Double-sided feedback phase recovery method based on optically limited imaging system

Abstract

The invention provides a double-sided feedback phase recovery method based on an optically limited imaging system. The method comprises the following steps: acquiring first and second diffraction plane intensities; according to whether the intensity of the second diffraction plane is cut off or not, the phase recovery imaging method of the first type or the second type is executed, the phase recovery imaging method comprises multiple iterations and a double-face feedback mechanism, and when the phase recovery imaging method of the first type is executed, the double-face feedback mechanism is executed. And applying spatial spectrum limited feedback of the second diffraction plane light field and amplitude constrained feedback of the first and second diffraction planes. When the second type of phase recovery imaging method is executed, limited illumination feedback of the first diffraction plane light field and amplitude feedback of the first diffraction plane and the second diffraction plane are applied. The amplitude feedback of the first and second diffraction planes is determined by the difference between the current output light field and the detection light field. According to the double-sided feedback phase recovery method, the defects of prior and multiple exposure of an object are overcome, and meanwhile the problem that an algorithm is prone to falling into local minimum and depends on initialization is solved.

Description

Technical Field

[0001] The present invention relates to the field of phase recovery imaging, and more specifically to a double-sided feedback phase recovery method based on an optically limited imaging system. Background Art

[0002] The imaging process of the camera projects a 3D scene onto a 2D image to capture the intensity distribution of the reflected light. While this approach is commonly used to record objects, it is difficult to effectively represent 3D scenes or uniformly absorbing objects. In physics and mathematics, "phase" plays a vital role as a real-valued scalar that determines the relative position of each point in a periodic signal. Due to the wave nature of light, the optical delay that occurs when light is projected onto a scattering medium can be defined as the phase change of the periodic light wave during the propagation process, which contains important optical path information and thus provides a means to quantify the depth information of the imaged object. By acquiring both amplitude and phase simultaneously, all information about the light field of the scatterer can be reconstructed.

[0003] Phase imaging technology is a powerful label-free imaging method that can recover phase information from intensity measurement. Interferometry, as a classic phase imaging method, mainly includes digital holographic microscopy, phase contrast microscopy, differential interference microscopy, optical diffraction tomography (ODT) and other technologies. This type of method can visualize phase information by interfering with a known reference beam or two polarized beams. However, in order to achieve quantitative recovery of the phase information of an object, this type of method usually needs to be combined with phase shifting technology or tomography technology to collect multiple frames of interference patterns, which makes this type of technology have the disadvantage of long measurement time and is not conducive to the application requirements of real-time imaging. Iterative phase recovery technology, as a non-interference method, mainly includes coherent diffraction imaging (CDI), self-interference holographic imaging, ptychography, Fourier ptychographic microscopy (FPM) and other technologies, providing another efficient imaging method for quantitative phase imaging technology. As a lensless imaging method, CDI records the diffraction image of the object, uses an iterative projection algorithm and imposes constraints such as the size of the object to inversely solve the phase of the object. Similarly, self-interference holographic imaging records the diffraction image after the interference of the object light and the illumination light, uses an iterative algorithm to obtain the phase and solve the twin image problem. These technologies have the ability to image in a single frame and can obtain good temporal resolution. However, the uniqueness of the solution of this type of method depends on oversampling, and its space-bandwidth product (i.e., information capacity) is inversely proportional to the sampling rate, so oversampling reduces the information capacity of the imaging system. In addition, the speed and robustness of phase recovery are heavily dependent on the convergence of the algorithm, making the accurate spatial size of the object and other prior constraints very important. However, the accurate object size is difficult to obtain in the application of transparent biological imaging. Even if the accurate object size is obtained, the convergence effect will also obtain different results with different initializations, and the success rate cannot be effectively guaranteed. Therefore, single recovery cannot be achieved.

[0004] In order to improve the robustness of phase recovery, speed up the calculation, and solve the problem of single-shot recovery, Rodenburg et al. proposed stacked diffraction imaging in 2004. Multiple diffraction images were obtained by scanning different overlapping local illumination areas of the sample, and the redundant information of the overlapping area was used for iteration, and a large field of view image was obtained at the same time. In 2005, Pedrini et al. proposed self-interference holographic imaging for multi-transmission distance measurement. Iterative phase recovery was performed by measuring the diffraction patterns of multiple transmission distances. In 2013, Guoan Zheng et al. proposed FPM technology based on a microscope system. Multiple microscopic images were obtained by overlapping multi-angle illumination, and the redundant information of the overlapping area was used for iteration. At the same time, a low-power objective lens was used to obtain a large field of view image, and a synthetic aperture was used to improve the spatial resolution. In 2016, Horstmeyer et al. proposed ODT technology without interference. Multiple images were obtained by multi-angle illumination. In the process of iterating the redundant information of the overlapping area, diffraction tomography models such as the Born approximation were introduced to achieve three-dimensional imaging of thick objects. These technologies are widely used in living cell imaging.

[0005] However, all of the above technologies require redundant measurements of multiple frames, thus reducing the temporal resolution of imaging. Although the existing non-interference phase recovery technology reduces the system complexity of interferometric phase imaging, it is an ill-posed mathematical problem due to the existence of fuzzy solutions to the phase problem. It requires additional redundant information such as oversampling, object size priors, or stacking and aperture synthesis to achieve good algorithm convergence. The need for redundant information in phase recovery reduces the efficiency of acquiring imaging image information, requiring phase imaging to collect multiple images to meet the uniqueness requirement.

[0006] Phase recovery is essentially a non-convex problem, which makes traditional projection algorithms easily fall into local minima. In addition, the convergence accuracy of the projection iteration algorithm is closely related to the initialization. Different initialization processes result in different final phase recovery accuracies, so phase recovery is not stable.

[0007] Existing algorithms solve the above problems mainly through two solutions: the first is to use semi-definite relaxation and increase the matrix dimension to transform the non-convex problem of the phase retrieval algorithm into a convex problem to avoid falling into the local minimum. However, this method has two defects. First, the implementation of semi-definite relaxation changes the traditional Fourier measurement method. The measurement requires random measurement to meet the sparse equidistance requirements, so it is not suitable for existing mainstream phase retrieval methods such as CDI and FPM. Secondly, the method of increasing the matrix dimension makes the algorithm pose a great challenge to computer memory. The memory required by the algorithm is N times that of the traditional projection algorithm. Among them, N is the number of sampling points for reconstructing the phase.

[0008] In addition, the algorithm can also obtain the global optimum by optimizing non-convex problems. The algorithm represented by Wirtinger Flow uses the spectral method to select the appropriate initialization, calculates the Wirtinger derivative to optimize the error function, and selects the appropriate step size for each step to make the algorithm globally convergent. However, the algorithm requires changes to the measurement method, and needs to design a random mask and perform random measurements. In addition, the Wirtinger Flow algorithm also requires multi-frame acquisition (at least 10 frames or more) to ensure that the algorithm has a 100% success rate.

[0009] Therefore, it is necessary to provide a double-sided feedback phase recovery method based on an optically confined imaging system. On the one hand, it can solve the defects of the existing phase recovery method that the uniqueness depends on object priors and multiple exposures, and on the other hand, it can solve the problems that the traditional iterative projection algorithm is prone to fall into local minima and depends on initialization.

[0010] In fact, all existing optical imaging systems are limited imaging systems. Due to the limited size of the imaging lens, the optical imaging system is actually a low-pass filter that filters out the high-frequency components of the object and only allows low-frequency components within a certain range to pass through the imaging system. The camera system and the microscope system are the two most typical optical limited imaging systems, and their structures are as follows: Figure 1 , Figure 2 shown.

[0011] The limitations of the camera system lie in the limited size of the imaging lens, the aperture size, and the field of view angle. On the Fourier plane, the limited size of the imaging lens and aperture filters out the high-frequency components of the object and determines the pupil function of the imaging system. On the real image plane, the limited size of the field of view angle limits the size of the real space that the image sensor can cover. Suppose the focal length of the camera is f, the half-height width of the sensor is h, the field of view angle is θ, the object moment is u, and the field of view height is FOV, then there is the following relationship:

[0012]

[0013]

[0014] The limitation of the microscope system lies in the limited pupil size, numerical aperture and field of view of the microscope objective. In the Fourier plane, the limited numerical aperture filters out the high-frequency components of the object and determines the pupil function of the imaging system. For the coherent light illumination system, let the cutoff frequency be f c , the numerical aperture of the objective is NA, and the illumination wavelength is λ, then there is the following relationship:

[0015]

[0016] On the real image plane, the field number FN of the objective lens and the magnification M jointly determine the field of view of the microscope system. Assume that the maximum field of view diameter of the microscope system is d FOV , then there is the following relationship:

[0017]

[0018] In order to collect the intensity distribution of the image plane and the intensity distribution of the Fourier plane of the imaging target, such as Figure 3 An optically confined imaging system is shown, which includes at least the following components: a light source 101, a first imaging lens 102, a beam splitter 103, a second imaging lens 104, a second two-dimensional array detector 105 (Fourier surface intensity, i.e., second diffraction plane intensity), and a first two-dimensional array detector 106 (image plane intensity, i.e., first diffraction plane intensity) that receives light from the first imaging lens 102 and is reflected by the beam splitter 103.

[0019] The first imaging lens 102 may be a photographic system or a microscope system. The specific acquisition process is as follows: when acquiring the image plane intensity, the incident light sequentially passes through the first imaging lens 102, the beam splitter 103, and the first two-dimensional array detector 106; when acquiring the Fourier surface intensity, the incident light sequentially passes through the first imaging lens 102, the beam splitter 103, the second imaging lens 104, and the second two-dimensional array detector 105. Summary of the invention

[0020] The present invention provides a double-sided feedback phase recovery method based on an optically limited imaging system to solve the defects of object prior and multiple exposures, and at the same time solve the problem that the algorithm is prone to fall into local minimum and depends on initialization.

[0021] In order to achieve the above object, the present invention provides a double-sided feedback phase recovery method based on an optically confined imaging system, comprising:

[0022] S1: collecting a first diffraction plane intensity and a second diffraction plane intensity of an imaging target through the optically limited imaging system;

[0023] S2: if the intensity of the second diffraction plane is truncated, the first type of phase recovery imaging method is executed, otherwise, the second type of phase recovery imaging method is executed;

[0024] The first type of phase recovery imaging method specifically includes:

[0025] S21: Based on the collected first diffraction plane intensity I(x n ,y m ) and the second diffraction plane intensity The amplitude of the light field in the first diffraction plane collected is obtained by square root calculation |f(x n ,ym )| and the amplitude of the light field collected in the second diffraction plane

[0026] S22: Generate the initial phase of the first diffraction plane light field and the amplitude of the light field in the first diffraction plane collected |f(x n ,y m )| multiply to get the first diffraction plane light field f1(x n ,y m ); At the same time, the input second diffraction plane light field of the first iteration Initialize;

[0027] S23: Input the first diffraction plane light field f for the i-th iteration i (x n ,y m ) performs the diffraction transformation calculation between the first diffraction plane and the second diffraction plane to obtain the output second diffraction plane light field of the i-th iteration

[0028] S24: Using the feedback mechanism to output the second diffraction plane light field of the i-th iteration Apply the amplitude constraint and spatial spectrum restriction constraint of the second diffraction plane light field to obtain the input second diffraction plane light field of the i+1th iteration

[0029] S25: Input second diffraction plane light field for the i+1th iteration Perform the diffraction transformation calculation between the second diffraction plane and the first diffraction plane to obtain the output first diffraction plane light field f of the i+1th iteration i ' +1 (x n ,y m ); then the output first diffraction plane light field f of the i+1th iteration is i ' +1 (x n ,y m ) is projected onto the amplitude of the light field of the first diffraction plane collected |f(x n ,y m )|, and obtain the first diffraction plane light field of the input to be corrected for the i+1th iteration

[0030] S26: according to the difference term f between the input first diffraction plane light field to be corrected and the output first diffraction plane light field of the i+1th iteration div (x n ,y m ), for the first diffraction plane light field to be corrected input at the i+1th iteration Apply constraint feedback to obtain the input image light field f of the i+1th iteration i+1 (x n ,y m );

[0031] The input image light field f of the i+1th iteration i+1 (x n ,y m )for:

[0032]

[0033] Among them, β2 is the feedback constant;

[0034] S27: add 1 to the current iteration number i as the current iteration number i of the new round, and return to step S23 to perform the next round of iteration; until the iteration end condition is met, the iteration ends at this time, and the input first diffraction plane light field f of the i+1th iteration is i+1 (x n ,y m ) as the reconstructed first diffraction plane light field;

[0035] The second type of phase recovery imaging method specifically includes:

[0036] S21': Based on the collected first diffraction plane intensity I(x n ,y m ) and the second diffraction plane intensity The amplitude of the light field in the first diffraction plane collected is obtained by square root calculation |f(x n ,y m )| and the amplitude of the light field collected in the second diffraction plane

[0037] S22': Generate the initial phase of the first diffraction plane light field And the amplitude of the light field collected in the second diffraction plane Multiply to get the input second diffraction plane light field of the first iteration At the same time, the first diffraction plane light field f1(x n ,y m ) to initialize;

[0038] S23': Input second diffraction plane light field for the i-th iteration Perform the diffraction transformation calculation between the second diffraction plane and the first diffraction plane to obtain the output first diffraction plane light field f of the i-th iteration i ′(x n ,y m );

[0039] S24': Using the feedback mechanism to output the first diffraction plane light field f of the i-th iteration i ′(x n ,y m ) applies the amplitude constraint of the first diffraction plane light field and the constraint of limited illumination or limited field of view to obtain the input first diffraction plane light field f of the i+1th iteration i+1 (x n ,y m );

[0040] S25': Input first diffraction plane light field f for the i+1th iteration i+1 (x n ,y m ) performs the diffraction transformation calculation between the first diffraction plane and the second diffraction plane to obtain the output second diffraction plane light field of the i+1th iteration Then the output second diffraction plane light field of the i+1th iteration is The amplitude of the light field projected onto the second diffraction plane collected Get the second diffraction plane light field to be corrected input for the i+1th iteration

[0041] S26': according to the difference term between the input second diffraction plane light field to be corrected and the output second diffraction plane light field of the i+1th iteration Apply constraint feedback to the input second diffraction plane light field to be corrected at the i+1th iteration to obtain the input second diffraction plane light field at the i+1th iteration

[0042] The second diffraction plane light field to be corrected in the i+1th iteration for:

[0043]

[0044] Among them, β2 is the feedback constant;

[0045] S27': add 1 to the current iteration number i as the current iteration number i of the new round, and return to step S23' to perform the next round of iteration; until the iteration end condition is met, the iteration ends at this time, and the input first diffraction plane light field f of the i+1th iteration is i+1 (x n ,y m ) as the reconstructed first diffraction plane light field.

[0046] The first diffraction plane is an image plane, and the second diffraction plane is a Fourier plane; in step S1, the intensity distribution of the second diffraction plane is a Fourier plane spatial spectrum, and whether the imaging target is a strong scattering object or a weak scattering object is determined according to the Fourier plane spatial spectrum; in step S2, the first type of phase recovery imaging method is a phase recovery imaging method for a strong scattering object, and the second type of phase recovery imaging method is a phase recovery method for a weak scattering object.

[0047] In step S23, step S25, step S23' and step S25', the diffraction transformation between the first diffraction plane and the second diffraction plane is calculated as a Fraunhofer diffraction transformation, and the diffraction transformation between the second diffraction plane and the first diffraction plane is calculated as an inverse Fraunhofer diffraction transformation.

[0048] Light scattered by the imaging target in an optically constrained imaging system causes a hard truncation of the Fourier plane spatial spectrum or the imaging field of view on the image plane due to the finite numerical aperture of the optical system; the finite numerical aperture of the optical system includes limitations on the size, direction and shape of the light source, the aperture limitation of the objective lens, the pupil, numerical aperture and imaging field angle of the imaging lens, the size limitation of the detector's photosensitive area, the size limitation of the rectangular or circular aperture, and the probe size limitation of the fiber optic detector.

[0049] The limited numerical aperture of the optical system corresponding to the limited spatial spectrum of the Fourier surface includes the pupil and / or numerical aperture size limitation of the imaging lens; the limited spatial spectrum of the Fourier surface causes hard truncation of the spatial spectrum of the Fourier surface; the limited illumination corresponds to the size limitation of the illumination light source on the object, and the limited field of view corresponds to the limited numerical aperture of the optical system including the pupil size limitation of the imaging lens and / or the limitation of the imaging field of view angle; the limited illumination or limited field of view causes hard truncation of the imaging field of view of the image plane.

[0050] The diffraction transformation between the first diffraction plane and the second diffraction plane is a Fresnel transformation, and the formula for calculating the diffraction transformation between the first diffraction plane and the second diffraction plane is:

[0051]

[0052] Among them, U zi (x′,y′) and U i (x, y) is the light field of the first diffraction plane and the second diffraction plane, z is the distance between the two planes, is the Fourier transform, k is the wave number, f x is the frequency in the x direction, f y is the frequency in the y direction, and λ is the wavelength.

[0053] In step S24, after applying the amplitude constraint and spatial spectrum constraint of the second diffraction plane light field, the input second diffraction plane light field of the i+1th iteration is for:

[0054]

[0055] in, is the input second diffraction plane light field of the i-th iteration; is the output second diffraction plane light field of the i-th iteration, is the negative feedback term of the second diffraction plane, β and β1 are iteration constants, and f max is the cutoff frequency of the calibrated pupil function;

[0056] In step S24', after applying the amplitude constraint and the finite illumination constraint of the first diffraction plane light field, the input first diffraction plane light field f of the i+1th iteration i+1 (x n ,y m )for:

[0057]

[0058] Among them, f i (x n ,y m ) is the input first diffraction plane light field of the i-th iteration, f i ′(x n ,y m ) is the output first diffraction plane light field of the i-th iteration, f di (x n ,y m ) is the negative feedback term of the first diffraction plane, β and β1 are iteration constants, and L is the cutoff radius of the calibrated illumination function or field distribution function.

[0059] The pupil function is calibrated, specifically including: placing a point light source in front of the optically limited imaging system, placing a two-dimensional array detector on the first diffraction plane to detect the image of the point light source, obtaining a point spread function from the intensity spatial distribution of the point light source image, and performing Fourier transform on the point spread function to obtain the pupil function of the optically limited imaging system; or placing a point light source in front of the optically limited imaging system, placing a two-dimensional array detector on the second diffraction plane to detect the second diffraction plane spatial spectrum distribution of the point light source, and directly using it as the calibrated pupil function of the optically limited imaging system; the illumination function is calibrated, specifically including: when the optically limited imaging system is subjected to limited illumination smaller than the field of view, removing the imaging target, placing a two-dimensional array detector on the first diffraction plane to detect the light intensity distribution function of the illumination light, as the illumination function; the field of view distribution function is calibrated, specifically including: under a limited field of view, the optically limited imaging system is irradiated with parallel light larger than the field of view, placing a two-dimensional array detector on the first diffraction plane to detect the light intensity distribution function of the illumination light, as the field of view distribution function.

[0060] Calibrating the pupil function also includes: determining the noise intensity according to the intensity distribution of the pupil function, and determining the cutoff frequency of the calibrated pupil function according to the noise intensity, so that within the range of the cutoff frequency of the calibrated pupil function, the pupil function is a detection value, and outside the range of the cutoff frequency of the calibrated pupil function, the pupil function is 0; when calibrating the illumination function or the field of view distribution function, determining the noise intensity according to the signal intensity distribution of the illumination function or the field of view distribution function, and setting the cutoff radius of the illumination function or the field of view distribution function according to the noise intensity, so that within the cutoff radius, the illumination function or the field of view distribution function signal is a detection value, and outside the cutoff radius, the illumination function or the field of view distribution function signal is 0.

[0061] In step S22 and step S22', the initial phase of the first diffraction plane light field is The initial phase of the light field in the first diffraction plane is obtained by random generation, or The phase part is obtained by Fourier transforming the amplitude of the collected first diffraction plane light field and retaining the phase part.

[0062] Compared with single-shot exposure technologies such as CDI, the dual-sided feedback phase recovery method based on the optically constrained imaging system of the present invention uses the intrinsic constraints of the optical system as algorithm constraints, without the need for object priors. The constraints on the intensity of the collected real image plane and the Fourier plane eliminate the interference of trivial solutions to traditional iterative algorithms, and solve the problem that they are easily trapped in local minima.

[0063] Compared with multiple exposure technologies such as FPM, the double-sided feedback phase recovery method based on the optically confined imaging system of the present invention only needs to collect the intensity information of the real image plane and the Fourier plane to complete the recovery without redundant measurement.

[0064] Compared with the traditional iterative projection algorithm, the double-sided feedback phase recovery method based on the optically confined imaging system of the present invention does not rely on the initialization process to achieve global convergence and has a 100% success rate.

[0065] Compared with existing WirtingerFlow and other algorithms, the double-sided feedback phase recovery method based on an optically confined imaging system of the present invention does not require the design of a mask to achieve random measurement, and only requires a single exposure to achieve global convergence.

[0066] In summary, the double-sided feedback phase recovery method based on the optically confined imaging system of the present invention not only solves the defects of the existing phase recovery method that the uniqueness depends on the object prior and multiple exposures, but also solves the problems that the traditional iterative projection algorithm is prone to fall into the local minimum and depends on initialization. It achieves global convergence that is independent of the initialization process without random measurement, additional computing resources, or multiple exposures, and has a 100% success rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 This is a typical optical path diagram of a camera system.

[0068] Figure 2 This is a typical optical path diagram of a microscope system.

[0069] Figure 3 It is a typical optical path diagram of an optically constrained imaging system that can capture both the image plane and the Fourier plane.

[0070] Figure 4-Figure 6 is a flow chart of a double-sided feedback phase recovery method based on an optically constrained imaging system according to a first embodiment of the present invention, wherein Figure 4 The overall flow chart is shown. Figure 5 shows the phase retrieval imaging method for strongly scattering objects, Figure 6 A phase retrieval imaging method for weakly scattering objects is shown.

[0071] Figure 7 Diagram of the truncation effect of an optically confined imaging system.

[0072] Figure 8 When the object is a strong phase object, the real image plane intensity image and the Fourier plane intensity image are collected, which shows the truncation effect of the pupil function.

[0073] Fig. 9 When the object is a weak phase object, the real image plane intensity image and the Fourier plane intensity image are collected, which shows the truncation effect of the limited field of view.

[0074] Fig.10 The complex amplitude distribution and phase image of the light field reconstructed by the phase recovery method of the present invention.

[0075] Fig.11 This is a comparison chart between the double-sided feedback phase recovery method based on the optically confined imaging system and the conventional projection iterative algorithm. DETAILED DESCRIPTION

[0076] The following describes the implementation of the present invention through specific embodiments, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific implementations, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention.

[0077] It should be noted that the following embodiments and features in the embodiments may be combined with each other if there is no conflict.

[0078] like Figure 4-Figure 6 The figure shows a double-sided feedback phase recovery method based on an optically confined imaging system according to the first embodiment of the present application, which can be applicable to any band of visible light and to an optically confined imaging system capable of collecting the image plane intensity distribution and Fourier plane intensity distribution of the imaging target.

[0079] Among them, the existing optical imaging systems are all limited imaging systems. Due to the limited size of the imaging lens, the optical imaging system is actually a low-pass filter, which filters out the high-frequency components of the object and only allows low-frequency components within a certain range to pass through the imaging system. Figure 3 As shown, the optically constrained imaging system capable of collecting the image plane intensity distribution and the Fourier plane intensity distribution of the imaging target includes at least the following components: a light source 101, a first imaging lens 102, a beam splitter 103, a second imaging lens 104, a second two-dimensional array detector 105 (Fourier plane intensity, i.e., second diffraction plane intensity), and a first two-dimensional array detector 106 (image plane intensity, i.e., first diffraction plane intensity) that receives light from the first imaging lens 102 and is reflected by the beam splitter 103.

[0080] like Figure 4-Figure 6 As shown, according to the first embodiment of the present invention, a double-sided feedback phase recovery method based on an optically constrained imaging system specifically includes:

[0081] Step S1: Collect the image plane intensity I(x n ,y m ) and Fourier surface intensity Therefore, the Fourier surface intensity can be used as the Fourier surface spatial spectrum, and whether the imaging target is a strong scattering object or a weak scattering object can be determined according to whether the Fourier surface spatial spectrum of the imaging target is truncated.

[0082] That is, the definition of strong scattering objects and weak scattering objects is based on whether the Fourier surface space spectrum is truncated by the pupil function. The Fourier surface space spectrum of strong scattering objects produces hard truncation. The specific truncation effect is as follows Figure 7 As shown in Figure 2, the Fourier plane spatial spectrum of the weakly scattering object is not truncated, but the imaging field of view of the image plane is hard truncated.

[0083] In this embodiment, for a strong scattering object, the image plane intensity I(x n ,y m ) and Fourier surface intensity like Figure 8 As shown in the figure, for weakly scattering objects, the image plane intensity I(x n ,y m ) and Fourier surface intensity like Fig. 9 shown.

[0084] In an optically constrained imaging system, the light scattered by the imaging target is hard-truncated in the Fourier plane spatial spectrum or the imaging field of view on the image plane due to the limited numerical aperture of the optical system.

[0085] Among them, the limited numerical aperture of the optical system corresponding to the limited Fourier surface space spectrum includes the pupil and / or numerical aperture size limitation of the imaging lens. The limited Fourier surface space spectrum causes hard truncation of the Fourier surface space spectrum. The collected data is suitable for the phase recovery imaging method of strongly scattering objects.

[0086] When the imaging field of the image plane is more limited due to limited illumination (or limited field of view), the limited illumination corresponds to the size limit of the illumination light source on the object, and the limited field of view corresponds to the limited numerical aperture of the optical system, including the pupil size limit of the imaging lens and / or the imaging field of view angle limit. Limited illumination or limited field of view causes hard truncation of the imaging field of the image plane, and the collected data is suitable for the phase recovery imaging method of weakly scattering objects.

[0087] In summary, the limited numerical aperture of the optical system includes, but is not limited to, the size, direction and shape limitations of the light source, the aperture limitations of the objective lens (if there is an objective lens), the pupil, numerical aperture and imaging field angle limitations of the imaging lens, the size limitations of the detector's photosensitive area, the size limitations of the rectangular or circular aperture (if there is an aperture), the probe size limitations of the fiber optic detector (if there is a fiber optic detector), and so on.

[0088] Step S2: Determine whether the Fourier plane spatial spectrum of the imaging target is truncated. If so, it indicates that it is a strong scattering object, and the phase recovery imaging method for strong scattering objects is executed accordingly. Otherwise, it indicates that it is a weak scattering object, and the phase recovery imaging method for weak scattering objects is executed.

[0089] like Figure 5 As shown, the phase recovery imaging method of a strongly scattering object specifically includes:

[0090] Step S21: Based on the acquired imaging target's image plane intensity I(x n ,y m ) and Fourier surface intensity (like Figure 8 As shown), the amplitude of the collected image light field |f(x n ,y m )| and the amplitude of the Fourier surface light field collected

[0091] Step S22: Randomly generate the initial phase of the image plane light field And the amplitude of the collected image light field |f(x n ,y m )| multiply to get the input image light field f1(x n ,y m ); At the same time, the input Fourier surface light field of the first iteration Initialize;

[0092] At this time, the current iteration number i = 1, that is, the input image plane light field f1(x n ,y m )for:

[0093]

[0094] Among them, |f(x n ,y m )| is the amplitude of the collected image light field, is the initial phase of the image light field.

[0095] When the current iteration number i = 1, the input Fourier surface light field of the first iteration is Initialized to 0.

[0096] Step S23: For the input image light field f of the i-th iteration i (x n ,y m ) performs Fraunhofer diffraction transform (i.e. standard two-dimensional Fourier transform) to obtain the output Fourier surface light field of the i-th iteration

[0097] That is, the output Fourier surface light field of the i-th iteration is for:

[0098]

[0099] Among them, f i (x n ,y m ) is the input image light field of the i-th iteration, is the Fourier transform.

[0100] Step S24: Using the feedback mechanism to output the Fourier surface light field of the i-th iteration Apply the amplitude constraint and spatial spectrum restriction constraint of the Fourier surface light field to obtain the input Fourier surface light field of the i+1th iteration

[0101] After applying the amplitude constraint and spatial spectrum constraint of the Fourier surface light field, the input Fourier surface light field of the i+1th iteration is for:

[0102]

[0103] in, is the input Fourier surface light field of the i-th iteration, which comes from the previous iteration. The input Fourier surface light field of the i-th iteration when i=1 comes from the initialization above; is the output Fourier surface light field of the i-th iteration, is the negative feedback term of the Fourier surface, β and β1 are iteration constants ranging from 0.5 to 1, and f max is the calibrated cutoff frequency of the pupil function. The calibration method of the pupil function is detailed below.

[0104] therefore, It represents the negative feedback of the finite Fourier signal so that the signal outside the cutoff frequency tends to 0 during the iteration process; Represents the negative feedback of the acquired Fourier surface intensity so that it tends to the acquired Fourier surface amplitude during the iteration process

[0105] That is to say, spatial spectrum constrained feedback and Fourier surface amplitude constrained feedback are applied to the Fourier surface light field. The Fourier surface amplitude feedback is determined by the difference between the current output light field and the detection light field, and the spatial spectrum constrained feedback is the difference between the current Fourier surface output light field and zero.

[0106] Among them, the Fourier surface negative feedback term Defined as:

[0107]

[0108] in, is the amplitude of the collected Fourier surface light field, is the output Fourier surface light field of the i-th iteration, is the amplitude of the output Fourier surface light field of the i-th iteration, is the input Fourier surface light field of the i-th iteration, is the amplitude of the input Fourier surface light field at the i-th iteration.

[0109] Step S25: Input Fourier surface light field of the i+1th iteration Perform the reverse Fraunhofer diffraction transform to obtain the output image light field f of the i+1th iteration i ' +1 (x n ,y m ), and then the output image light field f of the i+1th iteration is i ' +1 (x n ,y m ) is projected onto the collected image plane light field |f(x n ,y m )|, and obtain the input image plane light field to be corrected for the i+1th iteration

[0110] That is to say, the output image light field f of the i+1th iteration is i ' +1 (x n ,y m )for:

[0111]

[0112] The input image light field to be corrected at the i+1th iteration for:

[0113]

[0114] Among them, |f(x n ,y m )| is the amplitude of the collected image light field.

[0115] Step S26: Based on the difference term f between the input image plane light field to be corrected and the output image plane light field of the i+1th iteration div (x n ,y m ), apply constraint feedback to the input image plane light field to be corrected at the i+1th iteration to obtain the input image plane light field f at the i+1th iteration i+1 (xn ,y m );

[0116] Among them, the difference term f between the input image plane light field to be corrected and the output image plane light field at the i+1th iteration is div (x n ,y m ) is defined as:

[0117]

[0118] in is the input image light field to be corrected at the i+1th iteration, f i ' +1 (x n ,y m )The output image light field of the i+1th iteration.

[0119] Applying constraint feedback to the input image plane light field to be corrected at the i+1th iteration includes: calculating the difference term f between the input image plane light field to be corrected at the i+1th iteration and the output image plane light field div (x n ,y m ) acts on the input image light field to be corrected at the i+1th iteration Get the input image light field f of the i+1th iteration i+1 (x n ,y m ), the input image light field f of the i+1th iteration i+1 (x n ,y m )for:

[0120]

[0121] Among them, β2 is a feedback constant, which is used to ensure that the next output of the algorithm is closer to the image amplitude constraint, and is usually between 0.01 and 0.5.

[0122] That is to say, an image plane amplitude feedback is applied to the image plane, and the image plane amplitude feedback is determined by the difference between the current output light field and the detection light field.

[0123] Step S27: add 1 to the current iteration number i as the current iteration number i of the new round, and return to step S23 to perform the next round of iteration; until the iteration end condition is met, the iteration ends at this time, and the input image plane light field f of the i+1th iteration is i+1 (x n ,y m ) as the reconstructed image plane light field. Thus, phase recovery is completed, such as Fig.10 shown.

[0001] In this embodiment, the iteration end condition includes: error function ∑∑||U′ i |-|U||<ε, and the number of iterations i>N, at least one of the two holds true. Where ε is the noise level of the two-dimensional array detector, and N is usually 3000.

[0002] That is to say, if neither of them holds, it is necessary to continue the next round of iteration; if one or both of them hold, the iteration ends, and the input image light field f i+1 (x n ,y m ) is to reconstruct the image plane light field, that is, to complete the phase recovery.

[0003] like Figure 6 As shown, the phase recovery imaging method of a weakly scattering object specifically includes:

[0004] Step S21': Based on the acquired image plane intensity I(x n ,y m ) and Fourier surface intensity (like Fig. 9 As shown), the amplitude of the collected image light field |f(x n ,y m )| and the amplitude of the Fourier surface light field collected

[0005] Step S22': Randomly generate the initial phase of the image plane light field And compared with the amplitude of the Fourier surface light field collected Multiply to get the input Fourier surface light field of the first iteration At the same time, the input image light field f1(x n ,y m ) to initialize;

[0006] At this time, the number of iterations i = 1: that is, the input Fourier surface light field of the first iteration for:

[0007]

[0008] in, is the amplitude of the collected Fourier surface light field, is the initial phase of the image light field.

[0009] When the current iteration number i=1, the input image light field f1(x n ,y m ) is initialized to 0.

[0010] Step S23': Input Fourier surface light field of the i-th iteration Perform the reverse Fraunhofer diffraction transformation to obtain the output image light field f of the i-th iteration i ′(x n ,y m );

[0011] That is to say, the output image light field f of the i-th iteration i ′(x n ,y m )for:

[0012]

[0013] in, is the input Fourier surface light field of the i-th iteration, is the inverse Fourier transform.

[0014] Step S24': Using the feedback mechanism to generate the output image light field f of the i-th iteration i ′(x n ,y m ) imposes the amplitude constraint and limited illumination (or limited field of view) constraint on the image plane light field to obtain the input image plane light field f of the i+1th iteration i+1 (x n ,y m );

[0015] After applying the amplitude constraint and finite illumination constraint of the image plane light field, the input image plane light field f of the i+1th iteration is i+1 (x n ,y m )for:

[0016]

[0017] Among them, f i (x n ,y m ) is the input image light field of the i-th iteration. When i=1, f0(x n ,y m )=0,f i ′(x n ,y m ) is the output image light field of the i-th iteration, f di (x n ,y m ) is the image plane negative feedback term, β and β1 are iteration constants, ranging from 0.5 to 1, and L is the cutoff radius of the calibrated illumination function or field distribution function. The calibration method of the illumination function is detailed below.

[0018] Therefore, f i (x n ,y m )-βfi ′(x n ,y m ) represents the negative feedback of limited illumination (or limited field of view) so that its signal outside the illumination tends to 0 during the iteration process; f i ′(x n ,y m )+β1f di (x n ,y m ) represents the negative feedback of the intensity of the collected image plane light field, making it tend to the amplitude of the collected image plane light field |f(x n ,y m )|.

[0019] That is to say, limited illumination feedback and image amplitude constraint feedback are applied to the image plane light field, the image amplitude feedback is determined by the difference between the current output light field and the detection light field, and the limited illumination constrained feedback is the difference between the output light field of the image plane and zero.

[0020] Among them, the image plane negative feedback term f di (x n ,y m ) is defined as:

[0021]

[0022] Among them, |f(x n ,y m )| is the amplitude of the collected image light field, f i ′(x n ,y m ) is the output image light field of the i-th iteration, |f i ′(x n ,y m )| is the amplitude of the output image light field of the i-th iteration, f i (x n ,y m ) is the input image light field of the i-th iteration, |f i (x n ,y m )| is the amplitude of the input image light field of the i-th iteration.

[0023] Step S25': the input image light field f of the i+1th iteration i+1 (x n ,y m ) to perform Fraunhofer diffraction transform (i.e., standard two-dimensional Fourier transform) to obtain the output Fourier surface light field of the i+1th iteration Then the output Fourier surface light field of the i+1th iteration is The amplitude of the light field projected onto the collected Fourier surface Get the input Fourier surface light field to be corrected for the i+1th iteration

[0024] That is, the output Fourier surface light field of the i+1th iteration is for:

[0025]

[0026] Input Fourier surface light field to be corrected at the i+1th iteration for:

[0027]

[0028] in, is the amplitude of the collected Fourier surface light field.

[0029] Step S26': according to the difference term between the input Fourier surface light field to be corrected and the output Fourier surface light field of the i+1th iteration Apply constraint feedback to the input Fourier surface light field to be corrected at the i+1th iteration to obtain the input Fourier surface light field at the i+1th iteration

[0030] Among them, the difference term between the input Fourier surface light field to be corrected and the output Fourier surface light field at the i+1th iteration is is defined as:

[0031]

[0032] in, is the input Fourier surface light field to be corrected at the i+1th iteration, is the output Fourier surface light field of the i+1th iteration.

[0033] Apply constraint feedback to the input Fourier surface light field to be corrected at the i+1th iteration, specifically including: taking the difference term of the input Fourier surface light field to be corrected at the i+1th iteration and the output Fourier surface light field The input Fourier surface light field to be corrected for the i+1th iteration Get the input Fourier surface light field of the i+1th iteration Input Fourier surface light field of the i+1th iteration for:

[0034]

[0035] Among them, β2 is a feedback constant, which is used to ensure that the next output of the algorithm is closer to the Fourier surface light field amplitude constraint, and is usually between 0.01 and 0.5.

[0036] That is to say, Fourier surface amplitude constraint feedback is applied to the Fourier surface plane light field, and the Fourier surface amplitude feedback is determined by the difference between the current output light field and the detection light field.

[0037] Step S27': add 1 to the current iteration number i as the current iteration number i of the new round, and return to step S23' to perform the next round of iteration; until the iteration end condition is met, the iteration ends at this time, and the input image plane light field f of the i+1th iteration is i+1 (x n ,y m ) as the reconstructed image light field.

[0038] Thus, phase recovery is completed.

[0039] In this embodiment, the iteration end condition includes: the error function ∑∑||f i ′|-|f||<ε, number of iterations i>N, at least one of the two is true. Among them, ε is the noise level of the two-dimensional array detector, and N is usually 3000.

[0040] That is to say, if neither of them holds, it is necessary to continue the next round of iteration; if one or both of them hold, the iteration ends, and the input image light field f i+1 (x n ,y m ) is to reconstruct the image plane light field, that is, to complete the phase recovery.

[0041] Among them, calibrating the pupil function specifically includes:

[0042] A point light source is placed in front of the optically constrained imaging system, and a two-dimensional array detector is placed on the image plane to detect the image of the point light source. The point spread function is obtained from the spatial distribution of the intensity of the point light source image, and the pupil function of the optically constrained imaging system is obtained by Fourier transform. Alternatively, a point light source is placed in front of the optically constrained imaging system, and a two-dimensional array detector is placed on the Fourier plane to detect the Fourier plane spatial spectrum distribution of the point light source, and directly used as the calibrated pupil function of the optically constrained imaging system.

[0043] In particular, when the imaging system is a microscope system, fluorescent beads are placed as point light sources within the imaging depth of field of the front focal plane of the imaging system, a two-dimensional array detector is placed on the image plane to detect the image of the point light source, and a point spread function is obtained from the intensity spatial distribution of the point light source image, which is Fourier transformed to obtain the pupil function of the optically confined imaging system; or fluorescent beads are placed as point light sources within the imaging depth of field of the front focal plane of the imaging system, a two-dimensional array detector is placed on the Fourier plane to detect the Fourier plane spectrum distribution of the point light source, and directly used as the pupil function of the optically confined imaging system.

[0044] The method further comprises: determining the noise intensity of the pupil function according to the intensity distribution of the pupil function, and determining the cutoff frequency f of the calibrated pupil function according to the noise intensity. R , so that the cutoff frequency f of the calibrated pupil function R In the range of the pupil function, the detection value is at the cutoff frequency f R Outside the range of , the pupil function is 0.

[0045] At the cutoff frequency f of the calibrated pupil function R In the range, the detection intensity of the pupil function is greater than the noise intensity, so when the spatial frequency of the Fourier surface is less than the cutoff frequency f of the limited system R When f x 2 +f y 2 <f R 2 When , the pupil function is the detection value. If the spatial frequency of the Fourier surface is greater than the cutoff frequency of the restricted system, the pupil function is 0.

[0046] It should be noted that when obtaining the calibrated pupil function, the detected object, ie, the imaging target, needs to be removed, because the pupil function is irrelevant to the imaging target.

[0047] Among them, calibrating the illumination function specifically includes: when the optically limited imaging system is subjected to limited illumination smaller than the field of view (that is, the size of the illumination light cannot completely cover the pupil of the imaging lens), removing the imaging target and placing a two-dimensional array detector on the image plane to detect the intensity distribution function of the illumination light as the illumination function.

[0048] The field of view distribution function is calibrated, specifically including: under a limited field of view (i.e., the pupil size of the imaging lens is limited, and the field of view angle of the imaging system is limited, resulting in a limited field of view), irradiating the optically limited imaging system with parallel light larger than the field of view, and placing a two-dimensional array detector on the image plane to detect the light intensity distribution function of the illumination light as the field of view distribution function.

[0049] When calibrating the illumination function or the field of view distribution function, the noise intensity is determined according to the signal intensity distribution of the illumination function or the field of view distribution function, and the cutoff radius L of the illumination function or the field of view distribution function is set according to the noise intensity, so that the illumination function or the field of view distribution function signal within the cutoff radius is the detection value, and the illumination function or the field of view distribution function signal outside the cutoff radius is 0.

[0050] Within the cut-off radius, the detection intensity is greater than the noise intensity. Therefore, when the spatial coordinate range is less than the cut-off radius L, that is, x 2 +y 2 <L 2, the illumination function is the detection value; otherwise, outside the cutoff radius, the detection intensity is less than the noise intensity, so the illumination function is 0.

[0051] This method is significantly better than the iterative projection algorithm without double-sided feedback in terms of success rate and the number of iterations required for successful recovery. Fig.11 shown. Fig.11 In the figure, the horizontal axis OSR represents the oversampling rate, and the vertical axis represents the logarithm of the reconstruction error log 10 (e),Success rate and number of iterations required for successful recovery.

[0052] In other embodiments, the phase recovery method based on the optically constrained imaging system of the present invention is not limited to the iteration between the real image plane and the Fourier plane, but also includes the iteration between two diffraction planes in the near Fresnel zone, the Fresnel zone, the far field, and any combination thereof. The diffraction transformation between the real image plane and the Fourier plane can also be replaced by the diffraction transformation between two diffraction planes in one or more combinations of the near Fresnel zone, the Fresnel zone, and the far field.

[0053] For example, in the second embodiment of the present invention, the diffraction transformation between the real image plane and the Fourier plane is replaced by the diffraction transformation between two diffraction planes in the Fresnel zone. Therefore, in this embodiment, the other steps are the same as the steps of the phase recovery method based on the optically confined imaging system in the first embodiment of the present application. The only difference is that, in all steps, the image plane is replaced by the first diffraction plane, the Fourier plane is replaced by the second diffraction plane, the phase recovery imaging method for strongly scattering objects is replaced by the first type of phase recovery imaging method, and the phase recovery method for weakly scattering objects is replaced by the second type of phase recovery imaging method; accordingly, in step S23, step S25, step S23', and step S25', the Fraunhofer diffraction transform is replaced by a diffraction transform calculation (i.e., Fresnel transform) between the first diffraction plane and the second diffraction plane in the Fresnel zone, and the reverse Fraunhofer diffraction transform is replaced by a diffraction transform calculation between the second diffraction plane and the first diffraction plane in the Fresnel zone.

[0054] The formula for calculating the diffraction transformation between the first diffraction plane and the second diffraction plane is as follows:

[0055]

[0056] Among them, U zi (x′,y′) and U i (x, y) is the light field of the first diffraction plane and the second diffraction plane, z is the distance between the two planes, is the Fourier transform, k is the wave number, f x is the frequency in the x direction, f y is the frequency in the y direction, and λ is the wavelength.

[0057] It should be noted that in any embodiment of the present invention (such as the first diffraction plane and the second diffraction plane are in one or more combinations of the near Fresnel zone, the Fresnel zone, and the far field), the truncation of the first diffraction plane in the present invention corresponds to limited illumination or limited field of view, and the truncation of the second diffraction plane corresponds to limited spatial spectrum.

[0058] In the third embodiment of the present invention, the other steps are the same as those in the first embodiment of the present invention, except that the initial phase in step S22 and step S22′ can be obtained by using a geometric phase initialization method, that is, the amplitude of the collected image plane light field is Fourier transformed, and its phase part is retained as the initial phase.

[0059] Then, in step S22, the initial phase obtained by geometric phase initialization The amplitude of the image light field collected |f(x n ,y m )| multiply to get the input image light field f1(x n ,y m ); In step S22', the initial phase obtained by geometric phase initialization The amplitude of the Fourier surface light field collected Multiply to get the input Fourier surface light field of the first iteration This can speed up iterations.

[0060] Therefore, the phase recovery imaging method of the present invention includes multiple iterations and a double-sided feedback mechanism. When the first type of phase recovery imaging method is executed, spatial spectrum limited feedback and second diffraction plane amplitude constraint feedback are applied to the second diffraction plane light field, and the first diffraction plane amplitude feedback is applied to the first diffraction plane. Among them, the first or second diffraction plane amplitude feedback is determined by the difference between the current output light field and the detection light field. The spatial spectrum limited feedback is the difference between the output light field of the current second diffraction plane and zero. Similarly, when the second type of phase recovery imaging method is executed, limited illumination feedback and first diffraction plane amplitude constraint feedback are applied to the first diffraction plane light field, and the second diffraction plane amplitude feedback is applied to the second diffraction plane. Among them, the first and second diffraction plane amplitude feedback are determined by the difference between the current output light field and the detection light field, and the limited illumination limited feedback is the difference between the output light field of the first diffraction plane and zero. Therefore, the double-sided feedback phase recovery method based on the optically constrained imaging system of the present invention solves the defects of object prior and multiple exposures, and solves the problem that the algorithm is easy to fall into the local minimum and depends on initialization.

[0061] The above is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. The above embodiments of the present invention can also be modified in various ways. All simple, equivalent changes and modifications made according to the claims and the description of the present invention fall within the scope of protection of the claims of the present invention. The contents not described in detail in the present invention are all conventional technical contents.

Claims

1. A double-sided feedback phase recovery method based on an optically confined imaging system, characterized in that: include: Step S1: collecting a first diffraction plane intensity and a second diffraction plane intensity of an imaging target through the optically limited imaging system; Step S2: if the second diffraction plane intensity is truncated, then the first type of phase recovery imaging method is executed; otherwise, the second type of phase recovery imaging method is executed; The first type of phase recovery imaging method specifically includes: Step S21: Based on the collected first diffraction plane intensity I(x n ,y m ) and the second diffraction plane intensity The amplitude of the light field in the first diffraction plane collected is obtained by square root calculation |f(x n ,y m )| and the amplitude of the light field collected in the second diffraction plane Step S22: Generate the initial phase of the first diffraction plane light field and the amplitude of the light field in the first diffraction plane collected |f(x n ,y m )| multiply to get the first diffraction plane light field f1(x n ,y m ); At the same time, the input second diffraction plane light field of the first iteration Initialize; Step S23: Input the first diffraction plane light field f of the i-th iteration i (x n ,y m ) performs the diffraction transformation calculation between the first diffraction plane and the second diffraction plane to obtain the output second diffraction plane light field of the i-th iteration Step S24: Using the feedback mechanism to output the second diffraction plane light field of the i-th iteration Apply the amplitude constraint and spatial spectrum restriction constraint of the second diffraction plane light field to obtain the input second diffraction plane light field of the i+1th iteration Step S25: Input the second diffraction plane light field of the i+1th iteration Perform the diffraction transformation calculation between the second diffraction plane and the first diffraction plane to obtain the output first diffraction plane light field f of the i+1th iteration i ′ +1 (x n ,y m ); then the output first diffraction plane light field f of the i+1th iteration is i ′ +1 (x n ,y m ) is projected onto the amplitude of the light field of the first diffraction plane collected |f(x n ,y m )|, and obtain the first diffraction plane light field of the input to be corrected in the i+1th iteration Step S26: According to the difference term f between the input first diffraction plane light field to be corrected and the output first diffraction plane light field of the i+1th iteration div (x n ,y m ), for the first diffraction plane light field to be corrected input in the i+1th iteration Apply constraint feedback to obtain the input image light field f of the i+1th iteration i+1 (x n ,y m ); The input image light field f of the i+1th iteration i+1 (x n ,y m )for: Among them, β2 is the feedback constant; Step S27: add 1 to the current iteration number i as the current iteration number i of the new round, and return to step S23 to perform the next round of iteration; until the iteration end condition is met, the iteration ends at this time, and the input first diffraction plane light field f of the i+1th iteration is i+1 (x n ,y m ) as the reconstructed first diffraction plane light field; The second type of phase recovery imaging method specifically includes: Step S21': Based on the collected first diffraction plane intensity I(x n ,y m ) and the second diffraction plane intensity The amplitude of the light field in the first diffraction plane collected is obtained by square root calculation |f(x n ,y m )| and the amplitude of the light field collected in the second diffraction plane Step S22': Generate the initial phase of the first diffraction plane light field And the amplitude of the light field collected in the second diffraction plane Multiply to get the input second diffraction plane light field of the first iteration At the same time, the first diffraction plane light field f1(x n ,y m ) to initialize; Step S23': Input the second diffraction plane light field of the i-th iteration Perform the diffraction transformation calculation between the second diffraction plane and the first diffraction plane to obtain the output first diffraction plane light field f of the i-th iteration i ′ (x n ,y m ); Step S24': Using the feedback mechanism to output the first diffraction plane light field f of the i-th iteration i ′ (x n ,y m ) applies the amplitude constraint of the first diffraction plane light field and the constraint of limited illumination or limited field of view to obtain the input first diffraction plane light field f of the i+1th iteration i+1 (x n ,y m ); Step S25': Input the first diffraction plane light field f of the i+1th iteration i+1 (x n ,y m ) performs the diffraction transformation calculation between the first diffraction plane and the second diffraction plane to obtain the output second diffraction plane light field of the i+1th iteration Then the output second diffraction plane light field of the i+1th iteration is The amplitude of the light field projected onto the second diffraction plane collected Get the second diffraction plane light field to be corrected input for the i+1th iteration Step S26': according to the difference term between the input second diffraction plane light field to be corrected and the output second diffraction plane light field of the i+1th iteration Apply constraint feedback to the input second diffraction plane light field to be corrected at the i+1th iteration to obtain the input second diffraction plane light field at the i+1th iteration The second diffraction plane light field to be corrected in the i+1th iteration for: Among them, β2 is the feedback constant; Step S27': add 1 to the current iteration number i as the current iteration number i of the new round, and return to step S23' to perform the next round of iteration; until the iteration end condition is met, the iteration ends at this time, and the input first diffraction plane light field f of the i+1th iteration is i+1 (x n ,y m ) as the reconstructed first diffraction plane light field.

2. The double-sided feedback phase recovery method based on an optically confined imaging system according to claim 1, characterized in that: The first diffraction plane is an image plane, and the second diffraction plane is a Fourier plane; In the step S1, the second diffraction plane intensity distribution is a Fourier surface space spectrum, and whether the imaging target is a strong scattering object or a weak scattering object is determined according to whether the Fourier surface space spectrum is truncated; In step S2, the first type of phase recovery imaging method is a phase recovery imaging method for strongly scattering objects, and the second type of phase recovery imaging method is a phase recovery method for weakly scattering objects.

3. The double-sided feedback phase recovery method based on an optically confined imaging system according to claim 2, characterized in that: In step S23, step S25, step S23' and step S25', the diffraction transformation between the first diffraction plane and the second diffraction plane is calculated as a Fraunhofer diffraction transformation, and the diffraction transformation between the second diffraction plane and the first diffraction plane is calculated as an inverse Fraunhofer diffraction transformation.

4. The double-sided feedback phase recovery method based on an optically confined imaging system according to claim 2, characterized in that: In an optically constrained imaging system, the light scattered by the imaging target causes a hard truncation of the Fourier plane spatial spectrum or the imaging field of view on the image plane due to the limited numerical aperture of the optical system. The limited numerical aperture of the optical system includes the size, direction and shape of the light source, the aperture of the objective lens, the pupil, numerical aperture and imaging field angle of the imaging lens, the size of the detector's photosensitive area, the size of the rectangular or circular aperture, and the probe size of the fiber optic detector; The limited numerical aperture of the optical system corresponding to the limited Fourier surface spatial spectrum includes the pupil and / or numerical aperture size limitation of the imaging lens; the limited Fourier surface spatial spectrum causes the Fourier surface spatial spectrum to be hard truncated; Limited illumination corresponds to the size limitation of the illumination source on the object, and limited field of view corresponds to the limited numerical aperture of the optical system, including the pupil size limitation of the imaging lens and / or the limitation of the imaging field of view angle; limited illumination or limited field of view leads to hard truncation of the imaging field of view on the image plane.

5. The double-sided feedback phase recovery method based on an optically confined imaging system according to claim 1, characterized in that: The diffraction transformation between the first diffraction plane and the second diffraction plane is a Fresnel transformation, and the formula for calculating the diffraction transformation between the first diffraction plane and the second diffraction plane is: Among them, U zi (x ′ ,y ′ ) and U i (x, y) is the light field of the first diffraction plane and the second diffraction plane, z is the distance between the two planes, is the Fourier transform, k is the wave number, f x is the frequency in the x direction, f y is the frequency in the y direction, and λ is the wavelength.

6. The double-sided feedback phase recovery method based on an optically confined imaging system according to claim 1, characterized in that: The first diffraction plane and the second diffraction plane are two diffraction planes that are in one or more combinations of a near Fresnel zone, a Fresnel zone, and a far field.

7. The double-sided feedback phase recovery method based on an optically confined imaging system according to claim 1, characterized in that: In step S24, after applying the amplitude constraint and spatial spectrum constraint of the second diffraction plane light field, the input second diffraction plane light field of the i+1th iteration is for: in, is the input second diffraction plane light field of the i-th iteration; is the output second diffraction plane light field of the i-th iteration, is the negative feedback term of the second diffraction plane, β and β1 are iteration constants, and f max is the cutoff frequency of the calibrated pupil function; In step S24', after applying the amplitude constraint and the finite illumination constraint of the first diffraction plane light field, the input first diffraction plane light field f of the i+1th iteration i+1 (x n ,y m )for: Among them, f i (x n ,y m ) is the input first diffraction plane light field of the i-th iteration, f i ′ (x n ,y m ) is the output first diffraction plane light field of the i-th iteration, f di (x n ,y m ) is the negative feedback term of the first diffraction plane, β and β1 are iteration constants, and L is the cutoff radius of the calibrated illumination function or field distribution function.

8. The double-sided feedback phase recovery method based on an optically confined imaging system according to claim 7, characterized in that: Calibrate pupil function, including: A point light source is placed in front of the optically limited imaging system, and a two-dimensional array detector is placed on the first diffraction plane to detect the image of the point light source. A point spread function is obtained from the spatial distribution of the intensity of the point light source image, and a pupil function of the optically limited imaging system is obtained by Fourier transforming the point spread function; or a point light source is placed in front of the optically limited imaging system, and a two-dimensional array detector is placed on the second diffraction plane to detect the spatial spectrum distribution of the point light source in the second diffraction plane, and the distribution is directly used as the calibrated pupil function of the optically limited imaging system; The calibrating illumination function specifically includes: when the optically limited imaging system is subjected to limited illumination smaller than the field of view, removing the imaging target, placing a two-dimensional array detector on the first diffraction plane to detect the light intensity distribution function of the illumination light as the illumination function; The field of view distribution function is calibrated, specifically including: under a limited field of view, irradiating the optically limited imaging system with parallel light larger than the field of view, placing a two-dimensional array detector on the first diffraction plane to detect the light intensity distribution function of the illumination light as the field of view distribution function.

9. The double-sided feedback phase recovery method based on an optically confined imaging system according to claim 8, characterized in that: Calibrating the pupil function also includes: determining the noise intensity according to the intensity distribution of the pupil function, and determining the cutoff frequency of the calibrated pupil function according to the noise intensity, so that within the range of the cutoff frequency of the calibrated pupil function, the pupil function is a detection value, and outside the range of the cutoff frequency of the calibrated pupil function, the pupil function is 0; When calibrating the illumination function or the field of view distribution function, the noise intensity is determined according to the signal intensity distribution of the illumination function or the field of view distribution function, and the cutoff radius of the illumination function or the field of view distribution function is set according to the noise intensity, so that the illumination function or the field of view distribution function signal within the cutoff radius is the detection value, and the illumination function or the field of view distribution function signal outside the cutoff radius is 0.

10. The double-sided feedback phase recovery method based on an optically confined imaging system according to claim 1, characterized in that: In step S22 and step S22', the initial phase of the first diffraction plane light field is The initial phase of the light field in the first diffraction plane is obtained by random generation, or The phase part is obtained by Fourier transforming the amplitude of the collected first diffraction plane light field and retaining the phase part.

Images