A phase retrieval method for bright-field microscopy based on uniform light intensity
By simplifying the light intensity transmission equation to the Poisson equation and combining angular spectrum theory and gradient acceleration strategy, the error and instability problems of phase recovery of transparent samples are solved, achieving high-precision phase recovery and high-contrast imaging while reducing damage to the samples.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUANGZHOU MINGMEI PHOTOELECTRIC TECH CO LTD
- Filing Date
- 2026-03-12
- Publication Date
- 2026-05-26
AI Technical Summary
Traditional bright-field microscopy techniques have difficulty in effectively recovering the phase information of transparent samples. Existing phase recovery methods suffer from large errors, complex calculations, and instability, especially at large defocus distances where accuracy is insufficient.
The light intensity transmission equation is simplified to a Poisson equation by assuming uniform light intensity. A high-order error compensation model is constructed by combining angular spectrum theory, and a gradient acceleration strategy is introduced to recover the phase through finite difference method and iterative calculation.
It significantly improves the stability and accuracy of phase retrieval, enhances iterative convergence efficiency, improves the applicability and contrast of microscopic imaging, and reduces damage to samples.
Smart Images
Figure CN122085501A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the technical field of phase retrieval in optical measurement, specifically relating to a phase retrieval method for bright-field microscopy based on uniform light intensity. Background Technology
[0002] Traditional bright-field microscopy relies on the optical absorption properties of the sample itself to achieve imaging. However, most samples are transparent with uniform amplitude transmittance, resulting in minimal variation in light intensity. This makes it difficult for intensity-based imaging to reveal subtle features of the sample. To improve imaging results, researchers use staining techniques to increase contrast and achieve clearer images. However, staining agents have certain toxicity and photobleaching issues, which may cause irreversible damage to living cells. Because the thickness or refractive index of transparent samples is spatially non-uniform, when light waves pass through the sample, the amplitude changes very little, while the phase changes significantly. Phase information contains most of the object's information and can reveal important features. Therefore, obtaining the phase information of an object is of great significance in the field of optical imaging.
[0003] Phase detection techniques are mainly divided into interferometric and non-interferometric methods. Interferometric methods, represented by digital holography, can achieve accurate phase reconstruction, but they require sophisticated optical systems, necessitate phase unwrapping, and are computationally complex and prone to errors. In contrast, the Transport of Intensity Equation (TIE), as a non-interferometric phase measurement method, can quickly obtain phase information from intensity images. It has the advantages of simple optical path and no interference required. First derived by Teague in 1982 from the Helmholtz equation under paraxial approximation conditions, it describes the relationship between axial intensity variation and phase. Solving the TIE often simplifies it to the standard Poisson equation by introducing auxiliary functions. Several schemes are currently available: 1. Fast Fourier Transform (FFT) method; 2. Discrete Cosine Transform Method; 3. Iterative method of Poisson equation based on the maximum light intensity assumption; 4. Iterative method of Poisson equation based on positive error compensation model constructed based on angular spectrum theory; Among the above-mentioned solutions, there are errors introduced by auxiliary functions and instability caused by dividing the phase formula by the minimum value of light intensity. At the same time, when the defocus distance is large, the axial differential of light intensity calculated by the finite difference method has high-order errors, resulting in inaccurate phase recovery results. In addition, although the accuracy of phase recovery can be effectively improved by iterative methods, this method sacrifices efficiency for accuracy, which has significant limitations in practical application scenarios. Summary of the Invention
[0004] The purpose of this invention is to address the aforementioned shortcomings in the prior art by providing a phase recovery method for bright-field microscopy based on uniform light intensity, thereby solving the problems of errors caused by auxiliary functions and phase instability caused by dividing by a minimum value.
[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A phase retrieval method for bright-field microscopy based on uniform light intensity includes the following steps: S1. Acquire focused light intensity image, positive defocus image and negative defocus image along the optical axis; S2. Based on the positive and negative defocus images, the finite difference method is used to calculate the axial differential of the light intensity; S3. Introduce uniform light intensity and combine it with the axial differential of light intensity to simplify the light intensity transmission equation into the Poisson equation, and solve the Poisson equation to obtain the initial phase. S4. Based on the initial phase and focused light intensity image, construct a positive higher-order error compensation model for the axial differential of light intensity using angular spectrum theory; S5. Substitute the positive higher-order error compensation model into the initial phase calculation formula in S3 to obtain the phase; S6. Iteratively calculate the phase obtained in S5, repeating steps S4, S5, and S6, and introducing a gradient acceleration strategy during the iteration process until the iteration converges to obtain the final phase result.
[0006] Furthermore, in S2, based on the positive and negative defocus images, the finite difference method is used to calculate the axial differential of the light intensity, which is expressed as: In the formula, To focus the light intensity, Indicates the position along the optical axis. This represents the light intensity value corresponding to the positive defocus image. This represents the light intensity value corresponding to a negative defocus image. These represent the positive and negative defocus distances.
[0007] Furthermore, in S3, a uniform light intensity is introduced and combined with the axial differential of the light intensity, simplifying the light intensity transmission equation to the Poisson equation, which is expressed as: In the formula, For wavelength, For gradient operators, For phase; The initial phase is obtained by solving the Poisson equation; In the formula, For the initial phase, For wave number, For uniform light intensity, its value is 0.51. , This represents the maximum focused light intensity. For the Laplace operator.
[0008] Furthermore, in S4, a positive higher-order error compensation model for the axial differential of light intensity is constructed using angular spectrum theory, which is expressed as: in: In the formula, To measure the difference in light intensity, To construct the intensity difference using angular spectrum theory, The intensity difference constructed using angular spectrum theory when the light intensity is uniform. This represents the light intensity value corresponding to the theoretical defocused light intensity image calculated based on the measured focal plane using angular spectrum theory. This represents the light intensity value corresponding to the negative theoretical defocused light intensity image calculated using angular spectrum theory based on the measured focal plane. This represents the light intensity value corresponding to the theoretical defocused light intensity image calculated using angular spectrum theory under uniform light intensity. This represents the light intensity value corresponding to the negative theoretical defocused light intensity image calculated using angular spectrum theory when the light intensity is uniform.
[0009] Furthermore, the light intensity value corresponding to the theoretical defocused light intensity image is calculated based on the measured focal plane using angular spectrum theory. The light intensity value corresponding to the negative theoretical defocused light intensity image calculated based on the measured focal plane using angular spectrum theory. The light intensity value corresponding to the positive theoretical defocused light intensity image calculated using angular spectrum theory under uniform light intensity. The light intensity value corresponding to the negative theoretical defocused light intensity image calculated using angular spectrum theory under uniform light intensity. They are represented as follows: In the formula, This is the inverse Fourier transform. For Fourier transform, The imaginary unit, The spatial frequency in the x-direction. The spatial frequency is in the y-direction.
[0010] Furthermore, in step S5, the positive higher-order error compensation model is substituted into the initial phase calculation formula in step S3 to obtain the phase, which is expressed as: In the formula, This is the phase after positive higher-order error compensation.
[0011] Furthermore, in step S6, the phase after positive higher-order error compensation... Iterative calculations are performed, with a gradient acceleration strategy introduced during the iteration process, until the iteration converges, yielding the final phase result, which is expressed as: In the formula, The phase result after acceleration, To accelerate parameters, For the gradient direction, This represents the number of iterations.
[0012] Furthermore, the gradient direction Represented as: The acceleration parameters Represented as: In the formula, For the first The phase value after gradient acceleration in the next iteration For the first The phase value after gradient acceleration in the next iteration For the first The step size of the next iteration. For the first The step size of the next iteration.
[0013] Furthermore, the first Step size of the next iteration Represented as: .
[0014] The phase retrieval method for bright-field microscopy based on uniform light intensity provided by this invention has the following beneficial effects: This invention simplifies the light intensity transmission equation to a Poisson equation by assuming uniform light intensity, avoiding errors introduced by auxiliary functions and instability caused by minimum light intensity, thus significantly improving the stability and accuracy of phase recovery. At the same time, it constructs a higher-order axial differential error compensation model by combining angular spectrum theory and introduces a gradient acceleration strategy, which effectively corrects defocusing errors, greatly improves iterative convergence efficiency, and enhances the applicability of the method in practical microscopic imaging scenarios. Attached Figure Description
[0015] Figure 1 This is a flowchart of the phase retrieval method for bright-field microscopy based on uniform light intensity in the embodiments. Figure 1 .
[0016] Figure 2 This is a flowchart of the phase retrieval method for bright-field microscopy based on uniform light intensity in the embodiments. Figure 2 .
[0017] Figure 3 This is a measured light intensity image from the embodiment, wherein, Figure 3 In the image, (a) represents a negative defocus image. Figure 3 (b) in the image represents the focused image. Figure 3 (c) in the image represents a positive defocus image.
[0018] Figure 4 This is the phase recovery result in the example. Detailed Implementation
[0019] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0020] This embodiment of the phase retrieval method for bright-field microscopy based on uniform light intensity simplifies the light intensity transmission equation to a Poisson equation by assuming uniform light intensity. This effectively avoids errors introduced by auxiliary functions and phase instability caused by minimum light intensity. The initial phase is obtained by solving the simplified Poisson equation using the axial differential of light intensity calculated from measured light intensity, providing reliable phase results for subsequent iterations. Furthermore, a high-order error positive compensation model for the axial differential of light intensity, constructed based on angular spectrum propagation theory, improves the accuracy of the axial differential of light intensity at large defocus distances, further enhancing phase accuracy. In addition, a gradient acceleration strategy is introduced to improve the convergence efficiency of phase retrieval iterations and enhance the applicability of the algorithm. (Refer to...) Figure 1 and Figure 2 Specifically, it includes the following: S1. Acquire focused light intensity image, positive defocus image and negative defocus image along the optical axis; S2. Based on the positive and negative defocus images, the axial differential of light intensity is calculated using the finite difference method, which is expressed as: In the formula, To focus the light intensity, Indicates the position along the optical axis. This represents the light intensity value corresponding to the positive defocus image. This represents the light intensity value corresponding to a negative defocus image. These represent the positive and negative defocus distances.
[0021] S3. Introduce uniform light intensity and combine it with the axial differential of light intensity to simplify the light intensity transmission equation into the Poisson equation, and solve the Poisson equation to obtain the initial phase. The expression for the light intensity transmission equation is: In the formula, where λ is the wavelength and k is the wave number. For gradient operators, For phase; gradient operator Represented as: In the formula, ， These are the unit vectors in the x and y directions, respectively.
[0022] When the focused image has uniform light intensity Then, the light intensity transmission equation simplifies to the Poisson equation, which is expressed as: The initial phase is obtained by solving the Poisson equation; In the formula, For the initial phase, For uniform light intensity, its value is 0.51. , This represents the maximum focused light intensity. For the Laplace operator; Among them, calculation is performed using the Fast Fourier Transform. Represented as: In the formula, This is the inverse Fourier transform. For Fourier transform, The spatial frequency in the x-direction. The spatial frequency is in the y-direction.
[0023] S4. Based on the initial phase and focused light intensity image, a positive high-order error compensation model for the axial differential of light intensity is constructed using angular spectrum theory. Specifically, the initial phase obtained by S3 The light intensity value corresponding to the focused light intensity image acquired in S1 A positive higher-order error compensation model for the higher-order error of the axial differential of light intensity is constructed using angular spectrum theory, which is expressed as: in: In the formula, To measure the difference in light intensity, To construct the intensity difference using angular spectrum theory, The intensity difference constructed using angular spectrum theory when the light intensity is uniform. This represents the light intensity value corresponding to the theoretical defocused light intensity image calculated based on the measured focal plane using angular spectrum theory. This represents the light intensity value corresponding to the negative theoretical defocused light intensity image calculated using angular spectrum theory based on the measured focal plane. This represents the light intensity value corresponding to the theoretical defocused light intensity image calculated using angular spectrum theory under uniform light intensity. This represents the light intensity value corresponding to the negative theoretical defocused light intensity image calculated using angular spectrum theory when the light intensity is uniform.
[0024] The light intensity value corresponding to the theoretical defocused light intensity image calculated based on the measured focal plane using angular spectrum theory. The light intensity value corresponding to the negative theoretical defocused light intensity image calculated based on the measured focal plane using angular spectrum theory. The light intensity value corresponding to the positive theoretical defocused light intensity image calculated using angular spectrum theory under uniform light intensity. The light intensity value corresponding to the negative theoretical defocused light intensity image calculated using angular spectrum theory under uniform light intensity. The process of calculating the defocus plane using angular spectrum theory is as follows: In the formula, The imaginary unit; S5. Substitute the positive higher-order error compensation model into the initial phase calculation formula in S3, and solve for the phase, which is expressed as: In the formula, This is the phase after positive higher-order error compensation.
[0025] S6. Iteratively calculate the phase obtained in S5, repeating steps S4, S5, and S6, and introduce a gradient acceleration strategy during the iteration process until the iteration converges to obtain the final phase result. Specifically, for the phase after positive higher-order error compensation Iterative calculations are performed, with a gradient acceleration strategy introduced during the iteration process, until the iteration converges, yielding the final phase result, which is expressed as: In the formula, The phase result after acceleration, To accelerate parameters, For the gradient direction, This represents the number of iterations.
[0026] Furthermore, the gradient direction Represented as: The acceleration parameters Represented as: In the formula, For the first The phase value after gradient acceleration in the next iteration, if When the value is 0, it is the initial phase; otherwise, it is the phase after gradient acceleration iteration. For the first The phase value after gradient acceleration in the next iteration For the first The step size of the next iteration. For the first The step size of the next iteration.
[0027] Among them, the Step size of the next iteration Represented as: The present invention employs methods S1 to S6, which can effectively improve the accuracy of phase recovery and the efficiency of iterative convergence, thereby enhancing the applicability of the proposed method in practical application scenarios.
[0028] refer to Figure 3 and Figure 4 Images acquired under bright field conditions have low contrast and cannot clearly show details. However, after phase recovery using the method of this patent, the image contrast is significantly improved and details are clear. High-contrast observation of microscopic samples such as live cells can be achieved without invasive methods such as fluorescent labeling, reducing the damage of staining agents to samples and the time consumed in staining preparation, while realizing quantitative analysis of samples.
[0029] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.
Claims
1. A phase retrieval method for bright-field microscopy based on uniform light intensity, characterized in that, Includes the following steps: S1. Acquire focused light intensity image, positive defocus image and negative defocus image along the optical axis; S2. Based on the positive and negative defocus images, the finite difference method is used to calculate the axial differential of the light intensity; S3. Introduce uniform light intensity and combine it with the axial differential of light intensity to simplify the light intensity transmission equation into the Poisson equation, and solve the Poisson equation to obtain the initial phase. S4. Based on the initial phase and focused light intensity image, construct a positive higher-order error compensation model for the axial differential of light intensity using angular spectrum theory; S5. Substitute the positive higher-order error compensation model into the initial phase calculation formula in S3 to obtain the phase; S6. Iteratively calculate the phase obtained in S5, repeating steps S4, S5, and S6, and introducing a gradient acceleration strategy during the iteration process until the iteration converges to obtain the final phase result.
2. The phase retrieval method for bright-field microscopy based on uniform light intensity according to claim 1, characterized in that, In S2, based on the positive and negative defocus images, the finite difference method is used to calculate the axial differential of the light intensity, which is expressed as: In the formula, To focus the light intensity, Indicates the position along the optical axis. This represents the light intensity value corresponding to the positive defocus image. This represents the light intensity value corresponding to a negative defocus image. These represent the positive and negative defocus distances.
3. The phase retrieval method for bright-field microscopy based on uniform light intensity according to claim 2, characterized in that, In step S3, a uniform light intensity is introduced, and combined with the axial differential of the light intensity, the light intensity transmission equation is simplified to the Poisson equation, which is expressed as: In the formula, For wavelength, For gradient operators, For phase; The initial phase is obtained by solving the Poisson equation; In the formula, For the initial phase, For wave number, For uniform light intensity, its value is 0.
51. , To focus on the maximum light intensity, This refers to the light intensity value corresponding to the focused light intensity image; For the Laplace operator.
4. The phase retrieval method for bright-field microscopy based on uniform light intensity according to claim 3, characterized in that, In S4, a positive higher-order error compensation model for the axial differential of light intensity is constructed using angular spectrum theory, which is expressed as follows: in: In the formula, To measure the difference in light intensity, To construct the intensity difference using angular spectrum theory, The intensity difference constructed using angular spectrum theory when the light intensity is uniform. This represents the light intensity value corresponding to the theoretical defocused light intensity image calculated based on the measured focal plane using angular spectrum theory. This represents the light intensity value corresponding to the negative theoretical defocused light intensity image calculated using angular spectrum theory based on the measured focal plane. This represents the light intensity value corresponding to the theoretical defocused light intensity image calculated using angular spectrum theory under uniform light intensity. This represents the light intensity value corresponding to the negative theoretical defocused light intensity image calculated using angular spectrum theory when the light intensity is uniform.
5. The phase retrieval method for bright-field microscopy based on uniform light intensity according to claim 4, characterized in that, The light intensity value corresponding to the theoretical defocused light intensity image calculated based on the measured focal plane using angular spectrum theory. The light intensity value corresponding to the negative theoretical defocused light intensity image calculated based on the measured focal plane using angular spectrum theory. The light intensity value corresponding to the positive theoretical defocused light intensity image calculated using angular spectrum theory under uniform light intensity. The light intensity value corresponding to the negative theoretical defocused light intensity image calculated using angular spectrum theory under uniform light intensity. They are represented as follows: In the formula, This is the inverse Fourier transform. For Fourier transform, The imaginary unit, The spatial frequency in the x-direction. The spatial frequency is in the y-direction.
6. The phase retrieval method for bright-field microscopy based on uniform light intensity according to claim 4, characterized in that, In step S5, the positive higher-order error compensation model is substituted into the initial phase calculation formula in step S3 to obtain the phase, which is expressed as: In the formula, This is the phase after positive higher-order error compensation.
7. The phase retrieval method for bright-field microscopy based on uniform light intensity according to claim 1, characterized in that, In step S6, the phase after positive higher-order error compensation... Iterative calculations are performed, with a gradient acceleration strategy introduced during the iteration process, until the iteration converges, yielding the final phase result, which is expressed as: In the formula, The phase result after acceleration, To accelerate parameters, For the gradient direction, This represents the number of iterations.
8. The phase retrieval method for bright-field microscopy based on uniform light intensity according to claim 7, characterized in that, The gradient direction Represented as: The acceleration parameters Represented as: In the formula, For the first The phase value after gradient acceleration in the next iteration For the first The phase value after gradient acceleration in the next iteration For the first The step size of the next iteration. For the first The step size of the next iteration.
9. The phase retrieval method for bright-field microscopy based on uniform light intensity according to claim 8, characterized in that, The first Step size of the next iteration Represented as: 。