Phase order correction method for multi-frequency cascaded phase de-wrapping method

Abstract

A phase order correction method for multi-frequency cascaded phase unwrapping is proposed. First, the low-frequency unfolded phase is directly calculated using the multi-frequency fringe method, and then the mid-frequency unfolded phase is obtained to acquire the initial fringe order obtained through a small frequency ratio. Subsequently, based on the shifting wrapped phase method, a fringe order misaligned by half a cycle from the initial fringe order is obtained. Accurate phase reconstruction is achieved through fringe order correction. These two methods complement each other to simultaneously address the accuracy degradation caused by pseudo-2-step transitions and impulse noise errors, while preserving phase map details. This invention obtains the correct order corresponding to the high-frequency wrapped phase through a phase recovery method at two fringe frequencies, and uses this to calculate the high-frequency unfolded phase, achieving fast and accurate phase unwrapping.

Description

Technical Field

[0001] This invention relates to the fields of computer vision and 3D reconstruction technology, and in particular to a phase order correction method for multi-frequency cascaded phase unwrapping method. Background Technology

[0002] In the field of 3D sensing, Digital Fringe Projection Profilometry (DFPP) is an effective technique, playing a crucial role in non-contact, high-resolution, and high-speed 3D measurement across various fields such as computer vision, industrial defect detection, and smart manufacturing. Typically, the fringe phase collected by a DFPP system carries depth information of the measured object. Therefore, the implementation of DFPP mainly involves two steps: fringe pattern acquisition and phase retrieval. To achieve fast and accurate 3D reconstruction, numerous studies have explored the application of multi-frequency methods, complementary Gray codes, and phase-encoding-based techniques in acquiring the desired fringe pattern data. These methods are highly valued for their high accuracy in providing accurate measurement results in various industrial applications. Alongside data acquisition research, phase demodulation methods have also been extensively studied. Among various phase demodulation methods, phase-shifting methods are widely adopted due to their pixel-by-pixel measurement and robustness to reflectivity variations.

[0003] The application of phase-shifting methods is further divided into two types: phase extraction and phase unwrapping. Unlike traditional interferometry or moiré fringe profilometry, the DFPP system can always obtain accurate phase solutions through simple phase-shifting algorithms because the system is unaffected by phase shift errors. Therefore, when the measured surface remains stationary, many phase demodulation algorithms can be used to accurately obtain the phase map of the package of interest, such as the four-step algorithm.

[0004] However, phase unwrapping presents challenges due to the highly discontinuous contours of industrial objects. There are two main methods for phase unwrapping: spatial phase unwrapping (SPU) and temporal phase unwrapping (TPU). SPU is well-known for its sensitivity to noise and poses significant challenges during discontinuities and abrupt changes. In contrast, TPU produces stable and unrestricted results even in 3D measurements of large-scale complex surfaces, making it widely used for measuring isolated objects or discontinuous complex surfaces, covering computational complexity, robustness, and various parameter requirements. However, stable measurement results from existing DFPP systems can only be obtained using low- to mid-frequency fringes. A second problem with TPU is that it requires the additional projection of multiple frames of fringe patterns at different frequencies. Therefore, TPU involves a trade-off between speed and accuracy. Third, TPU is susceptible to certain errors that affect the accuracy of the reconstruction. One is gamma distortion caused by system settings, phase shift steps, and projected sinusoidal fringes. Another is phase error caused by calculating the inverse tangent function and fringe order in the presence of random noise. The former can be corrected through pre-calibration and compensation algorithms, while the latter is unavoidable and difficult to eliminate.

[0005] Although several phase unwrapping methods have been proposed to achieve reliable and accurate phase unwrapping for DFPP, ​​such as the noisy pixel identification criteria and iterative adaptive filtering proposed in "L. Feng, H. Du, F. Gu, J. Cui, Y. Li, Q. Zhu, T. Xu, and G. Zhang, "Enhancing phase unwrapping by noisy pixels identifying criteria and iterative adaptive filtering," Opt. Express 33(15), 31912 (2025)," which establishes a noisy pixel identification criterion for phase unwrapping to enhance TIE phase unwrapping technology, its efficiency and accuracy remain issues, especially in the presence of noise or drastic changes in the object's surface. Finally, this problem is further exacerbated when using high-frequency fringe patterns to measure objects with complex surface geometry and lighting conditions. In such cases, due to phase unwrapping error, a higher fringe frequency does not necessarily mean higher accuracy in 3D reconstruction. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, the present invention aims to provide a phase order correction method for a multi-frequency cascaded phase unwrapping method. First, the low-frequency expanded phase is directly calculated using the multi-frequency fringe method, and then the mid-frequency expanded phase is obtained to acquire an initial fringe order obtained through a small frequency ratio. Subsequently, based on a shifting wrapped phase method, a fringe order misaligned by half a cycle from the initial fringe order is obtained. Accurate phase reconstruction is achieved through fringe order correction. Both methods complement each other to simultaneously address pseudo-2. Addressing the accuracy degradation caused by jump and impulse noise errors while preserving phase map details.

[0007] To achieve the above objectives, the technical solution of the present invention is as follows: A phase order correction method for multi-frequency cascaded phase unwrapping methods includes the following steps: Step 1: Project the original fringe pattern onto the object under test using a projector, and acquire four-step phase-shifted fringe images at unit frequency, low frequency, medium frequency and high frequency using a camera. Then, calculate the wrapping phase corresponding to each frequency using the multi-step phase-shifting method. Step 2: Based on the multi-frequency fringe projection method, the initial low-frequency unfolded phase is calculated using the single-frequency phase and the low-frequency wrapping phase; Step 3: Using the multi-frequency fringe projection method and phase order correction technique, the intermediate frequency unfolded phase is further solved from the initial low-frequency unfolded phase and the intermediate frequency wrapped phase; Step 4: Similarly, using multi-frequency fringe projection and phase order correction techniques, the high-frequency unfolded phase is solved from the mid-frequency unfolded phase and the high-frequency wrapped phase.

[0008] The phase-shifted fringe image of step one is shown below: (1) in Indicates the first n The light intensity of the striped pattern Represents unit frequency, These represent low frequency, mid frequency, and high frequency, respectively. Indicates background light intensity. Representative adjustment system, f It is the fringe frequency. It is the phase, which carries the depth information of the object. It is the phase shift of the striped pattern, in which , N It is the number of phase shift steps. It is the initial phase; The formula for solving the phase using the multi-step phase shift algorithm is as follows: (2) In equation (2), This represents the phase obtained through demodulation, specifically the phase obtained using the arctangent function. Enclosed in the interval .

[0009] The multi-frequency fringe projection method in step two uses one or more sets of low-frequency fringe patterns to unwrap the higher-frequency phase through the algebraic relationship between two different frequency phases. One set is the fringe pattern used for actual measurement, and the other set is the single-frequency fringe pattern used for unwrapping. (3) In the formula: -Low-frequency stripe frequency; -Single-frequency stripe frequency, here ; For the fringe patterns shown in formula (3), let their demodulation phases be respectively , Because the phase distribution of the unit frequency stripes is in Inside, therefore Consistent with its unwrapping phase, let it be... ; The unwrapping phase is set as ;So, From formula (4), we can obtain: (4) As shown in formula (3), the following relationship exists between the low-frequency and single-frequency phases: (5) In the formula: (6) Combining formulas (4) and (5), the low-frequency fringe order is obtained as follows: (7) In the formula: round - rounding operation; Combining formulas (4) and (7), we can obtain the phase unwrapping formula (8) for low-frequency fringes: (8) The low-frequency expanded phase is then obtained from equation (8). .

[0010] The aforementioned multi-frequency fringe projection method and phase order correction technique are as follows: First, the wrapping phases of the four frequencies are obtained respectively. Then, the low-frequency unfolded phase, mid-frequency unfolded phase, and high-frequency unfolded phase are obtained sequentially from unit frequency to low, mid, and high. During the process from low to mid and mid to high, the phase order correction technique is used, that is, firstly by transforming the fringe pattern sequence; then, another shifted wrapping phase is obtained, and two orders are obtained respectively. The two fringe orders are filtered, and then a new correct fringe order is obtained based on the principle of complementarity. That is, all erroneous fringe order jumps are guided and removed by the second fringe order obtained by the shifted phase pattern.

[0011] Compared with the prior art, the advantages of the present invention are: 1. This invention only filters the order and does not process the phase, which can minimize phase distortion.

[0012] 2. The phase shift amount of the present invention is generated by changing the order of the fringe pattern, without the need for additional measurement.

[0013] In summary, this invention obtains the correct order corresponding to the high-frequency wrapped phase through the phase recovery method of two fringe frequencies, and uses it to solve the high-frequency unfolded phase, thus achieving fast and accurate phase unfolding. Attached Figure Description

[0014] Figure 1 This is a flowchart of phase recovery methods for four frequencies.

[0015] Figure 2 yes A schematic diagram. Detailed Implementation

[0016] This invention discloses a phase recovery method using four fringe frequencies. The technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. These are merely one embodiment of the invention and are not intended to limit the invention in any way. Therefore, any simple modifications, equivalent changes, or modifications made to the above embodiments based on the technical essence of this invention shall still fall within the scope of this invention.

[0017] The present invention will now be described in detail with reference to the accompanying drawings and embodiments. An overall flowchart is attached. Figure 1 .

[0018] Step 1: Project the original fringe pattern onto the object under test using a projector, and acquire four-step phase-shifted fringe images at unit frequency, low frequency, medium frequency and high frequency using a camera. Then, calculate the wrapping phase corresponding to each frequency using the multi-step phase-shifting method. 1.1 Phase Extraction Using the Phase Shift Method In a DFPP system employing phase-shift profilometry, the phase-shift fringe image captured by the camera is represented as follows: (1) in Indicates the first n The light intensity of the striped pattern Represents unit frequency, These represent low frequency, mid frequency, and high frequency, respectively. , Indicates background light intensity. Representative adjustment system, f It is the fringe frequency. It is the phase, which carries the depth information of the object. It is the phase shift of the striped pattern, in which , N It is the number of phase shift steps. It is the initial phase; Therefore, the formula for solving the phase using the multi-step phase shift algorithm is as follows: (2) In equation (2), This represents the phase obtained through demodulation. The phase obtained after applying the arctangent function. Enclosed in the interval .

[0019] Step 2: Based on the multi-frequency fringe projection method, the initial low-frequency unfolded phase is calculated using the single-frequency phase and the low-frequency wrapping phase. The phase wrapping of single frequency, low frequency, mid frequency, and high frequency is obtained through a multi-step phase shift algorithm. (This invention uses 4-step phase shifts for 1 frequency, 16 frequencies, 64 frequencies, and 128 frequencies as examples.) The specific operation of phase unfolding is as follows: First, the low-frequency unfolded phase is calculated from the single-frequency (1-frequency) phase, and then solved using the multi-frequency fringe projection method. The multi-frequency fringe projection method is another commonly used phase unwrapping method in fringe projection profilometry. It uses one or more sets of low-frequency fringe patterns to unwrap the higher-frequency phase through the algebraic relationship between two different frequency phases. In the dual-frequency unwrapping method, two sets of fringe patterns need to be projected: one set is the fringe pattern used for actual measurement, and the other set is the single-frequency fringe pattern used for unwrapping.

[0020] (3) In the formula: -Low-frequency stripe frequency; -Single-frequency stripe frequency, here .

[0021] For the fringe patterns shown in formula (3), let their demodulation phases be respectively , Because the phase distribution of the unit frequency stripes is in Inside, therefore Its unwrapping phase is consistent with its phase, let it be denoted as ; The unwrapping phase is set as ..So, From formula (4), we can obtain: (4) As shown in formula (3), the following relationship exists between the low-frequency and single-frequency phases: (5) In the formula: (6) Combining formulas (4) and (5), the order of the low-frequency stripes can be obtained as follows: (7) In the formula: round - rounding operation.

[0022] Combining formulas (4) and (7), we can obtain the phase unwrapping formula (8) for low-frequency fringes. Then, we can obtain the 16-frequency low-frequency unfolded phase from formula (8). : (8) Step 3: Using the multi-frequency fringe projection method and phase order correction technique, the mid-frequency unfolded phase is further solved from the initial low-frequency unfolded phase and mid-frequency wrapped phase. Step four, similarly, uses the multi-frequency fringe projection method and phase order correction technology to solve the high-frequency unfolded phase from the mid-frequency unfolded phase and the high-frequency wrapped phase.

[0023] Next, the mid- and high-frequency encapsulated phase maps are initially unfolded through a two-step process. First, phase order correction techniques are used, i.e., the fringe pattern sequence is transformed; then, another shifted encapsulated phase is obtained, and two orders are obtained separately; the two fringe orders are filtered to suppress spike-like outliers in the fringe order map; then, based on the principle of complementarity, a new correct fringe order is obtained, i.e., all erroneous fringe order jumps are guided and removed by the second fringe order mapping obtained from the shifted phase map. It focuses on processing the fringe order map rather than the phase map, thus obtaining a reliable unwrap phase by fully utilizing the measurement information of the obtained fringe pattern. Furthermore, this invention does not require an additional fringe pattern. Experimental results demonstrate that the proposed method has higher accuracy and speed than widely used methods.

[0024] In the following formula It is a mid-frequency wrap-around phase. It is the mid-frequency expanded phase. It is a high-frequency wrapped phase. It is a high-frequency expanded phase. (After obtaining...) Then, based on the stripe pattern sequence Obtain using equation (9) According to the stripe pattern sequence Obtain using formula (10) In the formula .

[0025] (9) (10) Corresponding stripe levels The results are obtained from equations (11) and (12) respectively.

[0026] (11) (12) Then respectively Median filtering is performed to obtain . The corresponding corrected stripe order The phase of the 64-frequency expansion can be obtained from equation (13) and then calculated from equation (14). .

[0027] (13) (14) After obtaining Then, here we base our analysis on the stripe pattern sequence. Obtain using equation (9) According to the stripe pattern sequence Obtain using formula (10) . , See attached diagram. Figure 2 As shown.

[0028] Corresponding stripe levels Obtained from equations (11) and (12) respectively. Then, respectively... Median filtering is performed to obtain . The corresponding corrected stripe order The phase of the 128-frequency expansion can be obtained from equation (13) and then calculated from equation (14). .

[0029] In summary, this invention proposes a phase order correction method for multi-frequency cascaded phase unwrapping, aiming to resolve the contradiction between measurement efficiency and accuracy in traditional multi-frequency phase unwrapping methods. By introducing a reasonable phase order correction strategy, this method can maintain high reliability and high accuracy in phase unfolding results even under measurement conditions with large frequency ratios and few projection frames, significantly improving the system's measurement speed and robustness. While ensuring accuracy, it effectively reduces the number of fringe frequencies and images required for projection, lowering sensitivity to dynamic scene changes and environmental interference, making it suitable for high-speed, real-time, or resource-constrained 3D measurement scenarios.

Claims

1. A phase order correction method for multi-frequency cascaded phase de-wrapping methods, characterized in that, Includes the following steps: Step 1: Project the original fringe pattern onto the object under test using a projector, and acquire four-step phase-shifted fringe images of single frequency, low frequency, medium frequency and high frequency using a camera. Then, calculate the wrapping phase corresponding to each frequency using the multi-step phase-shifting method. Step 2: Based on the multi-frequency fringe projection method, the initial low-frequency unfolded phase is calculated using the single-frequency phase and the low-frequency wrapping phase; Step 3: Using the multi-frequency fringe projection method and phase order correction technique, the intermediate frequency unfolded phase is further solved from the initial low-frequency unfolded phase and the intermediate frequency wrapped phase; Step 4: Similarly, using multi-frequency fringe projection and phase order correction techniques, the high-frequency unfolded phase is solved from the mid-frequency unfolded phase and the high-frequency wrapped phase.

2. The phase order correction method for the multi-frequency cascaded phase de-wrapping method according to claim 1, characterized in that, The phase-shifted fringe image of step one is shown below: （1） in Indicates the first n The light intensity of the striped pattern Represents unit frequency, These represent low frequency, mid frequency, and high frequency, respectively. Indicates background light intensity. Representative adjustment system, f It is the fringe frequency. It is the phase, which carries the depth information of the object. It is the phase shift of the striped pattern, in which , N It is the number of phase shift steps. It is the initial phase; The formula for solving the phase using the multi-step phase shift algorithm is as follows: (2) In equation (2), This represents the phase obtained through demodulation, specifically the phase obtained using the arctangent function. Enclosed in the interval .

3. The phase order correction method for the multi-frequency cascaded phase de-wrapping method according to claim 2, characterized in that, The multi-frequency fringe projection method in step two uses one or more sets of low-frequency fringe patterns to unwrap the higher-frequency phase through the algebraic relationship between two different frequency phases. One set is the fringe pattern used for actual measurement, and the other set is the single-frequency fringe pattern used for unwrapping. (3) In the formula: -Low-frequency stripe frequency; -Single-frequency stripe frequency, here ; For the fringe patterns shown in formula (3), let their demodulation phases be respectively , Because the phase distribution of the unit frequency stripes is in Inside, therefore Consistent with its unwrapping phase, let it be... ; The unwrapping phase is set to ;So, From formula (4), we can obtain: (4) As shown in formula (3), the following relationship exists between the low-frequency and single-frequency phases: (5) In the formula: (6) Combining formulas (4) and (5), the low-frequency fringe order is obtained as follows: (7) In the formula: round - rounding operation; Combining formulas (4) and (7), we can obtain the phase unwrapping formula (8) for low-frequency fringes: (8) The low-frequency expanded phase is then obtained from equation (8). .

4. The phase order correction method for the multi-frequency cascaded phase de-wrapping method according to claim 3, characterized in that, The aforementioned multi-frequency fringe projection method and phase order correction technique are as follows: First, the wrapping phases of the four frequencies are obtained respectively. Then, the low-frequency unfolded phase, mid-frequency unfolded phase, and high-frequency unfolded phase are obtained sequentially from unit frequency to low, mid, and high. During the process from low to mid and mid to high, the phase order correction technique is used, that is, firstly by transforming the fringe pattern sequence; then, another shifted wrapping phase is obtained, and two orders are obtained respectively. The two fringe orders are filtered, and then a new correct fringe order is obtained based on the principle of complementarity. That is, all erroneous fringe order jumps are guided and removed by the second fringe order obtained by the shifted phase pattern.

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