Phase difference method wavefront detection method and device combined with image sensor noise suppression
By calculating the noise suppression factor and optimizing the Zernike coefficient using an image sensor noise model, the problems of insufficient phase recovery accuracy and high computational complexity under noise influence in existing technologies are solved, achieving low-complexity and high-precision wavefront detection.
Patent Information
- Application Number
- CN202511237301.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-01
- Publication Date
- 2025-12-12
AI Technical Summary
Existing phase retrieval methods are affected by image sensor noise in optical measurements, resulting in insufficient retrieval accuracy and high computational complexity, making it difficult to meet real-time processing requirements.
The noise suppression factor is calculated using an image sensor noise model, applied to noisy images and optimized, and then the Zernike coefficient is updated using a nonlinear algorithm to recover the wavefront phase.
It achieves improved phase recovery accuracy with lower computational complexity, significantly reduces the root mean square value of the error wavefront, and improves the accuracy of wavefront detection.
Smart Images
Figure CN121120449A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of optical measurement and wavefront detection, and in particular to a phase difference wavefront detection method and apparatus that combines image sensor noise suppression. Background Technology
[0002] Phase retrieval is a technique that reconstructs the wavefront phase by acquiring the light intensity distribution from an image sensor. It is widely used in wavefront detection in astronomical telescopes and optical microscopes.
[0003] Phase retrieval algorithms are mainly divided into two categories: iterative and optimization-based. Iterative algorithms, represented by the Gerchberg-Saxton (GS) algorithm and its improvements, are based on Fourier transform and inverse Fourier transform. They iteratively approach the true wavefront phase by repeatedly traversing between the exit pupil plane and the image plane while applying constraints. Optimization-based algorithms, on the other hand, calculate the image plane image by setting the wavefront phase. Based on the difference between the calculated wavefront phase and the actual image, they construct an objective function and use optimization algorithms such as Newton's descent to minimize the objective function, thereby obtaining an accurate wavefront phase.
[0004] Phase difference method is an important phase recovery method. Its core idea is to acquire intensity images of the same object under different defocus states, combine the point spread function model of the imaging system and the known defocus information, construct an objective function and optimize it to recover the wavefront phase. This method has higher solution accuracy than single-image phase recovery algorithm.
[0005] In actual measurements, the detected light intensity distribution is affected by noise, including image sensor noise and environmental noise. Image sensor noise includes photon shot noise, dark shot noise, readout noise, and quantization noise, which are related to image sensor performance and signal strength, and have a significant impact on the accuracy of phase retrieval. To reduce the influence of noise, researchers have improved algorithms; for example, for phase difference algorithms, regularization methods are used to enhance their robustness to noise.
[0006] However, existing methods still have some shortcomings. While some improved algorithms have increased recovery accuracy, their computational complexity has increased significantly, making it difficult to meet the needs of real-time processing, and there is still room for improvement in recovery accuracy. Therefore, there is an urgent need for a new method that can guarantee high recovery accuracy while having low computational complexity and good generalization ability. Summary of the Invention
[0007] To address the shortcomings of existing technologies, this invention proposes a phase difference method and apparatus for wavefront detection that combines image sensor noise suppression. The method uses an image sensor noise model for theoretical analysis, calculates a noise suppression factor and applies it to the noisy image, and then substitutes the processed image into the objective function for optimization. This approach can ensure low computational complexity while significantly improving the accuracy of wavefront detection.
[0008] The specific technical solution is as follows:
[0009] A phase difference wavefront detection method combining image sensor noise suppression includes the following steps:
[0010] S1: The laser beam passes sequentially through the beam expander and the lens under test, and is received by the image sensor; the image sensor is moved to acquire multiple defocused spot images at different defocus positions.
[0011] S2: Calculate the effective diameter of the pupil area based on the wavelength of the laser, the focal length of the lens under test, and the pixels of the image sensor;
[0012] S3: Establish an exit pupil mask based on the aperture of the lens under test and the effective area diameter of the exit pupil surface;
[0013] S4: Set the Zernike polynomial coefficients, establish the exit pupil phase within the exit pupil mask, and obtain the generalized pupil function;
[0014] S5: Perform a two-dimensional Fourier transform on the generalized pupil function to obtain ideal spot images at different defocus positions;
[0015] S6: Average the intensity of multiple out-of-focus spot images acquired at each out-of-focus position to obtain the average noisy image at that out-of-focus position;
[0016] S7: Based on the average noisy image at each defocus position and the image sensor parameters, calculate the noise suppression factor at each defocus position, apply the noise suppression factor to the corresponding average noisy image, and obtain the corrected noisy image at each defocus position.
[0017] S8: Substitute the ideal spot image and the corrected noisy image at each defocus position into the objective function, optimize through a nonlinear algorithm, repeatedly update the Zernike coefficients and recalculate the ideal image, and finally obtain the restored wavefront phase.
[0018] Furthermore, the expressions for the exit pupil phase and the generalized pupil function are:
[0019]
[0020]
[0021] in, This is the defocus distance. For the first The generalized pupil function corresponding to each defocus position Represent the spatial coordinates of the pupil plane. Indicates the first Xiang Yuanze Nick polynomial, For the corresponding coefficient, Represents the imaginary unit. The exit pupil diameter is a function of the exit pupil diameter. This represents the fourth term of the Zehnek polynomial.
[0022] Furthermore, the formula for calculating the noise suppression factor is as follows:
[0023]
[0024] in, Out-of-focus position The noise suppression factor at that point, where m is the number of out-of-focus positions. Out-of-focus position The average noisy image at that location, Represents the image plane spatial coordinates.
[0025] Furthermore, the expression for the objective function E is:
[0026]
[0027] in, Indicates the out-of-focus position The intensity of the ideal light spot image at that location, Indicates the out-of-focus position The corrected noisy image.
[0028] Furthermore, S8 specifically includes:
[0029] Set up a random Zernike coefficient vector, calculate the objective function and its gradient with respect to the Zernike polynomial coefficients, and optimize the objective function using conjugate gradient descent; during optimization, calculate the search direction based on the gradient. The step size is determined using Armijo search. When the 1-norm of the gradient is less than a set threshold, an accurate wavefront Zernike coefficient vector is output, and the wavefront phase is established accordingly.
[0030] A phase difference wavefront detection device incorporating image sensor noise suppression includes one or more processors for implementing the phase difference wavefront detection method incorporating image sensor noise suppression.
[0031] An electronic device, comprising:
[0032] One or more processors;
[0033] A storage device for storing one or more programs that, when executed by the electronic device, enable the electronic device to implement a phase difference wavefront detection method incorporating image sensor noise suppression.
[0034] The beneficial effects of this invention are:
[0035] This invention theoretically analyzes the noise model of an image sensor, calculates a noise suppression factor and applies it to multiple out-of-focus noisy images, then substitutes the processed images into the objective function for optimization, achieving low computational complexity and significantly improving the accuracy of phase retrieval. Attached Figure Description
[0036] Figure 1 This is a flowchart of the method of the present invention.
[0037] Figure 2 This is a schematic diagram of an optical device according to one embodiment of the present invention. In the figure, 1 is a laser, 2 is a beam expander, 3 is the lens to be tested, and 4 is an image sensor.
[0038] Figure 3 This is an implementation result diagram of one embodiment of the present invention, wherein (a) is a noisy spot image at different defocus positions, (b) is the original wavefront phase, (c) is the error wavefront between the wavefront phase directly recovered from the noisy image and the original wavefront phase, and (d) is the error wavefront between the wavefront phase recovered after processing the noisy image and the original wavefront phase. Detailed Implementation
[0039] The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments. The purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.
[0040] like Figure 1 As shown, the phase difference wavefront detection method of the present invention, which combines image sensor noise suppression, includes the following steps:
[0041] S1: The laser beam emitted by laser 1 passes sequentially through beam expander 2 and lens under test 3, and is received by image sensor 4 (e.g., ...). Figure 2 (As shown); the moving image sensor 4 acquires multiple defocus spot images at different defocus positions.
[0042] S2: Based on the wavelength of the laser Focal length of the lens under test Pixels of an image sensor Calculate the effective diameter of the pupil area.
[0043] ;
[0044] S3: Based on the aperture of the lens to be tested and the effective area diameter of the exit pupil Establish an exit pupil mask;
[0045] S4: Set the Zernike polynomial coefficients, establish the exit pupil phase within the exit pupil mask, and obtain the generalized pupil function;
[0046] Defocus-induced exit pupil phase change The generalized pupil function satisfies the following relationship:
[0047]
[0048]
[0049] in, This is the defocus distance. For the first The generalized pupil function corresponding to each defocus position Represent the spatial coordinates of the pupil plane. Indicates the first Xiang Yuanze Nick polynomial, For the corresponding coefficient, Represents the imaginary unit. The exit pupil diameter is a function of the exit pupil diameter. This represents the fourth term of the Zehnek polynomial.
[0050] S5: Perform a two-dimensional Fourier transform on the generalized pupil function to obtain ideal spot images at different defocus positions.
[0051] The expression for the ideal spot image at the defocus position k is:
[0052]
[0053] in, Indicates the out-of-focus position The intensity of the ideal light spot image at that location, Represents a two-dimensional Fourier transform. Represents the image plane spatial coordinates.
[0054] S6: Average the intensity of multiple out-of-focus spot images acquired at each out-of-focus position to obtain the average noisy image at that out-of-focus position. .
[0055] S7: Based on the average noisy image at each out-of-focus position and the image sensor parameters, calculate the noise suppression factor for each out-of-focus position, and apply the noise suppression factor to the corresponding average noisy image. This yields a corrected, noisy image at each out-of-focus position.
[0056] The corrected noisy image is represented as follows:
[0057]
[0058] in, Indicates the out-of-focus position The noise suppression factor at a given location is calculated as follows:
[0059] For scientific-grade image sensors, under non-low light conditions, their dark shot noise, readout noise, and quantization noise are all much smaller than photon shot noise, and photon shot noise can be approximated by the following normal distribution:
[0060]
[0061] For out-of-focus positions The average of the M noisy images at point M is taken, which further reduces the variance of the noise, as shown below:
[0062]
[0063] Calculate the defocus position The sum of noise of all pixels in the corresponding average image Then the sum satisfies the distribution
[0064]
[0065] With constant light source power and the same exposure time, the sum of all photons is a constant. For different locations, the same distribution applies; for noisy images at different locations, the sum of their pixel intensities also follows the same distribution; therefore, the noise suppression factor is characterized as:
[0066]
[0067] in, Out-of-focus position The noise suppression factor at the point, where m is the number of out-of-focus positions.
[0068] By applying a noise suppression factor to a noisy image, the influence of noise on the objective function can be effectively suppressed, thereby improving the wavefront reconstruction accuracy.
[0069] S8: Compare the ideal image at each out-of-focus position with the corrected noisy image. Substituting the objective function, the Zernike coefficients are repeatedly updated and the ideal image is recalculated through a nonlinear optimization algorithm to obtain the restored wavefront phase at each defocus position.
[0070] The expression for the objective function E is as follows:
[0071]
[0072] The gradient g of the objective function with respect to the Zernike polynomial coefficients satisfies:
[0073]
[0074]
[0075] in, It is a process parameter and has no actual physical meaning;
[0076] The Zernike coefficient vector a is represented as
[0077]
[0078] Set up a random Zernike coefficient vector, compute the objective function, and optimize the objective function using conjugate gradient descent. During the optimization process, based on the analytical gradient... Expression calculation of search direction The step size is determined using Armijo search. The Zernike coefficient vector is updated after each iteration.
[0079]
[0080] When analyzing gradient The 1-norm is less than the threshold At that time, output accurate wavefront Zernike coefficient vector Based on this, the wavefront phase is established.
[0081] Corresponding to the aforementioned embodiments of the phase difference wavefront detection method incorporating image sensor noise suppression, the present invention also provides embodiments of a phase difference wavefront detection device incorporating image sensor noise suppression.
[0082] The phase difference wavefront detection device combined with image sensor noise suppression in this embodiment includes one or more processors for implementing the phase difference wavefront detection method combined with image sensor noise suppression in the above embodiment.
[0083] The phase difference wavefront detection device combining image sensor noise suppression in this embodiment can be applied to any device with data processing capabilities, such as a computer. The device embodiment can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of the device with data processing capabilities reading the corresponding computer program instructions from non-volatile memory into memory and executing them. From a hardware perspective, in addition to the processor, memory, network interface, and non-volatile memory, the device with data processing capabilities in this embodiment may also include other hardware depending on its actual functions; these will not be elaborated further.
[0084] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.
[0085] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without creative effort.
[0086] The following is a specific application embodiment of the method of the present invention to illustrate the technical effects of the method.
[0087] This embodiment verifies the wavefront detection method of the present invention through simulation, firstly including:
[0088] Step 1: Construct a simulation model of the optical system including laser 1, beam expander 2, lens under test 3, and image sensor 4. The laser beam emitted by laser 1 passes sequentially through beam expander 2 and lens under test 3, and is received by image sensor 4. Move image sensor 4 to minimize the light spot and obtain the focal plane position, moving it along the optical axis. Known defocus distance ; Collect data at each out-of-focus position Defocused light spot image.
[0089] Step 2: Based on the wavelength of the laser Focal length of the lens under test Pixels of an image sensor Calculate the effective diameter of the pupil area. .
[0090] Step 3: Based on the aperture of the lens to be tested and the effective area diameter of the exit pupil Create an exit pupil mask, which is a 256×256 matrix. The side length of the mask corresponds to the diameter of the effective area of the exit pupil surface. With the center of the mask as the center, the aperture of the lens to be measured Within a circular region with a diameter of 1, the mask value is 1; in other regions, the value is 0.
[0091] Step 4: Set the Zernike polynomial coefficients, establish the exit pupil phase within the exit pupil mask, and obtain the generalized pupil function.
[0092] In this embodiment, the Zernike coefficient has 36 terms, and the coefficient is a = [0, 0, 0, -0.211, -0.160, -0.109, -0.109, -0.127, -0.016, 0.039, -0.234, 0.191, -0.316, 0.043, -0.415, 0.065, -0.351, 0.356, 0.455, 0.069, -0.371, 0.248, 0.411, 0.256, 0.291, 0.267, 0.190, -0.068, 0.435, 0.319, 0.190, 0.241, 0.416, -0.432, -0.469, -0.487].
[0093] Step 5: Perform a two-dimensional Fourier transform on the generalized pupil function to obtain the ideal light spot intensity maps at the four defocus positions. .
[0094] Because the defocused spot images acquired in the simulated optical system do not contain noise during simulation verification, a noise model needs to be established first.
[0095] Step 6: Establish a noise model based on the image sensor parameters, and repeatedly apply the noise model to the ideal spot image at each defocus position to obtain 30 noisy images at each defocus position; then take the average intensity of the 30 noisy images at each defocus position as the average noisy image at each defocus position.
[0096] Image sensor noise can be added sequentially according to the imaging principle, first by converting image units into photon numbers:
[0097]
[0098] In the formula, Defocus position in units of photon count The intensity of the ideal light spot image at that location, This represents the quantum efficiency of the image sensor at the corresponding wavelength. This indicates the full-well capacity of the image sensor. Let c represent the maximum intensity value of a pixel in all m images, where c is a constant coefficient, satisfying... This is used to characterize the situation where the light intensity is increased as much as possible without overexposure. In this embodiment... , , .
[0099] Photons are received by the sensor target and converted into electrons. The number of electrons after conversion follows this distribution.
[0100]
[0101] in, Defocus position in units of electron count The intensity of the ideal light spot image at that location, This represents the Poisson distribution.
[0102] The noise generated before photons are converted into digital signals includes photon shot noise. Dark shot noise and readout noise , means as follows:
[0103]
[0104]
[0105]
[0106] in, It follows a Gaussian distribution. This represents the mean value of dark shot noise. To read out the standard deviation of the noise. The distribution, mean, and variance of the noise generated by photons until they are converted into digital signals are all related to the performance of the image sensor. Random numbers generated based on the corresponding distribution can be used to characterize the corresponding noise. In this embodiment, the mean of dark shot noise is... Read noise standard deviation .
[0107] Applying the noise model to the ideal spot image at each out-of-focus position, the intensity of the noisy image is obtained using the following formula. :
[0108]
[0109] in, Indicates the number of bits in the image sensor. This indicates rounding.
[0110] The intensity of 30 noisy images at each out-of-focus position is averaged to obtain the averaged noisy image at each out-of-focus position. .
[0111] Step 7: Based on the average noisy image at each out-of-focus position and the image sensor parameters, calculate the noise suppression factor for each out-of-focus position, and apply the noise suppression factor to the corresponding average noisy image. This yields a corrected, noisy image at each out-of-focus position.
[0112] In this embodiment, the noise suppression factor
[0113] Step 8: Randomly generate the initial Zernike polynomial coefficient matrix , Each term is limited to the range [-1, 1]. Based on this, the predicted ideal image at each defocus position is recalculated. The predicted ideal image at each defocus position is then compared with the corrected noisy image. Substitute the objective function, optimize it through a nonlinear optimization algorithm, repeatedly update the Zernike coefficients and recalculate the predicted ideal image until the objective function converges, and obtain the restored wavefront phase.
[0114] In this embodiment, the threshold .
[0115] In this embodiment, the conjugate gradient descent method is used to optimize the objective function. Figure 3 The figure shows the phase recovery result of the method proposed in this invention. As can be seen from the figure, compared with the uncorrected noisy image, the root mean square error of the recovered wavefront is reduced by more than 50%, which proves the effectiveness of this invention in improving the detection accuracy of the phase difference method phase recovery system.
[0116] It will be understood by those skilled in the art that the above descriptions are merely preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.
Claims
1. A phase difference wavefront detection method combining image sensor noise suppression, characterized in that, Includes the following steps: S1: The laser beam passes sequentially through the beam expander and the lens under test, and is received by the image sensor; the image sensor is moved to acquire multiple defocused spot images at different defocus positions. S2: Calculate the effective diameter of the pupil area based on the wavelength of the laser, the focal length of the lens under test, and the pixels of the image sensor; S3: Establish an exit pupil mask based on the aperture of the lens under test and the effective area diameter of the exit pupil surface; S4: Set the Zernike polynomial coefficients, establish the exit pupil phase within the exit pupil mask, and obtain the generalized pupil function; S5: Perform a two-dimensional Fourier transform on the generalized pupil function to obtain ideal spot images at different defocus positions; S6: Average the intensity of multiple out-of-focus spot images acquired at each out-of-focus position to obtain the average noisy image at that out-of-focus position; S7: Based on the average noisy image at each defocus position and the image sensor parameters, calculate the noise suppression factor at each defocus position, apply the noise suppression factor to the corresponding average noisy image, and obtain the corrected noisy image at each defocus position. S8: Substitute the ideal spot image and the corrected noisy image at each defocus position into the objective function, optimize through a nonlinear algorithm, repeatedly update the Zernike coefficients and recalculate the ideal image, and finally obtain the restored wavefront phase.
2. The phase difference wavefront detection method combined with image sensor noise suppression according to claim 1, characterized in that, The expressions for the exit pupil phase and the generalized pupil function are: in, This is the defocus distance. For the first The generalized pupil function corresponding to each defocus position Represent the spatial coordinates of the pupil plane. Indicates the first Xiang Yuanze Nick polynomial, For the corresponding coefficient, Represents the imaginary unit. The exit pupil diameter is a function of the exit pupil diameter. This represents the fourth term of the Zehnek polynomial.
3. The phase difference wavefront detection method combined with image sensor noise suppression according to claim 2, characterized in that, The formula for calculating the noise suppression factor is as follows: in, Out-of-focus position The noise suppression factor at that point, where m is the number of out-of-focus positions. Out-of-focus position The average noisy image at that location, Represents the image plane spatial coordinates.
4. The phase difference wavefront detection method combined with image sensor noise suppression according to claim 3, characterized in that, The expression for the objective function E is: in, Indicates the out-of-focus position The intensity of the ideal light spot image at that location, Indicates the out-of-focus position The corrected noisy image.
5. The phase difference wavefront detection method combined with image sensor noise suppression according to claim 4, characterized in that, S8 specifically includes: Set up a random Zernike coefficient vector, calculate the objective function and its gradient with respect to the Zernike polynomial coefficients, and optimize the objective function using conjugate gradient descent; during optimization, calculate the search direction based on the gradient. Armijo search is used to determine the step size. When the 1-norm of the gradient is less than a set threshold, an accurate wavefront Zernike coefficient vector is output, and the wavefront phase is established accordingly.
6. A phase difference wavefront detection device combining image sensor noise suppression, characterized in that, It includes one or more processors for implementing the phase difference wavefront detection method combined with image sensor noise suppression as described in any one of claims 1 to 5.
7. An electronic device, characterized in that, include: One or more processors; A storage device for storing one or more programs, which, when executed by the electronic device, cause the electronic device to implement the phase difference wavefront detection method combined with image sensor noise suppression as described in any one of claims 1 to 5.