A wavefront coding and decoding method based on angular sinusoidal square phase mask

Abstract

The application discloses a wavefront coding and decoding method based on an angular sine square phase mask, and relates to the field of photoelectric imaging. The method comprises the following steps: constructing a phase modulation function, making a phase mask according to the phase modulation function, placing the phase mask on a pupil plane or a conjugate plane of an optical system, and obtaining a modulated pupil function; determining a point spread function based on the modulated pupil function, and performing convolution operation on an original target image to obtain a blurred image; constructing a decoding model according to an optical transfer function, iteratively adjusting a power spectrum ratio in the decoding model, and decoding to obtain a plurality of candidate decoding images; and finally, performing similarity evaluation on the candidate decoding images, and selecting a best image as a clear image for output. The application can effectively avoid the generation of a modulation transfer function zero point, and still can obtain a clear target image under complex illumination conditions such as strong laser interference or backlight, and is suitable for occasions such as anti-laser blinding photoelectric imaging systems and backlight imaging.

Description

Technical Field

[0001] This application relates to the field of optical imaging, and in particular to a wavefront encoding and decoding method based on an angular sinusoidal square phase mask. Background Technology

[0002] In optical imaging systems, high-power laser incident light can easily lead to a high concentration of energy at the focal plane, causing irreversible damage to image sensors such as CMOS, such as pixel breakdown or saturation blurring. To solve this problem, an effective approach is to actively introduce specific phase modulation at the pupil plane. By changing the wavefront phase distribution, the energy of the focal spot is dispersed, reducing the peak power at the focal plane while keeping the total power constant, thereby protecting the sensor.

[0003] Existing wavefront coding techniques often employ vortex phase or cubic phase masks, which can extend depth of field or disperse energy to some extent. However, when defocusing conditions change, the point spread function of traditional vortex wavefront coding often exhibits significant rotation or structural changes, easily leading to directional blurring or accumulation of reconstruction errors during subsequent image reconstruction. More importantly, some wavefront coding methods may cause the modulation transfer function of the optical system to reach zero at specific spatial frequency locations, making it difficult to recover image detail information and severely affecting decoding quality.

[0004] In summary, there is an urgent need for a wavefront coding and decoding method that can suppress the generation of modulation transfer function zeros over a wide spatial frequency range and obtain clear target images under complex lighting conditions such as strong laser interference or backlighting. Summary of the Invention

[0005] The purpose of this application is to provide a wavefront encoding and decoding method based on an angular sinusoidal square phase mask, which can improve the stability of the system in the spatial frequency domain, improve the point spread function structure, and improve the image reconstruction quality.

[0006] To achieve the above objectives, this application provides the following solution: A wavefront encoding and decoding method based on an angular sinusoidal square-phase mask includes: A phase modulation function is constructed based on the angular sinusoidal square phase modulation term and the aberration phase term. Based on the phase modulation function, a phase mask is fabricated; The phase mask is placed on the pupil plane or conjugate plane of the optical system to perform phase modulation on the incident light field and obtain the modulated pupil function. Based on the modulated pupil function, the point spread function of the optical system at the image plane is determined; Based on the point spread function, a convolution operation is performed on the original target image to obtain a blurred image after wavefront coding; Perform a Fourier transform on the point spread function to obtain the optical transfer function; A decoding model is constructed based on the optical transfer function; The power spectral density ratio in the decoding model is iteratively adjusted, and the blurred image is decoded using the adjusted decoding model to obtain multiple candidate decoded images; The similarity of the multiple candidate decoded images is evaluated, and the candidate decoded image with the highest evaluation score is selected as the final clear image output.

[0007] Optionally, the phase modulation function is expressed as: , in, Represents the phase modulation function. This is the angular sinusoidal square phase modulation term. For aberration phase terms; For normalized radial coordinates, Angular coordinates, For topological load number, This represents the corresponding aberration coefficient. This represents the phase distribution of system aberrations.

[0008] Optionally, the expression for the modulated pupil function is: , in, This represents the modulated pupil function. Let be the pupil amplitude function. For phase modulation function, Represents the imaginary unit. This represents the phase modulation function in the exponential part.

[0009] Optionally, the expression for the point spread function is: , in, Represents the point spread function. Indicates Fourier transform, The modulated pupil function, This represents the complex amplitude distribution at the image plane.

[0010] Optionally, the blurred image is: , in, Represents a blurred image. For the original image, The point spread function is... , This represents convolution calculation. This is the noise term.

[0011] Optionally, the expression for the optical transfer function is: , in, Represents the optical transfer function. Indicates Fourier transform, This represents the point spread function.

[0012] Optionally, the expression for the decoding model is: , in, This represents the frequency spectrum of the decoded image. For the target image spectrum, by Obtained by Fourier transform; Represents the spectrum of the target image The conjugate; For the spectrum of the blurred image, by Obtained by Fourier transform; This represents the power spectral density ratio.

[0013] Optionally, the power spectral density ratio in the decoding model is iteratively adjusted, and the adjusted decoding model is used to decode the blurred image to obtain multiple candidate decoded images. This specifically includes the following steps: Set the search range for the power spectral ratio; The power spectral ratio is scanned step by step within the search range; The blurred image is decoded using the decoding model to obtain multiple candidate decoded images.

[0014] Optionally, a similarity evaluation is performed on the plurality of candidate decoded images, and the candidate decoded image with the highest evaluation score is selected as the final clear image output, specifically including the following steps: Calculate the structural similarity index and Pearson correlation coefficient between the multiple candidate decoded images and the original target image; The structural similarity index and Pearson correlation coefficient are weighted and calculated to obtain a comprehensive evaluation score; The candidate decoded image with the highest comprehensive evaluation score is selected from all candidate decoded images as the final clear image output.

[0015] Optionally, one side of the phase mask is a curved surface designed according to the phase modulation function, and the other side is a plane.

[0016] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a wavefront encoding and decoding method based on an angular sinusoidal square-phase mask. By employing angular sinusoidal square-phase modulation, the point spread function maintains a more stable energy distribution over a larger defocus range, effectively reducing the impact of defocus variations on the modulation transfer function, thereby expanding the depth of field. Furthermore, the structural consistency of the point spread function is significantly improved, with a more uniform energy distribution and smoother morphological changes, which enhances the stability of subsequent deconvolution algorithms and reduces the accumulation of reconstruction errors. Simultaneously, it maintains a high modulation transfer function value over a wide spatial frequency range, ensuring both the efficiency of computational imaging reconstruction and reducing sensitivity to processing and assembly errors. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating the wavefront encoding and decoding method based on an angular sinusoidal square phase mask in an embodiment of this application. Figure 2 This is a point distribution diagram of the optical system of the wavefront encoding and decoding method based on the angular sinusoidal square phase mask in the embodiments of this application; Figure 3 This is a schematic diagram of phase mask loading for the wavefront encoding and decoding method based on an angular sinusoidal square phase mask in an embodiment of this application. Figure 4 This is a schematic diagram of the modulation transfer function (MTF) of the wavefront coding and decoding method based on the angular sinusoidal square phase mask in the embodiments of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] like Figure 1As shown, a wavefront encoding and decoding method based on an angular sinusoidal square phase mask is provided, including the following steps: S1: Construct the phase modulation function based on the angular sinusoidal square phase modulation term and the aberration phase term.

[0022] The expression for the phase modulation function is: , in, Represents the phase modulation function. This is the angular sinusoidal square phase modulation term. For aberration phase terms; For normalized radial coordinates, Angular coordinates, For topological load number, This represents the corresponding aberration coefficient. This represents the phase distribution of system aberrations.

[0023] In a specific embodiment, the system aberration phase distribution It can be represented by a set of Zernike polynomials to describe aberrations in practical optical systems. Aberration phase term. It can describe a single aberration or a combination of aberrations. For example, a single spherical aberration can be represented as: The combination of ball difference and coma can be expressed as: ,in For the corresponding aberration coefficients, The wave number is defined as follows: , Indicates wavelength.

[0024] S2: Based on the phase modulation function, fabricate a phase mask.

[0025] In a specific embodiment, by constructing a thickness variation profile on an optical glass substrate using processing techniques, the phase modulation function constructed in S1 above can be converted into a phase mask. For example... Figure 2 The diagram shows the dot plot distribution of the optical system based on the aforementioned phase mask. The theoretical diffraction limit of the optical system corresponds to an Airy disk radius of 4.297 μm. Through ray tracing and dot plot analysis, the actual geometric root mean square (RMS) radius of the diffuse spot in the central field of view is determined to be 6.692 μm. The calculated ratio of the RMS radius to the Airy disk radius is approximately 1.56. In the evaluation system of traditional diffraction-limited optical systems, when this ratio is between 1.0 and 2.0, it indicates that the primary aberrations of the system have been effectively suppressed. It also demonstrates that the phase mask produces the expected controllable modulation effect on the wavefront, intentionally broadening the diffuse spot without causing irreversible collapse of the beam envelope.

[0026] S3: Place the phase mask on the pupil plane or conjugate plane of the optical system to perform phase modulation on the incident light field and obtain the modulated pupil function.

[0027] In a specific embodiment, such as Figure 3 As shown, a phase mask is placed on the pupil plane or conjugate plane of the optical system (such as the aperture stop position) to modulate the incident light field, obtaining the modulated pupil function. The expression for the modulated pupil function is: , in, This represents the modulated pupil function. Let be the pupil amplitude function. For phase modulation function, Represents the imaginary unit. This represents the phase modulation function in the exponential part.

[0028] The imaging characteristics of the system can be controlled through the above step S3.

[0029] S4: Determine the point spread function of the optical system at the image plane based on the modulated pupil function.

[0030] In a specific embodiment, the light field modulated by the phase mask propagates through the optical system and forms a corresponding point spread function (PSF) on the image plane. The point spread function describes the spatial response characteristics of the system to a point target.

[0031] The specific expression for the point spread function is: , in, Represents the point spread function. Indicates Fourier transform, The modulated pupil function, This represents the complex amplitude distribution at the image plane.

[0032] S5: Based on the point spread function, perform convolution operation on the original target image to obtain a blurred image after wavefront encoding.

[0033] In a specific embodiment, the imaging process in a spatially invariant linear imaging system can be represented as the convolution of the object and the system's point spread function. Based on the physical scenario of the optical signal being encoded and modulated by a phase mask at the pupil plane or conjugate plane of the optical system, the wavefront-coded imaging result, i.e., the blurred image, is obtained, and its expression is: , in, Represents a blurred image. For the original image, The point spread function is... , This represents convolution calculation. This is the noise term.

[0034] The above expression shows that the imaging system is a convolution operator in the spatial domain, resulting in a blurred image. It contains spatial information after phase modulation, providing input data for subsequent digital recovery processing.

[0035] S6: Perform a Fourier transform on the point spread function to obtain the optical transfer function. The expression for the optical transfer function is: , in, Represents the optical transfer function. Indicates Fourier transform, This represents the point spread function.

[0036] In a specific embodiment, to verify that the phase encoding method of this application can obtain stable MTF calculation results at a relatively low sampling rate, the optical transfer function is... Amplitude and phase decomposition are performed to obtain the modulation transfer function (MTF) and phase transfer function (PTF), which describe the amplitude transfer characteristics and phase transfer characteristics of the system in the spatial frequency domain. The specific expressions are as follows: , in, , ; is the optical transfer function, MTF is the modulation transfer function, and PTF is the phase transfer function. Let be the power of the natural exponential basis in the complex function, where The imaginary unit, The argument is the angle between the complex variable and the positive half-axis of the real axis in the complex plane.

[0037] like Figure 4 As shown, the angular sinusoidal square phase modulation term The encoded modulation transfer function (MTF) did not show any obvious zeros over a wide spatial frequency range, and the deviation of the MTF in the meridional and sagittal directions was effectively suppressed. This indicates that the spatial variation of the wavefront phase is relatively smooth and controllable, which not only ensures the high efficiency of computational imaging reconstruction but also reduces the sensitivity to processing and assembly errors. This verifies that the encoding method of this application has excellent frequency response continuity and directional consistency.

[0038] S7: Construct a decoding model based on the optical transfer function. In a specific embodiment, the decoding model is a Wiener filter decoding model, expressed as: , in, This represents the frequency spectrum of the decoded image. For the target image spectrum, by Obtained by Fourier transform; Represents the spectrum of the target image The conjugate; For the spectrum of the blurred image, by Obtained by Fourier transform; Indicates the power spectral density ratio. , Represents the power spectrum of image processing noise. This represents the power spectrum of the original image.

[0039] From the above formula, it can be concluded that only by obtaining the spectrum of the blurred image can... and the spectrum of the target image And adjust the power spectral ratio Only then can a balance between noise and sharpening effects be achieved.

[0040] Compared to other algorithms, Wiener filtering has lower computational complexity and produces better image quality after decoding, making it a commonly used algorithm. Furthermore, Wiener filtering uses the system's optical transfer function as a priori condition, making it suitable for image restoration. The system's point spread function can be accurately estimated, and experimental results also show that Wiener filtering performs well in restoring blurred images. In backlit backgrounds, the blurred image of the target after wavefront encoding is heavily suppressed. Using overall decoding may cause edge information distortion. Therefore, region-based decoding and restoration of the obtained intermediate blurred image can further reduce the pixel energy within the detector while avoiding the loss of information in the intermediate blurred image.

[0041] S8: Iteratively adjust the power spectral density ratio in the decoding model, and use the adjusted decoding model to decode the blurred image, obtaining multiple candidate decoded images. Specifically, this includes the following steps: S801: Sets the search range for the power spectral ratio. Power spectral ratio Used to characterize the proportional relationship between system noise and signal power, its value range is set to... to .

[0042] S802: Power spectral ratio within the search range Perform a step-by-step scan.

[0043] S803: The blurred image is decoded using a Wiener filter decoding model to obtain multiple candidate decoded images. This includes the following steps: First, the blurred image is decoded using the Wiener filter decoding model to obtain the frequency domain spectrum of the decoded image. The calculation formula is as follows: , Further, an inverse Fourier transform is performed on the frequency domain spectrum of the decoded image to convert the frequency domain to the spatial domain, thereby obtaining a preliminary restored image, i.e., multiple candidate decoded images. The calculation formula is as follows: , in, This represents the inverse Fourier transform.

[0044] S9: Evaluate the similarity of multiple candidate decoded images and select the candidate decoded image with the highest evaluation score as the final clear image output. This includes the following steps: S901: Calculate the structural similarity index (SSIM) and Pearson correlation coefficient (PCC) between multiple candidate decoded images and the original target image.

[0045] S902: A weighted average of the structural similarity index and the Pearson correlation coefficient is used to obtain a comprehensive evaluation score. The calculation formula is as follows: , Here, SSIM represents the structural similarity index, and PCC represents the Pearson correlation coefficient.

[0046] S903: Select the candidate decoded image with the highest comprehensive evaluation score from all candidate decoded images as the final clear image output.

[0047] Through the above iterative decoding optimization steps, appropriate Wiener filter parameters can be adaptively selected under different noise levels and system response conditions, thereby further improving image restoration quality and enhancing algorithm stability.

[0048] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. In summary, the content of this specification should not be construed as a limitation of this application.

Claims

1. A wavefront encoding and decoding method based on an angular sinusoidal square-phase mask, characterized in that, The wavefront encoding and decoding method based on the angular sinusoidal square phase mask includes: A phase modulation function is constructed based on the angular sinusoidal square phase modulation term and the aberration phase term. Based on the phase modulation function, a phase mask is fabricated; The phase mask is placed on the pupil plane or conjugate plane of the optical system to perform phase modulation on the incident light field and obtain the modulated pupil function. Based on the modulated pupil function, the point spread function of the optical system at the image plane is determined; Based on the point spread function, a convolution operation is performed on the original target image to obtain a blurred image after wavefront coding; Perform a Fourier transform on the point spread function to obtain the optical transfer function; A decoding model is constructed based on the optical transfer function; The power spectral density ratio in the decoding model is iteratively adjusted, and the blurred image is decoded using the adjusted decoding model to obtain multiple candidate decoded images; The similarity of the multiple candidate decoded images is evaluated, and the candidate decoded image with the highest evaluation score is selected as the final clear image output.

2. The wavefront encoding and decoding method based on an angular sinusoidal square-phase mask according to claim 1, characterized in that, The expression for the phase modulation function is: ， in, Represents the phase modulation function. This is the angular sinusoidal square phase modulation term. For aberration phase terms; For normalized radial coordinates, Angular coordinates, For topological load number, This represents the corresponding aberration coefficient. This represents the phase distribution of system aberrations.

3. The wavefront encoding and decoding method based on an angular sinusoidal square-phase mask according to claim 2, characterized in that, The expression for the modulated pupil function is: ， in, This represents the modulated pupil function. Let be the pupil amplitude function. For phase modulation function, Represents the imaginary unit. This represents the phase modulation function in the exponential part.

4. The wavefront encoding and decoding method based on an angular sinusoidal square-phase mask according to claim 3, characterized in that, The expression for the point spread function is: ， in, Represents the point spread function. Indicates Fourier transform, The modulated pupil function, This represents the complex amplitude distribution at the image plane.

5. The wavefront encoding and decoding method based on an angular sinusoidal square-phase mask according to claim 4, characterized in that, The blurred image is: ， in, Represents a blurred image. For the original image, The point spread function is... , This represents convolution calculation. This is the noise term.

6. The wavefront encoding and decoding method based on an angular sinusoidal square-phase mask according to claim 3, characterized in that, The expression for the optical transfer function is: ， in, Represents the optical transfer function. Indicates Fourier transform, This represents the point spread function.

7. The wavefront encoding and decoding method based on an angular sinusoidal square-phase mask according to claim 5, characterized in that, The expression for the decoding model is: ， in, This represents the frequency spectrum of the decoded image. For the target image spectrum, by Obtained by Fourier transform; Represents the spectrum of the target image The conjugate; For the spectrum of the blurred image, by Obtained by Fourier transform; This represents the power spectral density ratio.

8. The wavefront encoding and decoding method based on an angular sinusoidal square-phase mask according to claim 7, characterized in that, The power spectral density ratio in the decoding model is iteratively adjusted, and the adjusted decoding model is used to decode the blurred image to obtain multiple candidate decoded images. This process specifically includes the following steps: Set the search range for the power spectral ratio; The power spectral ratio is scanned step by step within the search range; The blurred image is decoded using the decoding model to obtain multiple candidate decoded images.

9. The wavefront encoding and decoding method based on an angular sinusoidal square-phase mask according to claim 1, characterized in that, The similarity of the multiple candidate decoded images is evaluated, and the candidate decoded image with the highest evaluation score is selected as the final clear image output. This process includes the following steps: Calculate the structural similarity index and Pearson correlation coefficient between the multiple candidate decoded images and the original target image; The structural similarity index and Pearson correlation coefficient are weighted and calculated to obtain a comprehensive evaluation score; The candidate decoded image with the highest comprehensive evaluation score is selected from all candidate decoded images as the final clear image output.

10. The wavefront encoding and decoding method based on an angular sinusoidal square-phase mask according to claim 1, characterized in that, One side of the phase mask is a curved surface designed according to the phase modulation function, and the other side is a plane.

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