CN104614970A - Optical scanning holographic image edge extracting method based on double-hole pupil - Google Patents

Abstract

The invention relates to an edge extraction method of an optical scanning holographic image based on a double hole pupil, which belongs to the technical field of optical scanning holography. The technical solution includes: Step 1: Set the double-hole pupil as P _2a (x,y)=δ(xx ₁ ,yy ₁ ), obtain the first Fresnel zone plate h ₁ , and perform the first two-dimensional Scan the hologram to obtain the hologram s ₁ . Step 2: Set the double aperture pupil as P _2b (x,y)=δ(xx ₂ ,yy ₂ ), obtain the second Fresnel zone plate h ₂ , conduct the second two-dimensional holographic scan, and obtain The hologram s ₂ is used to record more high-frequency information of the object. Step 3: Perform Fourier transform on the hologram of the two-dimensional holographic scanning, and introduce the conjugate gradient method to solve the inverse problem. The invention is simple in structure, easy to operate, has strong practicability, can realize clear object image edge extraction, and has important application value.

Description

A Method of Edge Extraction of Optical Scanning Holographic Image Based on Dual-hole Pupil

technical field

The invention belongs to the field of optical holographic imaging, and relates to optical scanning holographic technology and three-dimensional imaging technology.

Background technique

Optical Scanning Holography (OSH) is a kind of digital holography technology. By dividing the beam into two different wavefronts and interfering to form a Fresnel Zone Plate (FZP), and then realize the target High-resolution three-dimensional imaging of objects has broad application prospects in the fields of biomedical imaging, deformation measurement, particle field testing, optical microscopy, and optical remote sensing.

The two-dimensional hologram obtained by optical scanning holography technology contains the complete three-dimensional information of the sample, so how to extract the edge information of the sample image from the hologram has become a research hotspot in optical scanning holography. The edge of an image is the most basic feature of an image, and image edge detection is also one of the important basic contents of image processing. Specifically for optical scanning holography, the difficulty lies in how to extract effective reproduction from a two-dimensional hologram. Image edge information.

The document 'Edge detection of three-dimensional objects by manipulating pupil functions in an optical scanning holography system' proposed a preprocessing edge extraction method based on pupil design, by designing the two pupils in the OSH system as point pulse functions (Diracdelta function) and Laplacian of the Guassian function (Laplacian of the Guassian), so as to realize the edge extraction of the object image, but it needs to make major changes to the experimental system.

The document 'Edge-preserving sectional image reconstruction in optical scanningholography' proposes a method using the non-negative constraint method of total variation and gradient projection. This method can strengthen the slice object image to extract edge information, but the algorithm complexity is high .

The document 'Edge extraction using a time-varying vortex beam in incoherent digitalholography' proposes a method of using time-varying vortex beams to extract edge information of holograms. By introducing a spiral phase plate in the OSH system as one of the pupils, the time-varying vortex beam in coherent digitalholography is obtained. Change the vortex beam to extract objects like edges. This method can obtain clearer edge information, but the complexity of the experimental system also increases to a certain extent.

Contents of the invention

The invention provides a method for extracting the edge of an optical scanning holographic image based on a double-hole pupil. In the holographic imaging recording stage, two different Fresnel zone plates are produced by introducing a double-hole pupil, and then the same sample to be tested is scanned by these two Fresnel zone plates to obtain two sets of Hologram to record more high-frequency information of the object; in the holographic imaging reproduction stage, the hologram in the spatial domain is converted to the frequency domain through Fourier transform, and then the conjugate gradient method and inverse Fourier transform are used to realize the object Representation of the image edge and itself. The method is simple in structure, easy to operate, has strong practicability, and can realize clear object image edge extraction.

The technical solution of the present invention is: an optical scanning holographic image edge extraction method based on a dual-hole pupil, the system structure of which is shown in Figure 1, including the following steps:

Step 1: A polarization beam splitter (Beam Splitter, BS) splits the light with an angular frequency ω into two parts, one of which passes through the first pupil P ₁ (x, y) to form a plane wave P ₁ (x, y)=1; The other part passes through the second pupil P ₂ (x, y) after passing through the Acoustic Optical Frequency Shifter (AOFS) to generate a frequency shift of Ω. Here, the second pupil P ₂ (x, y) is realized by a transmissive liquid crystal spatial light modulator (Spatial LightModulator, SLM). By adjusting the voltage distribution of the spatial light modulator, the second pupil P ₂ (x,y) can work in two states: (1) P _2a (x,y)=δ(xx ₁ ,yy ₁ ), and (2)P _2b (x,y)=δ(xx ₂ ,yy ₂ ), to generate two spherical waves with different center positions; where, x ₁ ≠x ₂ , y ₁ ≠y ₂ , respectively represent the second light The spatial offset of pupil P ₂ (x, y) on the x, y axis; when the first hologram is recorded, it will pass through the first pupil P ₁ (x, y) and the second pupil P _2a ( The two beams of light x, y) are combined by a polarizing beam splitter to generate interference on the object to be measured to form a Fresnel zone plate h ₁ , and the deflection of h ₁ is controlled by a two-dimensional scanning mirror, thereby realizing the three-dimensional sample two-dimensional scanning. Lens 3 is used to collect the transmitted and scattered light passing through the sample and send it to the photodetector. The generated heterodyne current output is processed by frequency mixing, filtering, amplification, etc. to generate demodulation information and store it in the computer. The stored information is h ₁ coded image, which is essentially a hologram containing three-dimensional information of the sample.

The spatial impulse response of this optical scanning holographic system, that is, the Fresnel zone plate _h can be expressed as

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;z</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Where x, y, z represent space coordinates, and k is the wave number of light. It can be seen from formula (1) that for a certain axial position z, the Fresnel zone plate is a two-dimensional symmetric function about x, y, and the center of symmetry is (x ₁ , y ₁ ).

Assuming a complex function represents the amplitude information of the sample, then the two-dimensional hologram obtained after the sample is scanned by the optical system can be expressed as

where * represents two-dimensional convolution. Considering the sample to be tested as a collection of a series of discrete slices, the axial coordinate z can be discretized, expressed as z ₁ , z ₂ ,...,z _n , which represent the axial positions of different slices respectively. Then the two-dimensional hologram represented by (2) can be expressed as

Assuming that the sample contains only one slice, formula (3) can be simplified as

we will Convert to a 1D vector matrix ψ. If the sample to be tested is an N×N matrix, then ψ is a one-dimensional vector matrix with length ^N2 . Similarly, the two-dimensional hologram s ₁ (x, y) of the sample and the Fresnel zone plate h ₁ (x, y, z ₁ ) can also be transformed into one-dimensional vector matrices S ₁ and H of length N ² ₁ .

In this way, (4) can be expressed as

S ₁ ＝H ₁ ψ+n ₁ (5)

where n ₁ represents the white Gaussian noise of the system, which is a one-dimensional vector matrix of length N ² .

Step 2: Adjust the voltage of the spatial light modulator, set P ₂ (x,y) as P _2b (x,y)=δ(xx ₂ ,yy ₂ ), where x ₁ ≠x ₂ , y ₁ ≠y ₂ , so as to obtain the spherical wave whose center position is shifted. Combine the new spherical wave and another beam of plane wave through the polarization beam splitter, and generate interference on the measured object to form the second Fresnel zone plate (h ₂ ).

The spatial impulse response of the optical scanning holographic system, that is, the Fresnel zone plate (h ₂ ), can be expressed as

${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;z</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Comparing Equation (6) with Equation (1), it can be seen that by adjusting the second pupil P ₂ (x,y), the same optical system can be used to design different Fresnel zone plates to obtain more High-frequency information of many objects.

By scanning the same sample to be tested, a second group of sample holograms can be obtained. Likewise, this process can be characterized as

The matrix equation is

(8)

S ₂ =H ₂ ψ+n ₂

Integrating the matrix equations of the two 2D holographic scans, it can be expressed as

$\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]\mathrm{<span\; class="notranslate">\; \&psi;</span>}<span\; class="notranslate">\; +</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; H\&psi;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

Step 3: Reconstruct the holographic imaging by using the hologram scanned twice in two dimensions. In the stage of holographic imaging reproduction, the hologram in the spatial domain is first converted to the frequency domain by Fourier transform, and then the conjugate gradient method and inverse Fourier transform are used to realize the imaging of the edge of the object image and itself respectively. The reconstruction of holographic imaging is to solve the target vector ψ under the condition of known S. The solution of this problem can be transformed into the following minimization problem,

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&psi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; H\&psi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; C</span>}\mathrm{<span\; class="notranslate">\; \&psi;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Where ||.|| represents the second-order norm, λ>0 is the penalty coefficient, and C is the Laplacian Gaussian operator, which is essentially a high-pass filter and can be used for edge extraction of objects. The solution to this minimization problem can be expressed as

(H ⁺ H + λC ⁺ C)f(ψ) = H ⁺ G (11)

where H ⁺ is the conjugate transpose of matrix H. By introducing the conjugate gradient algorithm, edge extraction and object image reproduction can be realized.

The beneficial effects of the present invention are: by using the double-hole pupils to form different Fresnel zone plates to scan the sample to be tested respectively, two two-dimensional holograms are obtained, thereby recording more high-frequency information of the object, and then through Fourier The hologram in the spatial domain is transformed into the frequency domain, and then the conjugate gradient method and the inverse Fourier transform are used to realize the imaging of the edge of the object image and itself. The method is simple in structure, easy to operate, and can realize clear object image edge extraction, which has important application value.

Description of drawings

Fig. 1 is a basic structural diagram of the present invention (BS: polarization beam splitter, AOFS: acousto-optic modulator, lens: lens, 2D scan: two-dimensional scanning, detector: photodetector);

Fig. 2 is a schematic diagram of a sample to be tested in a specific embodiment of the present invention;

Fig. 3 is the Fresnel zone figure corresponding to the second pupil P _2a (x, y) and P _2b (x, y) in the specific embodiment of the present invention;

4 is a sinusoidal hologram obtained by scanning the second pupil P _2a (x, y) and P _2b (x, y) respectively in a specific embodiment of the present invention;

Figure 5 is the sample image reproduction effect obtained by traditional methods;

Fig. 6 is a sample image reproduction effect obtained in a specific embodiment of the present invention: including the object image itself and its edge information.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings.

A method for extracting the edge of an optical scanning holographic image based on a double-hole pupil, comprising the following steps:

Step 1: Set the double aperture pupil as P _2a (x,y)=δ(xx ₁ ,yy ₁ ), obtain the first Fresnel zone plate h ₁ , perform the first two-dimensional holographic scan, and obtain Hologram.

Step 2: Set the double aperture pupil as P _2b (x,y)=δ(xx ₂ ,yy ₂ ), obtain the second Fresnel zone plate h ₂ , conduct the second two-dimensional holographic scan, and obtain Hologram.

Step 3: Perform Fourier transform on the hologram of the two-dimensional holographic scanning, and introduce the conjugate gradient method to solve the inverse problem.

The specific structure of this embodiment is shown in FIG. 1 , and the center wavelength of the single-wavelength light source used is 632 nm. The sample to be tested used in this embodiment is shown in FIG. 2 , the axial position of the sample is z=34mm, the slice size is 1mm×1mm, and the matrix size is 512×512.

First, set the second pupil as P _2a (x,y)=δ(xx ₁ ,yy ₁ ), where x ₁ =0mm, y ₁ =0mm, perform the first two-dimensional holographic scanning, and obtain the hologram s ₁ .

Next, set the second pupil as P ₂ (x,y)=δ(xx ₂ ,yy ₂ ), where x ₂ =0.8mm, y ₂ =0mm, and conduct the second two-dimensional holographic scanning to obtain the hologram s ₂ .

Fresnel zone diagrams obtained with different pupils in the two scans are shown in Figure 3. It can be seen from Figure 3(a) and (b) that by changing the position of the pupil, more high-frequency information of the object can be recorded, thereby realizing the enhancement and extraction of the edge information of the object image. The sinusoidal hologram obtained by two scans is shown in Fig. 4. It can be seen from Figure 4 that we cannot obtain any information about the sample to be tested from the hologram.

Next, we compared two slice imaging methods: (1) the traditional sample image reconstruction method, which convolutes the sample hologram with the Fresnel zone plate conjugate function at the slice; Pupil edge extraction method. Figure 5(a) and (b) show the results of traditional image reconstruction using hologram s ₁ and hologram s ₂ , respectively. It can be seen that the effect of traditional image reproduction is not ideal, and the edges of the image are blurred. With the method of the present invention, the object image and its edge information can be completely distinguished, and the results are shown in Fig. 6 (a) and (b). This means that the method of the present invention successfully extracts the edge information of the object image.

The embodiment proves that by introducing a double-hole pupil, different Fresnel zone plates can be used to scan the sample to be tested to obtain two sets of holograms, thereby recording more high-frequency information of the object, and then using Fourier transform to convert the hologram The graph is converted to the frequency domain, and the conjugate gradient algorithm is introduced to solve it. The method is simple in structure, easy to operate, has strong practicability, can realize clear image edge extraction, and has important application value.

Claims (2)

1. a kind of optical scanning holographic image edge extraction method based on dual aperture pupil, is characterized in that: comprise the following steps: Step 1: The light beam passes through the polarization beam splitter to split the light with angular frequency ω into two parts, one part passes through the first pupil P ₁ (x, y) to form a plane wave P ₁ (x, y)=1; the other part passes through The acousto-optic modulator produces a frequency shift of Ω and then passes through the second pupil P ₂ (x,y); By adjusting the voltage distribution of the second pupil, the second pupil P ₂ (x,y) can work in two states: (1) P _2a (x,y)=δ(xx ₁ ,yy ₁ ), and (2)P _2b (x,y)=δ(xx ₂ ,yy ₂ ), to generate two spherical waves with different center positions, where x ₁ ≠x ₂ , y ₁ ≠y ₂ , respectively represent the second light The spatial offset of pupil P ₂ (x, y) on the x, y axis; When the first hologram is recorded, the two beams of light respectively passing through the first pupil P ₁ (x,y) and the second pupil P _2a (x,y) are combined through a polarizing beam splitter, and the measured Interference occurs on the object to form a Fresnel zone plate h ₁ , and the deflection of h ₁ is controlled by a two-dimensional scanning mirror to realize two-dimensional scanning of the three-dimensional sample; the lens 3 is used to collect the transmitted light and scattered light passing through the sample, and Send it into the photodetector; the generated heterodyne current output is processed by frequency mixing, filtering, amplification, etc. to generate demodulation information and store it in the computer; the stored information is h ₁ coded image, which essentially contains the three-dimensional sample holograms of information; The spatial impulse response of this optical scanning holographic system, that is, the Fresnel zone plate _h can be expressed as ${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;z</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ Among them, x, y, and z represent space coordinates, and k is the wave number of light; it can be seen from formula (1) that for a certain axial position z, the Fresnel zone plate is a two-dimensional symmetric function about x, y , the center of symmetry is (x ₁ ,y ₁ ); Assuming a complex function represents the amplitude information of the sample, then the two-dimensional hologram obtained after the sample is scanned by the optical system can represent Among them, * represents two-dimensional convolution; the sample to be tested is regarded as a collection of a series of discrete slices, and the axial coordinate z can be discretized, expressed as z ₁ , z ₂ ,..., z _n , representing The axial positions of different slices, then the two-dimensional hologram represented by (2) can be expressed as Assuming that the sample contains only one slice, formula (3) can be simplified as Will Converted to a one-dimensional vector matrix ψ, if the sample to be tested is an N×N matrix, then ψ is a one-dimensional vector matrix with a length of N ² ; similarly, the two-dimensional hologram s ₁ (x, y) of the sample and the phenanthrene The Nell zone plate h ₁ (x, y, z ₁ ) can also be transformed into one-dimensional vector matrices S ₁ and H ₁ with length N ² respectively; In this way, (4) can be expressed as S ₁ ＝H ₁ ψ+n ₁ (5) where n ₁ represents the white Gaussian noise of the system, which is a one-dimensional vector matrix of length N ² . Step 2: Adjust the voltage of the second pupil modulator, set P ₂ (x,y) as P _2b (x,y)=δ(xx ₂ ,yy ₂ ), where x ₁ ≠x ₂ , y ₁ ≠y ₂ , so as to obtain a spherical wave with a shifted center position, combine the new spherical wave with another beam of plane wave through a polarizing beam splitter, and generate interference on the measured object to form a second Fresnel zone plate (h ₂ ); The spatial impulse response of the optical scanning holographic system, that is, the Fresnel zone plate (h ₂ ), can be expressed as ${\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;z</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; (</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ By scanning the same sample to be tested, the second group of sample holograms can be obtained, and the process can also be characterized as The matrix equation is S ₂ =H ₂ ψ+n ₂ (8) Integrating the matrix equations of the two 2D holographic scans, it can be expressed as $\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]\mathrm{<span\; class="notranslate">\; \&psi;</span>}<span\; class="notranslate">\; +</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right]<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; H\&psi;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$ Step 3: Use two 2D scanned holograms to reproduce the holographic imaging; holographic imaging reproduction, that is, to solve the target vector ψ in the case of known S, the solution of this problem is transformed into the following minimization problem , $\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&psi;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; H\&psi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&lambda;</span>}{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; C\&psi;</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$ Where ||.|| represents the second-order norm, λ>0 is the penalty coefficient, and C is the Laplacian Gaussian operator, which is essentially a high-pass filter and can be used for edge extraction of objects; the minimization problem solution expressed as (H ⁺ H + λC ⁺ C)f(ψ) = H ⁺ G (11) Among them, H ⁺ is the conjugate transposition of matrix H; by introducing the conjugate gradient algorithm, edge extraction and object image reproduction can be realized. 2 . The method for extracting the edge of an optical scanning holographic image based on a dual-hole pupil according to claim 1 , wherein the second pupil is a transmissive liquid crystal spatial light modulator. 3 .