Digital phase-shifting phase retrieval method for ESPI fringe pattern based on distance mapping

Abstract

The application discloses a digital phase-shifting phase recovery method of ESPI fringe pattern based on distance mapping, which comprises the following steps: 1) extracting the direction of each pixel point of the fringe pattern, and then calculating the normal curve of the fringe according to the fringe direction to obtain the moving direction of the fringe; 2) extracting the center line of the dark fringe, calculating the width of the fringe according to the center line of the fringe, and obtaining the moving distance of the fringe through distance mapping; 3) comprehensively moving the direction and the distance, and performing digital phase-shifting on the initial fringe pattern point by point, and adopting the bilinear gray interpolation to obtain the fringe pattern after digital phase-shifting; 4) calculating the wrapped phase corresponding to the fringe pattern; and 5) performing unwrapping processing on the wrapped phase to recover the full-field phase of the fringe pattern. The application extracts the phase through the digital image processing technology on the single fringe pattern, avoids the problem of inaccurate phase-shifting existing in the traditional physical phase-shifting technology in dynamic measurement, and can effectively improve the accuracy of the phase recovery of the single fringe pattern.

Description

Technical Field

[0001] This invention relates to a distance-mapping-based digital phase shift recovery method for ESPI fringe patterns. This method requires only one interference fringe pattern and uses image processing to indirectly calculate the shift distance through distance mapping, achieving a four-step phase shift and enabling accurate phase information extraction. This invention can be applied to fields such as deformation measurement of optically rough surfaces and non-destructive testing of composite materials. Background Technology

[0002] Electronic speckle pattern interferometry (ESPI) is a full-field, non-contact optical non-destructive testing technique widely used for deformation measurement of optically rough surfaces and non-destructive testing of composite materials. This technique uses optical interference to record the speckle interference field of the test object before and after deformation. By comparing the difference in the speckle field before and after deformation, an interference fringe pattern reflecting the deformation of the object is obtained. Therefore, the deformation or displacement information of the test piece is hidden in the fringe pattern formed by the speckle interference. The ultimate goal of electronic shear speckle interferometry is to obtain the phase information of the fringe pattern, thereby acquiring the minute displacement or deformation of the object for defect detection and quantitative analysis. Therefore, accurately extracting the phase from the interference fringe pattern is of great significance for measuring the displacement, strain, and vibration of an object. However, because the fringe pattern contains random speckle noise, the image signal-to-noise ratio is extremely low, making processing difficult and greatly limiting the application of this technique in many areas. Currently, there is no universal and completely reliable method for phase recovery of speckle fringe patterns. Therefore, researching phase recovery methods for speckle fringe patterns is of great significance for promoting the application of ESPI measurement technology and advancing the informatization and intelligentization of this non-destructive testing technology.

[0003] Phase shifting technology is one of the most important developments and achievements in the field of fringe pattern processing research, and it is also one of the most widely used phase retrieval techniques. It boasts high sensitivity, good real-time performance, and the ability to obtain the entire phase field, giving it unparalleled advantages over other phase retrieval techniques. However, phase shifting methods have significant drawbacks: first, the specimen surface cannot be deformed during the multi-step phase shift acquisition of speckle field images, which poses a significant challenge to many dynamic deformation measurements; second, most phase shifting methods achieve fringe displacement through piezoelectric ceramics (PZT). Although PZT is widely used, its inherent hysteresis effect results in a nonlinear relationship between the driving voltage and the PZT's expansion and contraction, interfering with the measurement results. Therefore, exploring new phase shifting schemes is imperative to address these issues.

[0004] Digital phase-shifting (DPPS) offers a novel approach to phase retrieval, extracting fringe information using image processing techniques without relying on physical phase-shifting devices. Digital image processing algorithms then enable digital phase shifting of a single fringe pattern. This method determines the direction and distance of fringe movement during phase shift by analyzing the direction and spacing of the fringes in the image. Interpolation techniques are then used to generate three fringe patterns corresponding to π / 2, π, and 3π / 2 phase shifts. Finally, a four-step phase shift formula is used to calculate the overall phase. DPPS not only completely solves the problem of dynamic measurement but also effectively avoids a series of errors introduced by hardware devices, thus improving the measurement accuracy of phase-shifted electronic shear speckle interferometry (ESPI). During digital phase shifting, the movement distance and direction of each pixel are key factors affecting the accuracy. Therefore, this invention proposes a distance-mapping-based ESPI fringe pattern digital phase-shifting recovery method, accurately recovering the fringe phase from a single fringe pattern. Summary of the Invention

[0005] This invention proposes a digital phase-shifted phase recovery method for ESPI stripe patterns based on distance mapping. The algorithm first calculates the direction value of each pixel in the stripe pattern, then calculates the normal curve of the stripes as the stripe movement direction. Simultaneously, it extracts the center line of the stripe pattern, calculates the distance between each pixel and the next in-phase pixel to obtain the stripe width, and determines the stripe movement distance using distance mapping. Combining the movement direction and distance, digital phase shifting is performed through full-field interpolation to obtain the phase-shifted stripe pattern. A wrapped phase map is calculated on the digitally phase-shifted stripe pattern, and the full-field phase of the stripe pattern is recovered using an unwrapping method. The technical solution achieving the objective of this invention includes the following steps:

[0006] Step 1: Input a single ESPI stripe image, and use a combination of gradient method and plane fitting method to extract the direction of the preprocessed stripe image. The direction of stripe movement during digital phase shift is determined by the stripe direction.

[0007] (1) Fringe direction: The direction of the fringe image is determined by combining the gradient method and the plane fitting method. First, the gradient is calculated using the plane fitting method, and then the fringe direction is calculated using the gradient method.

[0008]

[0009] Among them, I x I y These represent the gradients of the current pixel along the x and y directions, respectively, and θ(x, y) represents the tangent direction of the stripe.

[0010] (2) Direction of movement: The direction of the normal curve in the fringe pattern is the direction of movement of the fringe. Let the coordinates of a point n in the fringe pattern be (x...). n y n), the coordinates (x, y) of two adjacent points on the normal curve. n+1 y n+1 ) and (x n-1 y n-1 This can be represented as:

[0011]

[0012] Step 2: Determine the distance the stripes move during digital phase shift based on the stripe distance mapping.

[0013] (1) Find the center line of the dark stripe;

[0014] (2) Calculate the width FS of the stripe containing pixel A. A The width FS of the stripe containing pixel B after four consecutive phase shifts from point A. B ;

[0015] (3) Find the normal curve of point A;

[0016] (4) Along the direction of the normal curve at point A, find the intersection of the normal curve and the stripe center line L located between points A and B, and then calculate the normal distance from point A to the stripe center line L, denoted as d. AL ;

[0017] (5) Using the distance mapping approach, calculate the distance d between the current pixel A and the target pixel B according to the proportional relationship shown in the following formula. AB Meanwhile, the distance point A moves along its normal curve direction during phase shift is obtained as kd / 4 (k = 1, 2, 3) (corresponding to phase shifts of kπ / 2 (k = 1, 2, 3) respectively).

[0018] d AB =d AL +d BL

[0019]

[0020] Where, d AB Let d be the distance between pixels A and B. AL Let d be the normal distance between point A and the center line L of the fringe. BL FS is the normal distance between point B and the center line L of the fringe. A FS represents the width of the stripe containing point A. B The width of the stripe containing point B.

[0021] Step 3: Based on the direction and distance of the fringe movement, bilinear interpolation can be used to obtain the phase shift fringe pattern corresponding to the fixed phase deviation.

[0022] Step 4: Perform digital phase shifting to calculate the wrap-around phase map;

[0023] Step 5: Unwrap the package to restore the overall phase.

[0024] Compared with the prior art, the beneficial effects of the present invention are:

[0025] 1. This invention utilizes a distance-mapping-based digital phase-shifting algorithm, requiring only one interference fringe pattern. It achieves four-step phase shifting through image processing technology to extract phase information, resulting in higher accuracy compared to the traditional fringe centerline method.

[0026] 2. This invention can overcome the phase shift error caused by the nonlinearity of piezoelectric ceramics, and at the same time avoid the influence of the deformation of the specimen surface during the multi-step phase shift acquisition of speckle field images. Attached Figure Description

[0027] Figure 1 Digital phase shift implementation steps

[0028] Figure 2 Electron speckle interference fringe pattern

[0029] Figure 3 Stripe direction diagram

[0030] Figure 4 Schematic diagram of stripe contour lines and normal curves

[0031] Figure 5 (a) Speckle pattern;

[0032] Figure 5 (b) Stripe pattern;

[0033] Figure 6 (a) Schematic diagram of distance calculation during digital phase shift of simulated stripes;

[0034] Figure 6 (b) Schematic diagram of the calculation of the moving distance during digital phase shift of experimental fringes;

[0035] Figure 7 (a) Simulated stripe pattern;

[0036] Figure 7 (b) Digital phase shift results of the simulated fringe pattern (phase shift amount is π / 2);

[0037] Figure 7 (c) Digital phase shift results of the simulated fringe pattern (phase shift amount is π);

[0038] Figure 7 (d) Digital phase shift results of the simulated fringe pattern (phase shift amount is 3π / 2);

[0039] Figure 7(e) The phase map enveloping the simulated fringe pattern;

[0040] Figure 7 (f) Unwrapped phase diagram of simulated fringe pattern;

[0041] Figure 8 Phase-shifted electronic speckle interferometry system;

[0042] Figure 9 (a) Experimental stripe pattern;

[0043] Figure 9 (b) The center line of the experimental fringe pattern;

[0044] Figure 9 (c) The phase map enveloping the experimental fringe pattern;

[0045] Figure 9 (d) Unwrapped phase diagram of experimental fringe pattern. Detailed Implementation

[0046] The present invention will now be described in further detail with reference to specific embodiments.

[0047] Currently, in digital phase shifting, the distance and direction of movement of each pixel are key factors affecting the phase shifting accuracy. This invention proposes a distance-mapping-based digital phase shifting phase recovery method for ESPI fringe patterns, which achieves higher accuracy than the traditional fringe centerline method.

[0048] The present invention determines the stripe direction and stripe distance through the following steps, the specific steps of which are as follows:

[0049] Step 1: Input a single ESPI stripe image, extract the direction of the preprocessed stripe image using the gradient method, and determine the direction of stripe movement during digital phase shift based on the stripe direction.

[0050] (1) Formula for calculating the direction of the stripes:

[0051]

[0052] Among them, I x I y These represent the gradients of the current pixel along the x and y directions, respectively, and θ(x, y) represents the tangent direction of the stripe.

[0053] (2) Direction of movement: The direction of the normal curve in the fringe pattern is the direction of movement of the fringe. The method for calculating the normal curve point by point is to set the position coordinates (x, y, y) of a point n in the fringe pattern. n y n ), the coordinates (x, y) of two adjacent points on the normal curve. n+1 y n+1 ) and (x n-1y n-1 This can be represented as:

[0054]

[0055] Step 2: Determine the distance the fringes move during digital phase shift using the fringe width and distance mapping method.

[0056] (1) The center line of the dark fringes in the interference fringe pattern was extracted using an image skeleton extraction method based on partial differential equations;

[0057] (2) Calculate the width FS of the stripe containing pixel A. A The width FS of the stripe containing pixel B after four consecutive phase shifts from point A. B ;

[0058] (3) Find the normal curve of point A;

[0059] (4) Along the direction of the normal curve at point A, find the intersection of the normal curve and the stripe center line L located between points A and B, and then calculate the normal distance from point A to the stripe center line L, denoted as d. AL ;

[0060] (5) Using the distance mapping approach, calculate the distance d between the current pixel A and the target pixel B according to the proportional relationship shown in the following formula. AB Meanwhile, the distance point A moves along its normal curve direction during phase shift is obtained as kd / 4 (k = 1, 2, 3) (corresponding to phase shifts of kπ / 2 (k = 1, 2, 3) respectively).

[0061] d AB =d AL +d BL

[0062]

[0063] Where, d AB Let d be the distance between pixels A and B. AL Let d be the normal distance between point A and the center line L of the fringe. BL FS is the normal distance between point B and the center line L of the fringe. A FS represents the width of the stripe containing point A. B The width of the stripe containing point B.

[0064] Step 3: Based on the direction and distance of the fringe movement, generate three phase-shifted fringe images corresponding to phase offsets of π / 2, π, and 3π / 2. Use bilinear interpolation to perform sub-pixel grayscale interpolation on the phase-shifted fringe images to correct the grayscale values ​​of each pixel.

[0065] Step 4: Calculate the wrap phase using the following formula.

[0066]

[0067] Where I0, I1, I2, and I3 are phase-shifted interference fringe patterns corresponding to phases of 0, π / 2, π, and 3π / 2, respectively. For the wrapping phase.

[0068] Step 5: Perform unpacking to restore continuous phase across the entire field.

[0069] The entire process will now be described in detail with reference to the accompanying drawings:

[0070] 1. The steps for implementing digital phase shift are as follows: Figure 1 As shown. First, input a single ESPI stripe pattern, such as... Figure 2 As shown.

[0071] 2. Determine the direction of stripe movement

[0072] The gradient method is used to determine the direction of the preprocessed fringe image. A schematic diagram of the fringe direction is shown below. Figure 3 As shown. Figure 4 As shown, contour lines are defined as curves that are locally parallel to the current direction of the fringe, and normal curves are curves that are locally perpendicular to the current direction of the fringe. The direction of movement is the direction of the normal curve. Figure 5 (b) Figure 5 (a) Obtain the direction diagram.

[0073] 3. Determine the stripe movement distance

[0074] For a four-step phase shift, the single phase shift is π / 2, meaning each pixel in the fringe pattern moves along the normal curve of the fringe by 1 / 4 of the fringe spacing. For example... Figure 4 As shown, let F be a pixel in the i-th level stripe. i Located exactly at the center line L of the stripe i If the fringe undergoes four consecutive phase shifts of π / 2, the corresponding NF at that point... i It will be located at L i Adjacent centerline L i+1 Above, to be precise, NF i At the center line L i+1 At the intersection of its normal curve, therefore F i With NF i The normal distance between them is the width of the i-th order fringe. After obtaining the normal curves of each point in the fringe pattern, the curve distance between two pixels on the same normal curve along the direction of the normal curve can be calculated. This curve distance is the local fringe spacing FS. iAt the same time, the moving distances for a single-step phase shift can be obtained as FS. i / 4、FS i / 2 and 3FS i / 4.

[0075] When point F i When dealing with pixels not located on the center line of the stripes, this invention calculates the stripe movement distance using distance mapping. First, it considers stripe patterns with the same direction but different widths, such as... Figure 6 As shown in (a) and 6(b), the center line of the dark stripes and the direction of the normal curve for each point in the figure are determined. The digital phase shift is performed along the direction of the normal curve. Let there be an arbitrary point A in the figure, and B be the position corresponding to point A after four consecutive phase shifts. Point A and the target point B are located on the same normal curve. Therefore, after obtaining the normal curve of point A, the position of the target point B should be located along the direction of the normal curve, and the distance moved by point A during the digital phase shift should be calculated.

[0076] This invention proposes the following distance mapping method to calculate the position of point B and the movement distance of point A during each phase shift.

[0077] (1) Find the center line of the dark stripe;

[0078] (2) Calculate the width FS of the stripe containing point A. A and the width FS of its neighboring fringe along its phase shift direction (i.e., the fringe where point B is located). B ;

[0079] (3) Find the normal curve of point A;

[0080] (4) Along the direction of the normal curve at point A, find the intersection of the normal curve and the stripe center line L located between points A and B, and then calculate the normal distance from point A to the stripe center line L, denoted as d. AL ;

[0081] (5) Using the distance mapping approach, calculate the distance d between the current pixel A and the target pixel B according to the proportional relationship shown in the following formula. AB At the same time, the distance that point A moves when it undergoes a phase shift along its normal curve direction is kd / 4 (k = 1, 2, 3).

[0082] d AB =d AL +d BL

[0083]

[0084] Where, d AB Let d be the distance between pixels A and B. AL Let d be the normal distance between point A and the center line L of the fringe. BLFS is the normal distance between point B and the center line L of the fringe. A FS represents the width of the stripe containing point A. B The width of the stripe containing point B.

[0085] 4. Generate phase-shifted fringe patterns

[0086] For example Figure 7 The simulated fringe pattern shown in (a) generates three phase-shifted fringe patterns corresponding to phase shifts of π / 2, π, and 3π / 2 based on the fringe movement direction and distance, as shown below. Figure 7 As shown in (b)-7(d), bilinear interpolation is used to perform sub-pixel grayscale interpolation on the phase-shifted stripe image in order to correct the grayscale value of each pixel.

[0087] 5. Calculate the package phase and perform unpacking.

[0088] The wrapping phase is calculated using the following formula, and the result is as follows: Figure 7 (e) is shown

[0089]

[0090] Where I0, I1, I2, and I3 are phase-shifted interference fringe patterns corresponding to phases of 0, π / 2, π, and 3π / 2, respectively. This involves unpacking the phase map (e.g., using least squares) to recover the full-field phase, as shown below. Figure 7 As shown in (f).

[0091] For example Figure 9 The experimental fringe pattern shown is processed in the same way as the simulated fringe pattern. Figure 9 (a) is adopted Figure 8 The experimental setup shown was used to collect data (including a laser, a Michelson interferometer optical path, and a piezoelectric ceramic phase shifter). Figure 9 (b) is the center line of the dark stripe in (a). Figure 9 (c) is the wrap-around phase map obtained using the digital phase shift method. Figure 9 (d) is the full-field phase recovered after unwrapping.

[0092] 6. Phase recovery effect

[0093] As can be seen from the figure, for both simulated fringe patterns and experimental images, the digital phase-shifting method provides a more accurate phase recovery result for speckle fringe images. The step information between phases is clear, and the grayscale information can transition smoothly. The phase unfolding effect is ideal, and the phase map can be continuously distributed. Therefore, this method can effectively solve dynamic measurement problems and, to a certain extent, avoid systematic errors caused by hardware equipment.

Claims

1. A distance-mapping-based digital phase-shift recovery method for ESPI fringe patterns, comprising the following steps: Step 1: Determine the direction of fringe movement during digital phase shift based on the fringe direction; Step 1-1: Determine the direction of the stripes at each point in the image. in, I x I y These represent the gradients of the current pixel (x, y) along the x-direction and along the y-direction, respectively, and θ(x, y) represents the tangent direction of the stripe. Step 1-2: Calculate the normal curve of each point in the image as the direction of fringe movement, and then apply the formula... The normal curve is calculated point by point, which is the direction of the stripe movement during digital phase shift, where n represents the number of pixels in the stripe pattern, (x n y n (x) represents the position coordinates of point n. n+1 y n+1 ) and (x n-1 y n-1 ) are the coordinates of two points adjacent to n along the normal curve; Step 2: Determine the distance the stripes move during digital phase shift by performing distance mapping based on the stripe centerline; Step 2-1: Find the center line of the dark stripes; Step 2-2: Calculate the width FS of the stripe containing pixel A. A The width FS of the stripe containing pixel B after four consecutive phase shifts from point A. B ; Steps 2-3: Find the normal curve of point A; Steps 2-4: Along the direction of the normal curve at point A, find the intersection of this normal curve and the fringe centerline L located between points A and B. Calculate the normal distance from point A to the fringe centerline L, denoted as d. AL ; Steps 2-5: Calculate the distance d between the current pixel A and the target pixel B according to the distance mapping and proportional relationship. AB Meanwhile, the distance point A moves along its normal curve direction during phase shift is obtained as kd. AB / 4, k takes the values ​​1, 2, and 3, which correspond to the phase shift kπ / 2 respectively. d AB =d AL +d BL Where, d AB Let d be the normal distance between pixels A and B. AL Let d be the normal distance between point A and the center line L of the fringe. BL FS is the normal distance between point B and the center line L of the fringe. A FS represents the width of the stripe containing point A. B The width of the stripe containing point B; Step 3: Based on the moving direction obtained in Step 1 and the moving distance obtained in Step 2, perform digital phase shifting on the initial fringe pattern I0 point by point, and use bilinear grayscale interpolation to obtain three fringe patterns I1, I2, and I3 corresponding to phase offsets of π / 2, π, and 3π / 2, respectively. Step 4: Calculate the package phase Wherein, I0, I1, I2, and I3 are the phase shift interference fringe patterns corresponding to phase shifts of 0, π / 2, π, and 3π / 2, respectively; Step 5: Unwrap the wrapped phase to recover the full-field phase of the fringe pattern.

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