Phase recovery method based on optically limited imaging system

Abstract

The invention provides a phase recovery method based on an optically limited imaging system. The phase recovery method comprises the following steps: acquiring first and second diffraction plane intensities; a first type of phase recovery imaging method or a second type of phase recovery imaging method is executed according to whether the intensity of the second diffraction plane is cut off or not, and the phase recovery imaging methods comprise multiple iterations; and applying amplitude constraint and spatial spectrum limited constraint or limited illumination or limited view field constraint to the diffraction plane light field by using a feedback mechanism during each iteration. According to the phase recovery method based on the optical limited system constraint, optical system intrinsic limitation is used as algorithm constraint, object prior is not needed, interference of trivial solutions on a traditional iterative algorithm is eliminated through the constraint of the intensity of a collected real image surface and a Fourier leaf surface, and the problem that the algorithm is prone to falling into local minimum is solved; in addition, recovery can be completed only by collecting intensity information of a real image surface and a Fourier surface, and redundant measurement is not needed.

Description

Technical Field

[0001] The present invention relates to the field of phase recovery imaging, and more specifically to a 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 information detection. Interference method is a classic phase imaging method, mainly including 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 the object, this type of method usually needs to be combined with phase shift 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 is a non-interference method, mainly including 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, GuoanZheng 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, and 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 requirements of phase recovery.

[0006] Therefore, it is necessary to propose a phase recovery method and algorithm based on optically confined system constraints to solve the problems that the uniqueness of existing phase recovery methods depends on object priors, multiple exposures, and the reconstruction algorithm is prone to fall into local optimality.

[0007] 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.

[0008] 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:

[0009]

[0010]

[0011] 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:

[0012]

[0013] 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:

[0014]

[0015] 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 (to obtain Fourier surface intensity, i.e., second diffraction plane intensity), and a first two-dimensional array detector 106 (to obtain image plane intensity, i.e., first diffraction plane intensity) that receives light from the first imaging lens 102 and reflected by the beam splitter 103.

[0016] 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

[0017] The purpose of the present invention is to provide a phase recovery method based on optically constrained system constraints, so as to solve the problems that the uniqueness of existing phase recovery methods depends on object priors, multiple exposures, and the reconstruction algorithm is prone to fall into local optimality.

[0018] In order to achieve the above object, the present invention provides a phase recovery method based on limited system constraints, comprising:

[0019] S1: collecting a first diffraction plane intensity and a second diffraction plane intensity of an imaging target through the optically limited imaging system;

[0020] 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;

[0021] The first type of phase recovery imaging method specifically includes:

[0022] 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

[0023] S22: Randomly 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;

[0024] 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

[0025] 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

[0026] 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 input first diffraction plane light field f of the i+1th iteration i+1 (x n ,y m );

[0027] S26: 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;

[0028] The second type of phase recovery imaging method specifically includes:

[0029] 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

[0030] S22': Randomly 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;

[0031] 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 );

[0032] 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 );

[0033] 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 input second diffraction plane light field of the i+1th iteration

[0034] S26': 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 first diffraction plane is an image plane, and the second diffraction plane is a Fourier plane;

[0036] 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;

[0037] 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.

[0038] 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 (i.e., a standard two-dimensional Fourier transformation), and the diffraction transformation between the second diffraction plane and the first diffraction plane is calculated as an inverse Fraunhofer diffraction transformation.

[0039] 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 the size limitation 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.

[0040] 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; 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.

[0041] The formula for calculating the diffraction transformation between the first diffraction plane and the second diffraction plane is:

[0042]

[0043] 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.

[0044] 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:

[0045]

[0046] 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 fmax is the cutoff frequency of the calibrated pupil function;

[0047] 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:

[0048]

[0049] 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.

[0050] Calibrate pupil function, including:

[0051] 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;

[0052] 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;

[0053] 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.

[0054] 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;

[0055] 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.

[0056] 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.

[0057] Compared with single-shot exposure technologies such as CDI, the phase recovery method based on the constraint of the optically constrained system of the present invention uses the intrinsic constraint of the optical system as the algorithm constraint, and does not require object priori. The constraint of the intensity of the collected real image plane and the Fourier plane eliminates the interference of the trivial solution to the traditional iterative algorithm, and solves the problem that it is easy to fall into the local minimum; and compared with multiple exposure technologies such as FPM, 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a typical optical path diagram of a camera system.

[0059] Figure 2 This is a typical optical path diagram of a microscope system.

[0060] Figure 3 This is a typical optical path diagram of an optically constrained imaging system.

[0061] Figure 4-Figure 6 is a flow chart of a phase recovery method based on optically constrained system constraints according to an 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.

[0062] Figure 7 Graph of the truncation effect for an optically confined system.

[0063] 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.

[0064] 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.

[0065] Fig.10 The complex amplitude distribution and phase image of the light field reconstructed by the phase recovery method of the present invention. DETAILED DESCRIPTION

[0066] 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.

[0067] It should be noted that the following embodiments and features therein may be combined with each other if there is no conflict.

[0068] like Figure 4-Figure 6 The figure shows a 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.

[0069] Among them, existing optical imaging systems are all limited imaging systems. 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 (for obtaining the Fourier plane intensity, i.e., the second diffraction plane intensity), and a first two-dimensional array detector 106 (for obtaining the image plane intensity, i.e., the first diffraction plane intensity) which receives light from the first imaging lens 102 and is reflected by the beam splitter 103.

[0070] like Figure 4-Figure 6 As shown, according to the first embodiment of the present invention, a phase recovery method based on an optically constrained imaging system specifically includes:

[0071] Step S1: Collect the image plane intensity I(x n ,y m ) and Fourier surface intensity The Fourier surface intensity is used as the Fourier surface spatial spectrum, and whether the imaging target is a strong scattering object or a weak scattering object is determined according to whether the Fourier surface spatial spectrum of the imaging target is truncated;

[0072] 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 a strong scattering object is truncated. The specific truncation effect is as follows: Figure 7 The Fourier space spectrum of a weakly scattering object is not truncated.

[0073] In this embodiment, for a strong scattering object, the image plane intensity I(x n ,y m ) and Fourier surface intensity F(f xn ,f ym )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.

[0074] In an optically constrained imaging system, the light scattered by the imaging target has a hard truncation of the Fourier plane spatial spectrum or the imaging field of view of the image plane due to the limited numerical aperture of the optical system. When the Fourier plane spatial spectrum is further limited by the numerical aperture of the optical imaging system, the limitation of the Fourier plane spatial spectrum is mainly caused by the pupil and / or numerical aperture size limitation of the imaging lens, and the limitation of the Fourier plane spatial spectrum leads to a hard truncation of the Fourier plane spatial spectrum, and the collected data is suitable for the phase recovery imaging method of strongly scattering objects.

[0075] When the imaging field of the image plane is more limited due to limited illumination (or limited field of view), where limited illumination corresponds to the size limit of the illumination source on the object; 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 phase recovery imaging methods of weakly scattering objects.

[0076] In summary, the limited numerical aperture of the optical system includes, but is not limited to, the size limitation of the light source, the aperture limitation 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 limitation of the detector's photosensitive area, the size limitation of the rectangular or circular aperture (if there is an aperture), the probe size limitation of the fiber optic detector (if there is a fiber optic detector), and so on.

[0077] Step S2: Depending on whether the imaging target is a strong scattering object or a weak scattering object, a phase recovery imaging method for a strong scattering object or a phase recovery imaging method for a weak scattering object is executed accordingly.

[0078] Among them, the phase recovery imaging method of strongly scattering objects specifically includes:

[0079] Step S21: Based on the acquired 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 collected Fourier surface light field

[0080] 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;

[0081] At this time, the current iteration number i=1; that is, the input image plane light field f1(x n ,y m )for:

[0082]

[0083] 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.

[0084] When the current iteration number i = 1, the input Fourier surface light field of the first iteration is Initialized to 0.

[0085] 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

[0086] That is, the output Fourier surface light field of the i-th iteration is for:

[0087]

[0088] Among them, f i (x n ,y m ) is the input image light field of the i-th iteration, is the Fourier transform.

[0089] 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

[0090] 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:

[0091]

[0092] 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 cutoff frequency of the calibrated pupil function. The calibration method of the pupil function is detailed below.

[0093] therefore, It represents the negative feedback of the finite Fourier surface intensity signal so that the signal outside the cutoff frequency tends to 0 during the iteration process; Represents the negative feedback of the intensity of the collected Fourier surface light field so that it tends to the amplitude of the collected Fourier surface light field during the iteration process

[0094] Among them, the Fourier surface negative feedback term is defined as:

[0095]

[0096] 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.

[0097] Step S25: Input Fourier surface light field of the i+1th iteration Perform the reverse Fraunhofer diffraction transformation to obtain the output image light field f of the i+1th iteration i ' +1 (x n ,y m ); 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 light field f of the i+1th iteration i+1 (x n ,y m ).

[0098] That is to say, the output image light field f of the i+1th iteration is i ' +1 (x n ,y m )for:

[0099]

[0100] The input image light field f of the i+1th iteration i+1 (x n ,y m )for:

[0101]

[0102] Among them, |f(x n ,y m )| is the amplitude of the collected image light field.

[0103] Step S26: 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.

[0104] 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.

[0105] 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.

[0106] The phase recovery imaging method of weakly scattering objects specifically includes:

[0107] 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 collected Fourier surface light field

[0108] 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;

[0109] At this time, the number of iterations i = 1: that is, the input Fourier surface light field of the first iteration for:

[0110]

[0111] in, is the amplitude of the collected Fourier surface light field, is the initial phase of the image light field.

[0112] When the current iteration number i=1, the input image light field f1(x n ,y m ) is initialized to 0.

[0113] 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 );

[0114] That is to say, the output image light field f of the i-th iterationi ′(x n ,y m )for:

[0115]

[0116] in, is the input Fourier surface light field of the i-th iteration, is the inverse Fourier transform.

[0117] 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 );

[0118] 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:

[0119]

[0120] Among them, f i (x n ,y m ) is the input image plane light field of the i-th iteration, which comes from the previous iteration. The input image plane light field of the i-th iteration when i=1 comes from the initialization above. 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.

[0121] Therefore, f i (x n ,y m )-βf i ′(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 )+β1fdi (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 )|.

[0122] Among them, the image plane negative feedback term f di (x n ,y m ) is defined as:

[0123]

[0124] 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.

[0125] Step S25': for 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 of the i+1th iteration

[0126] That is, the output Fourier surface light field of the i+1th iteration is for:

[0127]

[0128] Input Fourier surface light field of the i+1th iteration for:

[0129]

[0130] in, is the amplitude of the collected Fourier surface light field.

[0131] Step S26': 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.

[0132] In this embodiment, the iteration end condition includes: 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.

[0133] 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.

[0134] Among them, calibrating the pupil function specifically includes:

[0135] 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.

[0136] 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.

[0137] 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.

[0138] 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.

[0139] 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.

[0140] 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.

[0141] 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.

[0142] 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.

[0143] 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.

[0144] In other embodiments of the present invention, the phase recovery method based on the optically confined imaging system of the present invention is not limited to the diffraction transformation between the real image plane and the Fourier plane and its iteration. The diffraction transformation between the real image plane and the Fourier plane can also be replaced by a diffraction transformation between two diffraction planes in one or more combinations of the near Fresnel zone, the Fresnel zone, and the far field.

[0145] Among them, in the second embodiment of the present invention, the Fraunhofer diffraction transform between the real image plane and the Fourier plane is replaced by the diffraction transform between the two diffraction planes in the Fresnel zone. Therefore, the other steps of this embodiment are the same as the steps of the phase recovery method based on the optically confined imaging system of 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.

[0146] Accordingly, in step S23, step S25, step S23', and step S25', the Fraunhofer diffraction transform between the real image plane and the Fourier plane is replaced by the diffraction transform between the first diffraction plane and the second diffraction plane in the Fresnel zone, and the reverse Fraunhofer diffraction transform between the Fourier plane and the real image plane is replaced by the diffraction transform calculation between the second diffraction plane and the first diffraction plane in the Fresnel zone. Therefore, in the second embodiment, the formula for the diffraction transform calculation between the first diffraction plane and the second diffraction plane is as follows:

[0147]

[0148] 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.

[0149] 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.

[0150] 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 contents of the specification 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 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, 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: Randomly 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 input first diffraction plane light field f of the i+1th iteration i+1 (x n ,y m ); Step S26: 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': Randomly 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 input second diffraction plane light field of the i+1th iteration Step S26': 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 phase recovery method based on the 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 phase recovery method based on the 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 phase recovery method based on the 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 limitation of the light source, the aperture limitation of the objective lens, the pupil of the imaging lens, the numerical aperture and imaging field angle limitation, the size limitation of the detector photosensitive area, the size limitation of the rectangular or circular aperture, and the probe size limitation of the fiber optic detector.

5. The phase recovery method based on the optically confined imaging system according to claim 4, characterized in that: 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; Limited illumination corresponds to the size limitation of the illumination source on the object; 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.

6. The 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 diffraction transformation between the first diffraction plane and the second diffraction plane satisfies the following calculation formula: 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.

7. The 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 phase recovery method based on the 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 phase recovery method based on the 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 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.

Images