Synthetic aperture quantitative phase imaging method based on hybrid of digital holography and fourier ptychography

Abstract

A synthetic aperture quantitative phase imaging method based on a hybrid of digital holography and Fourier ptychography. A programmable LED array which is annularly arranged is mounted on an off-axis digital holographic system for providing oblique illumination at varying angles; accurate noise-containing low-frequency information of an object is obtained by means of digital holography and is used as initial estimation; and then, high-frequency information of the object is reconstructed by means of a Fourier ptychographic algorithm based on intensity measurement, so as to realize synthetic aperture quantitative phase imaging. Using the accurate low frequency provided by holography as initial estimation ensures the accuracy of phase retrieval and wavefront aberration reconstruction, without strictly meeting matching illumination conditions, and reduces the number of intensity graphs required by Fourier ptychography; and a non-interferometric phase retrieval method based on Fourier ptychography improves the imaging resolution to an incoherent diffraction limit, and also effectively solves the problem of inherent speckle noise in digital holography.

Description

A synthetic aperture quantitative phase imaging method combining hybrid digital holography and Fourier layer stacking Technical Field

[0001] This invention pertains to optical microscopy measurement and synthetic aperture quantitative phase imaging technology, and in particular to a microscopic imaging method that combines digital holography and Fourier layer stacking. Background Technology

[0002] In the field of biomedical microscopy, living cells and unstained biological samples exhibit variations in refractive index and thickness due to differences in their internal fine structures. When light waves pass through, the wavelength and amplitude remain unchanged, only the phase changes, but this phase difference is invisible to the human eye. Over the past few decades, scientists have developed various fluorescence microscopy techniques to stain or label cells using chemical or biological methods, such as wide-field, confocal, total internal reflection fluorescence, two / multiphoton, and light-sheet fluorescence microscopy. In these techniques, fluorescent labels attached to specific molecular structures are excited by short-wavelength lasers, emitting long-wavelength fluorescence that makes colorless and transparent biological samples specific, thus enabling imaging. Since the beginning of the 21st century, there has been a persistent need to improve imaging resolution to observe subcellular characteristics of biological samples. This demand has driven the development of many unique sub-diffraction imaging techniques that have had a significant impact on biofluorescence imaging. These techniques, through single-molecule localization (such as stochastic optical reconstruction microscopy (STORM) and photoactivated localization microscopy (PALM)) or spatially modulated excitation (such as stimulated emission depletion microscopy (STED) and structured illumination microscopy (SIM)), enable the visualization of sample features far beyond the diffraction limit. However, these imaging techniques require fluorescent dyes and proteins as biolabels, making them unsuitable for non-fluorescent samples or samples that are difficult to label with fluorescence. Furthermore, the photobleaching and phototoxicity of fluorescent agents hinder the imaging of live cells over extended periods.

[0003] In recent years, quantitative phase imaging (QPI) has become a highly valuable optical tool in biomedical research. Thanks to its unique capabilities, it can image optical thickness variations in living cells and tissues without the need for specific staining or exogenous contrast agents (such as dyes or fluorophores). Quantitative phase profiling of cells allows for the determination of cell structure and biophysical parameters with minimal sample manipulation. QPI offers an important alternative, especially when traditional preparation techniques (such as fixation, staining, or fluorescent labeling) can affect cell function and limit biological insights. By introducing the principles of interferometry and holography into microscopy, amplitude and phase information of microscopic samples can be demodulated simultaneously from recorded interference patterns. Furthermore, various optical diffraction tomography methods have been developed to infer the three-dimensional refractive index distribution of biological samples through object rotation or illumination scanning, enabling three-dimensional label-free microscopy, which has been successfully applied to the study of various types of biological samples, including blood cells, neurons, cancer cells, and bacteria. However, since interferometric phase measurement techniques typically use lasers as the light source, interferometric techniques under highly coherent illumination are susceptible to noise from imperfections in the optical system and environmental disturbances. Furthermore, the imaging resolution of this technology is limited by the coherent diffraction limit, making it impossible to achieve high-resolution, high-signal-to-noise ratio quantitative phase imaging.

[0004] Unlike interferometric quantitative phase measurement techniques, which face numerous challenges, non-interferometric quantitative phase imaging techniques reconstruct the phase information of an object from acquired intensity maps. These techniques offer excellent signal-to-noise ratios and can achieve imaging resolutions that reach the incoherent diffraction limit (i.e., twice the coherent diffraction limit). Currently, typical non-interferometric quantitative phase imaging techniques include the Transport-of-Intensity Equation (TIE), Differential Phase Contrast (DPC), and Fourier Ptychographic Imaging (FPI). Among these techniques, Fourier Ptychographic Imaging can achieve high-resolution phase imaging with a large field of view. However, based on phase transfer function analysis under tilted illumination, accurate low-frequency phase recovery and wavefront aberration reconstruction can only be achieved when the illumination source is strictly matched to the objective lens's numerical aperture. This process is extremely difficult to achieve in practical experiments, especially in microscopic systems with limited system bandwidth, where achieving the matching condition is virtually impossible with high numerical aperture objectives such as oil immersion objectives. Therefore, how to solve the two major problems in interferometric phase measurement (imaging resolution and noise), while avoiding the matching illumination problem faced in non-interferometric phase imaging, and achieve accurate quantitative phase imaging and aberration characterization is a major technical challenge. Summary of the Invention

[0005] The purpose of this invention is to provide a synthetic aperture quantitative phase imaging method that combines digital holography and Fourier layer stacking.

[0006] The technical solution to achieve the objective of this invention is: a synthetic aperture quantitative phase imaging method combining hybrid digital holography and Fourier layer stacking, comprising:

[0007] Step 1: Acquire a target hologram with vertical illumination and several low-resolution intensity maps with oblique illumination;

[0008] Step 2: Reconstruct the complex amplitude from the acquired target hologram using a digital holographic quantitative phase reconstruction algorithm;

[0009] Step 3: Fill the Fourier transform of the complex amplitude obtained by digital holography in Step 2 into the center of the empty spectrum as the initial spectrum. Use the Fourier stacked phase recovery algorithm based on adaptive step size to reconstruct the high-frequency information of the object, and at the same time update the aperture information under constraints to estimate the wavefront aberration.

[0010] Step 4: Use the wavefront aberration estimated in Step 3 to perform aberration compensation on the reconstructed complex amplitude. Fill the compensated complex amplitude into the center of the spectrum obtained in Step 3 and use it as the initial spectrum again. Repeat Step 3 once to achieve accurate reconstruction of object information and aperture aberration. Use the phase unwrapping algorithm to obtain the synthetic aperture quantitative phase imaging result.

[0011] Preferably, a synthetic aperture microscopy platform is used to acquire holograms under vertical illumination and low-resolution intensity maps under tilted illumination. The synthetic aperture microscopy platform includes a programmable LED array arranged in a ring, a laser, a microscope objective, a collimating lens, a fiber optic beam splitter, a beam splitter prism, a first reflecting mirror, a second reflecting mirror, an imaging tube, and a camera. The center of the programmable LED array coincides with the optical axis of the microscope objective, the back focal plane of the microscope objective coincides with the front focal plane of the imaging tube, and the imaging plane of the camera is placed on the back focal plane of the imaging tube.

[0012] The laser emitted by the laser is split into an object beam and a reference beam by an optical fiber beam splitter. The object beam illuminates the sample and is reflected by the microscope objective, the imaging tube, and the first reflecting mirror in sequence to reach the beam splitter. The reference beam is reflected by the collimating lens and the second reflecting mirror and then merges with the object beam at the beam splitter, causing interference to form a hologram, which is then captured by the camera.

[0013] The laser is turned off, and the LEDs in the programmable LED array are lit in sequence to illuminate the sample at an angle. The plane waves emitted by the LEDs illuminate the sample and are reflected by the microscope objective, imaging tube, and first reflecting mirror to reach the beam splitter, where they are captured by the camera as a low-resolution intensity image.

[0014] Preferably, the illumination wavelength of the programmable LED array is the same as the laser wavelength.

[0015] Preferably, the intensity distribution I of the target hologram H (x,y) specifically refers to: I H (x,y)=|O 2 +|R 2 +|R|Oexp(-iksinθx)+|R|O * exp(iksinθx)

[0016] In the formula, the object wave O represents the complex amplitude information modulated by the object, R is the reference wave, (x,y) are the spatial coordinates, θ is the angle between the object wave and the reference wave, k is the wave vector, and O * It represents the conjugate of the complex amplitude of the object light wave.

[0017] Preferably, the specific method for reconstructing the complex amplitude from the acquired target hologram using a digital holographic quantitative phase reconstruction algorithm is as follows:

[0018] The acquired hologram is subjected to Fourier transform to obtain its corresponding spectrum. The positive first-order spectrum containing the complex amplitude information of the object is found. The positive first-order spectrum is obtained by frequency domain filtering. The spectrum is shifted to the center of the empty spectrum according to the maximum value of the positive first-order spectrum. The complete complex amplitude is recovered by inverse Fourier transform.

[0019] Preferably, the Fourier transform of the complex amplitude obtained through digital holography in step 2 is filled to the exact center of the spectrum as the initial spectrum. The high-frequency information of the object is reconstructed using a Fourier stacked phase retrieval algorithm based on adaptive step size, and the aperture information is updated to estimate the wavefront aberration. The specific method is as follows:

[0020] Step 31: Fill the Fourier transform of the complete complex amplitude O obtained through digital holography in Step 2 to the exact center of the spectrum, as the initial spectrum. The spectrum is updated using the low-resolution intensity map of the j-th illumination angle;

[0021] Step 32: Update the aperture function;

[0022] Step 33: Let j = j + 1, and repeat steps 31 and 32 until the spectrum and aperture function are updated using the low-resolution intensity maps of all tilted illuminations. The updated spectrum is then used as the high-resolution spectrum for the nth iteration.

[0023] Step 34: Calculate the cost function for the nth spectrum update;

[0024] Step 35, according to the cost function ε nThe iteration step size is adaptively changed, and it is determined whether the updated step size meets the threshold condition. If it does not meet the threshold condition, the process returns to step 31 and repeats the above iteration. Otherwise, the aperture function obtained in the last iteration is used as the estimated wavefront aberration.

[0025] Preferably, the spectrum update formula is as follows:

[0026] Where, α n Let be the iteration step size for the nth iteration, and δ be the regularization parameter. Represents the complex transmittance function of an object at the j-th illumination angle. Fourier transform, This represents the unconstrained Fourier spectrum under the j-th illumination direction. This represents the spectrum updated using the low-resolution intensity map of tilted illumination at the j-th illumination angle during the n-th iteration. This represents the updated spectrum obtained by using the low-resolution intensity map of tilted illumination at the (j-1)th illumination angle in the nth iteration. Initially, in the first iteration, the Fourier transform of the complex amplitude obtained from the digital holography is filled to the center of the frequency domain as the initial spectrum. Intensity maps at different illumination angles are used as amplitude constraints for spectral updating, where (u j ,v j ) represents the frequency domain coordinates corresponding to the j-th illumination angle. In the object's complex transmittance function, a(x,y) represents the object's absorption. Represents the phase of the object, (x,y) are the spatial domain coordinates, (u,v) are the corresponding frequency domain coordinates, P j-1 (u,v) is the aperture function at the (j-1)th illumination angle. P represents the maximum amplitude of the aperture function at the (j-1)th illumination angle. j-1 * (u,v) is the conjugate of the aperture function at the (j-1)th illumination angle.

[0027] Preferably, the aperture function update formula is:

[0028] Where β is the aperture update step size and γ is the regularization factor. The synthesized spectrum after frequency domain shifting under the j-th tilted illumination in the n-th iteration, for .

[0029] Preferably, the cost function for the nth spectrum update is:

[0030] Among them, I j(x,y) represents the low-resolution intensity map corresponding to the j-th illumination angle. It is the synthesized spectrum after frequency domain shift at the j-th illumination angle in the n-th iteration, where (u j ,v j ) represents the frequency domain coordinates corresponding to the j-th illumination angle; P j-1 (u,v) represents the aperture function after the (j-1)th update.

[0031] Preferably, the step size update formula is:

[0032] In the formula, α n Let ε be the step size for the nth iteration. n This is the cost function calculated in the nth iteration.

[0033] Compared with the prior art, the present invention has the following significant advantages:

[0034] (1) The synthetic aperture quantitative phase imaging technology of hybrid digital holography and Fourier layer does not require a complex tilting illumination rotation device and structured light device. The use of ring-arranged LED illumination greatly simplifies the synthetic aperture imaging system and improves the stability and robustness of the system.

[0035] (2) When using Fourier layer stacking to reconstruct the high-frequency part of the object, a quasi-monochrome LED illumination source was used to acquire a high-quality intensity map, which avoided speckle noise and parasitic interference caused by high temporal coherence laser source and improved the imaging quality.

[0036] (3) The synthetic aperture technology based on Fourier stacks is different from the synthetic aperture technology based on interference. It has the convenience and flexibility of non-interference synthetic aperture, and is easy to implement and operate.

[0037] (4) The accurate low-frequency information of the object obtained by digital holographic reconstruction can be used as the initial estimate of the Fourier stack, which can ensure accurate low-frequency phase recovery without meeting strict matching illumination conditions. Even when using high numerical aperture objectives in a microscopic imaging system, accurate phase recovery can still be achieved, which has better practicality.

[0038] (5) The accurate low-frequency information of the object obtained by digital holographic reconstruction can be used as the initial estimate of the Fourier stack, which can ensure that the Fourier stack algorithm can reconstruct the wavefront aberration without satisfying the strict matching illumination condition.

[0039] (6) The accurate low-frequency information of the object obtained by digital holographic reconstruction is used as the initial estimate of the Fourier stack. While ensuring accurate phase recovery and aberration reconstruction, the number of intensity maps required for the Fourier stack is reduced.

[0040] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0041] Figure 1 is a flowchart of a synthetic aperture quantitative phase imaging method that combines digital holography and Fourier layer stacking.

[0042] Figure 2 shows the optical path diagrams corresponding to the digital holographic imaging mode and the Fourier stacked imaging mode in the synthetic aperture microscopy platform that combines digital holography and Fourier stacked imaging. Figure 2(a) shows the optical path of digital holographic imaging, and Figure 2(b) shows the optical path of Fourier stacked imaging.

[0043] Figure 3 compares the phase reconstruction results with and without wavefront aberration calibration. Figure 3(a) shows the phase reconstruction result before aberration correction, Figure 3(b) shows the phase reconstruction result after aberration correction, Figure 3(c) is an enlarged view of the region of interest in the phase reconstruction result before aberration correction, Figure 3(d) is a cross-section of the 5th element in the 10th group, Figure 3(e) is an enlarged view of the region of interest in the phase reconstruction result after aberration correction, and Figure 3(f) is a cross-section of the 6th element in the 10th group. Figure 4 is a data processing flowchart for phase reconstruction using simulated data and applying the synthetic aperture quantitative phase imaging algorithm of hybrid digital holography and Fourier stacking.

[0044] Figure 5 shows the phase reconstruction results of oral epithelial cells using a synthetic aperture quantitative phase imaging algorithm that combines digital holography and Fourier transform. Figure 5(a) shows the phase reconstruction result based on digital holography, Figure 5(b) shows the phase reconstruction result based on Fourier transform imaging, Figure 5(c) shows the phase reconstruction result of the present invention, Figure 5(d) shows the result of digital holographic microscopy, Figure 5(e) shows the magnified comparison result of region 1 of the present invention, Figure 5(f) shows the comparison result of Fourier transform imaging of region 2 and the present invention, Figure 5(g) shows a cross-sectional view of the cell nucleus region, and Figure 5(h) shows a three-dimensional rendering. Detailed Implementation

[0045] The present invention is a synthetic aperture quantitative phase imaging method that combines digital holography and Fourier stacking. It acquires one vertically illuminated hologram and eight intensity maps with tilted illumination. Accurate, but noisy, low-frequency information of the object is obtained from the hologram using digital holographic phase reconstruction technology. This information serves as an accurate initial estimate to fill the spectral center. Subsequently, a Fourier stacking algorithm based on intensity measurements updates the spectral reconstruction of the object's high-frequency information, thereby achieving synthetic aperture quantitative phase imaging. This method combines the advantages of both interferometric and non-interferometric phase measurements, resolving the inherent problems of both methods. Accurate low-frequency initial estimation ensures accurate phase recovery and wavefront aberrations without requiring strict matched illumination conditions, while also reducing the number of intensity maps required for Fourier stacking. The synthetic aperture algorithm based on Fourier stacking improves the imaging resolution to the incoherent diffraction limit while effectively solving the speckle noise problem inherent in digital holography. Furthermore, the non-interferometric synthetic aperture strategy based on a ring-shaped programmable LED array illumination simplifies the imaging system and ensures its robustness and stability.

[0046] As shown in Figure 1, a synthetic aperture quantitative phase imaging method combining hybrid digital holography and Fourier layer stacking is implemented using the following steps:

[0047] Step 1: Collect one hologram of vertical illumination and eight intensity maps of tilted illumination.

[0048] This step involved designing a synthetic aperture microscopy platform that combines hybrid digital holography and Fourier transform. Specifically, a ring-shaped programmable LED array was mounted on the off-axis digital holographic microscopy system, with each LED illuminated sequentially while a CCD camera simultaneously acquired intensity maps.

[0049] The specific implementation process is as follows: This invention is a hybrid digital holographic and Fourier layered synthetic aperture microscopy imaging system. The actual hardware platform of this system includes a programmable LED array arranged in a ring with a wavelength of 532nm, a 532nm laser, an Arduino control board, a sample to be tested, a microscope objective, a collimating lens, a beam splitter, a reflecting mirror, an imaging tube, and a camera. The center of the programmable LED array coincides with the optical axis of the microscope objective and is placed at a set distance from the sample. The back focal plane of the microscope objective coincides with the front focal plane of the imaging tube, and the imaging plane of the camera is placed on the back focal plane of the imaging tube. Figure 2 shows example diagrams of the digital holographic imaging mode and the Fourier layered imaging mode in the hybrid digital holographic and Fourier layered synthetic aperture microscopy imaging platform. In the example, as shown in Figure 2(a), a 532nm laser is lit, collimated by a lens, and then split into an object wave and a reference wave by a beam splitter. The object wave illuminates the sample, passes through the objective lens and tube lens, and is reflected by a mirror to reach another beam splitter. The reference wave, after collimation and reflection, merges with the object wave at another beam splitter, causing interference to form a hologram, which is then captured by a CCD camera. This structure is a classic Mach-Zehnder interference optical path. Because there is an optical path difference between the object wave and the reference wave, a laser source with high coherence is often used in this optical path. However, high coherence often introduces interference artifacts and speckle noise, and the imaging resolution is limited by the coherence diffraction limit. Nevertheless, since interferometry can accurately reconstruct complete complex amplitude information, this method can obtain accurate low frequencies of the object and use them as an initial estimate.

[0050] As shown in Figure 2(b), in Fourier stacked imaging mode, the laser is turned off, and LEDs are sequentially lit via the Arduino control board for tilted illumination. Since the wavelength used by the laser is 532nm, the LED illumination wavelength is also 532nm to ensure consistent phase reconstruction accuracy. Table 1 shows the parameters of the LEDs used. During the installation of the ring-shaped programmable LEDs, their center is aligned with the optical axis of the microscope objective. The height between the LED array and the objective is adjusted to match the objective's numerical aperture as closely as possible. Although perfectly matching the objective's numerical aperture is difficult to achieve, approaching the objective's numerical aperture will effectively improve imaging resolution. The sequentially lit LEDs emit plane waves that illuminate the object, which pass through the objective and converge at the tube lens before falling onto the camera's imaging plane. The data acquisition computer software communicates with the camera and LEDs through a programming interface and program. The camera and LED array are synchronized via the same controller using two coaxial cables, providing triggering and monitoring of the exposure status. The hardware control circuit provides a series of trigger signals to control the camera's trigger sequence for acquiring eight intensity maps.

[0051] Table 1 Physical parameters of programmable LED array

[0052] Step 2: The complex amplitude is reconstructed from the acquired target hologram using a digital holographic quantitative phase reconstruction algorithm. Specifically, a Fourier transform is performed on the acquired hologram to obtain its corresponding spectrum. The positive first-order spectrum containing the object's complex amplitude information is located, and frequency domain filtering is used to obtain the positive first-order spectrum. The spectrum is then shifted to the center of the empty spectrum based on the maximum value of the positive first-order spectrum, and an inverse Fourier transform is used to recover the complete complex amplitude. This complex amplitude contains accurate low-frequency information about the object.

[0053] The specific implementation process is as follows: For off-axis digital holographic imaging, the object light wave, after being modulated by the object, carries complete complex amplitude information (O(x,y)) and interferes with the reference light wave at a certain angle θ to form an off-axis hologram. The intensity distribution of the off-axis hologram is I. H (x,y) is: I H (x,y)=|O 2 +|R 2 +|R|Oexp(-iksinθx)+|R|O * exp(iksinθx)

[0054] A Fourier transform is performed on the acquired hologram. The angle θ between the object wave and the reference wave shifts the positive and negative first-order spectra, carrying complete complex amplitude information, from the center of the spectrum to the high-frequency region, effectively separating the positive and negative first-order and zero-order spectra in Fourier space. Filtering in the frequency domain using a bandpass filter yields the positive first-order spectrum R. * O = |R|Oexp(-iksinθx). Since the reference light wave is a quasi-plane wave, the amplitude term is constant, but there is a tilted phase term exp(-iksinθx). Therefore, by shifting the positive first-order spectrum to the center of the empty spectrum in Fourier space to eliminate the tilted phase term, a complete complex amplitude O with accurate low-frequency information of the object is obtained.

[0055] According to the frequency response theory of diffraction-limited systems, the cutoff frequency of the coherent transfer function in digital holography is half that of the incoherent transfer function. Therefore, compared to incoherent imaging systems, the imaging resolution of digital holography is limited by the coherent diffraction limit. Despite the resolution limitation and the influence of speckle noise, digital holographic interferometry effectively records and reconstructs accurate complex amplitude information of the object, ensuring good accuracy in low-frequency reconstruction without the need for additional illumination.

[0056] Step 3: Fill the complex amplitude obtained from digital holography in Step 2 to the exact center of the spectrum as the initial state for spectrum updating. Use an adaptive step-size Fourier stacked phase retrieval algorithm to reconstruct the object's high-frequency information, while simultaneously updating the aperture information under Zernike mode constraints to estimate wavefront aberrations. During the update process, low-resolution intensity maps at different illumination angles serve as amplitude constraints, and the finite objective lens numerical aperture in Fourier space serves as the support domain constraint for iterative spectrum updating to reconstruct the object's high-frequency information, thus achieving synthetic aperture. The specific implementation process is as follows:

[0057] Step 31: Fill the Fourier transform of the complete complex amplitude O obtained through digital holography in Step 2 to the exact center of the spectrum, as the initial spectrum. The spectrum is then updated using a low-resolution intensity map of the j-th illumination angle.

[0058] Where, α n Let δ be the iteration step size for the nth iteration, and δ be the regularization parameter. Represents the complex transmittance function of an object at the j-th illumination angle. Fourier transform, This represents the unconstrained Fourier spectrum under the j-th illumination direction. This represents the spectrum updated using the low-resolution intensity map of tilted illumination at the j-th illumination angle during the n-th iteration. This represents the updated spectrum after using the low-resolution intensity map of tilted illumination at the (j-1)th illumination angle in the nth iteration; initially, in the first iteration, the Fourier transform of the complex amplitude obtained from the digital holography is filled to the positive center of the frequency domain as the initial spectrum. Intensity maps at different illumination angles are used as amplitude constraints for spectral updating, where (u j ,v j ) represents the frequency domain coordinates corresponding to the j-th illumination angle. In the object's complex transmittance function, a(x,y) represents the object's absorption. Represents the phase of the object. (x,y) are the spatial domain coordinates, and (u,v) are the corresponding frequency domain coordinates.

[0059] Step 32: Considering the mechanical disturbances and thermal fluctuations of the microscope, as well as the optical inhomogeneities of biological samples that introduce aberrations leading to imaging distortion and significantly reducing imaging contrast and quality, the aperture function is updated simultaneously with the object's spectrum update to estimate wavefront aberrations, as shown in Figures 3(a) to 3(f). The initial aperture function P0(u,v) is a low-pass filter calculated based on the objective lens's numerical aperture.

[0060] Where β is the aperture update step size and γ is the regularization factor.

[0061] Step 33: Let j = j + 1, and repeat steps 31 and 32 until the spectrum and aperture function are updated using the low-resolution intensity maps of all tilted illuminations. The updated spectrum is then used as the high-resolution spectrum for the nth iteration.

[0062] Step 34: Calculate the cost function ε for the nth spectrum update. n :

[0063] Among them, I j (x,y) represents the low-resolution intensity map corresponding to the j-th illumination angle. It is the synthesized spectrum after frequency domain shift at the j-th illumination angle in the n-th iteration, where (u j ,v j ) represents the frequency domain coordinates corresponding to the j-th illumination angle. P j-1 (u,v) represents the aperture function after the (j-1)th update.

[0064] Step 35, according to the cost function ε n Adaptively changing the iteration step size ensures convergence speed while avoiding getting trapped in local optima, and also avoids reconstruction instability caused by the noisy holographic complex amplitude O during iteration.

[0065] In the hybrid digital holography and Fourier stacked imaging system proposed in this invention, the complex amplitude O obtained from holographic reconstruction is used as the initial estimate. Due to the inevitable introduction of speckle noise from the high-coherence light source, the robustness and stability of the Fourier stacked reconstruction will be reduced. Although the instability of Fourier stacked reconstruction is often attributed to the non-convex nature of phase recovery when there is non-negligible noise, it is actually more closely related to the choice of step size. In formula (1), the choice of step size is very important. A larger constant step size can achieve fast convergence in the early stage, but it usually causes the algorithm to oscillate strongly in the neighborhood of the solution, so it may not converge accurately to the global optimum. For a constant but sufficiently small step size, although the stability of convergence is improved, the convergence speed is limited. Therefore, the specific update condition is as follows:

[0066] When step size α n+1 When the value is less than a given threshold (recommended value is 0.001), the iteration stops, and the aperture function obtained from the last update is used as the estimated wavefront aberration. The specific process is shown in Figure 4.

[0067] Step 4: Using the wavefront aberrations estimated in Step 3, aberration compensation is performed on the complex amplitude obtained from the digital holographic reconstruction. The compensated complex amplitude is then Fourier transformed and refilled to the center of the spectrum obtained in Step 3. The filled spectrum is then used as the initial spectrum, and Step 3 is repeated once to achieve accurate reconstruction of object information and aperture aberrations. After the phase unwrapping algorithm, the final high-precision, speckle-free synthetic aperture quantitative phase imaging result is obtained.

[0068] The specific implementation process is as follows: In the hybrid digital holography and Fourier layered synthetic aperture imaging system, in addition to wavefront aberrations in the intensity map under tilted illumination, wavefront aberrations are also present in the hologram under vertical illumination. However, the above steps estimate the wavefront aberrations based on the Fourier layered algorithm of the intensity map, and the low-frequency part provided by the digital holography does not participate in the iterative reconstruction. Therefore, this invention utilizes the wavefront aberrations initially estimated in step 32 to compensate for the complex amplitude obtained from the digital holographic reconstruction. After compensation, it is refilled to the center of the spectrum, and step 3 is repeated to achieve the final quantitative phase imaging. Because the synthetic aperture quantitative imaging recovery algorithm of hybrid digital holography and Fourier layered method introduces the correct low-frequency initial estimation, the final phase reconstruction result will have a wrapping problem when the sample is a large-phase object. This invention adopts a reliability-oriented phase unwrapping algorithm. This algorithm uses the wrapped phase as input to calculate the reliability, and performs parallel local phase unwrapping based on the calculated reliability, ultimately achieving high-precision, speckle-free, and high-accuracy synthetic aperture quantitative phase imaging. Figures 5(a) to 5(f) show the results of imaging oral epithelial cells using a hybrid digital holography and Fourier layered synthetic aperture quantitative phase imaging method.

[0069] This invention employs an LED as the illumination source in its Fourier stacking algorithm based on intensity measurement. Because LEDs have low temporal coherence as illumination sources, the acquired intensity maps have a high signal-to-noise ratio. Using these intensity maps as amplitude constraints in the Fourier stacking algorithm to reconstruct the object's high-frequency information can effectively suppress the inherent speckle noise problem in digital holographic phase imaging, achieving high-precision, speckle-free, and high-resolution quantitative phase imaging.

[0070] This invention employs a Fourier stack algorithm based on intensity measurement to reconstruct the high frequencies of an object, thereby achieving quantitative phase imaging using synthetic aperture. Unlike synthetic aperture methods using tilted or structured light illumination in traditional digital holographic structures, the non-interferometric synthetic aperture method based on Fourier stacks offers greater ease of implementation and can effectively expand the numerical aperture of the objective lens, reaching or even exceeding the incoherent diffraction limit (i.e., twice the coherent diffraction limit).

[0071] This invention employs a reliability-oriented phase unwrapping algorithm. Due to the accurate low-frequency initialization provided by digital holography, accurate quantitative phase recovery can be achieved for large-phase objects. However, the range limitation of the arctangent operator leads to phase wrapping in the reconstruction of large-phase objects. The reliability-oriented unwrapping algorithm first calculates the reliability based on the phase map, and then performs fast and parallel unwrapping operations on the wrapped phases according to the magnitude of the reliability.

Claims

1. A synthetic aperture quantitative phase imaging method combining hybrid digital holography and Fourier layer stacking, characterized in that, include: Step 1: Acquire a target hologram with vertical illumination and several low-resolution intensity maps with oblique illumination; Step 2: Reconstruct the complex amplitude from the acquired target hologram using a digital holographic quantitative phase reconstruction algorithm; Step 3: Fill the Fourier transform of the complex amplitude obtained by digital holography in Step 2 into the center of the empty spectrum as the initial spectrum, and use the Fourier stacked phase recovery algorithm based on adaptive step size to reconstruct the high-frequency information of the object, while updating the aperture information to estimate the wavefront aberration. Step 4: Use the wavefront aberration estimated in Step 3 to perform aberration compensation on the reconstructed complex amplitude. Fill the compensated complex amplitude into the center of the spectrum obtained in Step 3 and use it as the initial spectrum again. Repeat Step 3 once to achieve accurate reconstruction of object information and aperture aberration. Use the phase unwrapping algorithm to obtain the synthetic aperture quantitative phase imaging result.

2. The synthetic aperture quantitative phase imaging method based on hybrid digital holography and Fourier layer stacking according to claim 1, characterized in that, Holograms under vertical illumination and low-resolution intensity maps under tilted illumination are acquired using a synthetic aperture microscopy platform. The synthetic aperture microscopy platform includes a ring-shaped programmable LED array, a laser, a microscope objective, a collimating lens, a fiber beam splitter, a beam splitter prism, a first reflecting mirror, a second reflecting mirror, an imaging tube, and a camera. The center of the programmable LED array coincides with the optical axis of the microscope objective, the back focal plane of the microscope objective coincides with the front focal plane of the imaging tube, and the imaging plane of the camera is placed on the back focal plane of the imaging tube. The laser emitted by the laser is split into an object beam and a reference beam by an optical fiber beam splitter. The object beam illuminates the sample and is reflected by the microscope objective, the imaging tube, and the first reflecting mirror in sequence to reach the beam splitter. The reference beam is reflected by the collimating lens and the second reflecting mirror and then merges with the object beam at the beam splitter, causing interference to form a hologram, which is then captured by the camera. The laser is turned off, and the LEDs in the programmable LED array are lit in sequence to illuminate the sample at an angle. The plane waves emitted by the LEDs illuminate the sample and are reflected by the microscope objective, imaging tube, and first reflecting mirror to reach the beam splitter, where they are captured by the camera as a low-resolution intensity image.

3. The synthetic aperture quantitative phase imaging method based on hybrid digital holography and Fourier layer stacking according to claim 2, characterized in that, The illumination wavelength of the programmable LED array is the same as that of the laser.

4. The synthetic aperture quantitative phase imaging method based on hybrid digital holography and Fourier layer stacking according to claim 2, characterized in that, Intensity distribution I of the target hologram H (x,y) specifically refers to: I H (x,y)=|O| 2 +|R| 2 +|R|O exp(-ik sinθx)+|R|O * exp(ik sinθx) In the formula, the object wave O represents the complex amplitude information modulated by the object, R is the reference wave, (x,y) are the spatial coordinates, θ is the angle between the object wave and the reference wave, k is the wave vector, and O * It represents the conjugate of the complex amplitude of the object light wave.

5. The synthetic aperture quantitative phase imaging method based on hybrid digital holography and Fourier layer stacking according to claim 1, characterized in that, The specific method for reconstructing the complex amplitude from the acquired target hologram using a digital holographic quantitative phase reconstruction algorithm is as follows: The acquired hologram is subjected to Fourier transform to obtain its corresponding spectrum. The positive first-order spectrum containing the complex amplitude information of the object is found. The positive first-order spectrum is obtained by frequency domain filtering. The spectrum is shifted to the center of the empty spectrum according to the maximum value of the positive first-order spectrum. The complete complex amplitude is recovered by inverse Fourier transform.

6. The synthetic aperture quantitative phase imaging method based on hybrid digital holography and Fourier layer stacking according to claim 1, characterized in that, The Fourier transform of the complex amplitude obtained through digital holography in step 2 is filled to the center of the spectrum as the initial spectrum. The high-frequency information of the object is reconstructed using the Fourier stacked phase retrieval algorithm based on adaptive step size. At the same time, the aperture information is updated to estimate the wavefront aberration. The specific method is as follows: Step 31: Fill the Fourier transform of the complete complex amplitude O obtained through digital holography in Step 2 to the exact center of the spectrum, as the initial spectrum. The spectrum is updated using the low-resolution intensity map of the j-th illumination angle; Step 32: Update the aperture function; Step 33: Let j = j + 1, and repeat steps 31 and 32 until the spectrum and aperture function are updated using the low-resolution intensity maps of all tilted illuminations. The updated spectrum is then used as the high-resolution spectrum for the nth iteration. Step 34: Calculate the cost function for the nth spectrum update; Step 35, according to the cost function ε n The iteration step size is adaptively changed, and it is determined whether the updated step size meets the threshold condition. If it does not meet the threshold condition, the process returns to step 31 and repeats the above iteration. Otherwise, the aperture function obtained in the last iteration is used as the estimated wavefront aberration.

7. The synthetic aperture quantitative phase imaging method based on hybrid digital holography and Fourier layer stacking according to claim 6, characterized in that, The specific formula for updating the spectrum is as follows: Where, α n Let be the iteration step size for the nth iteration, and δ be the regularization parameter. Represents the complex transmittance function of an object at the j-th illumination angle. Fourier transform, This represents the unconstrained Fourier spectrum under the j-th illumination direction. This represents the spectrum updated using the low-resolution intensity map of tilted illumination at the j-th illumination angle during the n-th iteration. This represents the updated spectrum obtained by using the low-resolution intensity map of tilted illumination at the (j-1)th illumination angle in the nth iteration. Initially, in the first iteration, the Fourier transform of the complex amplitude obtained from the digital holography is filled to the exact center of the frequency domain as the initial spectrum. Intensity maps at different illumination angles are used as amplitude constraints for spectral updating, where (u j ,v j ) represents the frequency domain coordinates corresponding to the j-th illumination angle. In the object's complex transmittance function, a(x,y) represents the object's absorption. Represents the phase of the object, (x,y) are the spatial domain coordinates, (u,v) are the corresponding frequency domain coordinates, P j-1 (u,v) is the aperture function at the (j-1)th illumination angle. P represents the maximum amplitude of the aperture function at the (j-1)th illumination angle. j-1 * (u,v) is the conjugate of the aperture function at the (j-1)th illumination angle.

8. The synthetic aperture quantitative phase imaging method based on hybrid digital holography and Fourier layer stacking according to claim 6, characterized in that, The aperture function update formula is: Where β is the aperture update step size and γ is the regularization factor. The synthesized spectrum after frequency domain shifting under the j-th tilted illumination in the n-th iteration, for .

9. The synthetic aperture quantitative phase imaging method based on hybrid digital holography and Fourier layer stacking according to claim 6, characterized in that, The cost function for the nth spectrum update is: Among them, I j (x,y) represents the low-resolution intensity map corresponding to the j-th illumination angle. It is the synthesized spectrum after frequency domain shift at the j-th illumination angle in the n-th iteration, where (u j ,v j ) is the frequency domain coordinate corresponding to the j-th illumination angle, P j-1 (u,v) represents the aperture function after the (j-1)th update.

10. The synthetic aperture quantitative phase imaging method of hybrid digital holography and Fourier layer stacking according to claim 6, characterized in that, The step size update formula is: In the formula, α n Let ε be the step size for the nth iteration. n This is the cost function calculated in the nth iteration.

Images