Phase unwrapping method, device and storage medium

Abstract

The present application discloses a phase unwrapping method, device and storage medium, which belongs to the field of optical measurement technology. The method includes: performing polar coordinate conversion on the wrapped phase information of the measured object to obtain a fringe phase map in a polar coordinate system; unwrapping and unfolding the fringe phase map to obtain an unfolded phase map in a polar coordinate system; converting the unfolded phase map in the polar coordinate system to a Cartesian coordinate system to obtain an unwrapped phase map. The embodiment of the present application converts the phase unwrapping problem from a Cartesian coordinate system to a polar coordinate system, so that the phase jump point can be converted into a gradient change in the polar direction, making the phase change of noise points and singular points easier to identify, reducing the errors caused by noise points and singular points in the phase unwrapping process, and improving the accuracy of phase unwrapping.

Description

Technical Field

[0001] The present application belongs to the field of optical measurement technology, and in particular, relates to a phase unwrapping method, device and storage medium. Background Art

[0002] Phase recovery technology is widely used in the field of optical measurement, such as interferometry and holographic measurement. In phase measurement, interference fringe technology is usually used to obtain phase information. Since the phase information changes periodically between 0 and 2π, the phase value obtained by direct reconstruction is usually wrapped in the main value interval of [-π, π] or [0, 2π], thus presenting a discontinuous step-type phase distribution pattern. Therefore, phase unwrapping is required to obtain the true continuous phase distribution. This process is also called phase unwrapping.

[0003] In the wrapped phase diagram, the edge of the phase jump is an important criterion for phase unwrapping. Since the noise points and singular points in the actual measurement results also have phase jump characteristics, the phase jumps corresponding to the noise points and singular points will be mistakenly identified as normal jumps during the phase unwrapping process, interfering with the judgment of the real phase change, resulting in deviations in the unwrapping results and affecting the accuracy of the phase unwrapping. Summary of the invention

[0004] The present application aims to solve at least one of the technical problems existing in the prior art. To this end, the present application proposes a phase unwrapping method, device and storage medium to improve the accuracy of phase unwrapping.

[0005] In a first aspect, the present application provides a phase unwrapping method, comprising:

[0006] The wrapped phase information of the measured object is converted into polar coordinates to obtain a fringe phase image in a polar coordinate system;

[0007] Unwrapping and unfolding the fringe phase image to obtain an unfolded phase image in a polar coordinate system;

[0008] The phase diagram after unfolding in the polar coordinate system is converted to the Cartesian coordinate system to obtain the unwrapped phase diagram.

[0009] According to the phase unwrapping method of the present application, the wrapped phase information of the measured object is converted into polar coordinates to obtain a fringe phase image in a polar coordinate system; the fringe phase image is unwrapped and unfolded to obtain an unfolded phase image in a polar coordinate system; the unfolded phase image in the polar coordinate system is converted to a Cartesian coordinate system to obtain an unwrapped phase image. The embodiment of the present application converts the phase unwrapping problem from a Cartesian coordinate system to a polar coordinate system, so that the phase jump point can be converted into a gradient change in the polar direction, making the phase changes of noise points and singular points easier to identify, reducing the errors caused by noise points and singular points in the phase unwrapping process, and improving the accuracy of phase unwrapping.

[0010] According to an embodiment of the present application, before performing polar coordinate conversion on the wrapped phase information of the measured object to obtain a fringe phase image in a polar coordinate system, the method includes:

[0011] Acquire a target signal obtained by measuring the object to be measured;

[0012] According to the signal strength of the target signal, a phase recovery algorithm is used to iteratively calculate and obtain the wrapped phase information of the object under test.

[0013] In this embodiment, the wrapped phase information of the object under test is iteratively calculated from the signal strength of the target signal through a phase recovery algorithm. The phase information can be inferred from the known signal strength without directly measuring the phase, thereby improving the accuracy of the wrapped phase information.

[0014] According to an embodiment of the present application, the step of performing polar coordinate conversion on the wrapped phase information of the object to be measured to obtain a fringe phase image in a polar coordinate system includes:

[0015] Calculating the polar diameter and angle of each discrete grid point in the wrapped phase information in a polar coordinate system;

[0016] Uniformly sampling each discrete grid point in a preset polar diameter interval and a preset angle interval to obtain a plurality of sampling points; wherein the maximum value of the polar diameter interval is less than or equal to the maximum polar diameter of each discrete grid point in the polar coordinate system;

[0017] The sampling points are interpolated using a preset interpolation algorithm to obtain a fringe phase map of the wrapped phase information in a polar coordinate system.

[0018] In this embodiment, by calculating the polar diameter and angle of each discrete grid point in the wrapped phase information in the polar coordinate system, the two-dimensional phase information in the Cartesian coordinate system can be converted into a representation in the polar coordinate system, and then uniform sampling is performed within the preset polar diameter interval and angle interval to make the distribution of data points more uniform, reducing information loss or error increase due to uneven sampling, and filtering out some noise points and singular points through interpolation to generate a smoother and more continuous fringe phase image, further improving the accuracy of phase unwrapping.

[0019] According to an embodiment of the present application, the uniform sampling of each discrete grid point in a preset polar radius interval and a preset angle interval respectively includes:

[0020] Determine the number of sampling times, and determine a first sampling step length in the polar radius interval and a second sampling step length in the angle interval;

[0021] Each discrete grid point is uniformly sampled in a preset polar radius interval and a preset angle interval according to the sampling number, the first sampling step length, and the second sampling step length.

[0022] In this embodiment, by determining the number of sampling times and the sampling step size within the polar radius and angle interval, the sampling density and distribution can be flexibly adjusted to reduce the possibility of missing poles, obtain sufficient data points in key areas to capture the details of phase changes, and reduce the number of sampling points in areas with gentler changes to save computing resources.

[0023] According to an embodiment of the present application, the step of interpolating the sampling points using a preset interpolation algorithm to obtain a fringe phase diagram of the wrapped phase information in a polar coordinate system includes:

[0024] Determine the data volume of the sampling points obtained by sampling;

[0025] An interpolation algorithm corresponding to the data volume is selected to interpolate the sampling points to obtain a fringe phase diagram of the wrapped phase information in a polar coordinate system.

[0026] In this embodiment, the density and distribution of the sampling can be evaluated by the amount of data at the sampling points. Since different interpolation algorithms are suitable for different data amounts and distributions, the most appropriate interpolation method is selected according to the number and characteristics of the sampling points, so that the interpolation process is both accurate and efficient, and can generate high-quality fringe phase images, thereby providing a reliable data basis for subsequent phase unwrapping and analysis.

[0027] According to an embodiment of the present application, the step of unwrapping the fringe phase image to obtain an unfolded phase image in a polar coordinate system includes:

[0028] constructing a Poisson equation according to the fringe phase diagram;

[0029] Perform discrete cosine transform on Poisson's equation to obtain Poisson's equation in discrete cosine transform frequency domain;

[0030] The Poisson equation in the discrete cosine transform frequency domain is solved by combining the least squares unwrapping algorithm, and the frequency domain representation of the unwrapped phase value after discrete cosine transform is obtained;

[0031] The unwrapped phase value is transformed from the discrete cosine transform frequency domain to the spatial domain representation to obtain the phase map after expansion in the polar coordinate system.

[0032] In this embodiment, the Poisson equation is constructed according to the fringe phase diagram to describe the variation law of the phase field. The Poisson equation is converted to the frequency domain through discrete cosine transform. The periodic jump problem of the phase can be more easily handled in the frequency domain. In the unwrapping calculation process, the phase gradient in the polar direction is mainly considered, rather than the phase gradient in the horizontal and vertical directions. Compared with the method of directly unwrapping the phase in the Cartesian coordinate system, the calculation process is simplified. The Poisson equation in the frequency domain is solved by combining the least squares unwrapping algorithm, and the optimal solution in the least squares sense can be obtained. Not only the accuracy of the phase unwrapping is improved, but also the computational efficiency of the discrete cosine transform is utilized to speed up the unwrapping process.

[0033] According to an embodiment of the present application, constructing a Poisson equation according to the fringe phase diagram includes:

[0034]

[0035] Solve the Poisson equation in the discrete cosine transform frequency domain, and get the unwrapped phase value in the discrete cosine transform frequency domain as:

[0036]

[0037] Among them, φ(r i ,θ j ) represents the representation of the unwrapped phase value in the spatial domain, i = 0, 1…, M-1, j = 0, 1,…, N-1 are the indices in the spatial domain, ρ i,j represents the total differential of the strip phase image gradient, It indicates that the unwrapped phase value is represented in the frequency domain after discrete cosine transform, m = 0, 1..., M-1, n = 0, 1,..., N-1 are the indices of the frequency domain, is i,j Frequency domain representation after discrete cosine transform.

[0038] In a second aspect, the present application provides a phase unwrapping device, comprising:

[0039] The first conversion module is used to convert the wrapped phase information of the measured object into polar coordinates to obtain a fringe phase image in a polar coordinate system;

[0040] An unwrapping module, used for unwrapping and unfolding the fringe phase image to obtain an unfolded phase image in a polar coordinate system;

[0041] The second conversion module is used to convert the phase image after being unfolded in the polar coordinate system into a Cartesian coordinate system to obtain the unwrapped phase image.

[0042] According to the phase unwrapping device of the present application, the wrapped phase information of the measured object is converted into polar coordinates to obtain a fringe phase image in a polar coordinate system; the fringe phase image is unwrapped and unfolded to obtain an unfolded phase image in a polar coordinate system; the unfolded phase image in the polar coordinate system is converted to a Cartesian coordinate system to obtain an unwrapped phase image. The embodiment of the present application converts the phase unwrapping problem from a Cartesian coordinate system to a polar coordinate system, so that the phase jump point can be converted into a gradient change in the polar direction, making the phase change of noise points and singular points easier to identify, reducing the errors caused by noise points and singular points in the phase unwrapping process, and improving the accuracy of phase unwrapping.

[0043] In a third aspect, the present application provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the phase unwrapping method as described in the first aspect above when executing the computer program.

[0044] In a fourth aspect, the present application provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the phase unwrapping method as described in the first aspect above.

[0045] In a fifth aspect, the present application provides a chip, comprising a processor and a communication interface, wherein the communication interface is coupled to the processor, and the processor is used to run programs or instructions to implement the phase unwrapping method as described in the first aspect above.

[0046] In a sixth aspect, the present application provides a computer program product, including a computer program, which, when executed by a processor, implements the phase unwrapping method as described in the first aspect above.

[0047] The above one or more technical solutions in the embodiments of the present application have at least one of the following technical effects:

[0048] According to the phase unwrapping method of the present application, the wrapped phase information of the measured object is converted into polar coordinates to obtain a fringe phase image in a polar coordinate system; the fringe phase image is unwrapped and unfolded to obtain an unfolded phase image in a polar coordinate system; the unfolded phase image in the polar coordinate system is converted to a Cartesian coordinate system to obtain an unwrapped phase image. The embodiment of the present application converts the phase unwrapping problem from a Cartesian coordinate system to a polar coordinate system, so that the phase jump point can be converted into a gradient change in the polar direction, making the phase changes of noise points and singular points easier to identify, reducing the errors caused by noise points and singular points in the phase unwrapping process, and improving the accuracy of phase unwrapping.

[0049] Furthermore, in some embodiments, the wrapped phase information of the object under test is obtained by iteratively calculating the signal strength of the target signal through a phase recovery algorithm. The phase information can be inferred from the known signal strength without directly measuring the phase, thereby improving the accuracy of the wrapped phase information.

[0050] Furthermore, in some embodiments, by calculating the polar diameter and angle of each discrete grid point in the wrapped phase information in the polar coordinate system, the two-dimensional phase information in the Cartesian coordinate system can be converted into a representation in the polar coordinate system, and then uniform sampling is performed within the preset polar diameter interval and angle interval to make the distribution of data points more uniform, thereby reducing information loss or error increase caused by uneven sampling. By interpolation, some noise points and singular points can be filtered out to generate a smoother and more continuous fringe phase image, thereby further improving the accuracy of phase unwrapping.

[0051] Furthermore, in some embodiments, by determining the number of sampling times and the sampling step size within the polar radius and angle interval, the sampling density and distribution can be flexibly adjusted to reduce the possibility of missing poles, obtain sufficient data points in key areas to capture the details of phase changes, and reduce the number of sampling points in areas with gentler changes to save computing resources.

[0052] Furthermore, in some embodiments, the density and distribution of the sampling can be evaluated by the amount of data at the sampling points. Since different interpolation algorithms are suitable for different data amounts and distributions, the most appropriate interpolation method is selected according to the number and characteristics of the sampling points, so that the interpolation process is both accurate and efficient, and can generate high-quality fringe phase images, thereby providing a reliable data basis for subsequent phase unwrapping and analysis.

[0053] Furthermore, in some embodiments, by constructing the Poisson equation based on the fringe phase diagram to describe the variation of the phase field, and converting the Poisson equation to the frequency domain through discrete cosine transform, the periodic jump problem of the phase can be more easily handled in the frequency domain, and in the unwrapping calculation process, the phase gradient in the polar direction is mainly considered, rather than the phase gradient in the horizontal and vertical directions. Compared with the method of directly unwrapping the phase in the Cartesian coordinate system, the calculation process is simplified, and the Poisson equation in the frequency domain is solved by combining the least squares unwrapping algorithm, so that the optimal solution in the least squares sense can be obtained, which not only improves the accuracy of the phase unwrapping, but also utilizes the computational efficiency of the discrete cosine transform to speed up the unwrapping process.

[0054] Additional aspects and advantages of the present application will be given in part in the description below, and in part will become apparent from the description below, or will be learned through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0056] Figure 1 is a flow chart of a phase unwrapping method provided in an embodiment of the present application;

[0057] Figure 2 It is a schematic diagram of the flow of the simulation experiment provided in the embodiment of the present application;

[0058] Figure 3 It is a schematic diagram of the surface structure of a physical object provided in an embodiment of the present application;

[0059] Figure 4 is a schematic diagram of the package phase information of a physical object provided in an embodiment of the present application;

[0060] Figure 5 is a fringe phase diagram provided by an embodiment of the present application;

[0061] Figure 6 The phase unwrapping diagram is obtained by performing unwrapping operation in the polar coordinate system provided in the embodiment of the present application;

[0062] Figure 7 is a re-wrapped phase diagram provided in an embodiment of the present application;

[0063] Figure 8 The absolute phase image after conversion to Cartesian coordinates and unwrapping provided by the embodiment of the present application;

[0064] Fig. 9 is a schematic diagram of the structure of a phase unwrapping device provided in an embodiment of the present application;

[0065] Fig.10It is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0066] The following will be combined with the drawings in the embodiments of the present application to clearly describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments in the present application belong to the scope of protection of this application.

[0067] The terms "first", "second", etc. in the specification and claims of the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described here, and the objects distinguished by "first", "second", etc. are generally of one type, and the number of objects is not limited. For example, the first object can be one or more. In addition, "and / or" in the specification and claims represents at least one of the connected objects, and the character " / " generally indicates that the objects associated with each other are in an "or" relationship.

[0068] The unwrapping algorithms in the related art are roughly divided into two types. One is the path-related path tracking algorithm. When the wrapped phase information has noise, shadows, stripe breaks and serious undersampling, this path tracking algorithm usually encounters problems such as missing some poles or non-unique paths when selecting the integral path, which may lead to non-unique unwrapping results, large differences from the true phase, and even "islands" appearing and unable to complete unwrapping. The other is a path-independent algorithm. This algorithm generally solves the objective function by the least squares algorithm to obtain the least squares norm solution as the phase unwrapping result. This method is global and can provide a smooth solution, avoiding the influence of some poles and paths on the results. However, this algorithm cannot limit the propagation of the phase error caused by unreliable data points in space. The unwrapped phase obtained has a tendency of peak sharpening, valley filling, and steep slope slowing down, which leads to global errors in the phase. The phase unwrapping method based on the solution of the discrete Poisson equation does not require threshold judgment of the interference pattern. It uses fast discrete cosine transform to solve the discrete Poisson equation with Neumann boundary conditions to obtain the least squares solution, and then obtains the unwrapped phase distribution.

[0069] However, these methods usually perform unwrapping operations in a Cartesian coordinate system. In Cartesian coordinates, phase jump points appear as sudden changes in phase values. Noise points and singular points in actual measurement results also have phase jump characteristics. Therefore, during the phase unwrapping process, the phase jumps corresponding to noise points and singular points will be mistakenly identified as normal jumps, interfering with the judgment of the actual phase change, resulting in deviations in the unwrapping results and affecting the accuracy of phase unwrapping.

[0070] In some high-precision measurement fields such as holographic interferometry and various imaging and sensing technologies based on phase information, whether the reconstructed phase information can be correctly unfolded directly affects the accuracy of the final measurement results. Therefore, the accuracy of phase unwrapping needs to be improved.

[0071] To solve at least one of the above technical problems, the present application provides a phase unwrapping method, device and storage medium. The phase unwrapping method and device provided by the present application are described in detail below with reference to the accompanying drawings through specific embodiments and their application scenarios.

[0072] The phase unwrapping method may be applied to a terminal, and may be specifically executed by hardware or software in the terminal.

[0073] The terminal includes, but is not limited to, a portable communication device such as a mobile phone or tablet computer with a touch-sensitive surface (e.g., a touch screen display and / or a touch pad). It should also be understood that in some embodiments, the terminal may not be a portable communication device, but a desktop computer with a touch-sensitive surface (e.g., a touch screen display and / or a touch pad).

[0074] In the following various embodiments, a terminal including a display and a touch-sensitive surface is described. However, it should be understood that the terminal may include one or more other physical user interface devices such as a physical keyboard, a mouse and a joystick.

[0075] The phase unwrapping method provided in the embodiment of the present application may be executed by an electronic device or a functional module or functional entity in the electronic device that can implement the phase unwrapping method. The electronic devices mentioned in the embodiment of the present application include but are not limited to mobile phones, tablet computers, computers, cameras, and wearable devices. The phase unwrapping method provided in the embodiment of the present application is described below using an electronic device as an example of the execution subject.

[0076] like Figure 1 As shown, the phase unwrapping method includes: step 110, step 120 and step 130.

[0077] Step 110: Perform polar coordinate conversion on the wrapped phase information of the object to be measured to obtain a fringe phase image in a polar coordinate system.

[0078] In the embodiment of the present application, the wrapped phase information refers to the phase jump phenomenon caused by the phase change exceeding 2π in the phase measurement technology, which makes the actual phase value "wrapped" in a 2π period. This wrapped phase value contains the height information of the surface of the measured object, but it is periodic, that is, if the phase change exceeds 2π, it will return to the starting point, thus presenting a discontinuous step-type phase distribution pattern.

[0079] In some embodiments, the package phase information of the measured object can be obtained by structured light three-dimensional measurement technology. In this method, the phase information is obtained by projecting a specific grating image onto the surface of the measured object and capturing its reflected image. For example, the four-step phase shift method or other structured light three-dimensional measurement technology can be used to obtain the package phase information of the measured object, which is not limited in the embodiments of the present application.

[0080] In some embodiments, a target signal obtained by measuring the measured object may be obtained;

[0081] According to the signal strength of the target signal, the phase recovery algorithm is used to iteratively calculate the wrapped phase information of the object under test.

[0082] In this embodiment, the target signal can be obtained by projecting a specific grating pattern onto the surface of the object to be measured, and using a camera to capture the reflected image signal. Specifically, a projector can be used to project a series of grating patterns onto the surface of the object to be measured. These grating patterns can be sinusoidal waveforms, and their phases will change according to the ups and downs of the object surface. Use a camera to photograph the surface of the object illuminated by the grating pattern to obtain an image signal. The image signal captured by the camera contains information about the phase change caused by the shape of the object surface. Of course, necessary preprocessing can also be performed on the captured image, such as denoising, contrast enhancement, etc., to improve the accuracy of subsequent phase extraction.

[0083] After acquiring the target signal, a suitable phase recovery algorithm, such as the Gerchberg-Saxton algorithm, the Fienup phase recovery algorithm, etc., can be selected according to the signal strength (amplitude information) of the target signal to calculate the wrapped phase information of the object under test. The iterative process may include: initializing the phase: randomly setting the phase or providing an initial estimate based on other information; calculating the complex signal: combining the measured amplitude information and the current phase information to construct a complex signal; updating the phase: updating the phase information based on the integrity constraints of the frequency domain or the spatial domain according to the rules of the phase recovery algorithm; checking convergence: determining whether the current phase estimate meets the convergence criteria, if so, stopping the iteration, otherwise continuing.

[0084] In the polar coordinate system, the polar diameter describes the distance from the point to the pole, which can be expressed in millimeters or other units; the angle describes the radial angle, which can be expressed in radians or degrees. The formula for converting the wrapped phase information P to the fringe phase image P_polar in the polar coordinate system is as follows:

[0085]

[0086] Among them, r represents the polar coordinate in the polar coordinate system, θ represents the angular coordinate in the polar coordinate system, x represents the horizontal coordinate of the package phase information P in the Cartesian coordinate system, and y represents the vertical coordinate of the package phase information P in the Cartesian coordinate system.

[0087] In this embodiment, the wrapped phase information of the object under test is iteratively calculated from the signal strength of the target signal through a phase recovery algorithm. The phase information can be inferred from the known signal strength without directly measuring the phase, thereby improving the accuracy of the wrapped phase information.

[0088] Step 120: unwrap and unfold the fringe phase image to obtain an unfolded phase image in a polar coordinate system.

[0089] In an embodiment of the present application, an unwrapping algorithm, such as a phase gradient-based algorithm, a path-based algorithm, or a minimum energy strategy, can be used to unwrap the fringe phase image P_polar. According to the unwrapping algorithm, the change of the phase in the fringe phase image can be determined, and the real phase can be reconstructed by increasing or decreasing multiples of 2π, thereby obtaining the phase image P_polar_unwrap after being unfolded in the polar coordinate system.

[0090] Step 130: convert the phase diagram after unfolding in the polar coordinate system into a Cartesian coordinate system to obtain an unwrapped phase diagram.

[0091] In the embodiment of the present application, the unwrapped phase image P_cart_unwrap can be obtained by converting P_polar_unwrap into a Cartesian coordinate system using the following formula:

[0092]

[0093] According to the phase unwrapping method of the present application, the wrapped phase information of the measured object is converted into polar coordinates to obtain a fringe phase image in a polar coordinate system; the fringe phase image is unwrapped and unfolded to obtain an unfolded phase image in a polar coordinate system; the unfolded phase image in the polar coordinate system is converted to a Cartesian coordinate system to obtain an unwrapped phase image. The embodiment of the present application converts the phase unwrapping problem from a Cartesian coordinate system to a polar coordinate system, so that the phase jump point can be converted into a gradient change in the polar direction, making the phase changes of noise points and singular points easier to identify, reducing the errors caused by noise points and singular points in the phase unwrapping process, and improving the accuracy of phase unwrapping.

[0094] In some embodiments, performing polar coordinate conversion on the wrapped phase information of the object to be measured to obtain a fringe phase image in a polar coordinate system includes:

[0095] Calculate the polar diameter and angle of each discrete grid point in the wrapped phase information in the polar coordinate system;

[0096] Uniformly sampling each discrete grid point in a preset polar diameter interval and a preset angle interval to obtain a plurality of sampling points; wherein the maximum value of the polar diameter interval is less than or equal to the maximum polar diameter of each discrete grid point in the polar coordinate system;

[0097] The sampling points are interpolated using a preset interpolation algorithm to obtain a fringe phase map that wraps the phase information in a polar coordinate system.

[0098] In this embodiment, the obtained fringe phase image in the polar coordinate system is not obtained by performing coordinate transformation on all discrete grid points in the wrapped phase information, but by sampling a portion of the discrete grid points. Specifically, the conversion formula from the Cartesian coordinate system to the polar coordinate system can be used to calculate the discrete grid points (x i ,y j ) in the polar coordinate system and the angle (r i,j ,θ i,j ).

[0099] Determine the polar radius interval. Since the wrapped phase information P is usually a rectangular graph, the polar radius r i,j The larger the radius, the closer it is to the edge of the graph, and the fewer grid points with phase information under this radius. In this case, subsequent interpolation may introduce singular points, resulting in large errors, which in turn affect the final measurement results. Therefore, the maximum value of the polar radius interval should be less than or equal to the maximum value of the polar radius of all discrete grid points in the polar coordinate system, that is, the maximum value of the polar radius interval R <max{r i,j}.

[0100] Determine the angle interval. For a complete circle, the angle interval is usually 0 to 2π radians, so the angle interval can be [-π,π] or [0,2π].

[0101] After determining the radial interval and the angular interval, each discrete grid point can be uniformly sampled in the radial interval and the angular interval to obtain multiple sampling points. Uniform sampling refers to the process of selecting sample points at equal intervals within a specified numerical range. In this embodiment, uniform sampling can be performed in the radial interval and uniform sampling can be performed in the angular interval. Through uniform sampling, the entire interval can be covered.

[0102] In some embodiments, uniform sampling can be performed in the following manner. The diameter interval is divided into a number of equally spaced sub-intervals, and the angle interval is divided into a number of equally spaced sub-intervals. One or more sampling points are determined in each diameter and angle sub-interval. The sampling points can be evenly distributed in each sub-interval. For example, the center point of each sub-interval can be selected as the sampling point, or multiple sampling points can be evenly distributed in each sub-interval. The sampling process can be completed based on the diameter and angle of each discrete grid point in the wrapped phase information calculated above in the polar coordinate system.

[0103] In this embodiment, a preset interpolation algorithm such as nearest neighbor interpolation, linear interpolation, cubic spline interpolation, etc. can be selected to interpolate the sampling points to estimate the phase values ​​of those grid points that are not directly sampled, fill in the grid points in the polar coordinate system, and thus obtain a fringe phase map in the polar coordinate system.

[0104] In this embodiment, by calculating the polar diameter and angle of each discrete grid point in the wrapped phase information in the polar coordinate system, the two-dimensional phase information in the Cartesian coordinate system can be converted into a representation in the polar coordinate system, and then uniform sampling is performed within the preset polar diameter interval and angle interval to make the distribution of data points more uniform, reducing information loss or error increase due to uneven sampling, and filtering out some noise points and singular points through interpolation to generate a smoother and more continuous fringe phase image, further improving the accuracy of phase unwrapping.

[0105] In some embodiments, uniformly sampling each discrete grid point in a preset polar radius interval and a preset angle interval respectively includes:

[0106] Determine the number of sampling times, and determine a first sampling step length in the polar radius interval and a second sampling step length in the angle interval;

[0107] Each discrete grid point is uniformly sampled in a preset polar radius interval and a preset angle interval according to the sampling number, the first sampling step length and the second sampling step length.

[0108] In this embodiment, the sampling times refer to the number of sample points to be collected in the radial interval and the angle interval respectively, and the sampling times can be determined according to the required resolution requirements so that the sampled image can meet the accuracy requirements of the analysis. Of course, the sampling times can also be determined in combination with computing resources.

[0109] The first sampling step of the radial interval represents the distance between two adjacent sampling points in the radial interval, and the second sampling step of the angular interval represents the angular difference between two adjacent sampling points in the angular interval. By determining the first sampling step and the second sampling step, uniform sampling can be achieved in the radial interval and the angular interval.

[0110] It should be noted that the first sampling step and the second sampling step need to be appropriately selected. If the step is too small, the data volume is large and the time is long. If the step is too small, some poles will be missed, thus affecting the accuracy of the final unwrapping result. Therefore, the first sampling step and the second sampling step can be calibrated in advance, so that the appropriate first sampling step and the second sampling step can be selected.

[0111] In this embodiment, by determining the number of sampling times and the sampling step size within the polar radius and angle interval, the sampling density and distribution can be flexibly adjusted to reduce the possibility of missing poles, obtain sufficient data points in key areas to capture the details of phase changes, and reduce the number of sampling points in areas with gentler changes to save computing resources.

[0112] In some embodiments, a preset interpolation algorithm is used to interpolate the sampling points to obtain a fringe phase diagram of the wrapped phase information in a polar coordinate system, including:

[0113] Determine the data volume of the sampling points obtained by sampling;

[0114] An interpolation algorithm corresponding to the amount of data is selected to interpolate the sampling points to obtain a fringe phase map containing phase information in a polar coordinate system.

[0115] In this embodiment, the total number of sampling points obtained by sampling may be counted, or the data volume of the sampling points may be estimated according to parameters such as the sampling step length and the number of sampling times.

[0116] According to the amount of data at the sampling points, select a suitable interpolation algorithm. The correspondence between the amount of data and the interpolation algorithm can be determined in advance. For example, if the amount of data is small, the nearest neighbor interpolation method can be selected to establish the correspondence. If the amount of data is large, the linear interpolation method can be selected to establish the correspondence. Of course, other interpolation algorithms can also be selected, such as cubic spline interpolation. After determining the amount of data at the sampling points, the corresponding interpolation algorithm can be determined according to the correspondence.

[0117] In this embodiment, the density and distribution of the sampling can be evaluated by the amount of data at the sampling points. Since different interpolation algorithms are suitable for different data amounts and distributions, the most appropriate interpolation method is selected according to the number and characteristics of the sampling points, so that the interpolation process is both accurate and efficient, and can generate high-quality fringe phase images, thereby providing a reliable data basis for subsequent phase unwrapping and analysis.

[0118] In some embodiments, unwrapping and unfolding the fringe phase image to obtain an unfolded phase image in a polar coordinate system includes:

[0119] Construct Poisson's equation based on the fringe phase diagram;

[0120] Perform discrete cosine transform on Poisson's equation to obtain Poisson's equation in discrete cosine transform frequency domain;

[0121] The Poisson equation in the discrete cosine transform frequency domain is solved by combining the least squares unwrapping algorithm, and the frequency domain representation of the unwrapped phase value after discrete cosine transform is obtained;

[0122] The unwrapped phase value is transformed from the discrete cosine transform frequency domain to the spatial domain representation to obtain the phase map after expansion in the polar coordinate system.

[0123] In this embodiment, the wrapped phase of the fringe phase image can be The gradient in the direction of the polar radius r The gradient in the direction of angle θ Total differential of stripe phase pattern gradient ε∈[0,1] is the weight coefficient, i=0,1…,M-1, j=0,1,…,N-1 are the indices in the spatial domain, let φ(r i ,θ j ) is the representation of the unwrapped phase value in the spatial domain, and the following Poisson equation is constructed:

[0124]

[0125] Let the cosine function Sine function m=0,1…,M-1、n=0,1,…,N-1 are the indices in the frequency domain, then the two-dimensional discrete cosine transform (DCT) pair can be written as follows:

[0126]

[0127]

[0128] in, is the frequency domain representation of function f after discrete cosine transform, f i,j is the representation of the function f in the spatial domain.

[0129] Performing DTC transformation on Poisson equation (3) yields the Poisson equation in DCT frequency domain:

[0130]

[0131] in, is the frequency domain representation of the unwrapped phase value after discrete cosine transform, is i,j Frequency domain representation after discrete cosine transform.

[0132] because So we have:

[0133]

[0134] Substituting (7) into the Poisson equation (6) in the DCT frequency domain, we can obtain:

[0135]

[0136] The solution is:

[0137]

[0138] The corresponding Ennomann boundary conditions are:

[0139]

[0140] According to formula (8), the frequency domain representation of the unwrapped phase value after discrete cosine transform is obtained: Then, through formula (5) Perform an inverse two-dimensional DCT transform to obtain the representation of the unwrapped phase value in the spatial domain φ(r i ,θ j ), that is, the phase diagram P_polar_unwrap after unfolding in the polar coordinate system is obtained.

[0141] Then, the phase map P_polar_unwrap after expansion in the polar coordinate system is transformed from the discrete cosine transform frequency domain to the spatial domain according to the following formula, and the phase map P_cart_unwrap after expansion in the polar coordinate system is obtained:

[0142]

[0143] In this embodiment, the Poisson equation is constructed according to the fringe phase diagram to describe the variation law of the phase field. The Poisson equation is converted to the frequency domain through discrete cosine transform. The periodic jump problem of the phase can be more easily handled in the frequency domain. In the unwrapping calculation process, the phase gradient in the polar direction is mainly considered, rather than the phase gradient in the horizontal and vertical directions. Compared with the method of directly unwrapping the phase in the Cartesian coordinate system, the calculation process is simplified. The Poisson equation in the frequency domain is solved by combining the least squares unwrapping algorithm, and the optimal solution in the least squares sense can be obtained. Not only the accuracy of the phase unwrapping is improved, but also the computational efficiency of the discrete cosine transform is utilized to speed up the unwrapping process.

[0144] The following simulation experiment is used to illustrate the technical effect of the phase unwrapping method provided in the embodiment of the present application. The process of this simulation experiment is as follows: Figure 2 As shown. In this simulation experiment, the operating platform: LAPTOP-24R382DR; processor: Intel(R)Core(TM)i5-10210U CPU@1.60GHz 2.11GHz; software: Matlab. Construct a 256*256 grid point [-127:128, -127:128], and the wrapped phase center is at the center of the grid. Given a wrapped phase information P and the corresponding unwrapped phase as the surface structure of the object, Figure 3 and Figure 4 This simulation experiment uses the least squares unwrapping algorithm based on DCT to unwrap the wrapped phase information ( Figure 4 ) to expand and compare the expanded absolute phase with the surface structure of the real object ( Figure 3 ) to evaluate the performance of the unpacking algorithm.

[0145] like Figure 5-Figure 7 As shown, the wrapped phase P is converted to the polar coordinate system through step 1 to obtain the fringe phase image P_polar ( Figure 5 ), and then the phase unwrapping diagram P_polar_unwrap is obtained by performing unwrapping operation in the polar coordinate system in step 2 ( Figure 6 ). In order to compare the changes of fringe phase images before and after unwrapping, Figure 7 The image after P_polar_unwrap is shown. Finally, the unwrapped phase P_polar_unwrap in the polar coordinate system is converted to the Cartesian coordinate system through step 3 to obtain the absolute phase image P_cart_unwrap after unwrapping. The result is as follows Figure 8As shown. The distance between the absolute phase map P_cart_unwrap obtained by unwrapping and the original surface structure is measured by PSNR (Peak Signal-to-Noise Ratio), SSIM (Structural Similarity Index) and MSE (Mean Squared Error), respectively, and are PSNR=29.0480db, SSIM=0.9715 and MSE=0.0012. Compared with the original surface structure, it can be found that the unwrapping method provided in the embodiment of the present application can effectively unfold the wrapped phase, obtain the absolute phase map, and then restore the surface structure of the object.

[0146] The phase unwrapping method provided in the embodiment of the present application may be executed by a phase unwrapping device. In the embodiment of the present application, the phase unwrapping device performing the phase unwrapping method is taken as an example to illustrate the phase unwrapping device provided in the embodiment of the present application.

[0147] The embodiment of the present application also provides a phase unwrapping device.

[0148] like Fig. 9 As shown, the phase unwrapping device comprises:

[0149] The first conversion module 910 is used to convert the wrapped phase information of the measured object into polar coordinates to obtain a fringe phase image in a polar coordinate system;

[0150] An unwrapping module 920 is used to unwrap the fringe phase image to obtain an unfolded phase image in a polar coordinate system;

[0151] The second conversion module 930 is used to convert the phase image after being unfolded in the polar coordinate system into a Cartesian coordinate system to obtain an unwrapped phase image.

[0152] According to the phase unwrapping device of the present application, the wrapped phase information of the measured object is converted into polar coordinates to obtain a fringe phase image in the polar coordinate system; the fringe phase image is unwrapped and unfolded to obtain the unfolded phase image in the polar coordinate system; the unfolded phase image in the polar coordinate system is converted to a Cartesian coordinate system to obtain the unwrapped phase image. The embodiment of the present application converts the phase unwrapping problem from the Cartesian coordinate system to the polar coordinate system, which can convert the phase jump point into the gradient in the polar direction, reduce the influence of the phase jump on the unwrapping, effectively remove the influence of noise and singular points, and improve the accuracy of the phase unwrapping. In addition, in the unwrapping calculation process, the phase gradient in the polar direction is mainly considered, rather than the phase gradient in the horizontal and vertical directions, which simplifies the calculation process and improves the calculation efficiency of the phase unwrapping.

[0153] In some embodiments, the first conversion module 910 is further configured to:

[0154] Acquire a target signal obtained by measuring the object to be measured;

[0155] According to the signal strength of the target signal, the phase recovery algorithm is used to iteratively calculate the wrapped phase information of the object under test.

[0156] In some embodiments, the first conversion module 910 is further configured to:

[0157] Calculate the polar diameter and angle of each discrete grid point in the wrapped phase information in the polar coordinate system;

[0158] Uniformly sampling each discrete grid point in a preset polar diameter interval and a preset angle interval to obtain a plurality of sampling points; wherein the maximum value of the polar diameter interval is less than or equal to the maximum polar diameter of each discrete grid point in the polar coordinate system;

[0159] The sampling points are interpolated using a preset interpolation algorithm to obtain a fringe phase map that wraps the phase information in a polar coordinate system.

[0160] In some embodiments, the first conversion module 910 is further configured to:

[0161] Determine the number of sampling times, and determine a first sampling step length in the polar radius interval and a second sampling step length in the angle interval;

[0162] Each discrete grid point is uniformly sampled in a preset polar radius interval and a preset angle interval according to the sampling number, the first sampling step length and the second sampling step length.

[0163] In some embodiments, the first conversion module 910 is further configured to:

[0164] Determine the data volume of the sampling points obtained by sampling;

[0165] An interpolation algorithm corresponding to the amount of data is selected to interpolate the sampling points to obtain a fringe phase map containing phase information in a polar coordinate system.

[0166] In some embodiments, the unpacking module 920 is further configured to:

[0167] Construct Poisson's equation based on the fringe phase diagram;

[0168] Perform discrete cosine transform on Poisson's equation to obtain Poisson's equation in discrete cosine transform frequency domain;

[0169] The Poisson equation in the discrete cosine transform frequency domain is solved by combining the least squares unwrapping algorithm, and the frequency domain representation of the unwrapped phase value after discrete cosine transform is obtained;

[0170] The unwrapped phase value is transformed from the discrete cosine transform frequency domain to the spatial domain representation to obtain the phase map after expansion in the polar coordinate system.

[0171] In some embodiments, constructing a Poisson equation based on a fringe phase map includes:

[0172]

[0173] Solve the Poisson equation in the discrete cosine transform frequency domain, and get the unwrapped phase value in the discrete cosine transform frequency domain as:

[0174]

[0175] Among them, φ(r i ,θ j ) represents the representation of the unwrapped phase value in the spatial domain, i = 0, 1…, M-1, j = 0, 1,…, N-1 are the indices in the spatial domain, ρ i,j represents the total differential of the strip phase image gradient, It indicates that the unwrapped phase value is represented in the frequency domain after discrete cosine transform, m = 0, 1..., M-1, n = 0, 1,..., N-1 are the indices of the frequency domain, and the cosine function Sine function is i,j Frequency domain representation after discrete cosine transform.

[0176] The phase unwrapping device in the embodiment of the present application can be an electronic device or a component in the electronic device, such as an integrated circuit or a chip. The electronic device can be a terminal or other devices other than a terminal. Exemplarily, the electronic device can be a mobile phone, a tablet computer, a laptop computer, a PDA, a vehicle-mounted electronic device, a mobile Internet device (Mobile Internet Device, MID), an augmented reality (augmented reality, AR) / virtual reality (virtual reality, VR) device, a robot, a wearable device, an ultra-mobile personal computer (ultra-mobile personal computer, UMPC), a netbook or a personal digital assistant (personal digital assistant, PDA), etc. It can also be a server, a network attached storage (Network Attached Storage, NAS), a personal computer (personal computer, PC), a television (television, TV), a teller machine or a self-service machine, etc., which is not specifically limited in the embodiment of the present application.

[0177] The phase unwrapping device in the embodiment of the present application may be a device having an operating system. The operating system may be a Microsoft (Windows) operating system, an Android (Android) operating system, an IOS operating system, or other possible operating systems, which are not specifically limited in the embodiment of the present application.

[0178] In some embodiments, Fig.10 As shown, an embodiment of the present application also provides an electronic device 1000, including a processor 1001, a memory 1002, and a computer program stored in the memory 1002 and executable on the processor 1001. When the program is executed by the processor 1001, each process of the above-mentioned phase unwrapping method embodiment is implemented, and the same technical effect can be achieved. To avoid repetition, it will not be repeated here.

[0179] It should be noted that the electronic devices in the embodiments of the present application include the above-mentioned mobile electronic devices and non-mobile electronic devices.

[0180] An embodiment of the present application also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the various processes of the above-mentioned phase unwrapping method embodiment are implemented, and the same technical effect can be achieved. To avoid repetition, it will not be repeated here.

[0181] The processor is the processor in the electronic device in the above embodiment. The readable storage medium includes a computer readable storage medium, such as a computer read-only memory ROM, a random access memory RAM, a magnetic disk or an optical disk.

[0182] An embodiment of the present application also provides a computer program product, including a computer program, which implements the above-mentioned phase unwrapping method when executed by a processor.

[0183] The processor is the processor in the electronic device in the above embodiment. The readable storage medium includes a computer readable storage medium, such as a computer read-only memory ROM, a random access memory RAM, a magnetic disk or an optical disk.

[0184] An embodiment of the present application further provides a chip, which includes a processor and a communication interface, wherein the communication interface and the processor are coupled, and the processor is used to run programs or instructions to implement the various processes of the above-mentioned phase unwrapping method embodiment, and can achieve the same technical effect. To avoid repetition, it will not be repeated here.

[0185] It should be understood that the chip mentioned in the embodiments of the present application can also be called a system-level chip, a system chip, a chip system or a system-on-chip chip, etc.

[0186] It should be noted that, in this article, the terms "comprise", "include" or any other variant thereof are intended to cover non-exclusive inclusion, so that the process, method, article or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise one..." do not exclude the presence of other identical elements in the process, method, article or device including the element. In addition, it should be pointed out that the scope of the methods and devices in the embodiments of the present application is not limited to performing functions in the order shown or discussed, and may also include performing functions in a substantially simultaneous manner or in reverse order according to the functions involved, for example, the described method may be performed in an order different from that described, and various steps may also be added, omitted, or combined. In addition, the features described with reference to certain examples may be combined in other examples.

[0187] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a computer software product, which is stored in a storage medium (such as ROM / RAM, a disk, or an optical disk), and includes a number of instructions for a terminal (which can be a mobile phone, a computer, a server, or a network device, etc.) to execute the methods described in each embodiment of the present application.

[0188] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present application, ordinary technicians in this field can also make many forms without departing from the purpose of the present application and the scope of protection of the claims, all of which are within the protection of the present application.

[0189] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "illustrative embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0190] Although the embodiments of the present application have been shown and described, those skilled in the art will appreciate that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present application, and that the scope of the present application is defined by the claims and their equivalents.

Claims

1. A phase unwrapping method, characterized in that: include: The wrapped phase information of the measured object is converted into polar coordinates to obtain a fringe phase image in a polar coordinate system; Unwrapping and unfolding the fringe phase image to obtain an unfolded phase image in a polar coordinate system; The phase diagram after unfolding in the polar coordinate system is converted to the Cartesian coordinate system to obtain the unwrapped phase diagram.

2. The method according to claim 1, characterized in that Before performing polar coordinate conversion on the wrapped phase information of the measured object to obtain a fringe phase image in a polar coordinate system, the following steps are included: Acquire a target signal obtained by measuring the object to be measured; According to the signal strength of the target signal, a phase recovery algorithm is used to iteratively calculate and obtain the wrapped phase information of the object under test.

3. The method according to claim 1, characterized in that The method of performing polar coordinate conversion on the wrapped phase information of the object to be measured to obtain a fringe phase image in a polar coordinate system includes: Calculating the polar diameter and angle of each discrete grid point in the wrapped phase information in a polar coordinate system; Uniformly sampling each discrete grid point in a preset polar diameter interval and a preset angle interval to obtain a plurality of sampling points; wherein the maximum value of the polar diameter interval is less than or equal to the maximum polar diameter of each discrete grid point in the polar coordinate system; The sampling points are interpolated using a preset interpolation algorithm to obtain a fringe phase map of the wrapped phase information in a polar coordinate system.

4. The method according to claim 3, characterized in that The uniform sampling of each discrete grid point in a preset polar radius interval and a preset angle interval respectively comprises: Determine the number of sampling times, and determine a first sampling step length in the polar radius interval and a second sampling step length in the angle interval; Each discrete grid point is uniformly sampled in a preset polar radius interval and a preset angle interval according to the sampling number, the first sampling step length, and the second sampling step length.

5. The method according to claim 3, characterized in that: The method of interpolating the sampling points using a preset interpolation algorithm to obtain a fringe phase diagram of the wrapped phase information in a polar coordinate system includes: Determine the data volume of the sampling points obtained by sampling; An interpolation algorithm corresponding to the data volume is selected to interpolate the sampling points to obtain a fringe phase diagram of the wrapped phase information in a polar coordinate system.

6. The method according to claim 1, characterized in that The step of unwrapping and unfolding the fringe phase image to obtain an unfolded phase image in a polar coordinate system includes: constructing a Poisson equation according to the fringe phase diagram; Perform discrete cosine transform on Poisson's equation to obtain Poisson's equation in discrete cosine transform frequency domain; The Poisson equation in the discrete cosine transform frequency domain is solved by combining the least squares unwrapping algorithm, and the frequency domain representation of the unwrapped phase value after discrete cosine transform is obtained; The unwrapped phase value is transformed from the discrete cosine transform frequency domain to the spatial domain representation to obtain the phase map after expansion in the polar coordinate system.

7. The method according to claim 6, characterized in that The constructing of the Poisson equation according to the fringe phase diagram comprises: Solve the Poisson equation in the discrete cosine transform frequency domain, and get the unwrapped phase value in the discrete cosine transform frequency domain as: Among them, φ(r i ,θ j ) represents the representation of the unwrapped phase value in the spatial domain, i = 0, 1…, M-1, j = 0, 1,…, N-1 are the indices in the spatial domain, ρ i,j represents the total differential of the strip phase image gradient, It indicates that the unwrapped phase value is represented in the frequency domain after discrete cosine transform, m = 0, 1..., M-1, n = 0, 1,..., N-1 are the indices of the frequency domain, is i,j Frequency domain representation after discrete cosine transform.

8. A phase unwrapping device, characterized in that: include: The first conversion module is used to convert the wrapped phase information of the measured object into polar coordinates to obtain a fringe phase image in a polar coordinate system; An unwrapping module, used for unwrapping and unfolding the fringe phase image to obtain an unfolded phase image in a polar coordinate system; The second conversion module is used to convert the phase image after being unfolded in the polar coordinate system into a Cartesian coordinate system to obtain the unwrapped phase image.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 7 is implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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