Phase recovery method of interference-free coded aperture correlation holography

Abstract

The invention discloses a phase recovery method based on non-interference coding aperture holography, and belongs to the field of computational optical imaging. According to the technology, phase information of an object is directly extracted from a single hologram through a physically-driven numerical optimization framework in combination with Wiener inverse filtering and an improved G-S (Gerchberg-Saxton) algorithm. A frequency domain inverse filter is constructed based on system modeling of a point diffusion hologram, noise interference is effectively suppressed, meanwhile, a historical gradient acceleration strategy is provided, a convergence path is optimized by dynamically adjusting an iteration step length, and the calculation efficiency is improved. The technology has the core advantages that the limitation of a traditional interference light path is broken through, precise optical alignment or multi-time out-of-focus surface data acquisition is not needed, the system architecture is simplified, the environmental adaptability is enhanced, and quantitative phase distribution reconstruction of transparent and weak scattering samples can be realized through single exposure.

Description

Technical Field

[0001] The present invention belongs to the field of computational optical imaging, and particularly relates to a phase recovery method for interferenceless coded aperture correlation holography, which is applicable to label-free quantitative phase imaging of transparent cells in biomedicine, sub-wavelength surface topography detection of micro-electromechanical systems (MEMS), optical elements, and other scenarios. Background Art

[0002] Interferenceless Coded Aperture Correlation Holography (I-COACH) is a non-coherent digital holography technology that can record and reconstruct the three-dimensional information of an object without the interference of two light waves. This feature greatly simplifies the optical path structure, reduces the requirements for system stability, improves power efficiency, and avoids complex optical alignment procedures. Currently, I-COACH has received attention in the fields of quantitative phase imaging and biomedical endoscope imaging, providing new solutions for phase measurement of transparent samples and high-resolution imaging of biological cells.

[0003] Traditional phase imaging techniques such as schlieren method, digital holographic tomography, etc. rely on beam interference or complex iterative optimization, and have problems such as high requirements for optical path stability and large computational complexity. In quantitative imaging based on the I-COACH system, although the intensity transport equation technique can directly solve the phase distribution, it is necessary to record intensity images of multiple defocus planes, which has problems of complex data processing, sensitivity to noise, and high phase recovery time cost.

[0004] The present invention proposes a phase recovery method for interferenceless coded aperture correlation holography. This method is a driving mechanism method based on numerical optimization, focusing on the phase recovery of holograms, with the characteristic of being interferenceless, thus reducing system complexity. Through systematic modeling of the point spread hologram, the phase distribution is directly solved, and combined with Wiener inverse filtering and an improved Gerchberg-Saxton (G-S) algorithm, the computational efficiency and noise robustness are balanced. In addition, the historical gradient weight optimization technique is adopted to reduce the number of iterations and improve the convergence speed. This method can directly recover the complex amplitude distribution of the object from a single hologram, realizing quantitative phase imaging under interferenceless conditions. Summary of the Invention

[0005] A phase retrieval method for non-interferometric coded aperture holography. The I-COACH optical device for implementing this method specifically includes a monochromatic LED light source, a first lens, an object or a pinhole, a microscope objective lens, a second lens, a polarizer, a phase-type spatial light modulator PSLM (Phase Spatial Light Modulator), and a CMOS image sensor. The light source uses incoherent light. After diffraction propagation and magnification by the microscope objective lens, it is modulated by the coded phase mask in the PSLM, and finally the intensity image is recorded by the image sensor. The coded phase mask is of a sparse dot type and is generated by an improved G-S (Gerchberg-Saxton) algorithm.

[0006] This method includes the following four steps:

[0007] S1: Record the object hologram and the point spread hologram;

[0008] Define the complex amplitude of the light field of the imaging object as O. The intensity of the object hologram OH (Object Hologram) recorded by the image sensor after being modulated by the coded phase mask CPM (Coded Phase Mask) is I OH , then replace the object with a pinhole, and the intensity of the point source hologram PSH (Point Spread Hologram) recorded by the image sensor is I PSH , and its formula description is I OH = O * I PSH Where, "*" represents the convolution operation.

[0009] Convert it to the frequency domain for calculation, and its formula is as follows Where, represents the Fourier transform, represents the inverse Fourier transform.

[0010] S2: Construct a Wiener inverse filter;

[0011] The Wiener inverse filter can be expressed as Where, (·) * represents the conjugate operation, and λ is the regularization parameter for suppressing noise.

[0012] The formula for the object preliminarily reconstructed after inverse filtering is expressed as

[0013] S3: Alternating projection optimization in the spatial domain and the frequency domain;

[0014] Constrain the initial amplitude |O 1 | and randomly initialize the phase θ (0) Optimize by alternately projecting in the spatial domain and the frequency domain through the GS algorithm. The spatial domain projection is expressed as where g (p) is the complex amplitude estimate at the p-th iteration, and θ (p) is the phase estimate at the p-th iteration.

[0015] Then calculate the frequency domain phase. The frequency domain projection is expressed as where G (p) is the frequency domain representation of the complex amplitude at the p-th iteration, A is the frequency domain amplitude constraint, calculated through the modulus of G (0) , and arg(·) is to take the phase.

[0016] Finally, back-project to update the phase, and its expression is where is the updated phase estimate.

[0017] S4: Accelerate the phase convergence with gradient;

[0018] Combined with the gradient acceleration strategy, normalize the initial phase generated in S3 and then optimize it. First, forward propagate the optical field to generate a hologram prediction, and its expression is where U 1 (n) is the predicted hologram at the n-th iteration, and θ n is the current phase estimate.

[0019] Calculate and correct the error of the predicted hologram through the recorded object hologram, and its expression is where U 2 (n) is the predicted hologram at the n-th iteration.

[0020] Back-propagate to the object plane to update the phase of the object plane, and its expression is where Δθ (n) is the phase update amount at the n-th iteration.

[0021] Use gradient to accelerate convergence, and iterate to obtain the phase of the reconstructed object, and its expression is Among them, r n represents the gradient acceleration factor of the nth iteration, <·> represents the inner product of two vectors, represents the square of the L2 norm, and θ (n) represents the phase estimation of the nth iteration, and θ (n-1) represents the phase estimation of the (n - 1)th iteration, and θ (n+1) represents the updated phase estimation. Description of the Drawings

[0022] Figure 1 Schematic diagram of non-interferometric coded aperture related holography adopted in the specific embodiment of the present invention.

[0023] Figure 2 Flowchart of a phase retrieval method based on non-interferometric coded aperture holography.

[0024] Figure 3 Imaging object: (a) Amplitude of the object, (b) Phase of the object.

[0025] Figure 4 Holograms recorded by the image sensor: (a) Object hologram, (b) Point spread hologram.

[0026] Figure 5 Reconstruction process and results: (a) Initial reconstructed amplitude, (b) Initial reconstructed phase, (c) Amplitude of the reconstructed object, (d) Phase of the reconstructed object.

[0027] Description of the reference numerals:

[0028] 1. Monochromatic LED light source, 2. First lens, 3. Target object or pinhole, 4. Microscope objective lens, 5. Second lens, 6. Imaging object plane, 7. Polarizer, 8. Phase-type spatial light modulator PSLM (Phase Spatial Light Modulator), 9. CMOS image sensor. Detailed Embodiment

[0029] In order to better explain the implementation process of the present invention, the present invention will be further described in detail below with an embodiment, but the present invention is not limited to this embodiment.

[0030] Embodiment

[0031] As Figure 1As shown, a monochromatic LED light source (1) with a wavelength of 532 nm is located on the front focal plane of the first lens (2). After being collimated by this lens, it forms a parallel light beam that irradiates the target object (3). The diffracted light of the object is magnified by a microscope objective lens (4) with a magnification of 40× and a focal length of 4 mm, and then is collimated again by a second lens (5) (with a focal length of 150 mm) that is 154 mm apart, forming an enlarged real image on the imaging plane (6). Then, this enlarged real image is regarded as an imaging object to participate in the subsequent imaging process. The light beam is incident on the polarizer (7), and the polarization angle of the polarizer (7) is the same as the modulation angle of the PSLM (8). The light beam passing through the polarizer (7) is modulated by the CPM loaded on the PSLM (8), and the modulated light beam is incident on the image sensor (9), and the hologram intensity distribution is recorded by the image sensor (9). Among them, CPM is of the sparse dot type and is generated by an improved G-S (Gerchberg-Saxton) algorithm.

[0032] The target object (3) uses a resolution plate with a pure phase distribution, whose amplitude is 1, and the amplitude and phase are respectively as Figure 3 (a) and Figure 3 (b) shown.

[0033] Recording the object hologram and the point spread hologram: Define the complex amplitude of the light field of the imaging object as O, and the intensity of OH recorded by the image sensor (9) after it is modulated by CPM is I OH , then replace the target object with a pinhole, and the intensity of PSH recorded by the image sensor is I PSH , and its formula description is I OH =O*I PSH Among them, "*" represents the convolution operation.

[0034] Convert it to the frequency domain for calculation, and its formula is as follows Among them, represents the Fourier transform, represents the inverse Fourier transform. Finally, the object hologram OH and the point source hologram PSH recorded by the image sensor (9) are respectively as Figure 4 (a) and Figure 4 (b) shown.

[0035] Constructing the Wiener inverse filter: For the convenience of analysis, the Wiener inverse filter can be expressed as Among them, (·) * represents the conjugate operation, λ is the regularization parameter for suppressing noise, and the value of the λ parameter is 1e-11.

[0036] The formula of the object initially reconstructed after inverse filtering is expressed as

[0037] Airspace-frequency domain alternating projection optimization: Take Figure 5 (a) The initial amplitude constraint |O 1 | and the randomly initialized phase θ (0) Perform airspace-frequency domain alternating projection optimization through the GS algorithm, and iterate 300 times to obtain the initial phase estimate. The airspace projection is expressed as where g (p) is the complex amplitude estimate of the p-th iteration, and θ (p) is the phase estimate of the p-th iteration.

[0038] Calculate the phase in the frequency domain. The frequency domain projection is expressed as where G (p) is the frequency domain representation of the complex amplitude of the p-th iteration, A is the frequency domain amplitude constraint, and is calculated by the modulus value of G (0) .

[0039] Back-project to update the phase to obtain the initial phase as shown in Figure 5 (b), and its expression is where is the updated phase estimate.

[0040] Gradient acceleration for phase convergence: Combine the gradient acceleration strategy to normalize and then optimize the initial phase generated in S3. First, forward-propagate the light field to generate a hologram prediction, and its expression is where U 1 (n) is the predicted hologram of the n-th iteration, and θ n is the current phase estimate.

[0041] Calculate and correct the error between the predicted hologram and the recorded object hologram, and its expression is where U 2 (n) is the predicted hologram of the n-th iteration.

[0042] Back-propagate to the object plane to update the phase in the object plane, and its expression is where Δθ (n) is the phase update amount of the n-th iteration.

[0043] Using gradient to accelerate convergence, the phase of the object is obtained after 200 iterations of the iterative loop, and its expression is where r n represents the gradient acceleration factor of the nth iteration, <·> represents the inner product of two vectors, represents the square of the L2 norm, θ (n) represents the phase estimate of the nth iteration, θ (n-1) represents the phase estimate of the (n - 1)th iteration, θ (n+1) represents the updated phase estimate. The reconstructed optical field amplitude and phase of the imaging object are respectively as Figure 5 (c) and Figure 5 (d) shown. From Figure 3 (b) and Figure 5 (d), it can be seen that the structural similarity between the phase distribution of the imaging object and the reconstructed phase distribution is 0.9578.

[0044] The above are only the preferred embodiments of the present invention, and do not represent the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the principle of the present invention are all included in the protection scope of the present invention.

Claims

1. A phase recovery method based on non-interference coded aperture holography, characterized in that: The method is specifically implemented by a device comprising a monochromatic LED light source, a first lens, a target object, a pinhole, a microscope objective lens, a second lens, a polarizer, a phase spatial light modulator PSLM (Phase Spatial Light Modulator), and a CMOS image sensor; the light source is incoherent light, which is propagated by diffraction and magnified by the microscope objective lens, and then modulated by a coded phase mask in the PSLM, and finally an intensity image is recorded by the image sensor, wherein the coded phase mask is a sparse point type and is generated by an improved GS (Gerchberg-Saxton) algorithm; The method comprises the following four steps: S1, recording object hologram and point spread hologram; The complex amplitude of the light field of the imaging object is defined as 0. After the complex amplitude of the light field is modulated by the coded phase mask CPM (Coded Phase Mask), the intensity of the object hologram OH (Object Hologram) recorded by the image sensor is I. OH Then the target object is replaced by a pinhole, and the intensity of the point source hologram PSH (Point Spread Hologram) recorded by the image sensor is I PSH , which is described by the formula I OH =O*I PSH Among them, "*" represents convolution operation; Convert the above formula to the frequency domain for calculation, the formula is as follows in, represents the Fourier transform, represents inverse Fourier transform; S2, construct the Wiener inverse filter; The Wiener inverse filter can be expressed as in,(·) * represents the conjugate operation, λ is the regularization parameter for suppressing noise; The formula for the object initially reconstructed after inverse filtering is expressed as S3, spatial-frequency domain alternating projection optimization; The initial amplitude constraint |O1| and the randomly initialized phase θ (0) The GS algorithm is used to perform spatial-frequency domain alternating projection optimization. The spatial domain projection is expressed as Among them, g (p) is the complex amplitude estimate of the pth iteration, θ (p) is the phase estimate of the pth iteration; Then calculate the frequency domain phase, and the frequency domain projection is expressed as Among them, G (p) is the frequency domain representation of the complex amplitude of the pth iteration, A is the frequency domain amplitude constraint, and G (0) The modulus value calculation, arg(·) is the phase; Finally, the back-projection updates the phase, which is expressed as in, is the updated phase estimate; S4, gradient accelerated phase convergence; Combined with the gradient acceleration strategy, the initial phase generated by S3 is normalized and then optimized. The forward light field is propagated to generate the hologram prediction, which is expressed as Among them, U1 (n) is the predicted hologram of the nth iteration, θ n is the current phase estimate; The error calculation and correction of the predicted hologram is performed through the recorded object hologram, and its expression is: Among them, U2 (n) is the predicted hologram of the nth iteration; Backward propagation to the object plane to update the object plane phase, the expression is: Among them, Δθ (n) is the phase update amount of the nth iteration; Using gradient acceleration to converge, the phase of the object is obtained by iterative cycle, and its expression is: Among them, r n represents the gradient acceleration factor of the nth iteration, <·> represents the inner product of two vectors, represents the square of the L2 norm, θ (n) represents the phase estimate of the nth iteration, θ (n-1) represents the phase estimate of the n-1th iteration, θ (n+1) represents the updated phase estimate.

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