A design method for a super-Gaussian aperture high-order differential filter, an image processing method and a device

Abstract

The present invention discloses a design method, an image processing method and a device for a super-Gaussian aperture high-order differential filter, and relates to the technical field of high-order differential image processing. The super-Gaussian aperture high-order differential filter is designed as follows: a super-Gaussian function is used as the aperture function corresponding to the transfer function of the high-order differential filter, and the aperture function is used to limit the range of the transfer function; further, an image processing method and a device based on super-Gaussian aperture high-order differential filtering are designed, and the super-Gaussian aperture high-order differential filter is placed on the spectrum plane of the 4f system to modulate the image spectrum, thereby obtaining a high-order differential image. Experiments have shown that the present invention can retain the characteristics of high-order image differentials and has low diffraction noise, and can accurately implement high-order differential operations, and can be effectively applied to optical simulation calculations and image processing.

Description

Technical Field

[0001] The present invention relates to the technical field of high-order differential image processing, and in particular to a design method, an image processing method and a device for a super-Gaussian aperture high-order differential filter. Background Art

[0002] Image processing and edge detection are at the core of many emerging technologies today, such as astronomical observations and biological imaging. Traditional methods use integrated circuits or digital computing to operate, which is limited by the size of the integration and the speed of the calculation. Today, optical analog computing has attracted widespread attention due to its ultra-fast operation speed, low power consumption, and large-scale parallel computing. In particular, image differential operations, as a type of analog computing, can highlight the edge information of sharp color transitions in the image; for invisible phase objects, differential operations can convert phase gradients into edge-visible intensity information, which is of great significance for microbial imaging. The differential mode based on Fourier spectrum filtering can provide a reference for the design of high-order differentiators in principle, and the transfer function in momentum space plays an important role in the design of differentiators.

[0003] Many differentiators using spectral filtering are based on designing transfer functions to modulate the transmission or reflection spectrum. Especially for integrated and miniaturized nano devices, such as metasurfaces, photonic crystals, chips, and liquid crystals, the transfer functions of differential operations usually have the form of total differential, partial differential, and topological differential. However, the transfer function is not infinite and needs to be limited by an aperture function. Previously, circular functions or Gaussian functions were commonly used as apertures to limit filters, which can achieve first-order or second-order differentials. In 2006, Optics Letters, Vol. 31, No. 10, "Radial Hilbert transform with Laguerre-Gaussian spatial filters" used Gaussian functions to limit Laguerre functions for differentiation and compared them with circular functions, achieving first-order isotropic differential operations and proving that Gaussian functions produce less noise than circular functions. The use of Gaussian functions as aperture filters was then continued, but whether the use of Gaussian functions as apertures is applicable to higher-order differentials has not been proven.

[0004] However, simulation experiments have shown that using a Gaussian function as an aperture tends to soften the high-frequency portion of high-order differentials, and it cannot accurately achieve high-order differentials. Summary of the invention

[0005] In view of the above problems, for high-order differential operations, the present invention proposes a design method, an image processing method and a device for a super-Gaussian aperture high-order differential filter.

[0006] According to one aspect of the present invention, a design method for a super-Gaussian aperture high-order differential filter is proposed, the design method comprising: using a super-Gaussian function as an aperture function corresponding to a transfer function of the high-order differential filter, the aperture function being used to limit the range of the transfer function; a transfer function T(k x ,k y ) is expressed as:

[0007]

[0008] In the formula, H(k x ,k y ) represents the momentum space transfer function without aperture restriction, k x ,k y Respectively represent the horizontal and vertical coordinates in momentum space; represents the super-Gaussian aperture function, k r represents the radial coordinate in momentum space, and w represents the beam waist radius of the super-Gaussian aperture function, m represents the order of the super-Gaussian function, and m≥3.

[0009] Furthermore, the momentum space transfer function H(k x ,k y )include:

[0010] The transfer function corresponding to the total differential is:

[0011] H1(k x ,k y )=(k x +k y ) n

[0012] Realize the transfer function corresponding to the partial differential:

[0013]

[0014] Realize the transfer function corresponding to the topological differentiation:

[0015]

[0016] In the formula, n represents the order of differentiation; Represents the polar coordinate azimuth on the Fourier plane.

[0017] According to another aspect of the present invention, an image processing method based on super-Gaussian aperture high-order differential filtering is proposed, the method comprising placing a super-Gaussian aperture high-order differential filter on a spectrum plane in a 4f system to modulate a two-dimensional image spectrum; performing an inverse Fourier transform on the modulated optical signal to obtain an image processing result; wherein, in the super-Gaussian aperture high-order differential filter, a super-Gaussian function is used as an aperture function corresponding to a transfer function of the filter, and the aperture function is used to limit the range of the transfer function; a transfer function T(k x ,k y ) is expressed as:

[0018]

[0019] In the formula, H(k x ,k y ) represents the momentum space transfer function without aperture restriction, k x ,k y Respectively represent the horizontal and vertical coordinates in momentum space; represents the super-Gaussian aperture function, k r represents the radial coordinate in momentum space, and w represents the beam waist radius of the super-Gaussian aperture function, m represents the order of the super-Gaussian function, and m≥3.

[0020] Furthermore, the momentum space transfer function H(k x ,k y )include:

[0021] The transfer function corresponding to the total differential is:

[0022] H1(k x ,k y )=(k x +k y ) n

[0023] Realize the transfer function corresponding to the partial differential:

[0024]

[0025] Realize the transfer function corresponding to the topological differentiation:

[0026]

[0027] In the formula, n represents the order of differentiation; Represents the polar coordinate azimuth on the Fourier plane.

[0028] According to another aspect of the present invention, an image processing device based on super-Gaussian aperture high-order differential filtering is also proposed, the device comprising a single-mode laser 31, a first lens 32, a pinhole filter 33, a second lens 34, a third lens 35, a first reflector 36, a spatial light modulator 37, a fourth lens 38, a second reflector 39, a pinhole 310, and a CCD camera 311, wherein the light beam emitted by the single-mode laser 31 is expanded by a 4f system composed of the first lens 32 and the second lens 34, and is low-pass filtered by the pinhole filter 33 in the 4f system, and then is transmitted to the optical fiber 311 through the optical fiber 312. The target object is located on the front focal plane of the third lens 35; the Fourier transform spectrum of the target object is reflected by the first reflector 36 at a small angle and incident on the spatial light modulator 37, and the spatial light modulator 37 is loaded with a prefabricated phase hologram as a filter to generate a phase hologram with a blazed grating, and the Fourier transform spectrum is filtered and modulated by the spatial light modulator 37 and diffracted to the positive first order; the diffracted light is Fourier inverse transformed by the fourth lens 38, and is reflected by the second reflector 39 through the pinhole 310 to extract the positive first order light; the differential image is obtained by the CCD camera 311;

[0029] The transfer function corresponding to the prefabricated phase hologram is a transfer function with aperture limitation, and a super-Gaussian function is used as the aperture function corresponding to the transfer function, and the aperture function is used to limit the range of the transfer function; the transfer function with aperture limitation T(k x ,k y ) is expressed as:

[0030]

[0031] In the formula, H(k x ,k y ) represents the momentum space transfer function without aperture restriction, k x ,k y Respectively represent the horizontal and vertical coordinates in momentum space; represents the super-Gaussian aperture function, k r represents the radial coordinate in momentum space, and w represents the beam waist radius of the super-Gaussian aperture function, m represents the order of the super-Gaussian function, and m≥3.

[0032] Furthermore, the momentum space transfer function H(k x ,k y )include:

[0033] The transfer function corresponding to the total differential is:

[0034] H1(k x ,k y )=(k x +k y )n

[0035] Realize the transfer function corresponding to the partial differential:

[0036]

[0037] Realize the transfer function corresponding to the topological differentiation:

[0038]

[0039] In the formula, n represents the order of differentiation; Represents the polar coordinate azimuth on the Fourier plane.

[0040] The beneficial technical effects of the present invention are:

[0041] The present invention proposes a design method for a super-Gaussian aperture high-order differential filter, using a super-Gaussian function as the aperture function corresponding to the transfer function of the high-order differential filter, the aperture function is used to limit the range of the transfer function, and the designed high-order differential filter is compared with the differential filter using a circular function as the aperture function and a Gaussian function as the aperture function. Experiments have shown that the super-Gaussian aperture can retain the characteristics of high-order image differentials and has low diffraction noise, and can accurately realize second-order to fifth-order, or even higher-order differential operations, and can be effectively applied to optical simulation calculations and image processing. Further, the present invention proposes an image processing method and device based on super-Gaussian aperture high-order differential filtering. Experimental results show that in the case of multi-order full differentials or multi-order partial differentials, clear edge lines with the same differential order may appear on the edge of the image, proving that when a super-Gaussian is used as an aperture filter, low-noise high-order differential image processing can be accurately achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily understood by reading the detailed description below with reference to the accompanying drawings. In the accompanying drawings, several embodiments of the present invention are shown in an exemplary and non-limiting manner, in which:

[0043] Figure 1 Schematic diagram of image differentiation operation.

[0044] Figure 2 The present invention is a flowchart of an image processing method based on super-Gaussian aperture high-order differential filtering according to an embodiment of the present invention.

[0045] Figure 3 It is a schematic diagram of the structure of an image processing device based on super-Gaussian aperture high-order differential filtering described in an embodiment of the present invention.

[0046] Figure 4The graphs are function curve comparison diagrams (a1-a5) of the circular function, Gaussian function and third to fifth order super Gaussian function in the embodiment of the present invention, the corresponding transfer function comparison diagram (b1-b5), the corresponding point spread function comparison diagram (c1-c5), the corresponding fifth order differential operation comparison diagram (d2-d6), and the white dotted line curve comparison diagram (e1-e5); wherein (d1) is the original circular image.

[0047] Figure 5 1 is a comparison diagram of the experimental results of performing fifth-order partial differentiation of a circular object using a circular domain function, a Gaussian function, and a super-Gaussian function as apertures in an embodiment of the present invention; wherein, (a1)-(a5) are holograms of the transfer functions of the circular domain aperture, the Gaussian aperture, and the super-Gaussian aperture, respectively, (b0) is a bright field image of the object, (b1)-(b4) are respectively the differential results corresponding to the above functions as apertures, and (c1)-(c4) are curves of the white dotted lines extracted from the differential results.

[0048] Figure 6 The graphs show the result of two-dimensional first-order to fourth-order total differential operations and second-order to fifth-order partial differential operations using a fourth-order super-Gaussian function as the filter aperture in an embodiment of the present invention; wherein (a1)-(a4) are the holograms required for first-order to fourth-order total differentials, and (b1)-(b4) are the corresponding differential results; (c1)-(c4) are the holograms required for second-order to fifth-order total differentials, and (d1)-(d4) are the corresponding differential results. DETAILED DESCRIPTION

[0049] The principles and spirit of the present invention will be described below with reference to several exemplary embodiments. It should be understood that these embodiments are provided only to enable those skilled in the art to better understand and implement the present invention, and are not intended to limit the scope of the present invention in any way. On the contrary, these embodiments are provided to make the present disclosure more thorough and complete, and to fully convey the scope of the present disclosure to those skilled in the art.

[0050] In order to solve the problem that circular aperture function and Gaussian aperture function in traditional spectrum filtering cannot realize accurate multi-order differentiation, the present invention proposes a design method, image processing method and device of super-Gaussian aperture high-order differential filter. The present invention uses super-Gaussian function as aperture limiting transfer function, which can accurately realize second-order to fifth-order or higher-order image differentiation operation.

[0051] The first embodiment of the present invention proposes a design method for a super-Gaussian aperture high-order differential filter. When designing the filter, in order to achieve accurate multi-order differentials, a super-Gaussian function is used as the aperture function corresponding to the transfer function of the high-order differential filter, and the aperture function is used to limit the range of the transfer function; then the transfer function T(k x ,k y) is expressed as:

[0052]

[0053] In the formula, H(k x ,k y ) represents the momentum space transfer function without aperture restriction, k x ,k y Respectively represent the horizontal and vertical coordinates in momentum space; represents the super-Gaussian aperture function, k r represents the radial coordinate in momentum space, and w represents the beam waist radius of the super-Gaussian aperture function, m represents the order of the super-Gaussian function, and m≥3.

[0054] In this embodiment, optionally, the momentum space transfer function H(k x ,k y )include:

[0055] The transfer function corresponding to the total differential is:

[0056] H1(k x ,k y )=(k x +k y ) n

[0057] Realize the transfer function corresponding to the partial differential:

[0058]

[0059] Realize the transfer function corresponding to the topological differentiation:

[0060]

[0061] In the formula, n represents the order of differentiation; Represents the polar coordinate azimuth on the Fourier plane.

[0062] The present embodiment is described in detail below.

[0063] Image differential operation is shown as follows Figure 1 As shown, the input image is Fourier transformed by lens L1, its spectrum is filtered by a filter, and after inverse Fourier transform by lens L2, the image differential result is output. Usually, the input electric field and the output electric field are shown in equations (1) and (2):

[0064]

[0065]

[0066] In the formula, and E in (x,y) and E out The spectrum of (x',y') satisfies equation (3):

[0067]

[0068] Among them, k x ,k y are the horizontal and vertical coordinates in momentum space, T(k x ,k y ) is the transfer function in momentum space.

[0069] In order to realize the differential operation in a certain direction, the transfer function must satisfy T(k x ,k y )∝k x or T(k x ,k y )∝k y At this time, after inverse Fourier transform, the output field as well as Thus, a one-dimensional differential operation in the x or y direction is realized. Similarly, the form of each transfer function that realizes the differential in the two-dimensional direction can be derived, as well as the form of the high-order differential transfer function. The transfer function with aperture limitation can be uniformly written in the form of formula (4):

[0070]

[0071] In the formula, H(k x ,k y ) represents the total differential (k x +k y ) n , partial differential or topological differentiation The momentum space transfer function without aperture restriction is the same as above, n represents the order of differentiation; represents the aperture function, which is used to limit the range of the transfer function, k r represents the radial coordinate in momentum space, and Represents the polar coordinate azimuth on the Fourier plane.

[0072] In the prior art, the circular domain function is usually used or Gaussian function As the aperture function, the present invention proposes to use a super-Gaussian function As the aperture, w is the beam waist radius of each aperture function, m is the order of the super Gaussian function, and m ≥ 3.

[0073] The second embodiment of the present invention proposes an image processing method based on super-Gaussian aperture high-order differential filtering, such as Figure 2 As shown, the method includes placing a super-Gaussian aperture high-order differential filter on the spectrum plane in the 4f system to modulate the two-dimensional image spectrum; performing inverse Fourier transform on the modulated optical signal to obtain an image processing result; wherein the super-Gaussian aperture high-order differential filter uses a super-Gaussian function as an aperture function corresponding to the transfer function of the filter, and the aperture function is used to limit the range of the transfer function; the transfer function T(k x ,k y ) is expressed as:

[0074]

[0075] In the formula, H(k x ,k y ) represents the momentum space transfer function without aperture restriction, k x ,k y Respectively represent the horizontal and vertical coordinates in momentum space; represents the super-Gaussian aperture function, k r represents the radial coordinate in momentum space, and w represents the beam waist radius of the super-Gaussian aperture function, m represents the order of the super-Gaussian function, and m≥3.

[0076] In this embodiment, optionally, the momentum space transfer function H(k x ,k y )include:

[0077] The transfer function corresponding to the total differential is:

[0078] H1(k x ,k y )=(k x +k y ) n

[0079] Realize the transfer function corresponding to the partial differential:

[0080]

[0081] Realize the transfer function corresponding to the topological differentiation:

[0082]

[0083] In the formula, n represents the order of differentiation; Represents the polar coordinate azimuth on the Fourier plane.

[0084] The third embodiment of the present invention provides an image processing device based on super-Gaussian aperture high-order differential filtering, such as Figure 3 As shown, the device includes a single-mode laser 31, a first lens 32, a pinhole filter 33, a second lens 34, a third lens 35, a first reflector 36, a spatial light modulator 37, a fourth lens 38, a second reflector 39, a pinhole 310, and a CCD camera 311; wherein the light beam emitted by the single-mode laser 31 is expanded by a 4f system composed of the first lens 32 and the second lens 34, and is low-pass filtered by the pinhole filter 33 in the 4f system, and then passes through a target object located on the front focal plane of the third lens 35; the Fourier transform spectrum of the target object is reflected by the first reflector 36 at a small angle and incident on the spatial light modulator 37, and the spatial A prefabricated phase hologram is loaded on the optical modulator 37 as a filter to generate a phase hologram with a blazed grating. The Fourier transform spectrum is filtered and modulated by the spatial light modulator 37 and then diffracted to the positive first order. The diffracted light is inversely Fourier transformed by the fourth lens 38, and is reflected by the second reflector 39 and the positive first order light is extracted through the pinhole 310. The differential image is obtained by using the CCD camera 311. The transfer function corresponding to the prefabricated phase hologram is a transfer function with aperture limitation, and a super Gaussian function is used as the aperture function corresponding to the transfer function, and the aperture function is used to limit the range of the transfer function. Then the transfer function T(k x ,k y ) is expressed as:

[0085]

[0086] In the formula, H(k x ,k y ) represents the momentum space transfer function without aperture restriction, k x ,k y Respectively represent the horizontal and vertical coordinates in momentum space; represents the super-Gaussian aperture function, k r represents the radial coordinate in momentum space, and w represents the beam waist radius of the super-Gaussian aperture function, m represents the order of the super-Gaussian function, and m≥3.

[0087] In this embodiment, optionally, the momentum space transfer function H(k x ,k y )include:

[0088] The transfer function corresponding to the total differential is:

[0089] H1(k x ,k y )=(k x +k y ) n

[0090] Realize the transfer function corresponding to the partial differential:

[0091]

[0092] Realize the transfer function corresponding to the topological differentiation:

[0093]

[0094] In the formula, n represents the order of differentiation; Represents the polar coordinate azimuth on the Fourier plane.

[0095] As an example, the image processing device described in this embodiment processes the image as follows: the outgoing light beam of the single-mode laser 31 with a wavelength of 532 nm is expanded by a 4-f system consisting of a first lens 32 (for example, the focal length of the lens is 75 mm), a second lens 34 (for example, the focal length of the lens is 150 mm), and a pinhole filter 33 (the pinhole filter is a low-pass filter) located in the 4-f system is filtered, and then passes through a target object located at the front focal plane of the third lens 35. The Fourier transform spectrum of the target object is reflected by the first reflector 36 at a small angle. Angle (for example, less than 15°) is incident on the spatial light modulator 37, and the spatial light modulator 37 is loaded with a computer-prefabricated phase hologram as a filter. According to formula (4) and a high-order differential filter using a super-Gaussian function as an aperture limiting function, a phase hologram with a blazed grating is generated. After filtering, the Fourier transform spectrum is diffracted to the positive first order, and the positive first order light is extracted by the fourth lens 38 through the inverse Fourier transform and the pinhole 310 (39 in the figure is the second reflector), and the differential image is collected by the CCD camera 311. By changing the hologram on the spatial light modulator 37, image differential results of different orders and isotropic or anisotropic can be generated.

[0096] The technical effect of the present invention is further verified through simulation experiments.

[0097] The super Gaussian function, Gaussian function and circular function are used as the transfer function of the aperture respectively in the high-order differential operation, which proves that when the super Gaussian function is used as the aperture filter, the high-order differential effects can be perfectly achieved.

[0098] Figure 4 Taking the fifth-order partial differential As an example, various simulations were performed using circular domain functions, Gaussian functions, and third to fifth order super Gaussian functions. Figure 4In the figure, (a1)-(a5) are the circular function, Gaussian function and super Gaussian function curves when m=3, 4, 5, respectively; (b1)-(b5) are the transfer functions when they are used as aperture function P, respectively, and are represented by different line types. Since the circular function does not affect the shape of the transfer function, the circular function is taken as the benchmark and compared with the Gaussian function and the super Gaussian function when m=3, 4, 5, respectively.

[0099] from Figure 4 It can be seen from (b1)-(b5) that the curve when the super-Gaussian is used as the aperture is closer to the circular function than the Gaussian function, that is, closer to the original transfer function. Figure 4 In (c1)-(c5), their point spread functions are calculated respectively. The point spread function is related to the diffraction noise and determines the quality of the final differential image. The circular domain function is prone to diffraction noise due to its steep edge. The point spread function sidelobes of the super Gaussian function are significantly lower and less than those of the circular domain function. The Gaussian function is prone to attenuate the high-frequency part of the high-order differential due to its smooth curve. Therefore, the use of the super Gaussian function can achieve a better high-order differential effect. Using a circular image ( Figure 4 (d1)) is simulated to perform fifth-order differential operation and extract the white dashed line curve, such as Figure 4 (d2)-(d6) and Figure 4 (e1)-(e5). It can be seen that using the circular domain function as a filter tends to generate more diffraction noise, while using the Gaussian function only produces three lines and no fifth-order differentials. With the increase of m for the super-Gaussian function, the five edge line values ​​become more and more obvious, but when it increases to a certain extent, some diffraction noise will also be generated. Therefore, the quality of high-order differentials and edge noise can be optimized by changing the beam waist radius w and the size of m.

[0100] Use the circular domain function, Gaussian function, and super Gaussian function as apertures to perform fifth-order partial differentials on a circular object. Experimental operation, experimental results such as Figure 5 shown. Figure 5 (a1)-(a5) are the holograms of the transfer functions of circular aperture, Gaussian aperture and super-Gaussian aperture (when m=3, 4, 5), Figure 5 (b0) is the bright field image of the object, Figure 5 (b1)-(b4) are the differential results of the above functions corresponding to the aperture, and the white dashed curves are also extracted, as shown in (c1)-(c4). It can be seen that when m=4, the filter differential effect of the super-Gaussian aperture is the best, which can produce a good fifth-order differential effect and almost no edge noise. The experimental results of the differential filters of various aperture functions (Exp.) and Figure 4 The results of the theoretical part (Sim.) are in good agreement.

[0101] In addition, using the fourth-order super-Gaussian function as the filter aperture, two-dimensional first-order to fourth-order total differential operations and second-order to fifth-order partial differential operations were performed, such as Figure 6 As shown; Figure 6 (a1)-(a4) and Figure 6 (b1)-(b4) are the holograms required for the first to fourth order total differentials and the corresponding differential results, respectively. Figure 6 (c1)-(c4) and Figure 6 (d1)-(d4) are the holograms required for the second to fifth order total differentials and the corresponding differential results, respectively. It can be seen that in the first to fourth order total differentials and the second to fifth order partial differentials, clear edge lines with the same order of differential appear on the edges, proving that when super Gaussian is used as aperture filtering, low-noise high-order differentials can be accurately achieved.

[0102] Although the operations of the method of the present invention are described in a specific order in the drawings, this does not require or imply that the operations must be performed in this specific order, or that all the operations shown must be performed to achieve the desired results. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step, and / or one step may be decomposed into multiple steps.

[0103] Although the spirit and principle of the present invention have been described with reference to several specific embodiments, it should be understood that the present invention is not limited to the disclosed specific embodiments, and the division of various aspects does not mean that the features in these aspects cannot be combined to benefit, and such division is only for the convenience of expression. The present invention is intended to cover various modifications and equivalent arrangements included in the spirit and scope of the attached claims.

Claims

1. An image processing method based on super-Gaussian aperture high-order differential filtering, characterized in that: The method comprises placing a super-Gaussian aperture high-order differential filter on a spectrum plane in a 4f system to modulate a two-dimensional image spectrum; performing inverse Fourier transform on the modulated optical signal to obtain an image processing result; wherein, in the super-Gaussian aperture high-order differential filter, a super-Gaussian function is used as an aperture function corresponding to a transfer function of the filter, and the aperture function is used to limit the range of the transfer function; a transfer function T(k x ,k y ) is expressed as: In the formula, H(k x ,k y ) represents the momentum space transfer function without aperture restriction, k x ,k y Respectively represent the horizontal and vertical coordinates in momentum space; represents the super-Gaussian aperture function, k r represents the radial coordinate in momentum space, and w represents the beam waist radius of the super-Gaussian aperture function, m represents the order of the super-Gaussian function, and m≥3.

2. The image processing method based on super-Gaussian aperture high-order differential filtering according to claim 1, characterized in that: The momentum space transfer function H(k x ,k y 0 includes: The transfer function corresponding to the total differential is: H1(k x ,k y )=(k x +k y ) n Realize the transfer function corresponding to the partial differential: Realize the transfer function corresponding to the topological differentiation: In the formula, n represents the order of differentiation; Represents the polar coordinate azimuth on the Fourier plane.

3. An image processing device based on super-Gaussian aperture high-order differential filtering, characterized in that: The invention comprises a single-mode laser (31), a first lens (32), a pinhole filter (33), a second lens (34), a third lens (35), a first reflector (36), a spatial light modulator (37), a fourth lens (38), a second reflector (39), a pinhole (310), and a CCD camera (311); wherein the light beam emitted by the single-mode laser (31) is expanded by a 4f system composed of the first lens (32) and the second lens (34), and is low-pass filtered by a pinhole filter (33) in the 4f system before passing through a focal plane located in front of the third lens (35). The target object is reflected by the first reflector (36) at a small angle and incident on the spatial light modulator (37). The spatial light modulator (37) is loaded with a prefabricated phase hologram as a filter to generate a phase hologram with a blazed grating. The Fourier transform spectrum is filtered and modulated by the spatial light modulator (37) and then diffracted to the positive first order. The diffracted light is Fourier inverse transformed by the fourth lens (38), and is reflected by the second reflector (39) and extracted through the pinhole (310). The differential image is obtained by using a CCD camera (311); The transfer function corresponding to the prefabricated phase hologram is a transfer function with aperture limitation, and a super-Gaussian function is used as the aperture function corresponding to the transfer function, and the aperture function is used to limit the range of the transfer function; the transfer function with aperture limitation T(k x ,k y ) is expressed as: In the formula, H(k x ,k y ) represents the momentum space transfer function without aperture restriction, k x ,k y Respectively represent the horizontal and vertical coordinates in momentum space; represents the super-Gaussian aperture function, k r represents the radial coordinate in momentum space, and w represents the beam waist radius of the super-Gaussian aperture function, m represents the order of the super-Gaussian function, and m≥3.

4. The image processing device based on super-Gaussian aperture high-order differential filtering according to claim 3, characterized in that: The momentum space transfer function H(k x ,k y )include: The transfer function corresponding to the total differential is: H1(k x ,k y )=(k x +k y ) n Realize the transfer function corresponding to the partial differential: Realize the transfer function corresponding to the topological differentiation: In the formula, n represents the order of differentiation; Represents the polar coordinate azimuth on the Fourier plane.

Images