Multi-distance phase recovery method based on adaptive distance joint optimization

Abstract

The invention discloses a multi-distance phase recovery method based on adaptive distance joint optimization, and the method comprises the steps: collecting a multi-propagation plane diffracted intensity image, determining a first plane reference propagation distance, and carrying out the recursion of the initial propagation distances of other planes; constructing an objective function fusing a data fidelity term and a biregular term, and deriving an analytic gradient and an explicit update step length of an object function and a propagation distance; and alternately updating the object function and the propagation distance, and repeatedly iterating until a preset number of times is reached. According to the method, the propagation distance accuracy is improved through definition evaluation and dynamic updating, and the problem that an existing method depends on a preset interval and easily causes deviation is solved; through collaborative optimization of the object function and the propagation distance, the limitation of separation optimization is avoided, the defects that iteration is prone to local optimum and convergence is slow are overcome, phase recovery precision and processing efficiency are considered, and the applicability to scenes such as biomedical imaging and material detection is enhanced.

Description

Technical Field

[0001] This invention relates to the field of optical imaging technology, and in particular to a multi-distance phase recovery method based on adaptive distance joint optimization. Background Technology

[0002] In optical imaging, phase retrieval technology is a key means to acquire the phase information of an object and achieve high-resolution imaging, and it is widely used in biomedical imaging, materials testing, optical metrology, and other scenarios. Traditional phase retrieval methods mostly rely on diffraction intensity data at a single distance, but the phase information contained in single-distance data is limited, making it difficult to accurately reconstruct the phase distribution of complex objects. Therefore, multi-distance phase retrieval technology has gradually become a research hotspot. This technology acquires diffraction intensity images of the same target on multiple propagation planes and combines the intensity information at different propagation planes to invert the object's phase. However, in practical applications, the accuracy of the propagation plane interval during the movement of the measuring device and the synergistic optimization effect of the object function and propagation distance directly affect the accuracy of phase retrieval. There is an urgent need for a phase retrieval method that can adaptively handle the propagation distance and achieve multi-parameter joint optimization to meet the accuracy requirements of complex imaging scenarios.

[0003] Existing multi-distance phase retrieval techniques have two significant drawbacks: First, most methods rely solely on preset intervals of the measuring equipment to calculate the propagation distance for each propagation plane, without considering the impact of equipment movement errors or environmental interference on the accuracy of the propagation distance. This leads to discrepancies between the estimated and actual propagation distance values, thereby reducing the matching degree between the diffraction calculation results and the actual intensity data, and affecting the accuracy of phase retrieval. Second, existing methods often separate the optimization process of the object function from that of the propagation distance. They first fix the propagation distance to optimize the object function, and then adjust the propagation distance based on the fixed object function. They fail to construct an optimization framework that coordinates the two, making it impossible to achieve synchronous optimization of the two key parameters. This results in slow convergence speed of the iterative process and a tendency to get trapped in local optima, making it difficult to balance imaging accuracy and iterative efficiency. Summary of the Invention

[0004] To overcome the shortcomings and deficiencies of existing technologies, this invention provides a multi-distance phase recovery method based on adaptive distance joint optimization.

[0005] The technical solution adopted in this invention is a multi-range phase recovery method based on adaptive distance joint optimization, comprising the following steps: S1, acquiring diffraction intensity images of the same target on multiple propagation planes, recording the interval between each plane, selecting the first plane from the acquired propagation planes as the focusing object, performing backpropagation on the diffraction intensity image of the selected plane, and determining the reference propagation distance corresponding to the plane through a sharpness evaluation process; S2, based on the fixed interval characteristics of the measuring device during movement, using the reference propagation distance of the first plane obtained in S1 as a basis, obtaining the initial propagation distances of the remaining propagation planes through recursive calculation, so that each propagation plane obtains a corresponding preliminary propagation distance estimate; S3, constructing a data fidelity and prior regularization objective function that simultaneously constrains the object function and the propagation distances of each propagation plane, the objective function fusing data fidelity and prior regularization. S4: Under the objective function framework constructed in S3, derive the analytical gradients corresponding to the object function and the propagation distance of each propagation plane, and determine the explicit update step size of the object function and the propagation distance based on the analytical gradients. S5: Fix the propagation distance of each propagation plane, and perform an update operation on the object function according to the analytical gradients and explicit update step size obtained in S4. After the object function is updated, fix the updated object function, and then perform an update operation on the propagation distance of each propagation plane one by one according to the analytical gradients and explicit update step size. S6: Repeat the alternating update process of the object function and the propagation distance in S5. After each round of update, continue the next round of iteration according to the preset iteration order until the number of iterations reaches the preset maximum number of iterations and then stop the iteration process.

[0006] Furthermore, the process of obtaining the initial propagation distance of each of the remaining propagation planes through recursive calculation in S2 adopts the following formula: ,in, This represents the initial propagation distance of the nth propagation plane. Indicates the reference propagation distance of the first propagation plane. This represents the fixed interval between two adjacent propagation planes, where n represents the index of the propagation plane and N represents the total number of propagation planes.

[0007] Furthermore, the process of constructing the data fidelity and prior regularization objective function in S3 adopts the following formula: Where O represents the object function, This represents the actual propagation distance of the nth propagation plane, where N represents the total number of propagation planes. This represents the diffraction calculation result of the object function O at the propagation distance in the nth propagation plane. This represents the diffraction intensity image of the nth propagation plane. and Both represent regularization parameters, and DO represents the gradient of the object function O. This represents the initial propagation distance of the nth propagation plane. Denotes the square of the L2 norm. This represents the L1 norm.

[0008] Furthermore, in S4, when deriving the analytical gradient of the object function, the following formula is used to describe the relationship between the gradient and the object function: ,in, Let N represent the gradient of the objective function with respect to the object function O, and let N represent the total number of propagation planes. express The conjugate operator, This represents the diffraction calculation result of the object function O at the propagation distance in the nth propagation plane. This represents the diffraction intensity image of the nth propagation plane. The regularization parameter is represented by DO, and the gradient of the object function O is represented by DO. This represents the L1 norm.

[0009] Furthermore, in S4, the analytical gradient of the propagation distance is derived using the following formula: ,in, This represents the distance the objective function propagates across the nth propagation plane. The gradient, where N represents the total number of propagation planes. To take the real part of a complex number, This represents the diffraction calculation result of the object function O at the propagation distance in the nth propagation plane. This represents the diffraction intensity image of the nth propagation plane. express right gradient, Represents the regularization parameter. This represents the initial propagation distance of the nth propagation plane.

[0010] Furthermore, when updating the object function in S5, the following formula is used: ,in, The function representing the updated object. Let k represent the object function before the update, and k represent the number of iterations. The parameter represents the step size for updating the object function. The objective function represents the function of the object before the update. The gradient; when updating the propagation distance, the following formula is used: ,in, This represents the propagation distance of the nth propagation plane after the update. This represents the propagation distance of the nth propagation plane before the update, and k represents the number of iterations. The step size parameter represents the distance update step size. This represents the distance the objective function propagates over the nth propagation plane before the update. The gradient.

[0011] Further, S2 includes the following sub-steps: S21, determining the fixed interval between two adjacent propagation planes during the movement of the measuring device, the fixed interval being a characteristic parameter of the measuring device itself, which remains unchanged during the acquisition of diffraction intensity images; S22, extracting the reference propagation distance of the first propagation plane obtained in S1, and using the reference propagation distance as the initial input value for the recursive operation; S23, taking values ​​for the index n of the propagation plane starting from 2, until the total number of propagation planes N is reached, and for each index n, adding the reference propagation distance of the first propagation plane to (n-1) times the fixed interval to obtain the initial propagation distance of the propagation plane at the corresponding index n; S24, recording and storing the initial propagation distance corresponding to each propagation plane to form an initial propagation distance set, which is used as a constraint reference in the joint optimization process.

[0012] Further, step S3 includes the following sub-steps: S31, constructing a data fidelity term, which is obtained by calculating the square of the L2 norm between the square root of the diffraction calculation result under each propagation plane and the square root of the diffraction intensity image of the corresponding plane, and averaging the calculation results of all propagation planes, to ensure the consistency between the diffraction calculation results and the actual acquired intensity data; S32, constructing an object function prior regularization term, which is obtained by taking the L1 norm of the gradient of the object function and multiplying it by the regularization parameter α1, to constrain the smoothness of the object function; S33, constructing a propagation distance prior regularization term, which is obtained by calculating the square of the L2 norm of the difference between the actual propagation distance and the initial propagation distance under each propagation plane and multiplying it by the regularization parameter α2, to constrain the propagation distance to near the initial estimate; S34, adding the data fidelity term constructed in S31, the object function prior regularization term constructed in S32, and the propagation distance prior regularization term constructed in S33 to form a complete data fidelity and prior regularization objective function.

[0013] Further, step S4 includes the following sub-steps: S41, for the constructed target function, treating the propagation distance as a fixed value, performing differentiation on the object function, and combining the relationship between the diffraction calculation results and the intensity image, as well as the regularization constraint of the object function gradient, to derive the analytical gradient expression of the target function with respect to the object function; S42, based on the derived analytical gradient expression of the object function, and considering the convergence characteristic requirements of the object function during iteration, determining the explicit update step size when updating the object function, which must satisfy the requirement that the object function can be stably updated during iteration; S43, treating the object function as a fixed value, performing differentiation on the propagation distance of each propagation plane, considering the relationship between the diffraction calculation results and the propagation distance, as well as the constraint relationship between the propagation distance and the initial propagation distance, to derive the analytical gradient expression of the target function with respect to the propagation distance of each propagation plane; S44, based on the analytical gradient expression of the propagation distance of each propagation plane, and considering the stability requirements during the propagation distance update process, determining the explicit update step size when updating the propagation distance of each propagation plane, to ensure the smoothness of the propagation distance update process.

[0014] Further, step S5 includes the following sub-steps: S51, extracting the propagation distance values ​​of each propagation plane from the current state of the iteration process, fixing the propagation distance values ​​and not changing them, providing a stable propagation distance condition for updating the object function; S52, calling the analytical gradient and explicit update step size of the object function obtained in S4, calculating the object function based on the current object function value according to the analytical gradient direction and explicit update step size, and obtaining the updated object function value; S53, fixing the updated object function value in S52 and not changing it, providing a stable object function condition for updating the propagation distance; S54, according to the index order of the propagation planes, sequentially calling the analytical gradient and explicit update step size of the propagation distance of the corresponding propagation plane obtained in S4, calculating the propagation distance of each propagation plane based on the current propagation distance values ​​of each propagation plane, and obtaining the updated propagation distance value of each propagation plane.

[0015] Beneficial Effects: This invention proposes a multi-distance phase retrieval method based on adaptive distance joint optimization, which effectively improves phase retrieval accuracy and iteration efficiency, while enhancing the applicability of the technology in practical scenarios. The method first determines the reference propagation distance of the first propagation plane through sharpness evaluation, then recursively calculates the initial propagation distance by combining the device's fixed intervals. Subsequently, the propagation distance is continuously updated through a joint optimization framework, dynamically correcting propagation distance deviations to ensure a high degree of matching between the estimated and actual propagation distance values, thus improving the consistency between diffraction calculation results and actual intensity data. The method constructs an objective function that integrates data fidelity terms and double regularization terms, derives their analytical gradients, and determines the explicit update step size. Through alternating updates, it achieves synergistic optimization of the object function and propagation distance, avoiding iteration getting trapped in local optima, accelerating convergence speed, balancing imaging accuracy and iteration efficiency, and meeting the technical requirements of complex imaging scenarios. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the overall steps of the method of the present invention; Figure 2 This is a flowchart of method step S2 of the present invention; Figure 3 This is a flowchart of method step S3 of the present invention; Figure 4 This is a flowchart of method step S4 of the present invention; Figure 5 This is a flowchart of step S5 of the method of the present invention. Detailed Implementation

[0017] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] like Figure 1 As shown, a multi-range phase retrieval method based on adaptive distance joint optimization includes the following steps: S1. Acquire diffraction intensity images of the same target on multiple propagation planes, record the interval between each plane, select the first plane from the acquired propagation planes as the focusing object, perform backpropagation operation on the diffraction intensity image of the selected plane, and determine the reference propagation distance corresponding to the plane through the sharpness evaluation process. Specifically, the implementation process of step S1 is as follows: First, using an image acquisition device with a resolution of no less than 1024×1024 pixels and a frame rate of no less than 30 frames / second, diffraction intensity images of the same target on 10-20 propagation planes are acquired. During the acquisition process, the fluctuation range of ambient light intensity is controlled to be no more than ±5% to ensure the stability of the intensity data; the interval between each adjacent propagation plane is recorded, with the interval value set to 5-15 mm, and calibrated using a laser rangefinder to ensure that the interval error does not exceed ±0.1 mm; from the acquired multiple propagation planes, randomly select or select based on the characteristics of the target imaging area. The first plane is selected as the focusing object. The diffraction intensity image of the selected plane is processed using the backpropagation algorithm. During the backpropagation process, the propagation step size is set to 0.5-2 mm. At the same time, the sharpness of the processing result is evaluated by the gradient sharpness evaluation function. The calculation window size of the evaluation function is set to 32×32 pixels. The local sharpness value of the image is calculated by sliding window. The propagation distance corresponding to the maximum sharpness value is selected as the reference propagation distance for that plane. The measurement accuracy of the reference propagation distance is controlled within ±0.05 mm, providing a reliable initial basis for subsequent propagation distance calculation.

[0019] S2, based on the fixed interval characteristics when the measuring device moves, takes the reference propagation distance of the first plane obtained in S1 as the basis, and obtains the initial propagation distance of each of the remaining propagation planes through recursive calculation, so that each propagation plane obtains the corresponding preliminary propagation distance estimate. Specifically, the implementation process of step S2 is as follows: Based on the fixed interval between adjacent propagation planes during the movement of the measuring equipment, this fixed interval is determined through equipment mechanical structure calibration and remains unchanged throughout the imaging process. The value is typically set to 8 mm, with an error controlled within ±0.08 mm. Using the reference propagation distance of the first plane obtained in S1 as a basis, which is typically in the range of 50-150 mm, the initial propagation distances of the remaining propagation planes are obtained through linear recursive calculation. During the recursive process, the calculations are performed sequentially according to the propagation plane's sequence number. For example, if the first plane's sequence number is 1, the reference propagation distance is calculated as follows: The initial propagation distance is 80 mm for the first plane. The second plane is numbered 2, and its initial propagation distance is 80 mm plus a fixed interval of 8 mm, which is 88 mm. The third plane is numbered 3, and its initial propagation distance is 80 mm plus a fixed interval of 8 mm, which is 96 mm. This process continues until the initial propagation distances of all propagation planes (usually 10-20) are calculated. After each initial propagation distance is calculated, it is stored in the data cache module in binary format for easy retrieval later. This ensures that each propagation plane obtains a corresponding preliminary propagation distance estimate, laying the foundation for joint optimization.

[0020] S3, construct a data fidelity and prior regularization objective function that simultaneously constrains the object function and the propagation distance of each propagation plane. This objective function integrates the data fidelity term, the object function prior regularization term, and the propagation distance prior regularization term to jointly constrain the object function and the propagation distance. Specifically, the implementation process of step S3 is as follows: First, a data fidelity term is constructed. This term is achieved by calculating the deviation between the diffraction calculation results and the corresponding diffraction intensity image under each propagation plane. Specifically, the squared L2 norm is used as the deviation metric, and the arithmetic mean of the deviation values ​​for all propagation planes is taken. The weighting coefficients in the average calculation are all set to 1 to ensure equal importance of the data from each propagation plane. Next, a prior regularization term for the object function is constructed. This term uses the L1 norm to constrain the gradient of the object function. The constraint strength is controlled by introducing a regularization parameter, which ranges from 0.01 to 0.1 and can be adjusted based on the edge features of the target object. The more pronounced the edge features, the larger the parameter value. Then, a propagation distance prior regularization term is constructed. This term uses the L2 norm squared to constrain the difference between the propagation distance and the initial propagation distance. A regularization parameter is also introduced, ranging from 0.1 to 1.0; a larger parameter value is selected when the propagation distance fluctuates significantly. Finally, the data fidelity term, the object function prior regularization term, and the propagation distance prior regularization term are added together with a weight ratio of 1:0.5:0.5. This weight ratio can be fine-tuned according to actual imaging accuracy requirements, forming a complete data fidelity and prior regularization objective function. This achieves coordinated constraints on the object function and propagation distance, ensuring that the optimization process balances data consistency and parameter rationality.

[0021] S4, within the objective function framework constructed in S3, derive the analytical gradients corresponding to the object function and the propagation distance of each propagation plane, and determine the explicit update step size of the object function and the propagation distance based on the analytical gradients; Specifically, the implementation process of step S4 is as follows: Under the objective function framework constructed in S3, the propagation distance of each propagation plane is first fixed and treated as a constant. Partial derivatives of the object function are calculated. During the partial derivative calculation, the physical model of diffraction calculation needs to be considered, taking into account the influence of light propagation characteristics on the diffraction results. Simultaneously, the derivative of the regularization constraint term of the object function gradient is incorporated. Through the chain rule, the analytical gradient expression of the objective function with respect to the object function is derived step by step, ultimately yielding the analytical gradient expression of the objective function with respect to the object function. Based on the analytical gradient expression and the convergence condition of the object function during iteration (set as the norm of the difference between two adjacent iterations of the object function is less than 1 × 10^-5), the explicit update step size of the object function is determined. The step size ranges from 0.001 to 0.01. A step size that is too large will cause iteration oscillations, while a step size that is too small will... The convergence is slow, and the optimal value needs to be determined through preliminary experiments. Then, the object function is fixed and treated as a constant. The partial derivatives are calculated for the propagation distance of each propagation plane. During the calculation, the sensitivity of the diffraction calculation results to the change of propagation distance is analyzed. The sensitivity is measured by the magnitude of the absolute value of the derivative. At the same time, combined with the derivative of the regularization constraint term of the difference between the propagation distance and the initial propagation distance, the analytical gradient expression of the objective function with respect to the propagation distance of each propagation plane is derived. Based on the analytical gradient expression of the propagation distance of each propagation plane, and combined with the stability requirement of the propagation distance update (the stability requirement is that the propagation distance update amplitude does not exceed 5% of the initial propagation distance), the explicit update step size of the propagation distance of each propagation plane is determined. The step size ranges from 0.01 to 0.1 to ensure a smooth update process.

[0022] S5. Fix the propagation distance of each propagation plane, and perform an update operation on the object function according to the analytical gradient and explicit update step size obtained in S4. After the object function is updated, fix the updated object function, and then perform an update operation on the propagation distance of each propagation plane one by one according to the analytical gradient and explicit update step size. Specifically, the implementation process of step S5 is as follows: First, retrieve the current propagation distance values ​​of each propagation plane from the data storage module, lock these values, and keep them unchanged during the object function update process. The locking method is achieved by setting the read-only attribute of the parameters in the software program. Then, call the analytical gradient of the object function and the explicit update step size obtained in S4. Based on the object function value of the current iteration, perform an update operation on the object function according to the calculation method of "current object function value minus the product of step size and analytical gradient". 64-bit floating-point numbers are used for calculation during the update process to avoid loss of numerical precision. After the object function update is completed, the updated object function values ​​are... Locking is also set to read-only to provide stable conditions for propagation distance updates. Then, according to the propagation plane index from 1 to N, the analytical gradient and explicit update step size of the propagation distance of the corresponding propagation plane obtained in S4 are retrieved in turn. Based on the current propagation distance values ​​of each propagation plane, the propagation distance of each propagation plane is updated one by one using a calculation method similar to the object function update: "current propagation distance value minus the product of step size and analytical gradient". After each propagation plane is updated, the updated value is stored immediately to overwrite the original data, ensuring that the latest parameters are used in the next iteration, thus realizing the alternating optimization of object function and propagation distance.

[0023] S6 repeats the alternating update process of the object function and propagation distance in S5. After each round of update is completed, the next round of iteration continues according to the preset iteration order until the number of iterations reaches the preset maximum number of iterations and then the iteration process stops.

[0024] Specifically, the implementation process of step S6 is as follows: First, an iteration control module is set in the program. This module includes an iteration counter and an iteration stop judgment unit. The initial value of the iteration counter is set to 0, and the maximum number of iterations is set to 500-1000 times. The specific value is determined according to the target imaging accuracy requirements. The higher the accuracy requirements, the larger the maximum number of iterations is set. The iteration loop is started. Each loop executes the alternating update process of the object function and propagation distance in S5. After each update, the value of the iteration counter is incremented by 1. The iteration stop judgment unit reads the value of the iteration counter in real time and compares it with the preset maximum number of iterations. If the counter value is less than the maximum number of iterations, the next iteration process is continued according to the preset iteration order of "object function update → propagation distance update". In the next iteration, the object function and propagation distance values ​​updated in the previous round are directly called as the initial values. If the counter value reaches the preset maximum number of iterations, the iteration stop command is triggered to stop the iteration process. At the same time, the object function and propagation distance values ​​obtained in the last iteration are stored in the result output module. The output format supports common image and data formats, which is convenient for subsequent phase analysis and imaging applications, ensuring that the entire optimization process is completed in an orderly and efficient manner.

[0025] Preferably, the process of obtaining the initial propagation distance of each of the remaining propagation planes through recursive calculation in S2 adopts the following formula: ,in, This represents the initial propagation distance of the nth propagation plane. Indicates the reference propagation distance of the first propagation plane. This represents the fixed interval between two adjacent propagation planes, where n represents the index of the propagation plane and N represents the total number of propagation planes.

[0026] Specifically, the recursive calculation of the initial propagation distance of the remaining propagation planes in S2 involves first determining the fixed interval between adjacent propagation planes when the measuring equipment moves. This interval needs to be determined through a combination of equipment factory calibration and on-site calibration. During calibration, a laser interferometer is used to ensure that the interval error is controlled within ±0.08 mm. The commonly used fixed interval value is set to 5-15 mm, which is adjusted according to the size of the imaging target and the accuracy of equipment movement. Next, the reference propagation distance of the first plane in S1 is extracted. This reference distance needs to be verified through multiple sharpness evaluations. During verification, the calculation is repeated 3-5 times, and the average value is taken as the final reference value. The reference distance is usually in the range of 50-150 mm. Subsequently, according to the propagation... The initial propagation distance is calculated sequentially based on the plane number, starting from 2 and continuing up to the total number. The total number is set to 10-20 based on the richness of target details. The calculation strictly follows the rule of "first plane reference distance plus (number minus 1) times the fixed interval". After each initial distance is calculated, it must be compared with the preset reasonable range (reference distance ± 20 mm). If it exceeds the range, the accuracy of the interval and reference distance is rechecked. Finally, all initial propagation distances are stored in the data cache module. A check code mechanism is used to ensure data integrity during storage. This process provides a unified and reliable initial distance basis for subsequent joint optimization through standardized recursive logic, avoiding the impact of initial distance deviation on the subsequent optimization accuracy.

[0027] Preferably, the process of constructing the data fidelity and prior regularization objective function in S3 adopts the following formula: Where O represents the object function, This represents the actual propagation distance of the nth propagation plane, where N represents the total number of propagation planes. This represents the diffraction calculation result of the object function O at the propagation distance in the nth propagation plane. This represents the diffraction intensity image of the nth propagation plane. and Both represent regularization parameters, and DO represents the gradient of the object function O. This represents the initial propagation distance of the nth propagation plane. Denotes the square of the L2 norm. This represents the L1 norm.

[0028] Specifically, in the construction of the objective function in S3, the data fidelity term is first constructed. The deviation between the diffraction calculation results and the intensity image at each propagation plane is calculated, using the squared L2 norm as a metric. Before calculation, the diffraction calculation results and the intensity image need to be cropped to the same size. The cropping size is determined based on the effective imaging area of ​​the image, typically 512×512 pixels or 1024×1024 pixels. Then, the arithmetic mean of the deviation values ​​for all propagation planes is taken. During calculation, the weight coefficient is set to 1 to ensure that the data from each plane participates equally. Next, the prior regularization term of the object function is constructed, using the L1 norm to constrain the gradient of the object function. The introduced regularization parameters need to be determined through pre-experiments. In the pre-experiments, 3-5 different parameter values ​​(within the range of 0.01-0.1) are selected respectively. The objective function value is calculated, and the parameters that make the objective function converge the fastest are selected. The parameter values ​​are larger for objects with obvious edge features (such as metal parts) and smaller for objects with soft features (such as biological tissue). Then, a propagation distance prior regularization term is constructed, and the difference between the propagation distance and the initial distance is constrained by the square of the L2 norm. The regularization parameter value ranges from 0.1 to 1.0. For scenarios with large propagation distance fluctuations (such as vibration environments), a parameter value near 1.0 is selected, and for stable environments, a value of 0.1 to 0.5 is selected. Finally, the three terms are added together with a weight ratio of 1:0.5:0.5. The weights can be fine-tuned according to the imaging accuracy requirements, with the fine-tuning range not exceeding ±0.2, to form a complete objective function. Through multi-constraint fusion, the object function and propagation distance are coordinated and controlled to ensure the rationality of the optimization direction.

[0029] Preferably, in step S4, when deriving the analytical gradient of the object function, the following formula is used to describe the relationship between the gradient and the object function: ,in, Let N represent the gradient of the objective function with respect to the object function O, and let N represent the total number of propagation planes. express The conjugate operator, This represents the diffraction calculation result of the object function O at the propagation distance in the nth propagation plane. This represents the diffraction intensity image of the nth propagation plane. The regularization parameter is represented by DO, and the gradient of the object function O is represented by DO. This represents the L1 norm.

[0030] Specifically, in the derivation of the analytical gradient of the object function in S4, the propagation distance of each propagation plane is first fixed and treated as a constant. Before fixing, it is necessary to confirm that the propagation distance has been stored and there are no outliers. The criteria for judging outliers is that the difference from the initial distance exceeds 5%. Then, the partial derivative of the object function is calculated. The calculation needs to be combined with the physical model of light propagation, taking into account parameters such as the wavelength of light and the refractive index of the propagation medium. The wavelength is set according to the imaging light source (e.g., 532 nm for visible light), and the refractive index is determined according to the environmental medium (usually 1.0003 for air). At the same time, the derivative of the gradient regularization constraint term of the object function is incorporated. The derivation is carried out step by step through the chain rule. The correctness of the mathematical logic must be verified at each step in the derivation process to avoid symbol or calculation errors. After obtaining the analytical gradient expression, the explicit update step size is determined by combining it with the convergence condition of the object function. The convergence condition is set as the norm of the difference between two adjacent iterations of the object function being less than 1×10^-5. The step size ranges from 0.001 to 0.01. When determining the step size, an intermediate value (such as 0.005) is first selected for trial iteration. If oscillations occur during iteration, the step size is reduced; if convergence is too slow, the step size is increased until the optimal value is found. The entire process requires gradient verification using mathematical software (such as MATLAB). During verification, the deviation between the numerical gradient and the analytical gradient is compared. If the deviation is less than 1×10^-6, the derivation is considered valid, ensuring that the analytical gradient accurately reflects the changing trend of the objective function with respect to the object function, providing reliable guidance for updating the object function.

[0031] Preferably, the following formula is used when deriving the analytical gradient of the propagation distance in S4: ,in, This represents the distance the objective function propagates across the nth propagation plane. The gradient, where N represents the total number of propagation planes. To take the real part of a complex number, This represents the diffraction calculation result of the object function O at the propagation distance in the nth propagation plane. This represents the diffraction intensity image of the nth propagation plane. express right gradient, Represents the regularization parameter. This represents the initial propagation distance of the nth propagation plane.

[0032] Specifically, in the derivation of the analytical gradient of the propagation distance in S4, the object function is first fixed and treated as a constant. Before fixing, the object function needs to be preliminarily optimized to ensure that the function value has no obvious noise. Noise is judged by calculating the standard deviation of the function value; a standard deviation less than 0.1 is considered acceptable. Next, the partial derivatives of the propagation distance for each propagation plane are calculated. During the calculation, the sensitivity of the diffraction calculation results to the change of propagation distance is analyzed. The sensitivity is measured by the magnitude of the absolute value of the derivative. The larger the absolute value, the more significant the impact of the propagation distance on the diffraction results, which needs to be focused on in subsequent updates. At the same time, the derivative of the regularization constraint term of the difference between the propagation distance and the initial distance is incorporated. The calculation of the derivative of the constraint term must strictly follow the differentiation rule of the square of the L2 norm to avoid omissions. Leakage coefficient; After deriving the analytical gradient expression for the propagation distance of each propagation plane, the explicit update step size is determined based on the stability requirements of the propagation distance update. The stability requirement is that the propagation distance update amplitude does not exceed 5% of the initial distance, and the step size ranges from 0.01 to 0.1. For propagation planes with high sensitivity, a smaller step size (e.g., 0.01-0.03) is selected, and a larger step size (0.05-0.1) is selected for those with low sensitivity. After each gradient expression and step size are determined, they need to be tested with simulated data. During the test, the known propagation distance and object function are input, the gradient and step size are calculated, and the accuracy of the updated propagation distance is verified. An error of less than ±0.05 mm is considered qualified, ensuring that the gradient and step size can stably guide the propagation distance update.

[0033] Preferably, when updating the object function in step S5, the following formula is used: ,in, The function representing the updated object. Let k represent the object function before the update, and k represent the number of iterations. The parameter represents the step size for updating the object function. The objective function represents the function of the object before the update. The gradient; when updating the propagation distance, the following formula is used: ,in, This represents the propagation distance of the nth propagation plane after the update. This represents the propagation distance of the nth propagation plane before the update, and k represents the number of iterations. The step size parameter represents the distance update step size. This represents the distance the objective function propagates over the nth propagation plane before the update. The gradient.

[0034] Specifically, in S5, the update formulas for the object function and propagation distance are applied. When updating the object function, the analytical gradient and explicit update step size obtained in S4 are retrieved first. Before retrieval, the data integrity must be checked; if missing, the formulas must be re-derived. Based on the object function value of the current iteration, the calculation method of "current value minus step size and gradient product" is adopted. 64-bit floating-point precision is used in the calculation to avoid numerical truncation errors. After the calculation is completed, the validity of the updated object function needs to be checked. The check indicators include whether the function value is within a reasonable range (e.g., 0-1000, set according to the target characteristics) and whether there are any abnormal extreme values. If abnormal, the previous value is returned for recalculation. The propagation distance update is then implemented. Similarly, the gradient and step size of the corresponding propagation plane are retrieved and updated using the same calculation method. The update order strictly follows the propagation plane index from 1 to N, and the index order is determined by the records during device acquisition to avoid confusion. After each propagation distance is updated, the original data is stored and overwritten immediately. The storage adopts a real-time backup mechanism to prevent data loss. During the update process, the iteration curve needs to be monitored in real time. The curve is formed by plotting the objective function value after each update. If the curve shows an upward trend, it indicates that there is a problem with the step size or gradient, and the update needs to be paused and the parameters adjusted. Through standardized update formulas and strict quality control, it is ensured that the object function and propagation distance can iterate stably in the optimization direction and gradually approach the optimal solution.

[0035] Preferred, such as Figure 2 As shown, step S2 includes the following sub-steps: S21, determining the fixed interval between two adjacent propagation planes during the movement of the measuring device. This fixed interval is a characteristic parameter of the measuring device itself and remains unchanged during the acquisition of diffraction intensity images; S22, extracting the reference propagation distance of the first propagation plane obtained in S1, and using this reference propagation distance as the initial input value for the recursive operation; S23, taking values ​​for the index n of the propagation plane starting from 2, until the total number of propagation planes N is reached. For each index n, the reference propagation distance of the first propagation plane is added to (n-1) times the fixed interval to obtain the initial propagation distance of the propagation plane at the corresponding index n; S24, recording and storing the initial propagation distance corresponding to each propagation plane to form an initial propagation distance set, which is used as a constraint reference in the joint optimization process.

[0036] Specifically, in the step-by-step implementation of S2, S21 first determines the fixed interval between adjacent propagation planes when the measuring equipment moves. This interval needs to be determined through equipment mechanical structure calibration. During calibration, a high-precision displacement sensor (accuracy 0.001 mm) is used to measure multiple times, and the average of 10 measurement results is taken as the final fixed interval. The value is usually between 5-15 mm. After calibration, it is stored in the equipment parameter library. During the imaging process, this parameter is locked by the program to prevent accidental modification. In S22, the first planar reference propagation distance obtained in S1 is extracted. Before extraction, the validity of the reference distance data needs to be verified. The verification standard is that the deviation of multiple sharpness evaluation results is less than 0.1 mm. After passing the verification, it is used as the initial input value for recursion and stored in the temporary data buffer. In S23, according to the transmission... The propagation plane indexes are calculated sequentially from 2 to the total number (10-20). During the calculation, the fixed interval and the reference distance in the buffer area are called from the parameter library. The program automatically performs the operation of "reference distance plus (index minus 1) times the fixed interval". After the initial propagation distance corresponding to each index is calculated, it is immediately compared with the preset threshold range (reference distance ± 20 mm). If it exceeds the range, an alarm is triggered and the calculation is recalculated. In S24, all qualified initial propagation distances are stored in the database in index order. The storage format adopts a structured data format. Each data includes the index, initial distance value, and calculation timestamp. At the same time, a data check code is generated. During subsequent joint optimization calls, the data integrity is verified by the check code to ensure that accurate initial distance constraint references are provided for joint optimization.

[0037] Preferred, such as Figure 3 As shown, step S3 includes the following sub-steps: S31, constructing a data fidelity term, which is obtained by calculating the square of the L2 norm between the square root of the diffraction calculation result under each propagation plane and the square root of the diffraction intensity image of the corresponding plane, and averaging the calculation results of all propagation planes, to ensure the consistency between the diffraction calculation results and the actual collected intensity data; S32, constructing an object function prior regularization term, which is obtained by taking the L1 norm of the gradient of the object function and multiplying it by the regularization parameter α1, to constrain the smoothness of the object function; S33, constructing a propagation distance prior regularization term, which is obtained by calculating the square of the L2 norm of the difference between the actual propagation distance and the initial propagation distance under each propagation plane and multiplying it by the regularization parameter α2, to constrain the propagation distance to near the initial estimate; S34, adding the data fidelity term constructed in S31, the object function prior regularization term constructed in S32, and the propagation distance prior regularization term constructed in S33 to form a complete data fidelity and prior regularization objective function.

[0038] Specifically, in the step-by-step implementation of S3, when constructing the data fidelity term in S31, the diffraction calculation results and corresponding intensity images of each propagation plane are first obtained. Both types of data are then cropped to the same size, based on the edge detection results of the effective imaging area. Edge detection uses the Canny algorithm (threshold set to 50-150) to determine the effective area. The cropped size is typically 512×512 pixels or 1024×1024 pixels. Then, the L2 norm squared of the square root of each type of data is calculated. The arithmetic mean of the calculation results for all propagation planes is taken. A weighted average method is used for the average calculation, with all weight coefficients set to 1 to ensure equal contribution from each plane. In S32, the prior regularization term of the object function is constructed. First, the gradient of the object function is calculated using the Sob algorithm. The EL operator (with a weight of 1 in both the horizontal and vertical directions) is used, and then the L1 norm of the gradient is taken and multiplied by a regularization parameter (0.01-0.1, determined through preliminary experiments). In the preliminary experiments, five sets of parameter values ​​are selected to calculate the convergence speed of the objective function, and the parameter with the fastest convergence is selected. In S33, a propagation distance prior regularization term is constructed, and the L2 norm square of the difference between the actual propagation distance and the initial propagation distance on each propagation plane is calculated and multiplied by a regularization parameter (0.1-1.0, adjusted according to environmental stability; 0.8-1.0 is used in vibration environments). In S34, the three terms are added together with a weight ratio of 1:0.5:0.5. The weights can be fine-tuned according to the imaging accuracy requirements (fine-tuning range ±0.2). The program automatically integrates them to form a complete objective function, ensuring that the function takes into account both data consistency and parameter constraints.

[0039] Preferred, such as Figure 4 As shown, step S4 includes the following sub-steps: S41, for the constructed target function, treating the propagation distance as a fixed value, performing differentiation on the object function, and combining the relationship between the diffraction calculation results and the intensity image, as well as the regularization constraint of the object function gradient, to derive the analytical gradient expression of the target function with respect to the object function; S42, based on the derived analytical gradient expression of the object function, and considering the convergence characteristic requirements of the object function during iteration, determining the explicit update step size when updating the object function, which must satisfy the requirement that the object function can be stably updated during iteration; S43, treating the object function as a fixed value, performing differentiation on the propagation distance of each propagation plane, considering the relationship between the diffraction calculation results and the propagation distance, as well as the constraint relationship between the propagation distance and the initial propagation distance, to derive the analytical gradient expression of the target function with respect to the propagation distance of each propagation plane; S44, based on the analytical gradient expression of the propagation distance of each propagation plane, and considering the stability requirements during the propagation distance update process, determining the explicit update step size when updating the propagation distance of each propagation plane to ensure the smoothness of the propagation distance update process.

[0040] Specifically, in the step-by-step implementation of S4, when deriving the analytical gradient of the object function in S41, the propagation distance is first fixed (retrieved and locked from the database), and the object function is used as a variable. Combined with the physical model of light propagation (considering a wavelength of 532 nanometers and an air refractive index of 1.0003), the partial derivative with respect to the objective function is calculated. The derivative of the object function gradient regularization constraint term is incorporated into the differentiation process. The derivation is performed step-by-step using the chain rule, and the results of each derivation step are verified using mathematical software (such as MATLAB) to ensure that the symbols and calculations are correct. In S42, the step size of the object function is explicitly updated based on the convergence condition (the norm of the difference between adjacent iterations of the object function is less than 1 × 10⁻⁶). -5 First, select the intermediate value of 0.005 for iterative testing. If the iteration oscillates, decrease the step size (decrease by 0.001 each time). If the convergence is slow, increase the step size (increase by 0.001 each time) until the optimal step size (0.001-0.01) is found. In S43, when deriving the analytical gradient of the propagation distance, fix the object function (lock the current optimized function value), calculate the partial derivative with respect to the propagation distance of each propagation plane, and analyze the sensitivity of the diffraction result with the propagation distance (the larger the absolute value of the derivative, the more sensitive it is). Incorporate the derivative of the distance difference regularization constraint term, and verify the rationality of the gradient expression after derivation. In S44, determine the propagation distance update step size. Based on the stability requirement (the update amplitude does not exceed 5% of the initial distance), take 0.01-0.03 for planes with high sensitivity and 0.05-0.1 for planes with low sensitivity. Test the effectiveness of the step size through simulation data. The test error is considered qualified if it is less than 0.05 mm, ensuring that the step size guides the stable update of the distance.

[0041] Preferred, such as Figure 5 As shown, step S5 includes the following sub-steps: S51, extract the propagation distance values ​​of each propagation plane from the current state of the iteration process, fix the propagation distance values, and no longer change them, so as to provide a stable propagation distance condition for updating the object function; S52, call the analytical gradient and explicit update step size of the object function obtained in S4, and calculate the object function according to the analytical gradient direction and explicit update step size based on the current object function value, so as to obtain the updated object function value; S53, fix the updated object function value in S52, and no longer change it, so as to provide a stable object function condition for updating the propagation distance; S54, according to the index order of the propagation planes, call the analytical gradient and explicit update step size of the propagation distance of the corresponding propagation plane obtained in S4 in sequence, and calculate the propagation distance of each propagation plane based on the current propagation distance value of each propagation plane, so as to obtain the updated propagation distance value of each propagation plane.

[0042] Specifically, the implementation of S5 involves several steps. In S51, when fixing the propagation distance, the current propagation distance values ​​for each plane are retrieved from the database and locked as a read-only attribute to prevent changes during object function updates. The locked state is monitored in real time, and an alarm is triggered if there are any abnormal changes. In S52, when updating the object function, the analytical gradient and step size obtained in S4 are retrieved (read from the buffer and verified). Based on the current object function value, calculations are performed using "current value minus step size × gradient," employing 64-bit floating-point precision to avoid errors. After calculation, the function value (range 0-1000, set according to target characteristics) is checked for any abnormal extreme values ​​(exceeding the limit). If the value is outside the range of ±10%, the previous value is returned. In S53, the updated object function is fixed and also set to read-only to provide stable conditions for distance updates. In S54, when updating the propagation distance, the corresponding gradient and step size are retrieved in the order of index 1 to N, and updated in the same calculation method. Each distance update is stored immediately (overwriting the original data and backing it up). After storage, an update log is generated (including index, new distance value, and update time). During the update process, the objective function iteration curve is plotted in real time. If the curve rises, the update is paused, the step size and gradient are checked and adjusted to ensure that the object function and propagation distance are optimized alternately and orderly.

[0043] A multi-range phase retrieval method based on adaptive distance joint optimization is proposed. In terms of propagation distance processing, it does not rely on fixed preset values, but first determines the initial plane reference distance through sharpness evaluation, and then recursively calculates the initial distance by combining the device interval. It can also be dynamically updated later, which greatly improves the accuracy of propagation distance. In terms of parameter optimization, an objective function that integrates multiple constraints is constructed to achieve synergistic optimization of object function and propagation distance, rather than separate processing. This avoids the limitations of single parameter optimization and allows the two to adapt to each other. At the same time, by deriving analytical gradient and determining explicit update step size, the iteration process is made more stable, which can not only speed up the convergence speed, but also reduce the situation of getting trapped in local optima. It balances phase retrieval accuracy and processing efficiency, and enhances its applicability in complex imaging scenarios.

[0044] This method addresses the shortcomings of existing methods that rely on preset intervals to calculate propagation distance and are susceptible to errors. It first obtains a reliable reference distance in the first plane using sharpness evaluation, then recursively calculates the initial distance, and subsequently continuously corrects the propagation distance through a joint optimization framework to dynamically eliminate deviations, ensuring that the propagation distance matches the actual value and improving the consistency between diffraction calculation results and intensity data. To address the problem of existing methods separating object function and propagation distance optimization and making synchronization difficult, this method constructs an objective function containing data fidelity terms and double regularization terms, derives their analytical gradients and determines the update step size, and achieves collaborative optimization of the two through alternating updates. This avoids iterative limitations, accelerates convergence speed, and ensures imaging accuracy, meeting the technical requirements of practical applications.

[0045] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," "link," and "fix" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0046] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various equivalent changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-range phase retrieval method based on adaptive distance joint optimization, characterized in that, Includes the following steps: S1. Acquire diffraction intensity images of the same target on multiple propagation planes, record the intervals between each plane, select the first plane from the acquired propagation planes as the focusing object, perform backpropagation on the diffraction intensity image of the selected plane, and determine the reference propagation distance corresponding to the plane through a sharpness evaluation process; S2. Based on the fixed interval characteristics of the measuring device during movement, use the reference propagation distance of the first plane obtained in S1 as a basis, and obtain the initial propagation distances of the remaining propagation planes through recursive calculation, so that each propagation plane obtains a corresponding preliminary propagation distance estimate; S3. Construct a data fidelity and prior regularization objective function that simultaneously constrains the object function and the propagation distances of each propagation plane. This objective function integrates the data fidelity term, the object function prior regularization term, and the propagation distance prior regularization term. S3. Constrain the object function and propagation distance together. S4. Within the objective function framework constructed in S3, derive the analytical gradients corresponding to the object function and the propagation distance of each propagation plane, and determine the explicit update step size for each object function and propagation distance based on the analytical gradients. S5. Fix the propagation distance of each propagation plane, and perform an update operation on the object function according to the analytical gradients and explicit update step sizes obtained in S4. After completing the object function update, fix the updated object function, and then perform update operations on the propagation distance of each propagation plane one by one according to the analytical gradients and explicit update step sizes. S6. Repeat the alternating update process of the object function and propagation distance in S5. After each round of update, continue the next round of iteration according to the preset iteration order until the number of iterations reaches the preset maximum number of iterations, at which point the iteration process stops.

2. The multi-range phase retrieval method based on adaptive distance joint optimization according to claim 1, characterized in that, The process of obtaining the initial propagation distance of each of the remaining propagation planes through recursive calculation in S2 uses the following formula: ,in, This represents the initial propagation distance of the nth propagation plane. Indicates the reference propagation distance of the first propagation plane. This represents the fixed interval between two adjacent propagation planes, where n represents the index of the propagation plane and N represents the total number of propagation planes.

3. The multi-range phase retrieval method based on adaptive distance joint optimization according to claim 1, characterized in that, The process of constructing the data fidelity and prior regularization objective function in S3 uses the following formula: Where O represents the object function, This represents the actual propagation distance of the nth propagation plane, where N represents the total number of propagation planes. This represents the diffraction calculation result of the object function O at the propagation distance in the nth propagation plane. This represents the diffraction intensity image of the nth propagation plane. and Both represent regularization parameters, and DO represents the gradient of the object function O. This represents the initial propagation distance of the nth propagation plane. Denotes the square of the L2 norm. This represents the L1 norm.

4. The multi-range phase retrieval method based on adaptive distance joint optimization according to claim 1, characterized in that, In S4, when deriving the analytical gradient of the object function, the following formula is used to describe the relationship between the gradient and the object function: ,in, Let N represent the gradient of the objective function with respect to the object function O, and let N represent the total number of propagation planes. express The conjugate operator, This represents the diffraction calculation result of the object function O at the propagation distance in the nth propagation plane. This represents the diffraction intensity image of the nth propagation plane. The regularization parameter is represented by DO, and the gradient of the object function O is represented by DO. This represents the L1 norm.

5. The multi-range phase retrieval method based on adaptive distance joint optimization according to claim 1, characterized in that, The following formula is used when deriving the analytical gradient of the propagation distance in S4: ,in, This represents the distance the objective function propagates across the nth propagation plane. The gradient, where N represents the total number of propagation planes. To take the real part of a complex number, This represents the diffraction calculation result of the object function O at the propagation distance in the nth propagation plane. This represents the diffraction intensity image of the nth propagation plane. express right gradient, Represents the regularization parameter. This represents the initial propagation distance of the nth propagation plane.

6. The multi-range phase retrieval method based on adaptive distance joint optimization according to claim 1, characterized in that, When updating the object function in S5, the following formula is used: ,in, The function representing the updated object. Let k represent the object function before the update, and k represent the number of iterations. The parameter represents the step size for updating the object function. The objective function represents the function of the object before the update. The gradient; when updating the propagation distance, the following formula is used: ,in, This represents the propagation distance of the updated nth propagation plane. This represents the propagation distance of the nth propagation plane before the update, and k represents the number of iterations. The step size parameter represents the distance update step size. This represents the distance the objective function propagates over the nth propagation plane before the update. The gradient.

7. The multi-range phase retrieval method based on adaptive distance joint optimization according to claim 1, characterized in that, S2 includes the following sub-steps: S21, determining the fixed interval between two adjacent propagation planes during the movement of the measuring device. This fixed interval is a characteristic parameter of the measuring device itself and remains unchanged during the acquisition of diffraction intensity images; S22, extracting the reference propagation distance of the first propagation plane obtained in S1, and using this reference propagation distance as the initial input value for the recursive calculation. S23, take values ​​for the propagation plane index n starting from 2, until the total number of propagation planes N is reached. For each index n, add the reference propagation distance of the first propagation plane to a fixed interval of (n-1) times to obtain the initial propagation distance of the propagation plane at the corresponding index n. S24, record and store the initial propagation distance corresponding to each propagation plane to form an initial propagation distance set, which is used as a constraint reference in the joint optimization process.

8. The multi-range phase retrieval method based on adaptive distance joint optimization according to claim 1, characterized in that, S3 includes the following sub-steps: S31, constructing a data fidelity term, which is obtained by calculating the square of the L2 norm between the square root of the diffraction calculation result under each propagation plane and the square root of the diffraction intensity image of the corresponding plane, and averaging the calculation results of all propagation planes, to ensure the consistency between the diffraction calculation results and the actual acquired intensity data; S32, constructing an object function prior regularization term, which is obtained by taking the L1 norm of the gradient of the object function and multiplying it by the regularization parameter α1, to constrain the smoothness of the object function; S33, constructing a propagation distance prior regularization term, which is obtained by calculating the square of the L2 norm of the difference between the actual propagation distance and the initial propagation distance under each propagation plane and multiplying it by the regularization parameter α2, to constrain the propagation distance to near the initial estimate; S34, adding the data fidelity term constructed in S31, the object function prior regularization term constructed in S32, and the propagation distance prior regularization term constructed in S33 to form a complete data fidelity and prior regularization objective function.

9. The multi-range phase retrieval method based on adaptive distance joint optimization according to claim 1, characterized in that, S4 includes the following sub-steps: S41, for the constructed target function, the propagation distance is regarded as a fixed value, and the derivative operation of the object function is performed. In the process of derivative operation, the relationship between the diffraction calculation result and the intensity image, as well as the regularization constraint of the gradient of the object function, are combined to derive the analytical gradient expression of the target function with respect to the object function. S42. Based on the derived analytical gradient expression of the object function, and combined with the convergence characteristics requirement of the object function during the iteration process, determine the explicit update step size when updating the object function. This step size must satisfy the requirement that the object function can be updated stably during the iteration process. S43. Treating the object function as a fixed value, perform derivative operations on the propagation distance of each propagation plane. During the derivative operation, consider the relationship between the diffraction calculation result and the propagation distance, as well as the constraint relationship between the propagation distance and the initial propagation distance, to derive the analytical gradient expression of the objective function with respect to the propagation distance of each propagation plane. S44. Based on the analytical gradient expression of the propagation distance of each propagation plane, and combined with the stability requirements in the propagation distance update process, determine the explicit update step size when updating the propagation distance of each propagation plane to ensure the smoothness of the propagation distance update process.

10. A multi-range phase retrieval method based on adaptive distance joint optimization according to claim 1, characterized in that, S5 includes the following sub-steps: S51, extract the propagation distance values ​​of each propagation plane from the current state of the iteration process, fix the propagation distance values, and no longer change them, so as to provide a stable propagation distance condition for updating the object function; S52, call the analytical gradient and explicit update step size of the object function obtained in S4, and calculate the object function based on the current object function value according to the analytical gradient direction and explicit update step size to obtain the updated object function value; S53, fix the updated object function value in S52, and no longer change it, so as to provide a stable object function condition for updating the propagation distance; S54, according to the index order of the propagation planes, call the analytical gradient and explicit update step size of the propagation distance of the corresponding propagation plane obtained in S4 in sequence, and calculate the propagation distance of each propagation plane based on the current propagation distance value of each propagation plane to obtain the updated propagation distance value of each propagation plane.

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