Iterative non-interference quantitative phase imaging method based on Cramo-Clike relationship

Abstract

The invention discloses an iterative non-interference quantitative phase imaging method based on a Cramo-Clike relationship, and the method comprises the steps: enabling a programmable LED array which is annularly arranged to be installed on an inverted bright-field microscope, providing inclined illumination for angle transformation, collecting a series of intensity images under a matched illumination condition, and carrying out the detection of the intensity images through a Cramo-Clike relationship. And the complex amplitude of the object is reconstructed as an initial value by using the Cramo-Clike relationship. And updating the real part of the complex amplitude in a logarithm domain through iteration, thereby recovering the complex amplitude distribution of the large-phase sample. According to the method, any object approximation process is not involved, the convergence speed can be greatly increased by using the object complex amplitude reconstructed by the Cramo-Cif relation as initial estimation, the reconstruction of a large-phase object can be realized only by a small amount of iteration, and the method exceeds the limitation of first-order Born and Ritov approximation in a non-interference quantitative imaging technology.

Description

Technical Field

[0001] The present invention belongs to optical microscopy and quantitative phase imaging technology, in particular to an iterative non-interference quantitative phase imaging method based on the Cramer-Krony relationship. Background Art

[0002] Quantitative phase imaging (QPI) enables label-free quantification of the optical thickness of living cells and tissues, making it an important optical tool in biological research and medical diagnostics. Phase distribution allows for the determination of cellular structure and biophysical parameters, which is crucial for studying intrinsic cellular properties. Traditional quantitative phase imaging typically relies on interferometry, requiring complex interferometric configurations and a stable environment. Furthermore, the inherent nature of interferometry leads to drawbacks such as limited lateral resolution and laser speckle noise, hindering widespread application. Non-interferometric quantitative phase imaging, on the other hand, addresses the inherent challenges of interferometry, simplifying the imaging system and improving the accuracy and quality of reconstruction. In recent years, researchers worldwide have proposed a variety of quantitative phase imaging methods, such as Fourier ptychography (FPM), transmission intensity equations (TIE), and differential contrast imaging (DPC). These techniques directly recover phase from intensity, which is considered an inverse problem requiring a rigorous "intensity-phase" model. Different imaging systems also require different imaging models of the object. Fourier ptychography is a coherent imaging system that is linear in complex amplitude. Despite this, the technique still has two weaknesses: (1) a large amount of data redundancy is required to ensure stable convergence; (2) a reliable solution requires a large number of iterations, which is very time-consuming. These limitations make it difficult to achieve the optimal balance between reconstruction speed and measurement accuracy, especially for large phase objects. The light intensity transmission equation and differential phase contrast imaging belong to partially coherent imaging systems. Their nonlinear image generation models will lead to the coupling of amplitude and phase. Their solutions usually require the introduction of Born / Retov (weak / slowly varying object) approximations to linearize the forward model of the imaging process. The first-order Born approximation assumes that the object is a weak scatterer, while the first-order Retov approximation assumes that the phase gradient of the object is relatively smooth. The certainty of phase recovery depends on these approximate conditions, which are not always strictly met in practical applications. Although these problems can be solved through iteration, the solution process is very complicated and still cannot get rid of the process of introducing approximate models. Therefore, non-interferometric measurement of samples with large phase values remains a challenge.

[0003] In recent years, the Cramer-Kronym relation has attracted widespread attention in the field of quantitative phase imaging due to its unique ability to decouple the real and imaginary parts of complex functions analyzed in the upper half plane within a single frame. Methods based on the spatial Cramer-Kronym relation convert spatial variations in intensity into spatial variations in phase, enabling the acquisition of phase images from single intensity measurements under oblique illumination. Essentially, this method establishes a linear model using the Cramer-Kronym relation. It uses the cepstrum to convert multiplicative modulation relationships into additive ones, without involving any object approximation. Notably, the cepstrum involves logarithmic operations, which increase the signal bandwidth. Logarithmic operations decompose the intensity image into a superposition of two conjugate polynomials. Phase retrieval requires the effective separation of the conjugate terms, ensuring that their higher-order terms do not diverge in the frequency domain. Due to the limited bandwidth of image sensors, high-order convolution terms can cause aliasing, resulting in high-frequency components appearing in the negative frequency domain, severely impacting the validity of the Cramer-Kronym relation. Therefore, the acquired intensity image is typically zero-padded in the frequency domain before performing the logarithmic operation. Conjugate high-order convolution terms are separated by increasing the numerical bandwidth. However, the zero-padding range in the Fourier domain is not constant; its area tends to grow exponentially with increasing phase, which can easily lead to problems such as excessive computation time and memory overload. Furthermore, adjusting the zero-padding area in the frequency domain based on the phase range of the measured object (which requires prior information) is a complex and time-consuming process. More importantly, for large-phase objects with strong scattering, the cepstrum diverges severely in the frequency domain, rendering zero-padding ineffective. The Cramer-Krony relation alone cannot recover the object's true phase range. Summary of the Invention

[0004] In order to achieve high-precision quantitative phase imaging of large-phase objects, the present invention proposes an iterative non-interferometric quantitative phase imaging method based on the Cramer-Kronym relation to solve the problems of slow reconstruction of large-phase objects and the need for object approximation in non-interferometric quantitative phase imaging, thereby achieving high-precision large-phase recovery and surpassing the limitations of first-order Born and Rettorf approximations.

[0005] The technical solution for achieving the purpose of the present invention is: an iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship, comprising the following steps:

[0006] Step 1: collect a series of raw intensity images under annular matching lighting conditions;

[0007] Step 2: Initialize the complex amplitude of the object under test based on the Cramer-Krony relationship;

[0008] In step 3, the real part of the complex amplitude of the corresponding sub-spectrum of the measured object is updated in the logarithmic domain using the collected intensity map, and a new complex amplitude distribution of the sample is obtained. In step 4, based on the new complex amplitude distribution of the sample, step 3 is repeated iteratively until the complex amplitude converges to obtain the final complex amplitude distribution of the sample, and the quantitative phase imaging result is obtained by combining the phase unwrapping algorithm.

[0009] Compared with the prior art, the present invention has the following significant advantages:

[0010] (1) The iterative non-interferometric quantitative phase imaging method based on the Cramer-Kronym relation uses an imaging model based on the Cramer-Kronym relation to initialize, which greatly accelerates the convergence speed of the iterative process, avoids the high-order nonlinear errors caused by the introduction of the first-order Born or Rettorf approximation model, and improves the accuracy of phase recovery;

[0011] (2) As a nonlinear optimization algorithm, the iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship is iterated in the logarithmic domain, breaking the dependence of non-interferometric quantitative phase imaging technology on the first-order Born and Rettorf approximations, achieving high-precision reconstruction of large phase objects, and combining with filtering technology to effectively suppress multiplicative noise, thereby improving imaging quality and accuracy;

[0012] The present invention is further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is a flow chart of the iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship.

[0014] Figure 2 is the frequency domain coverage of the iterative non-interferometric quantitative phase imaging method (6 images) based on the Cramer-Kronym relation.

[0015] Figure 3 It is a phase image comparison of microlens arrays reconstructed by an iterative non-interference quantitative phase imaging method based on the Cramer-Krony relationship, a method based on the Cramer-Krony relationship, a Fourier stack microscopy method, and a digital holographic microscopy method.

[0016] Figure 4 This is the phase image of COS7 cells reconstructed by the iterative non-interferometric quantitative phase imaging method based on the Cramer-Kronym relationship. DETAILED DESCRIPTION

[0017] like Figure 1 As shown in FIG, an iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship includes the following four steps:

[0018] Step 1: Collect a series of raw intensity images under annular matching lighting conditions.

[0019] The iterative non-interference quantitative phase imaging device based on the Cramer-Krony relationship of the present invention consists of three main components: a ring-shaped programmable LED array, a condenser, and a microscope imaging system. The multi-wavelength surface-mounted ring-shaped programmable LED array is placed at the front focal plane of the condenser (a cemented doublet lens with a focal length of 50 mm). The central wavelength of the green channel is 525 nm and the spectral linewidth is ~20 nm. During the imaging process, 6 LED elements evenly distributed on a ring with a radius of 20 mm sequentially illuminate the sample from different illumination angles. The numerical aperture (NA) of the objective lens is 20 nm. obj ) must be consistent with the numerical aperture (NA ill ) matches, i.e. NA obj =NA ill =0.16, such as Figure 2 The imaging system consists of two parts: a brightfield microscope, including a 4×, 0.16NA objective lens (which can be replaced with a 10×, 0.4NA objective lens) and a CMOS camera.

[0020] The specific implementation process is as follows: a circular programmable LED array is used to light up the LED elements in sequence to illuminate the sample, and a synchronous trigger signal is generated to the CMOS camera while sending the lighting control. The collected image is recorded as I n .

[0021] Step 2: Initialize the complex amplitude of the object under test based on the Cramer-Kronym relation.

[0022] The specific implementation process is:

[0023] Construct an analytic function that satisfies the Cramer–Cronym relation:

[0024] χ(r)=log[U n (r)]-ik inc ·r

[0025] in, (x,y) is the spatial coordinate, and Represents the unit vectors in the x and y directions, k inc is the shear wave vector of the incident plane wave, U n (r) is the complex amplitude of the object under the nth illumination angle, and the collected intensity map can be expressed as I n (x,y)=|U n (x,y)| 2 .

[0026] It is generally believed that the incident light is a quasi-monochromatic plane wave with unit amplitude, which can be expressed as The total field complex amplitude U(r) is the superposition of the incident field and the scattered field, that is, U(r) = U in (r)+U s(r). For the nth lighting angle, U n (r) = U(r). The analytical function can be rewritten as:

[0027]

[0028] The intensity and scattered field are converted into an additive relationship through the cepstrum:

[0029]

[0030] At this time, the real part of the analytic function is obtained

[0031] According to the Cramer-Kronym relation, the imaginary part of the analytical function is calculated by directional Hilbert transform to obtain the complete complex amplitude of the measured object:

[0032]

[0033] Where H{·} represents the directional Hilbert transform, I n is the acquired intensity image.

[0034] Step 3: In the logarithmic domain, the real parts of the complex amplitudes of the corresponding sub-spectra of the measured object are updated in sequence using the acquired intensity image, and a new complex amplitude distribution of the sample is obtained. The specific implementation process is as follows:

[0035] Step 3.1, for the sub-spectrum S corresponding to the nth lighting angle n The complex amplitude U of (u,v) n (x,y) is logarithmically calculated to obtain log[U n (x,y)], (u,v) is the frequency domain coordinate corresponding to (x,y); log[U n The complex amplitude of (x,y)] is expressed as A+iB, where A and B represent log[U n (x,y)];

[0036] Step 3.2: Calculate the intensity image based on the acquired image. Will As log[U calculated in step 3.1 n (x,y)];

[0037] In step 3.3, steps 3.1 and 3.2 are repeated until all sub-spectra corresponding to the illumination angles are updated, completing one round of iteration and obtaining the new complex amplitude distribution of the sample.

[0038] In step 4, based on the sample's new complex amplitude distribution, step 3 is repeated until the iterations converge, i.e., the cost function approaches zero. This yields the final complex amplitude distribution of the sample, which is then combined with the phase unwrapping algorithm to obtain quantitative phase imaging results. The reconstructed phase range is now much larger than the initial value reconstructed using only the Cramer-Kronym relation in step 2.

[0039] Construct the cost function:

[0040]

[0041] Compared to existing non-interferometric quantitative phase imaging methods, the present invention's iterative method, based on the Cramer-Krony relation, retains the advantage of the Cramer-Krony imaging model in that it does not require object approximation, while also overcoming the limitations of first-order Born and Rettorf approximations. This significantly improves the reconstruction accuracy of large-phase samples and, utilizing the Cramer-Krony relation, greatly accelerates the convergence of the iterative process. Furthermore, the present invention proposes a logarithmic domain iteration strategy that, combined with filtering, can suppress noise, particularly the effects of multiplicative noise, thereby further improving the quality of image reconstruction.

[0042] Figure 3 Comparison of phase images of a microlens array reconstructed using iterative non-interferometric quantitative phase imaging based on the Cramer-Krony relationship, a method based on the Cramer-Krony relationship, Fourier phantom microscopy, and digital holographic microscopy. It is clear that the iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship can achieve high-precision imaging of large phase objects with only a small number of iterations. Figure 4 The phase distribution of COS7 cells reconstructed using the method of the present invention can be used to measure the true three-dimensional morphology of transparent samples.

[0043] This method utilizes a ring-shaped programmable LED array to collect a series of light intensity images under matching lighting conditions. The complex amplitude of the object under test is then initialized based on the Cramer-Krony relationship. Based on this initialization, the real parts of the complex amplitudes of the corresponding sub-spectra of the object under test are sequentially updated in the logarithmic domain using the collected intensity images, ultimately yielding the complex amplitude distribution of the sample. This method eliminates the need for an interferometer, retaining the advantages of non-interferometric quantitative phase imaging techniques, such as high stability and low noise, while achieving imaging of large phase objects beyond the first-order Born and Rettorf approximations.

Claims

1. An iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship, characterized in that: The following steps are involved: Step 1: collect a series of raw intensity images under annular matching lighting conditions; Step 2: Initialize the complex amplitude of the object under test based on the Cramer-Krony relationship; Step 3: In the logarithmic domain, the real parts of the complex amplitudes of the corresponding sub-spectra of the measured object are updated in sequence using the collected intensity map, and a new complex amplitude distribution of the sample is obtained; Step 4: Repeat step 3 according to the new complex amplitude distribution of the sample until the complex amplitude converges to obtain the final complex amplitude distribution of the sample, and combine it with the phase unwrapping algorithm to obtain the quantitative phase imaging result.

2. The iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship according to claim 1, characterized in that: The original intensity image is collected using a non-interference microscopic imaging system, which includes a ring-shaped programmable LED array, a condenser, and a microscope imaging system. The programmable LED array is arranged at the front focal plane of the condenser, and the center of the programmable LED array coincides with the optical axis of the microscope objective of the microscope imaging system.

3. The iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship according to claim 1, characterized in that: The specific method for collecting a series of raw intensity images under annular matching lighting conditions is as follows: The LED elements of the ring-shaped programmable LED array are sequentially lit to illuminate the sample, and the original intensity image I is collected at the same time. i .

4. The iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship according to claim 1, characterized in that: The specific steps for initializing the complex amplitude of the object under test based on the Cramer-Krony relationship are: Construct an analytic function that satisfies the Cramer–Cronym relation: χ(r)6log[U n (r)]-ik inc ·r in, k inc is the shear wave vector of the incident plane wave, U n (r) is the total field complex amplitude of the object under the nth illumination angle, (x, y) is the spatial coordinate, and Represent the unit vectors in the x and y directions respectively; The total field complex amplitude is specifically: U(r) = U in (r)+U s (r) Where U s (r) is the scattered field, U in (r) is the incident field, and for the nth illumination angle, U(r) = U n (r); the analytical function is rewritten as: The intensity and scattered field are converted into an additive relationship through the cepstrum: At this time, the real part of the analytic function is obtained According to the Cramer-Kronym relation, the imaginary part of the analytical function is calculated by directional Hilbert transform to obtain the complete complex amplitude of the measured object: Where H{·} represents the directional Hilbert transform, I n is the acquired intensity image.

5. The iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship according to claim 1, characterized in that: The specific method of sequentially updating the real parts of the complex amplitudes of the corresponding sub-spectra of the measured object using the acquired intensity map in the logarithmic domain and obtaining the new complex amplitude distribution of the sample is as follows: Step 3.1, for the sub-spectrum S corresponding to the nth lighting angle n The complex amplitude U of (u,v) n (x,y) is logarithmically calculated to obtain log[U n (x,y)], (u,v) is the frequency domain coordinate corresponding to (x,y); log[U n The complex amplitude of (x,y)] is expressed as A+iB, where A and B represent log[U n (x,y)]; Step 3.2: Calculate the intensity image based on the acquired image. Will As log[U calculated in step 3.1 n (x,y)]; In step 3.3, repeat steps 3.1 and 3.2 until all sub-spectra corresponding to the illumination angles are updated to obtain the new complex amplitude distribution of the sample.

6. The iterative non-interferometric quantitative phase imaging method based on the Cramer-Krony relationship according to claim 5, characterized in that: The specific method for judging the convergence of the complex amplitude is that the value of the cost function is less than the set value, wherein the cost function is specifically:

Images