Optical image phase imaging method and device based on bisymmetric bias space differential

Abstract

The invention discloses an optical image phase imaging method and device based on bisymmetric bias space differentiation, and relates to the technical field of optical information processing. The method is characterized by comprising the following steps: placing a pure-phase target object on an object surface of a 4f system formed by two Fourier transform lenses, performing Fourier transform on signal light carrying image information of the pure-phase target object through a first lens, and forming a Fourier spectrum of an image on a spectrum surface; a complex amplitude filter is placed at the frequency spectrum surface, and is pre-loaded with a distributed symmetric bias space differential function and is superposed with a transfer function of the blazed grating, so as to modulate the Fourier spectrum of the image; fourier transform is carried out on the modulated frequency spectrum through a second lens, and two image differential operation results which do not influence each other are obtained on an image plane; and processing the image differential operation result to obtain the phase distribution of the pure phase target object. The information processing time is remarkably shortened, the system power consumption is reduced, and the method has practical application value.

Description

Technical Field

[0001] This invention relates to the field of optical information processing technology, and specifically to an optical image phase imaging method and apparatus based on dual-symmetric bias spatial differentiation. Background Technology

[0002] In image processing, differentiation is a crucial processing method. Traditional image differentiation is achieved through digital computation, i.e., digital image processing. Digital image processing typically uses convolution kernels (such as Sobel and Laplacian operators) with the original image in the spatial domain to achieve edge detection. However, due to the analog-to-digital conversion and discretization processes, digital differentiation requires frequent analog-to-digital conversions and discretization, resulting in low speed and low energy efficiency. Conversely, optical analog computation offers advantages such as high-speed computation, parallel processing, and low power consumption, allowing optical spatial differentiation to achieve edge detection of amplitude objects and the conversion of phase gradients to intensity information with high efficiency and low energy consumption. This has rekindled the research interest of many researchers in recent years. Related research focuses on achieving optical spatial differentiation using various methods, such as surface plasmon resonances, photonic crystals, spin-orbit interactions, the Brewster effect, the photonic spin Hall effect, and the geometric spin Hall effect. With the development of nanophotonics technology, nanophotonic devices such as metasurfaces, liquid crystal photonic platforms, and photonic chips based on the Pannan-Latnam-Berry phase are widely used in spatial differentiation and optical analog information processing due to their ease of integration. A typical application of optical differentiation is phase reconstruction, where the phase distribution usually contains more information about the sample's morphology, structure, and tissue properties than the intensity distribution.

[0003] However, due to the weak scattering and absorption characteristics of pure phase objects, intensity measurements are difficult to provide effective phase information, making it challenging to extract the phase structure from the incident light background. The paper "Analytic phase retrieval method via regional Fourier spectrum superposition," published in *Optics Letters*, Volume 50, Issue 18, page 5662, 2025, proposes an analytical phase retrieval method based on regional Fourier spectrum superposition. This method transforms the phase retrieval problem into an interferometric problem, constructing a system of linear equations through regional Fourier spectrum superposition to solve for the phase difference between regions. However, this method has the following limitations: the linear equations must satisfy linear independence; the sample region division must ensure phase uniformity within a single region; redundant variables exist when non-uniform samples are densely segmented, affecting computational speed; and the phase distribution cannot be recovered from a single acquisition. The paper "Direct single-shotphase retrieval from the diffraction pattern of separated objects," published in Volume 7, 2016, page 10820 of Nature Communications, proposes a method for direct phase recovery from the diffraction pattern of separated objects. This method achieves single-frame phase recovery, but requires at least two separated objects, making phase recovery impossible for a single object. Furthermore, it is necessary to ensure that the detector is located in the Fourier plane of the diffraction pattern to accurately acquire the diffraction intensity distribution. Summary of the Invention

[0004] In view of the above problems, the present invention proposes an optical image phase imaging method and device based on dual-symmetric bias spatial differentiation, which can realize phase imaging by acquiring multiple differentiation results in a single acquisition.

[0005] According to one aspect of the present invention, an optical image phase imaging method based on bisymmetric bias spatial differentiation is proposed, the method comprising:

[0006] A pure-phase target object is placed on the object plane of a 4f system consisting of two Fourier transform lenses. The signal light carrying the image information of the pure-phase target object undergoes a Fourier transform through the first lens, forming the Fourier spectrum of the image on the spectral plane. The complex amplitude filter is preloaded with a distributed symmetrical bias spatial differential function and superimposed with the transfer function of a blazed grating to modulate the Fourier spectrum of the image. The modulated spectrum undergoes a Fourier transform through the second lens, resulting in two independent image differential operation results on the image plane. The image differential operation results are processed to obtain the phase distribution of the pure-phase target object.

[0007] Furthermore, the distributed symmetric bias space differential function is: and Regarding It is symmetric in axis space, and its expression is as follows:

[0008] , ;

[0009] corresponding transfer function for:

[0010] ;

[0011] In the formula, and They are along Axial direction and The wave vector component in the axial direction is also shaft and Spatial frequency components along the axial direction; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the first horizontal and first vertical positions on the imaging plane; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the second horizontal position and the second vertical position on the imaging plane; Indicates the wavelength of the incident light; Indicates the focal length of the lens.

[0012] Furthermore, the formulas for calculating the first horizontal position and the first vertical position are as follows: , The formulas for calculating the second horizontal position and the second vertical position are: , ;in, and These represent the grating frequencies at the first horizontal position and the first vertical position, respectively. and These represent the grating frequencies at the second horizontal position and the second vertical position, respectively.

[0013] Furthermore, the distributed symmetric bias space differential function is: and Regarding It is symmetric in axis space, and its expression is as follows:

[0014] , ;

[0015] corresponding transfer function for:

[0016] ;

[0017] In the formula, and They are along Axial direction and The wave vector component in the axial direction is also shaft and Spatial frequency components along the axial direction; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the first horizontal and first vertical positions on the imaging plane; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the second horizontal position and the second vertical position on the imaging plane; Indicates the wavelength of the incident light; Indicates the focal length of the lens.

[0018] Furthermore, the formulas for calculating the first horizontal position and the first vertical position are as follows: , The formulas for calculating the second horizontal position and the second vertical position are: , ;in, and These represent the grating frequencies at the first horizontal position and the first vertical position, respectively. and These represent the grating frequencies at the second horizontal position and the second vertical position, respectively.

[0019] Furthermore, the results of the two independent image differentiation operations are expressed as follows: and :

[0020] , ;

[0021] In the formula, Represents spatial coordinates on the image plane; This represents the signal light field carrying pure phase target object image information.

[0022] Furthermore, processing the image differentiation results to obtain the phase distribution of the pure phase target object includes: processing the differentiation results of the two independent images... and The phase distribution of the pure phase target object is obtained by subtracting the intensity values ​​and then integrating.

[0023] Furthermore, the transfer function of the blazed grating is:

[0024] ;

[0025] In the formula, Represents spatial coordinates on the spectrum plane; and This indicates the position coordinates of the first-order diffraction fringes generated by the blazed grating on the imaging plane.

[0026] According to another aspect of the present invention, an optical image phase imaging device based on dual-symmetric bias spatial differentiation is proposed. The device includes: a laser, a pure phase target object, a first lens, a complex amplitude filter, a second lens, a camera, and a computer; wherein the first lens and the second lens form a 4f system, the pure phase target object is placed at the front focal plane of the first lens, the complex amplitude filter is placed at the rear focal plane of the first lens, the camera is placed at the rear focal plane of the second lens, and the camera and the computer are connected.

[0027] The complex amplitude filter is preloaded with a distributed symmetrical bias spatial differential function and superimposed with the transfer function of a blazed grating to modulate the Fourier spectrum of the image.

[0028] The computer is used to process the differential operation results of the image output by the camera to obtain the phase distribution of the pure phase target object.

[0029] Furthermore, the expression for the transfer function of the distributed symmetric bias spatial differential function superimposed with the blazed grating is:

[0030] ;

[0031] In the formula, and They are along Axial direction and The wave vector component in the axial direction is also shaft and Spatial frequency components along the axial direction; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the first horizontal and first vertical positions on the imaging plane; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the second horizontal position and the second vertical position on the imaging plane; Indicates the wavelength of the incident light; Indicates the focal length of the lens;

[0032] The process of processing the image differentiation results output by the camera to obtain the phase distribution of the pure phase target object includes: differentiating the results of two independent images output by the camera. and The phase distribution of the pure phase target object is obtained by subtracting the intensity values ​​and then integrating.

[0033] The beneficial technical effects of this invention are:

[0034] This invention provides an easy-to-implement and highly practical optical method for phase imaging of pure phase objects. By combining double-symmetric bias spatial differentiation with multiplexing technology, it achieves the acquisition of differential results in a single acquisition, which traditional methods require multiple detections. This fully leverages the advantages of fast optical processing speed and parallel computing capabilities, significantly shortening information processing time and reducing system power consumption. Furthermore, due to the symmetry of the differential function, only simple mathematical processing of the acquisition results is needed to reconstruct the phase distribution, effectively avoiding the limitations of mainstream phase reconstruction methods and possessing significant practical application value. Attached Figure Description

[0035] The above and other objects, features, and advantages of exemplary embodiments of the present invention will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. Several embodiments of the invention are illustrated in the drawings by way of example and not limitation, wherein:

[0036] Figure 1 This is a flowchart of the optical image phase imaging method based on dual-symmetric bias spatial differentiation according to an embodiment of the present invention;

[0037] Figure 2 This is a schematic diagram of the optical image phase imaging device based on dual-symmetric bias spatial differentiation according to an embodiment of the present invention;

[0038] Figure 3 This is an example diagram of the original phase distribution of a pure phase object in an embodiment of the present invention;

[0039] Figure 4 This is an example diagram of a symmetrical bias filter in the x-direction in an embodiment of the present invention;

[0040] Figure 5 This is an example diagram of a symmetrical bias filter in the y-direction in an embodiment of the present invention;

[0041] Figure 6 This is an example diagram of a filter after multiplexing the filters in the x and y directions in an embodiment of the present invention;

[0042] Figure 7 This is an example diagram showing the result obtained after differentiating the complex amplitude filter in an embodiment of the present invention;

[0043] Figure 8 This is an example diagram of the intensity difference in the x and y directions obtained after demultiplexing in an embodiment of the present invention;

[0044] Figure 9 This is an example diagram of the reconstructed phase distribution obtained after integration in an embodiment of the present invention;

[0045] Figure 10 This is an example image comparing the original phase and reconstructed phase of a non-binary object in an embodiment of the present invention;

[0046] Figure 11 This is the error distribution histogram in an embodiment of the present invention. Detailed Implementation

[0047] The principles and spirit of the invention will now be described with reference to several exemplary embodiments. It should be understood that these embodiments are given merely to enable those skilled in the art to better understand and implement the invention, and are not intended to limit the scope of the invention in any way. Rather, these embodiments are provided to make this disclosure more thorough and complete, and to fully convey the scope of this disclosure to those skilled in the art.

[0048] This invention proposes an optical image phase imaging method and device based on dual-symmetric bias spatial differentiation. Based on the characteristic of spatial differentiation to transform phase information into intensity distribution, and combining Fourier spatial filtering technology and holographic multiplexing technology, two symmetric bias one-dimensional spatial differential functions are selected to make filters, so as to achieve the effect of recovering the complete phase information of the phase object after a single optical acquisition and simple digital processing.

[0049] This invention proposes an optical image phase imaging method based on bisymmetric bias spatial differentiation, such as... Figure 1 As shown, the method includes:

[0050] S1. Place the pure phase target object 2 on the object surface of a 4f system composed of two Fourier transform lenses. The signal light carrying the image information of the pure phase target object undergoes Fourier transform through the first lens 3 to form the Fourier spectrum of the image on the spectrum surface.

[0051] S2. A complex amplitude filter 4 is placed at the spectral surface. The complex amplitude filter 4 is preloaded with a distributed symmetrical bias spatial differential function and a transfer function superimposed on a blazed grating to modulate the Fourier spectrum of the image.

[0052] S3. The modulated spectrum is subjected to Fourier transform through the second lens 5, and two independent image differential operation results are obtained on the image plane.

[0053] S4. Process the image differentiation operation result to obtain the phase distribution of the pure phase target object.

[0054] The optical image phase imaging method proposed in the embodiments of the present invention will be described in detail below.

[0055] Unlike traditional digital signal processing, optical analog signal processing achieves various calculations by modulating the light field. Based on Fourier optics theory, the relationship between the differential and the corresponding transfer function is first established, considering the incident light field carrying object information in a Cartesian coordinate system. and the filtered output light field According to Fourier optics theory, the incident and emitted light fields can be extended to the sum of a series of spatial frequency components, which can be expressed as:

[0056] (1)

[0057] (2)

[0058] (3)

[0059] in, and These are the index fields. and Spatial Fourier spectrum; and They are along Axial direction and The wave vector component in the axial direction is also shaft and Spatial frequency components along the axial direction; This represents the transfer function of the entire differential filter system.

[0060] To achieve the first-order differential in a specific direction without loss of generality, assume that along... Along the axial direction, the output light field should have the following distribution: Therefore, for the incident light field The Fourier expansion of equation (1) is obtained by taking the pairs of both sides. The partial derivative yields:

[0061] (4)

[0062] Comparing equations (2), (3), and (4), we can obtain the transfer function as follows:

[0063] (5)

[0064] As can be seen from equation (5), .

[0065] For a purely phase-dependent object, its complex amplitude expression is: ,in It is a constant. For phase; for conduct Directional differentiation yields: This operation achieves phase-amplitude conversion, and then... By extracting this term and integrating it, phase reconstruction can be achieved.

[0066] Modulating the optical field spectrum can affect the optical field distribution in its spatial domain. The key lies in the selection of the transfer function. By biasing the one-dimensional differential function shown in equation (5) above, two values ​​for the transfer function are obtained. Axially symmetric functions: and These two things about The axis-space symmetric distributed bias space differential functions are used as the system's transfer functions to modulate the spectrum, and the output results are as follows:

[0067] (6)

[0068] (7)

[0069] By taking the difference in strength between the two, we can obtain:

[0070] (8)

[0071] Right now: (9)

[0072] In the formula, This represents the intensity distribution of the outgoing light field. The intensity distribution is proportional to the differential of the original light field. If the original object is a purely phase-dependent object, the phase distribution of the object can be reconstructed by integration, i.e.:

[0073] .

[0074] Similarly, the same method can be used to perform the same operation in the y-direction to obtain the same result. Then regarding... The differential function of the axially symmetric distributed bias space is: and The expression is as follows:

[0075] , (10)

[0076] In actual fabrication, according to holographic multiplexing theory, to achieve effective separation of the differential image obtained after modulation of the input object on the imaging plane, a suitable grating needs to be selected and its frequency adjusted. Commonly used grating types include amplitude gratings (such as cosine amplitude gratings) and phase gratings (such as sinusoidal phase gratings and blazed gratings). Considering imaging quality and the characteristics of different gratings, this embodiment of the invention selects a blazed grating. The complex amplitude transmittance of the blazed grating is:

[0077] (11)

[0078] in Represents the spatial coordinates on the spectrum plane; u and v represent the grating frequencies in the vertical and horizontal directions, respectively.

[0079] To obtain the Fraunhofer diffraction pattern of the blazed grating, consider placing a lens with a focal length of f at a distance f from the spatial light modulator (i.e., the complex amplitude filter 4) to separate different diffraction orders. The final coordinates of the first-order diffraction fringe positions are then obtained. , With respect to the selected grating frequency (u, v), and lens focal length and incident light wavelength Relevant, namely: , Therefore, the transfer function of the blazed grating is in the form of:

[0080] (12)

[0081] In summary, the differential function corresponding to the distributed symmetric bias space and The transfer function that ultimately needs to be loaded on the spectral surface is in the form of:

[0082] (13)

[0083] In the formula, , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the first horizontal and first vertical positions on the imaging plane; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the second horizontal position and the second vertical position on the imaging plane; Indicates the wavelength of the incident light; This represents the lens focal length. The formulas for calculating the first horizontal and first vertical positions are: , The formulas for calculating the second horizontal position and the second vertical position are: , ;in, and These represent the grating frequencies at the first horizontal position and the first vertical position, respectively. and These represent the grating frequencies at the second horizontal position and the second vertical position, respectively.

[0084] Corresponding to the distributed symmetric bias space differential function and The transfer function that ultimately needs to be loaded on the spectral surface is in the form of:

[0085] (14)

[0086] In the formula, , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the first horizontal and first vertical positions on the imaging plane; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the second horizontal position and the second vertical position on the imaging plane; Indicates the wavelength of the incident light; This represents the lens focal length. The formulas for calculating the first horizontal and first vertical positions are: , The formulas for calculating the second horizontal position and the second vertical position are: , ;in, and These represent the grating frequencies at the first horizontal position and the first vertical position, respectively. and These represent the grating frequencies at the second horizontal position and the second vertical position, respectively.

[0087] In summary, to achieve optical image phase imaging of the pure-phase target object 2, the pure-phase target object 2 is placed on the object plane of a 4f imaging system composed of two convex lenses. The signal light carrying the image information of the pure-phase target object passes through the pure-phase target object 2 placed on the front focal plane of the first lens 3. The beam carrying the phase information of the object passes through the first lens 3 and obtains the Fourier transform spectrum of the object on its rear focal plane. A complex amplitude filter 4 (pre-loaded with the transfer function as shown in equation (13) or (14)) corresponding to the spatial differential operation superimposed on the blazed grating is placed at the rear focal plane of the first lens 3 to obtain the Fourier transform spectrum of the object. The modulated beam is subjected to Fourier transform again through the second lens 5. The differential results of the two independent images after exiting (as shown in equations (6) and (7)) are imaged onto the back focal plane of the second lens 5. The phase distribution can be reconstructed by performing the difference and integration of the acquired images (as shown in equations (8) and (9)).

[0088] This invention provides an easy-to-implement and highly practical optical method for phase imaging of pure phase objects. By combining double-symmetric bias spatial differentiation with multiplexing technology, it achieves the acquisition of differential results in a single acquisition, which traditional methods require multiple detections. This fully leverages the advantages of fast optical processing speed and parallel computing capabilities, significantly shortening information processing time and reducing system power consumption. Furthermore, due to the symmetry of the differential function, only simple mathematical processing of the acquisition results is needed to reconstruct the phase distribution, effectively avoiding the limitations of mainstream phase reconstruction methods and possessing significant practical application value.

[0089] This invention also proposes an optical image phase imaging device based on bisymmetric bias spatial differentiation, such as... Figure 2 As shown, the device includes: a laser 1, a pure-phase target object 2, a first lens 3, a complex amplitude filter 4, a second lens 5, a camera 6, and a computer 7; wherein, the first lens 3 and the second lens 5 form a 4f system, the pure-phase target object 2 is placed at the front focal plane of the first lens 3, the complex amplitude filter 4 is placed at the rear focal plane of the first lens 3, the camera 6 is placed at the rear focal plane of the second lens 5, and the camera 6 is connected to the computer 7; the complex amplitude filter 4 is preloaded with a distributed symmetrical bias spatial differential function and superimposed with the transfer function of a blazed grating to modulate the Fourier spectrum of the image; the computer 7 is used to process the image differential operation results output by the camera 6 to obtain the phase distribution of the pure-phase target object.

[0090] First, laser 1 emits a laser beam, which is incident on the pure-phase target object 2 placed at the front focal plane of the first lens 3. The beam carrying the phase information of the object is passed through the first lens 3 and the Fourier transform spectrum of the object is obtained at its rear focal plane. The complex amplitude filter 4 placed at the rear focal plane of the first lens 3 modulates the Fourier transform spectrum of the object. The modulated beam is then subjected to another Fourier transform by the second lens 5. After exiting, the differential results of the two independent images are imaged onto the rear focal plane of the second lens 5 where the camera 6 is located, and then transmitted to the computer 7 for processing. The computer 7 uses the difference and integration of the acquired images to obtain the reconstructed phase distribution.

[0091] The function of the optical image phase imaging device based on dual-symmetric bias spatial differential described in this embodiment of the invention can be explained by the aforementioned optical image phase imaging method based on dual-symmetric bias spatial differential. Therefore, for the parts not described in detail in the device embodiment, please refer to the above method embodiment, and they will not be repeated here.

[0092] The technical effects of the present invention were further verified through Matlab numerical simulation.

[0093] The simulation used a 632.8nm laser light source to illuminate the object, and the focal lengths of the two Fourier transform lenses forming the 4f system were both set to 200mm. The phase distribution of the object is as follows. Figure 3 As shown, since the lens's function is to perform Fourier transform, its spectrum is obtained through a two-dimensional Fourier transform; the transfer function is applied to the phase object spectrum for modulation to achieve differentiation of the object by a dual-symmetric bias spatial differentiator. The symmetric bias differentiating filter (i.e., the complex amplitude filter 4 proposed in this embodiment) is as follows: Figure 4 , 5 As shown, the symmetrical bias filters in the x and y directions are multiplexed, as follows: Figure 6 As shown. The modulated image obtained by Fourier transform through the second lens 5 is as follows. Figure 7 As shown, by reusing the solution and taking the difference in intensity, the difference in intensity in the x and y directions is obtained, as follows. Figure 8 As shown, where, Figure 8 The left image corresponds to the intensity difference in the x-direction, and the right image corresponds to the intensity difference in the y-direction; finally, the phase of the object is restored through integration. Figure 9 As shown, the example corresponds to the y-direction.

[0094] For non-binary objects, their phase distribution is as follows: Figure 10 As shown in the left figure, the phase reconstructed after the above process is as follows: Figure 10 As shown in the right figure. To further analyze the phase reconstruction effect, the point-to-point difference between the original phase and the reconstructed phase of the object is calculated, and the mean square error is analyzed as follows: Figure 11 As shown, the variance is 0.0033 and the standard deviation is 0.0571. This demonstrates that the present invention achieves good reconstruction results for the phase distribution.

[0095] While the spirit and principles of the invention have been described with reference to several specific embodiments, it should be understood that the invention is not limited to the disclosed specific embodiments, and the division of aspects does not imply that features in these aspects cannot be combined for benefit; such division is merely for ease of description. The invention is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims

1. An optical image phase imaging method based on double-symmetric bias spatial differentiation, characterized in that, include: A pure-phase target object (2) is placed on the object plane of a 4f system composed of two Fourier transform lenses. The signal light carrying the image information of the pure-phase target object is subjected to Fourier transform through the first lens (3) to form the Fourier spectrum of the image on the spectrum plane. A complex amplitude filter (4) is placed on the spectrum plane. The complex amplitude filter (4) is preloaded with a distributed symmetrical bias spatial differential function and superimposed with the transfer function of a blazed grating to modulate the Fourier spectrum of the image. The modulated spectrum is subjected to Fourier transform through the second lens (5) to obtain two independent image differential operation results on the image plane. The image differentiation operation result is processed to obtain the phase distribution of the pure phase target object.

2. The optical image phase imaging method based on double-symmetric bias spatial differentiation according to claim 1, characterized in that, The distributed symmetric bias space differential function is: and Regarding It is symmetric in axis space, and its expression is as follows: ， ； corresponding transfer function for: ； In the formula, and They are along Axial direction and The wave vector component in the axial direction is also shaft and Spatial frequency components along the axial direction; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the first horizontal and first vertical positions on the imaging plane; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the second horizontal position and the second vertical position on the imaging plane; Indicates the wavelength of the incident light; Indicates the focal length of the lens.

3. The optical image phase imaging method based on double-symmetric bias spatial differentiation according to claim 2, characterized in that, The formulas for calculating the first horizontal position and the first vertical position are as follows: , The formulas for calculating the second horizontal position and the second vertical position are: , ;in, and These represent the grating frequencies at the first horizontal position and the first vertical position, respectively. and These represent the grating frequencies at the second horizontal position and the second vertical position, respectively.

4. The optical image phase imaging method based on double-symmetric bias spatial differentiation according to claim 1, characterized in that, The distributed symmetric bias space differential function is: and Regarding It is symmetric in axis space, and its expression is as follows: ， ； corresponding transfer function for: ； In the formula, and They are along Axial direction and The wave vector component in the axial direction is also shaft and Spatial frequency components along the axial direction; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the first horizontal and first vertical positions on the imaging plane; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the second horizontal position and the second vertical position on the imaging plane; Indicates the wavelength of the incident light; Indicates the focal length of the lens.

5. The optical image phase imaging method based on double-symmetric bias spatial differentiation according to claim 4, characterized in that, The formulas for calculating the first horizontal position and the first vertical position are as follows: , The formulas for calculating the second horizontal position and the second vertical position are: , ;in, and These represent the grating frequencies at the first horizontal position and the first vertical position, respectively. and These represent the grating frequencies at the second horizontal position and the second vertical position, respectively.

6. The optical image phase imaging method based on bisymmetric bias spatial differentiation according to claim 3 or 5, characterized in that, The results of the differential operations on the two independent images are expressed as follows: and : ， ； In the formula, Represents spatial coordinates on the image plane; This represents the signal light field carrying pure phase target object image information.

7. The optical image phase imaging method based on double-symmetric bias spatial differentiation according to claim 6, characterized in that, The step of processing the image differentiation results to obtain the phase distribution of the pure phase target object includes: differentiating the results of the two independent images. and The phase distribution of the pure phase target object is obtained by subtracting the intensity values ​​and then integrating.

8. The optical image phase imaging method based on bisymmetric bias spatial differentiation according to claim 3 or 5, characterized in that, The transfer function of the blazed grating is: ； In the formula, Represents spatial coordinates on the spectrum plane; and This indicates the position coordinates of the first-order diffraction fringes generated by the blazed grating on the imaging plane.

9. An optical image phase imaging device based on dual-symmetric bias spatial differentiation, characterized in that, include: Laser (1), pure phase target object (2), first lens (3), complex amplitude filter (4), second lens (5), camera (6), computer (7); wherein, the first lens (3) and the second lens (5) form a 4f system, the pure phase target object (2) is placed at the front focal plane of the first lens (3), the complex amplitude filter (4) is placed at the rear focal plane of the first lens (3), the camera (6) is placed at the rear focal plane of the second lens (5), and the camera (6) and the computer (7) are connected; The complex amplitude filter (4) is preloaded with a distributed symmetrical bias spatial differential function and a transfer function superimposed on a blazed grating to modulate the Fourier spectrum of the image. The computer (7) is used to process the image differential operation results output by the camera (6) to obtain the phase distribution of the pure phase target object.

10. The optical image phase imaging device based on dual-symmetric bias spatial differentiation according to claim 9, characterized in that, The expression for the transfer function of the distributed symmetric bias spatial differential function superimposed with a blazed grating is: ； In the formula, and They are along Axial direction and The wave vector component in the axial direction is also shaft and Spatial frequency components along the axial direction; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the first horizontal and first vertical positions on the imaging plane; , Spatial differential functions The first-order diffraction light generated by the corresponding hologram is at the second horizontal position and the second vertical position on the imaging plane; Indicates the wavelength of the incident light; Indicates the focal length of the lens; The process of processing the image differentiation results output by the camera (6) to obtain the phase distribution of the pure phase target object includes: differentiating the two independent image results output by the camera (6). and The phase distribution of the pure phase target object is obtained by subtracting the intensity values ​​and then integrating.

Images