Synthetic aperture quantitative phase imaging method of mixed digital holography and Fourier lamination

Abstract

The invention discloses a synthetic aperture quantitative phase imaging method based on mixed digital holography and Fourier lamination, which comprises the following steps of: installing a programmable LED (light-emitting diode) array which is annularly arranged on an off-axis digital holography system for providing inclined illumination of angle transformation, obtaining accurate low-frequency information of an object which contains noise through digital holography, and taking the information as initial estimation; and then, object high frequency is reconstructed through a Fourier lamination algorithm based on intensity measurement, so that synthetic aperture quantitative phase imaging is realized. According to the invention, the accurate low frequency provided by holography is used as initial estimation, so that the accuracy of phase recovery and wavefront aberration reconstruction is ensured, a matched illumination condition does not need to be strictly met, and meanwhile, the number of intensity graphs required by Fourier lamination is reduced; the non-interferometric phase recovery method based on Fourier lamination improves the imaging resolution to an incoherent diffraction limit, and effectively solves the inherent speckle noise problem in digital holography.

Description

Technical Field

[0001] The invention belongs to optical microscopic measurement and synthetic aperture quantitative phase imaging technology, in particular to a microscopic imaging method of hybrid digital holography and Fourier stacking. Background Art

[0002] In the field of biomedical microscopic imaging, living cells and unstained biological samples have different refractive indices and thicknesses of their internal microstructures. When light waves pass through, the wavelength and amplitude do not change, only the phase changes, but this phase difference cannot be observed by the human eye. In the past few decades, scientists have developed a variety of fluorescence microscopic imaging methods by staining or marking cells through some chemical or biological means, such as widefield, confocal, total internal reflection fluorescence, dual / multiphoton and light sheet fluorescence microscopy technology. In these technologies, fluorescent markers attached to specific molecular structures are excited by short-wavelength lasers and radiate long-wavelength fluorescence, making colorless and transparent biological samples specific, thereby imaging. Since the beginning of the 21st century, there has been a 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 huge impact on biofluorescence imaging, enabling visualization of sample features far beyond the diffraction limit 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)). However, these imaging techniques require fluorescent dyes and fluorescent proteins as biomarkers and are therefore not suitable for non-fluorescent samples or samples that are difficult to fluorescently label. In addition, photobleaching and phototoxicity of fluorescent agents hinder the imaging of living cells over long periods of time.

[0003] In recent years, quantitative phase imaging (QPI) has become a valuable optical tool in biomedical research, thanks to its unique ability to image optical thickness changes in living cells and tissues without the need for specific staining or exogenous contrast agents (e.g., dyes or fluorophores). Quantitative phase profiles of cells allow the determination of cellular structures and biophysical parameters with minimal sample manipulation. QPI provides an important alternative, especially in cases where traditional preparation techniques (such as fixation, staining, or fluorescent labeling) may affect cell function and limit biological insights. By introducing the principles of interferometry and holography into microscopy, the amplitude and phase information of microscopic samples can be simultaneously demodulated from the recorded interference pattern. In addition, various optical diffraction tomography methods have been developed to infer the three-dimensional refractive index distribution of biological samples by object rotation or illumination scanning, making three-dimensional label-free microscopy possible and have been successfully applied to study various types of biological samples such as blood cells, neuronal cells, cancer cells, bacteria, etc. However, since lasers are usually used as light sources in interferometric phase measurement techniques, interferometric measurement techniques under high-coherence light source illumination are affected by noise caused by imperfections in the optical system and environmental disturbances. In addition, the imaging resolution of this technology is limited by the coherent diffraction limit, and high-resolution, high signal-to-noise ratio quantitative phase imaging cannot be achieved.

[0004] Different from the various problems faced by interference-based quantitative phase measurement technology, non-interference-based quantitative phase imaging technology reconstructs the phase information of the object through the collected intensity map, has a good imaging signal-to-noise ratio, and the imaging resolution can reach the incoherent diffraction limit (i.e., twice the coherent diffraction limit). At present, the more typical non-interference quantitative phase imaging technologies include the transport-of-intensity equation (TIE), differential phase contrast (DPC), Fourier ptychographic imaging (FPI), etc. Among these technologies, Fourier ptychographic imaging technology can achieve high-resolution phase imaging with a large field of view. However, according to the analysis of the phase transfer function under oblique illumination, accurate low-frequency phase recovery and wavefront aberration reconstruction can only be achieved when the illumination light source strictly matches the numerical aperture of the objective lens. However, this process is very difficult to implement in actual experiments, especially when using high numerical aperture objectives such as oil-immersion objectives in microscopy systems (limited system bandwidth), it is almost impossible to achieve matching conditions. 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 to achieve accurate quantitative phase imaging and aberration characterization is a major technical challenge. Summary of the invention

[0005] The object of the present invention is to provide a synthetic aperture quantitative phase imaging method of hybrid digital holography and Fourier stacking.

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

[0007] Step 1: Collect a vertically illuminated target hologram and several obliquely illuminated low-resolution intensity images;

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

[0009] Step 3, fill the Fourier transform of the complex amplitude obtained by digital holography in step 2 to the center of the empty spectrum as the initial spectrum, use the Fourier stacking phase recovery algorithm based on adaptive step size to reconstruct the high-frequency information of the object, and update the constrained aperture information 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 to 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, and use the phase unwrapping algorithm to obtain the synthetic aperture quantitative phase imaging result.

[0011] Preferably, a hologram under vertical illumination and a low-resolution intensity image under oblique illumination are collected by a synthetic aperture microscopic imaging platform, wherein the synthetic aperture microscopic imaging platform comprises a programmable LED array, a laser, a microscope objective lens, a collimating lens, a fiber beam splitter, a beam splitter prism, a first reflector, a second reflector, an imaging tube lens and a camera arranged in a ring, wherein the center of the programmable LED array coincides with the optical axis of the microscope objective lens, the rear focal plane of the microscope objective lens coincides with the front focal plane of the imaging tube lens, and the imaging plane of the camera is placed at the rear focal plane of the imaging tube lens;

[0012] The laser emitted by the laser is divided into an object light wave and a reference light wave by a fiber beam splitter. The object light wave irradiates the sample and then passes through the microscope objective lens, the imaging tube lens, and the first reflector to reach the beam splitter prism. The reference light wave is reflected by the collimating lens and the second reflector and then merges with the object light wave at the beam splitter prism to form a hologram by interference, which is captured by the camera.

[0013] Turn off the laser and light up the LEDs in the programmable LED array in turn to illuminate the sample obliquely. The plane wave emitted by the LED illuminates the sample and is reflected by the microscope objective, imaging tube lens and the first reflector in turn to reach the beam splitter prism, and the low-resolution intensity image is captured by the camera.

[0014] Preferably, the illumination wavelength of the programmable LED array and the laser wavelength are the same.

[0015] Preferably, the intensity distribution of the target hologram Specifically: , In the formula, the object light wave represents the complex amplitude information carried by the object after modulation, is the reference light wave, is the spatial domain coordinate, is the angle between the object light wave and the reference light wave, is the wave vector, represents the conjugate of the complex amplitude of the object light wave.

[0016] Preferably, the specific method of reconstructing the complex amplitude from the collected target hologram by using the digital holographic quantitative phase reconstruction algorithm is: The collected hologram is subjected to Fourier transform to obtain its corresponding spectrum, and 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, and the spectrum is moved to the center of the empty spectrum according to the maximum value of the positive first-order spectrum. The inverse Fourier transform is used to restore the complete complex amplitude.

[0017] Preferably, the Fourier transform of the complex amplitude obtained by digital holography in step 2 is filled to the center of the spectrum as the initial spectrum, and the high-frequency information of the object is reconstructed by using the Fourier stacked phase recovery algorithm based on the adaptive step size, and the specific method for estimating the wavefront aberration by updating the aperture information is as follows: Step 31: The complete complex amplitude obtained by digital holography in step 2 The Fourier transform of fills the spectrum to the center as the initial spectrum , and use the The spectrum is updated with a low-resolution intensity map of each illumination angle; Step 32: Update the aperture function; Step 33, let , repeat steps 31 and 32 until the spectrum and aperture function are updated using the low-resolution intensity images of all oblique illuminations, and the updated spectrum is used as the high-resolution spectrum of the nth iteration; Step 34, calculate the Cost function for sub-spectrum update; Step 35, according to the cost function The iteration step size is adaptively changed, and it is determined whether the updated step size satisfies the threshold condition. If not, the process returns to step 31 to repeat the above iteration. Otherwise, the aperture function obtained in the last iteration is used as the estimated wavefront aberration.

[0018] Preferably, the spectrum updating formula is specifically: , in, is the nth iteration step length, is the regularization parameter, Indicates Complex transmittance function of an object at different illumination angles The Fourier transform of Indicates Fourier spectrum without amplitude constraint under illumination directions, Indicates that in the nth round of iteration, The updated spectrum of the low-resolution intensity map of oblique illumination at illumination angles, Indicates that in the nth round of iteration, The updated spectrum of the low-resolution intensity map of the oblique illumination under the illumination angle. Initially, in the first round of iteration, the Fourier transform of the complex amplitude obtained by the digital hologram is filled to the center of the frequency domain as the initial spectrum , the intensity map at different lighting angles is used as the amplitude constraint to update the spectrum, where It is The frequency domain coordinates corresponding to the illumination angles are, in the complex transmittance function of the object, represents the absorption of the object, Represents the phase of the object, is the spatial domain coordinate, is the corresponding frequency domain coordinate.

[0019] Preferably, the aperture function update formula is: , in, is the aperture update step size, is the regularization factor, For the In the iteration The synthetic spectrum after frequency domain shift under oblique illumination, for The complex conjugate of .

[0020] Preferably, The cost function of the sub-spectrum update is: , in, Representative The low-resolution intensity map corresponding to the illumination angle, It is The Fourier transform of the complex transmittance function of the object at the illumination angle is It is The frequency domain coordinates corresponding to the lighting angles, Represents the aperture function.

[0021] Preferably, the step size update formula is: , In the formula, For the The step size of the iteration, For the The cost function calculated by iteration.

[0022] Compared with the prior art, the present invention has the following significant advantages:

[0023] (1) The synthetic aperture quantitative phase imaging technology that hybridizes digital holography and Fourier stacking does not require complex tilt illumination rotation devices and structured light devices. The use of circularly arranged LED illumination greatly simplifies the synthetic aperture imaging system and improves the stability and robustness of the system.

[0024] (2) When Fourier stacking is used to reconstruct the high-frequency part of the object, a quasi-monochromatic LED illumination light source is used to collect high-quality intensity images, avoiding the speckle noise and parasitic interference caused by the high temporal coherence laser light source, thereby improving the imaging quality.

[0025] (3) The synthetic aperture technology based on Fourier stacking 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.

[0026] (4) Digital holographic reconstruction obtains accurate low-frequency information of the object as the initialization estimate of the Fourier stack, which can ensure accurate low-frequency phase recovery without the need to meet strict matching illumination conditions. Even when using a high numerical aperture objective in a microscopic imaging system, accurate phase recovery can still be achieved, which has better practicality.

[0027] (5) Digital holographic reconstruction obtains accurate low-frequency information of the object as the initialization estimate of the Fourier stack, which can ensure that the Fourier stack algorithm reconstructs the wavefront aberration without meeting strict matching illumination conditions.

[0028] (6) Digital holographic reconstruction obtains accurate low-frequency information of the object as the initialization estimate of the Fourier stack, which reduces the number of intensity maps required for the Fourier stack while ensuring accurate phase recovery and aberration reconstruction.

[0029] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of the synthetic aperture quantitative phase imaging method of hybrid digital holography and Fourier stacking.

[0031] Figure 2 It is an optical path diagram corresponding to the digital holographic imaging mode and the Fourier stack imaging mode in a synthetic aperture microscopy imaging platform that mixes digital holography and Fourier stack. Figure 2 (a) is the optical path of digital holographic imaging. Figure 2 (b) is the optical path of Fourier stack imaging.

[0032] Figure 3 This is the comparison of phase reconstruction results with and without wavefront aberration calibration. Figure 3 (a) is the phase reconstruction result before aberration correction. Figure 3 (b) is the phase reconstruction result after aberration correction. Figure 3 (c) is a magnified image of the region of interest of the phase reconstruction result before aberration correction. Figure 3 (d) is the cross section of the 5th element of the 10th group, Figure 3 (e) is a magnified image of the region of interest of the phase reconstruction result after aberration correction. Figure 3 (f) is the cross section of the 6th element of the 10th group.

[0033] Figure 4 This is a data processing flow chart for phase reconstruction using a hybrid digital holographic and Fourier stack synthetic aperture quantitative phase imaging algorithm, taking simulation data as an example.

[0034] Figure 5 This is the result of phase reconstruction of oral epithelial cells using a synthetic aperture quantitative phase imaging algorithm that hybridizes digital holography and Fourier stacking. Figure 5 (a) is the phase reconstruction result based on digital holography. Figure 5 (b) is the phase reconstruction result of Fourier stack imaging. Figure 5 (c) Phase reconstruction results of the present invention, Figure 5 (d) is the result of digital holographic microscopy. Figure 5 (e) is the magnified comparison result of area 1 of the present invention, Figure 5 (f) is the comparison result of the Fourier stack imaging of region 2 and the present invention, Figure 5 (g) is a cross-sectional view of the cell nucleus region. Figure 5 (h) is a 3D rendering. DETAILED DESCRIPTION

[0035] The concept of the present invention is: a synthetic aperture quantitative phase imaging method of hybrid digital holography and Fourier stacking, by collecting a vertically illuminated hologram and eight obliquely illuminated intensity maps. Accurate but noisy low-frequency information of the object is obtained from the hologram through the phase reconstruction technology of digital holography technology, and filled into the center of the spectrum as an accurate initial estimate, and then the high-frequency information of the spectrum reconstruction object is updated by the Fourier stacking algorithm based on intensity measurement, thereby realizing synthetic aperture quantitative phase imaging. Since this method takes into account the advantages of interference and non-interference phase measurement, it solves the inherent problems of the two measurement methods. Accurate low-frequency initial estimation ensures the accuracy of phase recovery and wavefront aberration, and does not need to meet strict matching illumination conditions, while 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 inherent speckle noise problem in digital holography. In addition, the non-interference synthetic aperture strategy based on annular programmable LED array illumination simplifies the imaging system and ensures the robustness and stability of the system.

[0036] like Figure 1 As shown, a synthetic aperture quantitative phase imaging method of hybrid digital holography and Fourier stacking, the specific implementation steps are:

[0037] Step 1, collecting a vertically illuminated hologram and eight obliquely illuminated intensity maps;

[0038] In this step, a synthetic aperture microscopy platform for hybrid digital holography and Fourier stacking is designed. Specifically, a ring-shaped programmable LED array is added to the off-axis digital holographic microscopy system, and the LEDs are lit one by one and the CCD camera is triggered synchronously to collect the intensity map.

[0039] The specific implementation process is as follows: the present invention is a synthetic aperture microscopy imaging system that mixes digital holography and Fourier stacking. The actual hardware platform of the system includes a programmable LED array with a wavelength of 532 nm arranged in a ring, a 532 nm laser, an Arduino control board, a sample to be tested, a microscope objective, a collimating lens, a beam splitter, a reflector, an imaging tube lens, and a camera. The center of the programmable LED array coincides with the optical axis of the microscope objective and is placed at a distance from the sample. The rear focal plane of the microscope objective coincides with the front focal plane of the tube lens, and the imaging plane of the camera is placed at the rear focal plane of the imaging tube lens. Figure 2 The digital holographic imaging mode and the Fourier stacking imaging mode example diagrams in the hybrid digital holographic and Fourier stacking synthetic aperture microscopy imaging platform are given respectively. In the example, Figure 2As shown in (a), a laser with a wavelength of 532 nm is turned on, and after being collimated by a lens, it is divided into an object light wave and a reference light wave through a beam splitter prism. The object light wave irradiates the sample, passes through the objective lens and the tube lens, and is reflected by a reflector to reach another beam splitter prism. The reference light wave is collimated and reflected, and then merges with the object light wave on another beam splitter prism, where interference forms a hologram and is captured by a CCD camera. This structure is a classic Mach-Zehnder interference optical path. Since there is a direct optical path difference between the object light wave and the reference light wave, a laser light source with higher coherence is often used in this optical path. However, highly coherent light often brings interference artifacts and speckle noise, and the imaging resolution is limited by the coherent diffraction limit. Nevertheless, since the interferometric measurement technology can accurately reconstruct the complete complex amplitude information, this method can be used to obtain accurate object low frequencies and use them as initial estimates.

[0040] like Figure 2 As shown in (b), in the Fourier stack imaging mode, the laser is turned off, and the LEDs are lit up in sequence through the Arduino control board for oblique illumination. Since the wavelength used by the laser is 532 nm, the LED illumination wavelength used to ensure consistent phase reconstruction accuracy is also 532 nm. Table 1 shows the parameters of the LEDs used. In the process of adding a ring-shaped programmable LED, its center coincides with the optical axis of the microscope objective lens, and the height between the LED array and the objective lens is adjusted to match the objective lens numerical aperture as much as possible. Although it is difficult to perfectly match the objective lens numerical aperture, approaching the objective lens numerical aperture will effectively improve the imaging resolution. The LEDs that are lit one by one emit plane waves to illuminate the object, pass through the objective lens, converge through the tube lens, and fall on the imaging plane of the camera. The data acquisition computer software communicates with the camera and LED through the programming interface and program. The camera and the LED array are synchronized through the same controller using two coaxial cables to provide triggering and monitor the exposure status. The hardware control circuit provides a series of trigger signals to control the camera trigger sequence to collect eight intensity images.

[0041] Table 1 Physical parameters of programmable LED array

[0042] project parameter LED unit model LED unit wavelength WS2812B, SMD-5050532 nm LED unit bandwidth LED unit number ~20 nm8 LED unit power ~200 mW power supply 5V

[0043] Step 2: Reconstruct the complex amplitude from the collected target hologram through the digital holographic quantitative phase reconstruction algorithm, that is, perform Fourier transform on the collected hologram to obtain its corresponding spectrum, find the positive first-order spectrum containing the complex amplitude information of the object, obtain the positive first-order spectrum by frequency domain filtering, and move the spectrum to the center of the empty spectrum according to the maximum value of the positive first-order spectrum, and use inverse Fourier transform to restore the complete complex amplitude. This complex amplitude contains the accurate low-frequency information of the object.

[0044] The specific implementation process is as follows: For off-axis digital holographic imaging, the object light wave is modulated by the object and carries the complete complex amplitude information ( ) forms a certain angle with the reference light wave Interference occurs to form an off-axis hologram, and the intensity distribution of the off-axis hologram for:

[0045]

[0046] Perform Fourier transform on the collected hologram, and the angle between the object light wave and the reference light wave The positive and negative first-order spectra carrying complete complex amplitude information are moved from the center of the spectrum to the high-frequency region, so that the positive and negative first-order and zero-order are effectively separated in Fourier space. The positive first-order spectrum is obtained by filtering in the frequency domain through a bandpass filter. Since the reference light wave is a quasi-plane wave, the amplitude term is constant, but there is a tilted phase term. Therefore, by moving the positive first-order spectrum to the center of the empty spectrum in Fourier space to eliminate the tilted phase term, the complete complex amplitude with accurate low-frequency information of the object is obtained. .

[0047] According to the frequency response theory of diffraction-limited systems, the cutoff frequency of the coherent transfer function under digital holography is half of the cutoff frequency of the incoherent transfer function. Therefore, compared with the incoherent imaging system, the imaging resolution of digital holography is limited by the coherent diffraction limit. Although the resolution is limited and affected by speckle noise, the digital holographic interferometry method effectively records and reconstructs the accurate complex amplitude information of the object, which can well ensure the accuracy of low-frequency reconstruction without the need for additional lighting conditions.

[0048] Step 3, fill the complex amplitude obtained by digital holography in step 2 to the center of the spectrum as the initial state of spectrum update, use the Fourier stacking phase recovery algorithm based on adaptive step size to reconstruct the high-frequency information of the object, and update the aperture information under the Zernike mode constraint to estimate the wavefront aberration. In the updating process, the low-resolution intensity map under different illumination angles is used as the amplitude constraint, and the limited objective lens numerical aperture in Fourier space is used as the support domain constraint iteration to reconstruct the high-frequency information of the object to achieve synthetic aperture. The specific implementation process is:

[0049] Step 31: The complete complex amplitude obtained by digital holography in step 2 The Fourier transform of fills the spectrum to the center as the initial spectrum , and use the The spectrum is updated using a low-resolution intensity map of the illumination angles:

[0050] (1)

[0051] in, is the nth iteration step length, is the regularization parameter. Indicates Complex transmittance function of an object at different illumination angles The Fourier transform of Indicates Fourier spectrum without amplitude constraint under illumination directions, Indicates that in the nth round of iteration, The updated spectrum of the low-resolution intensity map of oblique illumination at illumination angles, Indicates that in the nth round of iteration, The updated spectrum of the low-resolution intensity map of the oblique illumination under the illumination angle; Initially, in the first round of iteration, the Fourier transform of the complex amplitude obtained by the digital hologram is filled to the center of the frequency domain as the initial spectrum , the intensity map at different lighting angles is used as the amplitude constraint to update the spectrum, where It is The frequency domain coordinates corresponding to the illumination angle. In the object complex transmittance function, represents the absorption of the object, Represents the phase of an object. is the spatial domain coordinate, is the corresponding frequency domain coordinate.

[0052] Step 32: Considering the mechanical disturbance and thermal fluctuation of the microscope, as well as the optical inhomogeneous structure of the biological sample, aberrations will be introduced, resulting in imaging distortion, which will significantly reduce the imaging contrast and quality. Therefore, the aperture function is updated synchronously while the object spectrum is updated to estimate the wavefront aberration, such as Figure 3 (a) ~ Figure 3 (f) shows the initial aperture function is the low-pass filter calculated based on the objective numerical aperture:

[0053] (2)

[0054] in, is the aperture update step size, is the regularization factor.

[0055] Step 33, let , repeat steps 31 and 32 until the spectrum and aperture function are updated using the low-resolution intensity images of all oblique illuminations, and the updated spectrum is used as the high-resolution spectrum of the nth iteration;

[0056] Step 34, calculate the Cost function for sub-spectral update :

[0057] (3)

[0058] in, Representative The low-resolution intensity map corresponding to the illumination angle, It is The Fourier transform of the complex transmittance function of the object at the illumination angle is It is The frequency domain coordinates corresponding to the illumination angle. Representative The aperture function after the update.

[0059] Step 35, according to the cost function Adaptively change the iteration step size to avoid falling into the local optimal solution while ensuring the convergence speed, and avoid the holographic complex amplitude with noise Reconstruction instability caused by iteration.

[0060] In the hybrid digital holography and Fourier stack imaging system proposed in the present invention, the complex amplitude obtained by holographic reconstruction As an initialization estimate, the high coherence light source used will inevitably introduce speckle noise, which will reduce the robustness and stability of Fourier stack reconstruction. Although the instability of Fourier stack reconstruction in the presence of non-negligible noise is often attributed to the non-convex nature of phase recovery, in fact, it is more closely related to the choice of step size. In formula (1), the choice of step size is very important. A large constant step size can achieve rapid convergence in the early stage, but it usually causes the algorithm to oscillate strongly in the neighborhood of the solution, so it may not accurately converge 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, according to the adaptive iterative step size of the cost function, the specific update condition is:

[0061] (4)

[0062] When step length When it is less than a given threshold (the recommended value is 0.001), the iteration stops and the aperture function obtained by the last update is used as the estimated wavefront aberration. The specific process is as follows: Figure 4 shown.

[0063] Step 4, use the wavefront aberration estimated in step 3 to perform aberration compensation on the complex amplitude obtained by digital holographic reconstruction, refill the compensated complex amplitude to the center of the spectrum obtained in step 3 after Fourier transformation, use the filled spectrum as the initial spectrum again, and repeat step 3 to achieve accurate reconstruction of object information and aperture aberration. After the phase unwrapping algorithm, the final high-precision, speckle-free synthetic aperture quantitative phase imaging result is obtained.

[0064] The specific implementation process is as follows: In the hybrid digital holography and Fourier stacking synthetic aperture imaging system, in addition to the wavefront aberration in the intensity map under oblique illumination, the hologram under vertical illumination also has aberrations. However, the above steps are based on the Fourier stacking algorithm of the intensity map to estimate the wavefront aberration, and the low-frequency part provided by the digital holography does not participate in the iterative reconstruction. Therefore, the present invention uses the wavefront aberration preliminarily estimated in step 32 and compensates for the complex amplitude obtained by digital holographic reconstruction. After compensation, refill to the center of the spectrum, and repeat step 3 again to achieve the final quantitative phase imaging. Since the correct low-frequency initial estimate is introduced into the synthetic aperture quantitative imaging recovery algorithm of the hybrid digital holography and Fourier stacking, there will be a wrapping problem in the final phase reconstruction result when the sample is a large phase object. The present invention adopts a reliability-guided phase unwrapping algorithm, which uses the wrapped phase as input to calculate the reliability, and performs parallel local phase unwrapping based on the calculated reliability, and finally achieves high-precision, speckle-free, and high-precision synthetic aperture quantitative phase imaging. Figure 5 (a) ~ Figure 5 (h) shows the results of imaging oral epithelial cells using a hybrid digital holography and Fourier stack synthetic aperture quantitative phase imaging method.

[0065] The Fourier stacking algorithm based on intensity measurement in the present invention uses LED as the illumination light source. Since LED as an illumination light source has low temporal coherence, the acquired intensity map has a high signal-to-noise ratio. It is used as the amplitude constraint condition in the Fourier stacking algorithm to reconstruct the high-frequency information of the object, which can effectively suppress the inherent speckle noise problem in digital holographic phase imaging. High-precision, speckle-free, high-resolution quantitative phase imaging is achieved.

[0066] The present invention uses a Fourier stacking algorithm based on intensity measurement to reconstruct the high frequency of the object to achieve synthetic aperture quantitative phase imaging. Different from the synthetic aperture method under oblique illumination or structured light illumination in the traditional digital holographic structure, the non-interference synthetic aperture method based on Fourier stacking has better convenience in implementation and can effectively expand the numerical aperture of the objective lens to reach or even break through the incoherent diffraction limit (i.e., twice the coherent diffraction limit).

[0067] This step uses a reliability-guided 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 problem of the inverse tangent operator leads to phase wrapping in the reconstruction of large phase objects. The reliability-guided unwrapping algorithm first calculates the reliability based on the phase map, and then implements fast and parallel unwrapping operations on the wrapped phase according to the size of the reliability.

Claims

1. A method for synthetic aperture quantitative phase imaging of hybrid digital holography and Fourier stacking, characterized in that: include: Step 1: Collect a vertically illuminated target hologram and several obliquely illuminated low-resolution intensity images; Step 2: Reconstruct the complex amplitude from the acquired target hologram through the digital holographic quantitative phase reconstruction algorithm; Step 3, fill the Fourier transform of the complex amplitude obtained by digital holography in step 2 to the center of the empty spectrum as the initial spectrum, use the Fourier stacking phase recovery algorithm based on adaptive step size to reconstruct the high-frequency information of the object, and update 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 to 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, and use the phase unwrapping algorithm to obtain the synthetic aperture quantitative phase imaging result.

2. The method for synthetic aperture quantitative phase imaging of hybrid digital holography and Fourier stacking according to claim 1, characterized in that: A hologram under vertical illumination and a low-resolution intensity image under oblique illumination are collected by a synthetic aperture microscopic imaging platform, wherein the synthetic aperture microscopic imaging platform comprises a programmable LED array, a laser, a microscope objective lens, a collimating lens, a fiber beam splitter, a beam splitter prism, a first reflector, a second reflector, an imaging tube lens and a camera arranged in a ring, wherein the center of the programmable LED array coincides with the optical axis of the microscope objective lens, the rear focal plane of the microscope objective lens coincides with the front focal plane of the imaging tube lens, and the imaging plane of the camera is placed at the rear focal plane of the imaging tube lens; The laser emitted by the laser is divided into an object light wave and a reference light wave by a fiber beam splitter. The object light wave irradiates the sample and is reflected by the microscope objective lens, the imaging tube lens and the first reflector in turn to reach the beam splitter prism. The reference light wave is reflected by the collimating lens and the second reflector and merges with the object light wave at the beam splitter prism to form a hologram by interference, which is captured by the camera. Turn off the laser and light up the LEDs in the programmable LED array in turn to illuminate the sample obliquely. The plane wave emitted by the LED illuminates the sample and is reflected by the microscope objective, imaging tube lens and the first reflector in turn to reach the beam splitter prism, and the low-resolution intensity image is captured by the camera.

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

4. The method for synthetic aperture quantitative phase imaging of hybrid digital holography and Fourier stacking according to claim 2, characterized in that: Intensity distribution of target hologram Specifically: , In the formula, the object light wave represents the complex amplitude information carried by the object after modulation, is the reference light wave, is the spatial domain coordinate, is the angle between the object light wave and the reference light wave, is the wave vector, represents the conjugate of the complex amplitude of the object light wave.

5. The method for synthetic aperture quantitative phase imaging of hybrid digital holography and Fourier stacking according to claim 1, characterized in that: The specific method of reconstructing the complex amplitude from the collected target hologram by using the digital holographic quantitative phase reconstruction algorithm is as follows: The collected hologram is subjected to Fourier transform to obtain its corresponding spectrum, and 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, and the spectrum is moved to the center of the empty spectrum according to the maximum value of the positive first-order spectrum. The complete complex amplitude is restored by inverse Fourier transform.

6. The method for synthetic aperture quantitative phase imaging of hybrid digital holography and Fourier stacking according to claim 1, characterized in that: The Fourier transform of the complex amplitude obtained by digital holography in step 2 is filled to the center of the spectrum as the initial spectrum, and the high-frequency information of the object is reconstructed using the Fourier stacking phase recovery algorithm based on adaptive step size. The specific method for estimating the wavefront aberration by updating the aperture information is as follows: Step 31: The complete complex amplitude obtained by digital holography in step 2 The Fourier transform of fills the spectrum to the center as the initial spectrum , and use the The spectrum is updated with a low-resolution intensity map of each illumination angle; Step 32: Update the aperture function; Step 33, let , repeat steps 31 and 32 until the spectrum and aperture function are updated using the low-resolution intensity images of all oblique illuminations, and the updated spectrum is used as the high-resolution spectrum of the nth iteration; Step 34, calculate the Cost function for sub-spectrum update; Step 35, according to the cost function The iteration step size is adaptively changed, and it is determined whether the updated step size satisfies the threshold condition. If not, the process returns to step 31 to repeat the above iteration. Otherwise, the aperture function obtained in the last iteration is used as the estimated wavefront aberration.

7. The method for synthetic aperture quantitative phase imaging of hybrid digital holography and Fourier stacking according to claim 6, characterized in that: The spectrum update formula is as follows: ， in, is the nth iteration step length, is the regularization parameter, Indicates Complex transmittance function of an object at different illumination angles The Fourier transform of Indicates Fourier spectrum without amplitude constraint under illumination directions, Indicates that in the nth round of iteration, The updated spectrum of the low-resolution intensity map of oblique illumination at illumination angles, Indicates that in the nth round of iteration, The updated spectrum of the low-resolution intensity map of the oblique illumination under the illumination angle. Initially, in the first round of iteration, the Fourier transform of the complex amplitude obtained by the digital hologram is filled to the center of the frequency domain as the initial spectrum , the intensity map at different lighting angles is used as the amplitude constraint to update the spectrum, where It is The frequency domain coordinates corresponding to the illumination angles are, in the complex transmittance function of the object, represents the absorption of the object, Represents the phase of the object, is the spatial domain coordinate, is the corresponding frequency domain coordinate, For the Aperture function at illumination angles, For the The maximum amplitude of the aperture function at the illumination angle, For the The conjugate of the aperture function at each illumination angle.

8. The method for synthetic aperture quantitative phase imaging of hybrid digital holography and Fourier stacking according to claim 7, characterized in that: The aperture function update formula is: ， in, is the aperture update step size, is the regularization factor, For the In the iteration The synthetic spectrum after frequency domain shift under oblique illumination, for The complex conjugate of .

9. The method for synthetic aperture quantitative phase imaging of hybrid digital holography and Fourier stacking according to claim 6, characterized in that: No. The cost function of the sub-spectrum update is: ， in, Representative The low-resolution intensity map corresponding to the illumination angle, It is The Fourier transform of the complex transmittance function of the object at the illumination angle is It is The frequency domain coordinates corresponding to the lighting angles, Represents the aperture function.

10. The method for synthetic aperture quantitative phase imaging of hybrid digital holography and Fourier stacking according to claim 6, characterized in that: The step size update formula is: ， In the formula, For the The step size of the iteration, For the The cost function calculated by the iteration.

Images