A coded aperture-based axial tomography method

Abstract

The invention proposes an axial tomography method based on coded aperture: First, generate a random phase aperture code through a random phase iterative algorithm based on intensity constraint; set the axial depth range [z min , z max . Taking a point light source at a distance z min on the principal optical axis as the target, adjust the object wavefront to capture images I1, I2, and I3 at three phase shifts of θ1, θ2, and θ3 respectively. Through three-step phase shift, obtain the point spread function H PSF of the point light source; with Δz as the step spacing, sequentially change the position of the point light source, and repeat the above process to record the point spread functions at different depths within the axial depth interval; taking a three-dimensional object as the target, adjust the object wavefront to capture images I1, I2, and I3 at three phase shifts of θ1, θ2, and θ3 respectively; use three-step phase shift to obtain the two-dimensional tomographic image H OBJ of the target; finally, perform target reconstruction. In the case of incoherent illumination, the invention can effectively improve the axial resolution of incoherent tomography while ensuring that the lateral resolution reaches the incoherent diffraction limit by using the phase-encoded aperture technology.

Description

Technical Field

[0001] The invention belongs to the field of tomography, and in particular relates to an axial tomography method based on coded aperture. Background Art

[0002] In the 21st century, mankind has entered the information age. As a good carrier of information, images have many advantages, such as large amount of information, intuitiveness, and easy to understand. As the main way to obtain images, the imaging system has increasingly higher requirements in terms of imaging resolution, imaging field of view, imaging speed, imaging dimension and other performance.

[0003] Traditional imaging systems are limited to two-dimensional imaging of the target scene and cannot record information at different depths of the target. The development of holographic technology and optical coherence tomography technology has realized the recording of information at different axial depths of the target. The basic principle of holographic technology is to record the depth information of the target through the interference of two coherent light beams. Since holographic technology has high requirements on the coherence of the light beam, it is usually necessary to use laser as the light source for active illumination. Optical diffraction tomography technology realizes tomographic imaging of the target at different axial depths by scanning, and has high axial resolution, but the imaging process using scanning usually takes a long time. Summary of the invention

[0004] The object of the present invention is to provide an axial tomography method based on coded aperture, so as to effectively improve the axial resolution of incoherent tomography while ensuring that the lateral resolution reaches the incoherent diffraction limit.

[0005] The technical solution of the present invention is as follows: an axial tomography method based on coded aperture, the steps are as follows:

[0006] Step 1. Generate a random phase coded aperture through a random phase iterative algorithm based on intensity constraints;

[0007] Step 2. Set the axial depth range , and the axial step distance ;

[0008] Step 3. Record the point spread function at different depths: The point light source is taken as the target, and the object light wavefront is adjusted to shoot , , Three phase-shifted images , , , through three-step phase shift, we get the diffusion function of the point light source ,by For the stepping interval, the position of the point light source is changed in sequence, and the above process is repeated to record the point spread function at different depths in the axial depth interval;

[0009] Step 4. Record the 2D tomographic image of the target: Take the 3D object as the target and adjust the object light wavefront to capture the , , Three phase-shifted images , , . Use three-step phase shift to obtain a two-dimensional tomographic image of the target ;

[0010] Step 5: Reconstruction of target tomographic image: Correlation operations are performed on the point spread functions at different axial depths and the two-dimensional tomographic image of the target, and a two-dimensional cross-sectional image of the target at the corresponding axial depth is reconstructed.

[0011] In step 1, the specific steps of the random phase iteration algorithm based on intensity constraints are as follows:

[0012] (1) Generate through random function Random real matrix uniformly distributed between and , get the initial matrix

[0013] ;

[0014] (2) Yes Perform a two-dimensional Fourier transform to obtain a complex matrix ,in The amplitude is ;

[0015] (3) Generate by random function Random phase uniformly distributed ,make

[0016] ;

[0017] (4) Yes Performing a two-dimensional Fourier transform, the phase in the frequency domain is obtained as ,make

[0018] ;

[0019] (5) Yes Perform a two-dimensional inverse Fourier transform to obtain its spatial phase: ,make

[0020] ;

[0021] (6) Calculated by the following formula , The root mean square residual between :

[0022] ,

[0023] And normalize the RMS;

[0024] (7) Repeat steps (4), (5), and (6) until the normalized mean square error is less than the threshold and the phase The convergence iteration ends. Extract the phase as random phase aperture coding.

[0025] In step 3, the transmission process of the point light source in the system is:

[0026] (1) Point light source on the main optical axis , the complex amplitude obtained by propagating through free space to the aperture plane of the system:

[0027] ;

[0028] (2) Complex amplitude in the aperture plane Complex amplitude distribution after passing through the collimating lens ,

[0029] Among them, the transmittance function of the collimating lens is: ,

[0030] The complex amplitude after passing through the collimating lens is: ;

[0031] (3) Use a beam splitter to split the light beam passing through the lens into two paths: object light and reference light. The object light is modulated by the coded aperture and then reflected to obtain: ,

[0032] The reference light is directly reflected from the plane mirror: ;

[0033] (4) After reflection, the object light and the reference light are superimposed to obtain:

[0034]

[0035] The superimposed beam propagates through free space to the CCD plane to record the light intensity .

[0036] In step 3, the phase information is recovered from the three intensity images using the three-step phase shift method to obtain the complex point spread function , select , , , complex point spread function for:

[0037] .

[0038] When reconstructing the intensity of the target two-dimensional cross-sectional image in step 5, the following formula is used to perform correlation operation on the target two-dimensional tomographic image and the point spread function:

[0039]

[0040] in and represent Fourier transform and inverse Fourier transform respectively, Indicates conjugation.

[0041] The beneficial effects of the present invention are: (1) the present invention can realize axial tomography of a three-dimensional target object through a single recording, reconstruct tomographic images of the target at different depths, and effectively improve the imaging efficiency; (2) the present invention can perform axial tomography of a three-dimensional object under incoherent light illumination, getting rid of the limitation of the coherence requirement of the light source. Compared with using a laser with strong coherence as a light source, incoherent light has the advantages of a high diffraction limit, no speckle noise, and a safer and more reliable light source. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 The present invention is a flowchart of an axial tomography method based on coded aperture according to an embodiment of the present invention.

[0043] Figure 2 is the target used for simulation test, where (a) is the axial depth The target, (b) is the axial depth goal.

[0044] Figure 3 is the point spread function obtained by recording the point light source at each axial position, where (a) is the axial depth of the point light source The point spread function recorded at (b) is the point light source at the axial depth The point spread function is recorded at .

[0045] Figure 4 It is a two-dimensional tomogram of a three-dimensional target obtained by three-step phase shift solution.

[0046] Figure 5 The results of reconstructing the target at different axial depths are shown in Figure 2, where (a) is the target at depth The result of reconstruction at depth (b) is the target at depth The result of reconstruction. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0048] by Figure 2 As a target of simulation test, this embodiment specifically describes an axial tomography method based on coded aperture, and the specific implementation steps are as follows.

[0049] Step 1. Generate a random phase coded aperture through a random phase iterative algorithm based on intensity constraints. The random phase coding generation process of the aperture is as follows:

[0050] (1) Generate through random function Random real matrix uniformly distributed between and , get the initial matrix

[0051] ;

[0052] (2) Yes Perform a two-dimensional Fourier transform to obtain a complex matrix ,in The amplitude is ;

[0053] (3) Generate by random function Random phase uniformly distributed ,make

[0054] ;

[0055] (4) Yes Performing a two-dimensional Fourier transform, the phase in the frequency domain is obtained as ,make

[0056] ;

[0057] (5) Yes Perform a two-dimensional inverse Fourier transform to obtain its spatial phase: ,make

[0058] ;

[0059] (6) Calculated by the following formula , The root mean square error between:

[0060] ,

[0061] And normalize the RMS;

[0062] (7) Repeat steps (4), (5), and (6) until the normalized mean square error is less than the threshold and the phase The convergence iteration ends. Extract the phase as random phase aperture coding.

[0063] Step 2. Set the axial depth range , and the axial step distance .

[0064] Step 3. Record the point spread function at different depths: The point light source is the target. At this time, the point light source is , the complex amplitude obtained by propagating through free space to the aperture plane of the system:

[0065] ;

[0066] The aperture plane complex amplitude The complex amplitude distribution is obtained through the collimating lens ,

[0067] Among them, the transmittance function of the collimating lens is:

[0068]

[0069] The complex amplitude after passing through the collimating lens is:

[0070]

[0071] The beam passing through the collimating lens is divided into two paths, object light and reference light, by using a beam splitter. The object light is modulated by the coded aperture and then reflected to obtain:

[0072]

[0073] The reference light is directly reflected from the plane mirror:

[0074]

[0075] After the object light and the reference light are reflected, they are superimposed to obtain:

[0076]

[0077] The superimposed beam propagates through free space to the CCD plane to record the light intensity , by changing the object light wavefront, the phase shift is adjusted to , , Take pictures separately , , , the diffusion function of the point light source is obtained through the three-step phase shift formula:

[0078]

[0079] by is the stepping interval, the position of the point light source is changed in sequence, and the above process is repeated to record the point spread function at different depths in the axial depth interval. The point spread function at the same axial depth position as the target is as follows: Figure 3 shown.

[0080] Step 4. Record the 2D tomographic image of the target: Take the 3D object as the target, place the target in the axial depth interval, and shoot the 3D tomographic image of the target by changing the object light wavefront. , , Three phase-shifted images , , . Use three-step phase shift to obtain a two-dimensional tomographic image of the target The target's two-dimensional tomographic image intensity is as follows: Figure 4 shown.

[0081] Step 5. Target tomographic image reconstruction: Using the formula:

[0082]

[0083] The point spread functions at different axial depths are correlated with the two-dimensional tomographic image of the target to reconstruct the two-dimensional cross-sectional image of the target at the corresponding axial depth, such as Figure 5 As shown, by using point spread functions of different depths, the images of the target at different depths can be reconstructed respectively.

[0084] It can be seen from the above steps that the present invention utilizes phase-coded aperture technology to achieve axial tomography of three-dimensional objects under incoherent light illumination, improve the axial resolution, and ensure that the lateral resolution of a single image reaches the incoherent diffraction limit.

[0085] The present invention uses random phase-coded aperture technology to achieve axial tomography of three-dimensional objects illuminated by incoherent light. In terms of light source, the present invention uses incoherent light so that the lateral resolution of the system can reach the incoherent diffraction limit, which is twice the coherent diffraction limit. That is, under the same system aperture, the lateral resolution of the imaging of the present invention can reach twice that of the traditional holographic method. At the same time, the present invention only needs to take a single shot of the three-dimensional object to reconstruct the tomographic image of the target at different axial positions. While ensuring the axial resolution, the imaging time of the system is reduced.

[0086] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A coded aperture based axial tomography method, Features Here are the steps: Step 1. Generate a random phase coded aperture through a random phase iterative algorithm based on intensity constraints; Step 2. Set the axial depth range , and the axial step distance ; Step 3. Record the point spread function at different depths: The point light source is taken as the target, and the object light wavefront is adjusted to shoot , , Three phase-shifted images , , , through three-step phase shift, we get the diffusion function of the point light source ,by For the stepping interval, the position of the point light source is changed in sequence, and the above process is repeated to record the point spread function at different depths in the axial depth interval; The transmission process of point light source in the system is: (1) Point light source on the main optical axis , the complex amplitude obtained by propagating through free space to the aperture plane of the system: ； (2) Complex amplitude in the aperture plane Complex amplitude distribution after passing through the collimating lens , Among them, the transmittance function of the collimating lens is: , The complex amplitude after passing through the collimating lens is: ; (3) Use a beam splitter to split the light beam passing through the lens into two paths: object light and reference light. The object light is modulated by the coded aperture and then reflected to obtain: , The reference light is directly reflected from the plane mirror: ; (4) After reflection, the object light and the reference light are superimposed to obtain: ， The superimposed beam propagates through free space to the CCD plane to record the light intensity ; Step 4. Record the 2D tomographic image of the target: Take the 3D object as the target and adjust the object light wavefront to capture the , , Three phase-shifted images , , , using three-step phase shift to obtain a two-dimensional tomographic image of the target ; Step 5: Reconstruction of target tomographic image: Correlation operations are performed on the point spread functions at different axial depths and the two-dimensional tomographic image of the target, and a two-dimensional cross-sectional image of the target at the corresponding axial depth is reconstructed.

2. A coded aperture based axial tomography method according to claim 1, Features In step 1, the specific steps of the random phase iteration algorithm based on intensity constraints are as follows: (1) Generate through random function Random real matrix uniformly distributed between and , get the initial matrix ； (2) Yes Perform a two-dimensional Fourier transform to obtain a complex matrix ,in The amplitude is ; (3) Generate by random function Random phase uniformly distributed ,make ； (4) Yes Performing a two-dimensional Fourier transform, the phase in the frequency domain is obtained as ,make ； (5) Yes Perform a two-dimensional inverse Fourier transform to obtain its spatial phase: ,make ； (6) Calculated by the following formula , The root mean square residual between : And normalize the RMS; (7) Repeat steps (4), (5), and (6) until the normalized mean square error is less than the threshold and the phase The convergence iteration is completed and the phase is extracted as random phase aperture encoding.

3. The coded aperture based axial tomography method according to claim 1, Features In step 3, the phase information is recovered from the three intensity images using the three-step phase shift method to obtain the complex point spread function , select , , , complex point spread function for: 。 4. The coded aperture based axial tomography method according to claim 1, Features When reconstructing the intensity of the target two-dimensional cross-sectional image in step 5, the following formula is used to perform correlation operation on the target two-dimensional tomographic image and the point spread function: in and represent Fourier transform and inverse Fourier transform respectively, Indicates conjugation.

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