Single-frame off-axis digital hologram zero-order suppression double-branch spectral fusion reconstruction method

Abstract

This invention discloses a zero-order suppressed bi-branch spectral fusion reconstruction method for single-frame off-axis digital holograms, specifically relating to the fields of digital holographic imaging and computational imaging. It utilizes a discrete cosine transform domain penalized least squares model to estimate and subtract slowly varying zero-order background; extracts a small-window core spectrum from the original spectrum and a large-window extended spectrum from the zero-order suppressed spectrum; performs complex gain calibration within the overlapping frequency band, and obtains a positive first-order spectrum based on radial cosine weighted fusion, then recovers amplitude and phase through inverse Fourier transform and numerical propagation. This invention eliminates the need for multi-frame acquisition, hardware modulation, or training data, balances center-band complex field fidelity with peripheral high-frequency recovery, reduces background fluctuations and reconstruction artifacts, and improves the stability of single-frame off-axis digital holographic reconstruction.

Description

Technical Field

[0001] This invention belongs to the fields of digital holographic imaging and computational imaging technology, specifically relating to a zero-order suppression dual-branch spectral fusion reconstruction method for single-frame off-axis digital holograms. Background Technology

[0002] Digital holography records the interference intensity distribution between the object beam and the reference beam, and combines this with numerical diffraction propagation to achieve quantitative recovery of target amplitude and phase information. Off-axis digital holography introduces a tilted carrier between the object beam and the reference beam, separating the zero-order, positive-first-order, and negative-first-order spectra in the Fourier domain. This allows for complex amplitude reconstruction from a single-frame hologram, making it suitable for dynamic sample imaging, real-time detection, and rapid phase measurement. However, in practical off-axis digital holographic systems, the zero-order spectrum is not strictly confined to the spectral center. Due to factors such as uneven illumination, object beam self-interference, sample scattering, coherent noise, and system aberrations, the zero-order spectrum extends outward and contaminates the region containing the positive-first-order spectrum. Using a smaller frequency domain filtering window to extract the positive-first-order spectrum can reduce the zero-order spectrum from entering the passband, but it will truncate peripheral high-frequency components, leading to loss of edge details, microstructure texture, and phase abrupt change information. Using a larger frequency domain filtering window can retain more high-frequency information, but residual zero-order spectrum and noise can easily enter the reconstruction passband, causing background fluctuations, ringing artifacts, and phase instability.

[0003] Existing technologies such as multi-frame acquisition, reference light modulation, polarization modulation, intensity ratio adjustment, and dual-plane recording can suppress zero-order terms, but they typically require additional hardware or multi-frame stable acquisition, which is not conducive to dynamic single-frame imaging and compact system applications. Some single-frame numerical methods reduce zero-order background through nonlinear filtering, iterative estimation, interpolation, transform domain suppression, or image decomposition, but they easily create new trade-offs between zero-order suppression and the preservation of intrinsic low-to-mid-frequency information of the target. Adaptive spectrum segmentation and deep learning methods improve the automation of spectrum extraction, but most methods still rely on a single spectral window; deep learning methods also typically require training data and may be affected by imaging systems, sample types, and variations in noise statistics. Summary of the Invention

[0004] The purpose of this invention is to provide a zero-order suppressed dual-branch spectral fusion reconstruction method for single-frame off-axis digital holograms to solve the above-mentioned problems.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a zero-order suppression dual-branch spectral fusion reconstruction method for single-frame off-axis digital holograms, the specific steps of which are as follows:

[0006] S1. Obtain a single-frame off-axis digital hologram and determine the positive first-order spectrum center in the original spectrum corresponding to the single-frame off-axis digital hologram; S2. Based on the penalized least squares model in the discrete cosine transform domain, perform zero-order background estimation on the single-frame off-axis digital hologram to obtain a zero-order background estimation hologram; S3. Subtract the zero-order background estimation hologram obtained in S2 from the single-frame off-axis digital hologram to obtain a zero-order suppressed hologram; S4. Perform Fourier transform on the single-frame off-axis digital hologram and the zero-order suppressed hologram respectively to obtain the original spectrum and the zero-order suppressed spectrum; S5. Extract a small window core spectrum from the original spectrum, centered on the positive first-order spectrum center;

[0007] S6. In the zero-order suppression spectrum, extract the large-window extended spectrum centered on the positive first-order spectrum center, wherein the passband range of the large-window extended spectrum is larger than the passband range of the small-window core spectrum; S7. In the overlapping frequency band of the small-window core spectrum and the large-window extended spectrum, estimate the complex gain factor used to compensate for amplitude ratio differences and overall phase shift, and calibrate the large-window extended spectrum using the complex gain factor; S8. According to the radial cosine weight, smoothly fuse the small-window core spectrum and the calibrated large-window extended spectrum to obtain the fused positive first-order spectrum; S9. Shift the fused positive first-order spectrum to the spectrum center and perform an inverse Fourier transform to obtain the complex amplitude field of the recording surface, and perform numerical propagation on the complex amplitude field of the recording surface to obtain the amplitude distribution and / or phase distribution at the target surface.

[0008] Preferably, the method for determining the positive first-order spectrum center in S1 is any one of the following: peak search after excluding the zero-order region of the spectrum center, system carrier frequency calibration, or manual input.

[0009] Preferably, the penalized least squares model in S2 includes a data consistency term and a second-order smoothing regularization term, expressed as:

[0010] ;

[0011] in, Here, Δ is the smoothing regularization parameter, and Δ is the discrete Laplace operator.

[0012] Under mirror boundary conditions, the discrete cosine transform can diagonalize the discrete Laplace operator; therefore, the background estimation can be efficiently solved in the discrete cosine transform domain as follows:

[0013] ;

[0014] Where DCT is the two-dimensional discrete cosine transform, IDCT is the two-dimensional inverse discrete cosine transform, and Λ is the eigenvalue matrix of the discrete Laplace operator in the discrete cosine transform domain.

[0015] Preferably, the detailed process of extracting the core spectrum of the small window centered on the positive first-level spectrum center in S5 is as follows: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] Construct a first elliptical Butterworth window centered on the ellipse; its normalized elliptical radius is expressed as:

[0016] ;

[0017] in, and These represent the semi-axis lengths of the first elliptical window in the two frequency directions; the first elliptical Butterworth window is represented as:

[0018] ;

[0019] in, The filter order; the core spectrum of the small window. pass Compared with the original spectrum Multiply them to get the result.

[0020] Preferably, the expansion process in S6, which extracts the large window spread spectrum centered on the positive first-level spectrum center, is based on the same positive first-level spectrum center. Construct a second elliptical Butterworth window centered on the ellipse; its normalized elliptical radius is expressed as:

[0021] ;

[0022] in, and Let be the semi-axis lengths of the second elliptical window, and satisfy . , The second elliptical Butterworth window is represented as:

[0023] ;

[0024] in, The filter order; large window spread spectrum pass With zero-order suppression spectrum Multiply them to get the result.

[0025] Preferably, the complex gain factor in S7 is obtained through the following complex-domain least squares model:

[0026] ;

[0027] Its closed-form solution is expressed as:

[0028] ;

[0029] in, Indicates complex conjugation. To prevent division by zero of small positive numbers; the large window spread spectrum after complex gain calibration is:

[0030] ;

[0031] Through this complex gain calibration, the two spectral branches have consistent complex amplitude and phase scales in the overlapping region, thereby reducing amplitude jumps and phase discontinuities caused by direct splicing.

[0032] Preferably, the detailed process of S8 is to fuse coordinates radially. The weighting function represents the normalized distance of a spectral point relative to the center of the positive first-order spectral spectrum.

[0033] ;

[0034] in, As the boundary of the core area, The outer boundary of the transition region; merging the positive first-order spectrum. Represented as:

[0035] ;

[0036] Within the core region, the fused spectrum is mainly derived from the small window core branch of the original spectrum to maintain the fidelity of the center band complex field; within the extended region, the fused spectrum is mainly derived from the large window extended branch of the zero-order suppressed spectrum to supplement the peripheral high-frequency information; within the transition region, the two branches transition continuously according to cosine weights to avoid spectrum discontinuity caused by hard handover.

[0037] Preferably, in step S9, the numerical propagation of the complex amplitude field of the recording surface is specifically performed using the angular spectrum propagation method to propagate the complex amplitude field of the recording surface to the object surface; the angular spectrum propagation transfer function can be expressed as:

[0038]

[0039] in, The wavelength of the light source, For wave number, For transmission distance, and Spatial frequency coordinates; complex amplitude field of the object surface The target amplitude distribution is obtained by inverse transformation after multiplying the complex amplitude field of the recording surface with the angular spectrum propagation transfer function; and phase distribution They are respectively:

[0040] .

[0041] The technical effects and advantages of this invention are as follows: 1. This invention completes complex field reconstruction using a single-frame off-axis digital hologram, without the need for multi-frame acquisition, reference light modulation, polarization modulation, or additional hardware structures, making it suitable for dynamic samples and online detection scenarios.

[0042] 2. This invention utilizes a penalized least squares model (PLS-DCT) constructed in the discrete cosine transform domain to estimate and subtract the slowly varying zero-order background, thereby reducing the contamination of the zero-order spectrum on the positive first-order spectrum region and providing conditions for expanding the spectrum extraction range.

[0043] 3. This invention extracts the core spectrum of a small window from the original spectrum and the extended spectrum of a large window from the zero-order suppressed spectrum, so that the center frequency band complex field fidelity and the recovery of the peripheral high spatial frequency are undertaken by different branches, thus alleviating the contradiction between resolution and zero-order contamination of a single window.

[0044] 4. This invention compensates for the amplitude ratio difference and overall phase shift between the two branches simultaneously through complex gain calibration within the overlapping frequency band, thereby reducing amplitude and phase discontinuities during the spectrum fusion process.

[0045] 5. This invention achieves smooth spectral fusion through radial cosine weighting, reducing ringing artifacts, background fluctuations and phase instability, while maintaining high amplitude and phase reconstruction resolution.

[0046] 6. This invention does not rely on training data and has good physical interpretability and cross-system applicability. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the off-axis digital holographic microscopy system of the present invention;

[0048] Figure 2 This is a flowchart of the single-frame off-axis digital hologram zero-order suppression dual-branch spectral fusion reconstruction method of the present invention.

[0049] Figure 3 This is a hologram of the USAF 1951 quantitative phase resolution plate in an embodiment of the present invention.

[0050] Figure 4 The phase is reconstructed by the USAF 1951 quantitative phase resolution plate in this embodiment of the invention.

[0051] Figure 5 This is a hologram of optical phase star target reconstruction in an embodiment of the present invention.

[0052] Figure 6 This refers to the phase reconstructed from the optical phase target in this embodiment of the invention.

[0053] In the diagram: 1. Laser; 2. Beam expander and collimator; 3. Beam splitter; 4. Adjustable attenuator; 5. Second reflector; 6. Microscope objective; 7. Reflector; 8. Object under test; 9. Second microscope objective; 10. Second beam splitter; 11. CCD camera; 12. Computer. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] This invention provides a zero-order suppression dual-branch spectral fusion reconstruction method for a single-frame off-axis digital hologram, as shown in the figure. The specific steps are as follows:

[0056] S1. Obtain a single-frame off-axis digital hologram and determine the positive first-order spectrum center in the original spectrum corresponding to the single-frame off-axis digital hologram; S2. Based on the penalized least squares model in the discrete cosine transform domain, perform slow-varying zero-order background estimation on the single-frame off-axis digital hologram to obtain a zero-order background estimation hologram; S3. Subtract the zero-order background estimation hologram obtained in S2 from the single-frame off-axis digital hologram to obtain a zero-order suppressed hologram; S4. Perform Fourier transforms on the single-frame off-axis digital hologram and the zero-order suppressed hologram respectively to obtain the original spectrum and the zero-order suppressed spectrum; S5. Extract a small window core spectrum from the original spectrum centered on the positive first-order spectrum center; S6. Extract a small window core spectrum from the zero-order suppressed spectrum centered on the positive first-order spectrum center. S7. Extract the large window extended spectrum centered on the small window core spectrum, wherein the passband range of the large window extended spectrum is larger than the passband range of the small window core spectrum; S8. Estimate the complex gain factor used to compensate for amplitude ratio differences and overall phase shift within the overlapping frequency band of the small window core spectrum and the large window extended spectrum, and calibrate the large window extended spectrum using the complex gain factor; S9. S1. S2. S3. S4. S5. S6. S7. S8. S9. S1. S2. S1. S2. S3. S4. S9. S1. S2. S1. S2. S3. S1. S2. S3. S4. S1. S2. S1. S2. S3. S1. S2. S3. S1. S2. S1. S2. S3. S1. S2. S1. S2. S3. S1. S2. S1. S2. S3. S1. S2. S1. S2. S3. S1. S2. S1. S2. S3. S1. S2. S1. S2. S3. S1. S2. S1. S2. S3. S1. S2. S1. S3. S1. S2. S1. S2. S3. S1. S1. S2. S1. S3. S1. S2 ...1. S2.

[0057] Specifically, the method for determining the positive first-level spectrum center in S1 is any one of the following: peak search after excluding the zero-level region of the spectrum center, system carrier frequency calibration, or manual input.

[0058] Specifically, the penalized least squares model in S2 includes a data consistency term and a second-order smoothing regularization term, expressed as:

[0059] ;

[0060] in, Here, Δ is the smoothing regularization parameter, and Δ is the discrete Laplace operator.

[0061] Under mirror boundary conditions, the discrete cosine transform can diagonalize the discrete Laplace operator; therefore, the background estimation can be efficiently solved in the discrete cosine transform domain as follows:

[0062] ;

[0063] Where DCT is the two-dimensional discrete cosine transform, IDCT is the two-dimensional inverse discrete cosine transform, and Λ is the eigenvalue matrix of the discrete Laplace operator in the discrete cosine transform domain.

[0064] Specifically, the detailed process of extracting the core spectrum of the small window centered on the positive first-level spectrum center in S5 is as follows: Using the positive first-level spectrum center... Construct a first elliptical Butterworth window centered on the ellipse; its normalized elliptical radius is expressed as:

[0065] ;

[0066] in, and These represent the semi-axis lengths of the first elliptical window in the two frequency directions; the first elliptical Butterworth window is represented as:

[0067] ;

[0068] in, The filter order; the core spectrum of the small window. pass Compared with the original spectrum Multiply them to get the result.

[0069] Specifically, the expansion process in S6, which extracts the large window spread spectrum centered on the positive first-level spectrum center, is based on the same positive first-level spectrum center. Construct a second elliptical Butterworth window centered on the ellipse; its normalized elliptical radius is expressed as:

[0070] ;

[0071] in, and Let be the semi-axis lengths of the second elliptical window, and satisfy . , The second elliptical Butterworth window is represented as:

[0072] ;

[0073] in, The filter order; large window spread spectrum pass With zero-order suppression spectrum Multiply them to get the result.

[0074] Specifically, the complex gain factor in S7 is obtained through the following complex-domain least squares model:

[0075] ;

[0076] Its closed-form solution is expressed as:

[0077] ;

[0078] in, Indicates complex conjugation. To prevent division by zero of small positive numbers; the large window spread spectrum after complex gain calibration is:

[0079] ;

[0080] Through this complex gain calibration, the two spectral branches have consistent complex amplitude and phase scales in the overlapping region, thereby reducing amplitude jumps and phase discontinuities caused by direct splicing;

[0081] Specifically, the detailed process of S8 is to fuse coordinates radially. The weighting function represents the normalized distance of a spectral point relative to the center of the positive first-order spectral spectrum.

[0082] ;

[0083] in, As the boundary of the core area, The outer boundary of the transition region; merging the positive first-order spectrum. Represented as:

[0084] ;

[0085] Within the core region, the fused spectrum is mainly derived from the small window core branch of the original spectrum to maintain the fidelity of the center band complex field; within the extended region, the fused spectrum is mainly derived from the large window extended branch of the zero-order suppressed spectrum to supplement the peripheral high-frequency information; within the transition region, the two branches transition continuously according to cosine weights to avoid spectrum discontinuity caused by hard handover.

[0086] Specifically, in S9, the numerical propagation of the complex amplitude field of the recording surface is performed using the angular spectrum propagation method to propagate the complex amplitude field of the recording surface to the object surface; the angular spectrum propagation transfer function can be expressed as:

[0087]

[0088] in, The wavelength of the light source, For wave number, For transmission distance, and Spatial frequency coordinates; complex amplitude field of the object surface The target amplitude distribution is obtained by inverse transformation after multiplying the complex amplitude field of the recording surface with the angular spectrum propagation transfer function; and phase distribution They are respectively:

[0089] ;

[0090] It also includes a laser 1, the output end of which is provided with a beam expander collimator 2, the output end of which is provided with a beam splitter 3, and the output end of which is provided with an adjustable attenuator 4 and a reflector 7 respectively.

[0091] The output end of the adjustable attenuator 4 is equipped with a second reflector 5. The output end of the second reflector 5 is equipped with a microscope objective 6.

[0092] The output end of the reflector 7 is provided with a second microscope objective 9, and the object to be tested 8 is placed between the second microscope objective 9 and the reflector 7. The output ends of the second microscope objective 9 and the second microscope objective 6 are both converged on the second beam splitter 10. The output end of the second beam splitter is provided with a CCD camera 11, and the CCD camera is electrically connected to the computer 15.

[0093] Example 1: Dual-branch spectral fusion reconstruction of a single-frame off-axis hologram

[0094] This embodiment inputs a single-frame off-axis digital hologram. First, a two-dimensional Fourier transform is performed on the hologram, and the positive first-order spectral center is determined after excluding the central zero-order spectral region. Subsequently, the slowly varying zero-order background is estimated using the PLS-DCT method. The smoothing regularization parameter in PLS-DCT can be set according to the degree of holographic background undulation and interference fringe density; when the background undulation is strong, the smoothing regularization parameter can be appropriately increased, and when the target has abundant low-frequency information, the parameter can be appropriately decreased to avoid excessively weakening the useful structure.

[0095] After obtaining the zero-order background estimation map, it is subtracted from the original hologram to obtain the zero-order suppressed hologram. The Fourier spectra of the original hologram and the zero-order suppressed hologram are calculated separately. The original spectrum is used to extract the core spectrum for the small window, and the zero-order suppressed spectrum is used to extract the extended spectrum for the large window.

[0096] The core spectrum of the small window is extracted using a first elliptical Butterworth window centered on the center of the positive first-order spectrum. This window has a smaller semi-axis to preserve reliable low-frequency and mid-frequency complex field information in the central region of the positive first-order spectrum. The extended spectrum of the large window is extracted using a second elliptical Butterworth window centered on the same positive first-order spectrum. This window has a larger semi-axis than the first elliptical Butterworth window, to preserve more peripheral high-frequency components.

[0097] Since the core spectrum of the small window originates from the original spectrum, while the extended spectrum of the large window originates from the zero-order suppressed spectrum, there may be differences in amplitude scaling and overall phase shift between the two. To avoid spectral discontinuities caused by direct splicing, a complex domain least squares problem is constructed within the overlapping frequency bands of the two branches to estimate the complex gain factor, and this complex gain factor is used to calibrate the extended spectrum of the large window.

[0098] After complex gain calibration, spectral fusion is performed using radial cosine weights. In the core region near the center of the positive first-order spectrum, the fused spectrum primarily uses the small window core branch of the original spectrum; in the extended region far from the center, the fused spectrum primarily uses the large window extended branch of the zero-order suppressed spectrum; in the transition region between the two, a continuous transition using cosine weights is employed. Finally, the fused positive first-order spectrum is shifted to the center of the spectrum, and an inverse Fourier transform is performed to obtain the complex amplitude field of the recording surface. This field is then propagated to the object surface using the angular spectrum propagation method to obtain the amplitude and phase distribution of the target.

[0099] Example 2: Transmission-type Off-axis Digital Holographic Microscopy Experiment

[0100] This embodiment uses a transmission-type off-axis digital holographic microscope system to verify the method of the present invention, and its schematic diagram is shown below. Figure 1 As shown. The light source wavelength is 633.1 nm. After beam expansion and collimation, the laser beam is split into object beam and reference beam by beam splitter 3. An adjustable attenuator 4 is set in the reference beam path to make the intensity ratio of the object beam and the reference beam close to 1:1. The object beam passes through the sample after reflecting mirror 7 and is collected by a 10x microscope objective 10 with a value aperture of 0.25. The reference beam is adjusted in propagation direction by reflecting mirror 5 and then re-beamed with the object beam at beam splitter 10 to form off-axis interference fringes. The hologram is acquired by CCD camera 11 with a resolution of 2592×1944 pixels and a pixel size of 2.2 μm. By adjusting the tilt angle of the reference beam to introduce a suitable spatial carrier, the zeroth, positive first, and negative first order spectra are separated in the Fourier domain.

[0101] The USAF 1951 quantitative phase resolution plate was used as the sample, and an effective hologram of 1024×1024 pixels was cropped from the original hologram. The hologram is shown below. Figure 3 As shown in the figure. Experimental results show that, compared with conventional Fourier filtering, Kronecker interpolation, and PLS-DCT large-window single-branch filtering, the method of this invention can reduce background phase fluctuations while maintaining high phase resolution. The standard deviations of the background region phase are 0.209 rad, 0.211 rad, 0.208 rad, and 0.197 rad, respectively. The method of this invention has the lowest corresponding phase standard deviation, and its reconstructed phase is shown in the figure. Figure 4 As shown.

[0102] In the second set of experiments, an optical phase star target was used as a complex phase sample, and an effective hologram of 1024×1024 pixels was cropped from the original hologram, as shown in the figure below. Figure 5 As shown. For the two background regions, the phase standard deviations obtained by the method of this invention are 0.191 rad and 0.107 rad, respectively; compared with the PLS-DCT large-window single-branch filtering method, the phase standard deviations are reduced by approximately 27.7% and 28.2%, respectively. This result demonstrates that the present invention can further suppress background phase fluctuations while recovering complex high spatial frequency phase structures. The phase reconstructed by this invention is shown in the figure. Figure 6 As shown.

[0103] Example 3: System and Device Implementation

[0104] The method of this invention can be implemented via software programs on general-purpose computers, workstations, embedded computing platforms, graphics processing units (GPUs), or digital signal processors (DSPs). The system may include an image acquisition interface, a processor, a memory, and a display module. The image acquisition interface receives a single-frame hologram acquired by an off-axis digital holographic system; the processor performs zero-order background estimation, bi-branch spectrum extraction, complex gain calibration, radial cosine fusion, and complex field reconstruction; the memory stores the input hologram, intermediate spectra, reconstruction results, and the computer program; and the display module displays the amplitude diagram, phase diagram, and spectral analysis results.

[0105] This invention can also be integrated into a digital holographic microscopy imaging device. After a single-frame off-axis hologram is acquired by a CCD or CMOS camera, it is input into a processor to execute the above algorithm, thereby outputting the amplitude and phase reconstruction results of the target in real time or near real time.

[0106] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for zero-order suppression and two-branch spectral fusion reconstruction of single-frame off-axis digital hologram, characterized in that: The specific steps are as follows: S1. Obtain a single-frame off-axis digital hologram and determine the positive first-order spectral center in the original spectrum corresponding to the single-frame off-axis digital hologram; S2. Based on the penalized least squares model in the discrete cosine transform domain, perform zero-order background estimation on the single-frame off-axis digital hologram to obtain a zero-order background estimation hologram; S3. Subtract the zero-order background estimation hologram obtained in S2 from the single-frame off-axis digital hologram to obtain a zero-order suppressed hologram; S4. Perform Fourier transforms on the single-frame off-axis digital hologram and the zero-order suppressed hologram respectively to obtain the original spectrum and the zero-order... Suppressing the spectrum; S5, extracting a small window core spectrum centered on the positive first-order spectrum center in the original spectrum; S6, extracting a large window extended spectrum centered on the positive first-order spectrum center in the zero-order suppressed spectrum, wherein the passband range of the large window extended spectrum is larger than the passband range of the small window core spectrum; S7, estimating a complex gain factor for compensating for amplitude ratio differences and overall phase shift within the overlapping frequency band of the small window core spectrum and the large window extended spectrum, and calibrating the large window extended spectrum using the complex gain factor; S8. Based on the radial cosine weight, the core spectrum of the small window and the calibrated extended spectrum of the large window are smoothly fused to obtain the fused positive first-order spectrum; S9. The fused positive first-order spectrum is shifted to the center of the spectrum and inverse Fourier transform is performed to obtain the complex amplitude field of the recording surface, and the complex amplitude field of the recording surface is numerically propagated to obtain the amplitude distribution and / or phase distribution at the target surface.

2. The method of zero-order suppression double-branch spectral fusion reconstruction of single-frame off-axis digital hologram according to claim 1, characterized in that: The method for determining the positive first-level spectrum center in S1 is any one of the following: peak search after excluding the zero-level region of the spectrum center, system carrier frequency calibration, or manual input.

3. The zero-order suppression dual-branch spectral fusion reconstruction method for a single-frame off-axis digital hologram according to claim 1, characterized in that: The penalized least squares model in S2 includes a data consistency term and a second-order smoothing regularization term, expressed as follows: ； wherein is a smoothing regularization parameter, and Δ is a discrete Laplacian operator. Under mirror boundary conditions, the discrete cosine transform can diagonalize the discrete Laplace operator; therefore, the background estimation can be efficiently solved in the discrete cosine transform domain as follows: ； Where DCT is the two-dimensional discrete cosine transform, IDCT is the two-dimensional inverse discrete cosine transform, and Λ is the eigenvalue matrix of the discrete Laplace operator in the discrete cosine transform domain.

4. The method of claim 1, wherein the method is a zero-order suppression bifurcated spectrum fusion reconstruction method of a single-frame off-axis digital hologram. The detailed process of extracting the small window core spectrum centered on the positive primary spectrum center in S5 is: constructing a first elliptical Butterworth window centered on the positive primary spectrum center ; Its normalized elliptic radius is expressed as: ； wherein, and are the semi-axes lengths of the first elliptical window in the two frequency directions, respectively; the first elliptical Bartlett window is represented as: ； wherein, is the filter order; small window core spectrum by and the original spectrum is multiplied.

5. The zero-order suppression dual-branch spectral fusion reconstruction method for a single-frame off-axis digital hologram according to claim 1, characterized in that: The extension process in the S6 of extracting a large window expansion spectrum with the positive primary spectrum center as the center is to construct a second elliptical Bartlett window with the same positive primary spectrum center as the center as the center Its normalized elliptic radius is expressed as: ； wherein, and are the semi-axes lengths of the second elliptical window, respectively, and satisfy , The second elliptical Bartlett window is expressed as: ； wherein is the filter order; large window spread spectrum by and zeroth order suppression spectrum multiplication.

6. The method of claim 1, wherein the method is a zero-order-rejection two-branch spectral fusion reconstruction method of a single-frame off-axis digital hologram. The complex gain factor in S7 is obtained through the following complex-domain least squares model: ； Its closed-form solution is expressed as: ； in, Indicates complex conjugation. To prevent division by zero of small positive numbers; the large window spread spectrum after complex gain calibration is: ； Through this complex gain calibration, the two spectral branches have consistent complex amplitude and phase scales in the overlapping region, thereby reducing amplitude jumps and phase discontinuities caused by direct splicing.

7. The zero-order suppression dual-branch spectral fusion reconstruction method for a single-frame off-axis digital hologram according to claim 1, characterized in that: The detailed process of S8 is to convert the radial fusion coordinates The normalized distance of the spectral point relative to the center of the positive primary spectrum is represented, and the weight function is represented as: ； in, As the boundary of the core area, The outer boundary of the transition region; merging the positive first-order spectrum. Represented as: ； Within the core region, the fused spectrum is mainly derived from the small window core branch of the original spectrum to maintain the fidelity of the center band complex field; within the extended region, the fused spectrum is mainly derived from the large window extended branch of the zero-order suppressed spectrum to supplement the peripheral high-frequency information; within the transition region, the two branches transition continuously according to cosine weights to avoid spectrum discontinuity caused by hard handover.

8. The method of claim 1, wherein the method is a zero-order-rejection two-branch spectral fusion reconstruction method of a single-frame off-axis digital hologram. The numerical propagation of the recording surface complex amplitude field in the S9 is specifically the angular spectrum propagation method for propagating the recording surface complex amplitude field to the object surface; and the angular spectrum propagation transfer function can be expressed as: in, The wavelength of the light source, For wave number, For transmission distance, and Spatial frequency coordinates; complex amplitude field of the object surface The target amplitude distribution is obtained by inverse transformation after multiplying the complex amplitude field of the recording surface with the angular spectrum propagation transfer function; and phase distribution They are respectively: 。

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