reference phase of the fringe pattern combination; Represents the absolute phase value corresponding to other different frequency stripe patterns; selects the difference between the absolute phase of other frequencies and the reference phase for each combination. The lowest order result is taken as the optimal solution, and the corresponding difference is also saved. .

8. The method for calculating the absolute phase of phase-shift-free multi-frequency fringes for dynamic three-dimensional measurement according to claim 3, characterized in that: The specific process of step ④, which involves traversing each pixel pair in the difference map to correct the phase error, is as follows: First, perform a pixel-by-pixel traversal and grouping. The smaller the sum, the higher the traversal priority; determine the absolute phase difference between two pixels in a pixel pair, if the phase difference is less than... Pixel pairs are grouped based on neighborhood connectivity, with a phase difference greater than or equal to 1. The pixel pairs are grouped separately, resulting in several groups; the pixel pairs in each group are then searched. The value, in The smallest group is used as the reference group. Merging and phase correction are performed on the remaining groups based on their adjacency relationships with the reference group, ultimately yielding the corrected phase result. During phase correction, the highest-priority pixel pair between the reference group and the current group's adjacent edges must be extracted. One pixel in this pair belongs to the reference group, and its phase is... Another pixel belongs to the current group and its phase is The process of eliminating phase transitions is expressed as: ； in It is the corrected phase. It is an integer function.

9. The method for calculating the absolute phase of phase-shift-free multi-frequency fringes for dynamic three-dimensional measurement according to claim 1, characterized in that: The phase result optimization process described in (2) specifically includes the following steps: ① Based on the frequency relationship between adjacent frame fringe patterns, the phase solution of adjacent frames is simplified to the phase solution of a single frame. With the obtained initial phase value, the phase search range is limited to the vicinity of the true value. Then, based on the constraints of the multi-frequency fringe pattern equation, the preliminary optimized phase result is obtained. ② Combining the smoothness characteristics of natural images, the fringe tone of neighboring pixels should also have a locally smooth distribution. This characteristic is added as a penalty constraint to the objective function to obtain a further optimized phase result.

10. The method for calculating the absolute phase of phase-shift-free multi-frequency fringes for dynamic three-dimensional measurement according to claim 9, characterized in that: In step ②, the objective function consists of a data fidelity term and a smoothing constraint term, and its expression is as follows: ； ； ； in, This is the absolute phase of the first frequency fringe pattern, which is the reference phase of the fringe pattern combination. and These represent the background light intensity and modulation of the striped pattern. The intensity of the striped pattern. For the corresponding frequency, The first parameter is used to adjust the strength of the modulation constraint. The data fidelity term originates from the phase relationship constraints between multi-frequency fringe patterns, ensuring that the optimized phase satisfies the physical model; the second term... To smooth the constraint term, The penalty coefficient is... This is the standard deviation of the modulation scheme within the current pixel neighborhood. This term utilizes the spatial smoothing properties of the fringe modulation scheme to penalize unreasonable phase abrupt changes.

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