A single-point quantitative phase extraction method for curved interference fringes and its application

Abstract

The present invention discloses a single-point quantitative phase extraction method and application of curved interference fringes. The present invention removes noise, improves contrast and performs binarization processing by shooting a zero-phase curved interference fringes image and a curved interference fringes image to be measured in a double-spot interference fringes formation area; then performs tilt correction on the interference fringes image; then uses a step-by-step pixel displacement algorithm to solve the fringes period T and the fringes displacement N; substitutes the fringes period T and the fringes displacement N into a formula to obtain the corresponding single-point phase value or phase difference value #imgabs0#, that is, to obtain the quantitative phase value of the phase object at the light point to be measured. The present invention has the advantages of being able to process curved interference fringes and parallel straight fringes images, strong adaptability, being able to automatically rotate the tilted interference fringes to a horizontal position, only needing to process the pixels contained in the selected area (greater than two interference fringes), saving processing time and improving computational efficiency.

Description

Technical Field

[0001] The invention belongs to the research field of optical measurement and image processing, and particularly relates to a single-point quantitative phase extraction method of curved interference fringes and an application thereof. Background Art

[0002] At present, there are two main types of quantitative imaging technologies for phase objects: full-field quantitative phase imaging technology and single-point scanning quantitative phase imaging technology. In the existing single-point scanning quantitative phase imaging technology, the key is to accurately and quantitatively extract the phase value of each point of the phase object. For example, in the phase object dual-point source quantitative phase scanning measurement and imaging technology, the object plane single-point phase extraction technology is only applicable to the case where the interference fringes formed by the dual-point far-field diffraction are parallel and equally spaced straight fringes, and is not applicable to the extraction of single-point phase of curved interference fringes formed by the dual-point near-field diffraction. In the field of laser interferometer microscopy, there are a large number of curved interference fringes, which brings certain difficulties and limitations to the promotion and application of this technology. Summary of the invention

[0003] The primary purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art and to provide a single-point quantitative phase extraction method for curved interference fringes - a step-by-step pixel displacement algorithm.

[0004] Another object of the present invention is to provide an application of the single-point quantitative phase extraction method of the curved interference fringes.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A single-point quantitative phase extraction method for curved interference fringes, such as Figure 1 As shown, the following steps are included:

[0007] (1) When no phase object is placed, an interference fringe image is photographed in the area where the double-spot interference fringe is formed, as a zero-phase curved interference fringe image; the phase object is moved by a stepper motor so that the light spot as the point to be measured hits the object, and the phase curved interference fringe image to be measured is photographed, and then the photographed zero-phase curved interference fringe image and the curved interference fringe image to be measured are preprocessed;

[0008] (2) performing tilt correction on the zero-phase curved interference fringe image and the phase curved interference fringe image to be measured obtained after processing in step (1) so that they are in a horizontal direction;

[0009] (3) using a step-by-step pixel displacement algorithm, the fringe period T is calculated for the zero-phase curved fringe image obtained after processing in step (2); and the fringe displacement N is calculated for the phase curved interference fringe image to be measured obtained after processing in step (2);

[0010] (4) Substitute the fringe period T and fringe displacement N obtained in step (3) into the formula to obtain the corresponding single-point phase value or phase difference That is, the quantitative phase value of the phase object at the measured light point is obtained. If the interference fringes move to the left, the phase of the sample can be obtained from obtained.

[0011] The two light points described in step (1) are two light points with relatively high brightness on the spectrum, which are the reference light point and the measured light point; the light point where the phase object to be measured is placed is the measured light point, and the other light point is the reference light point.

[0012] The shooting described in step (1) is preferably carried out using a digital camera.

[0013] The preprocessing described in step (1) is preferably to filter out noise, improve contrast and perform binarization processing.

[0014] The tilt correction described in step (2) is to first judge the correction direction of the interference fringe image of the zero phase through the program, then automatically rotate it to the horizontal position, and calculate the rotation angle θ°. Other interference fringes in the same series only need to be rotated by θ° in the same direction to be corrected to the horizontal state, without manual operation.

[0015] The program described is preferably a matlab program, and the specific steps are preferably as follows: Take the pixels in the middle row of the image and calculate the average period t of the gray-scale change; make the image rotate counterclockwise by a small angle σ° with its center point as the fixed point, and then calculate the average period t' of the gray-scale change of the pixels in the middle row of the image. Compare the sizes of t and t'. If t'<t, continue to rotate counterclockwise by σ°, repeat the above operation, and compare the average period sizes before and after each rotation until the smallest average period is obtained; if t'>t, rotate clockwise by σ°, and perform the same operation steps as before until the smallest average period is obtained. At this time, the image has been rotated to the horizontal state. Count the number of rotations n at this time, and then the rotation angle of the interference fringe images in the same series can be obtained from θ = n·σ.

[0016] The coordinates of the center point will change after each rotation of the image. This is because after each rotation, matlab will automatically fill the pixels with gray-scale 0 around the interference fringe image, increasing the number of pixels included in the output image. If the center point coordinates taken after each rotation remain unchanged, it will cause the center point selected each time not to be the same pixel point, resulting in rotation errors. Therefore, in order to ensure that the center point selected each time is the same pixel point, the size of the image should be calculated after each rotation of the image: the number of pixel rows is p, and the number of columns is q, and is used as the center point for the next rotation.

[0017] The steps for obtaining the fringe period T described in step (3) are preferably as follows: select a pixel area with a number of fringes greater than 2 as a moving window of the image variable I0; take the same area of ​​the same image and set it as the image variable I1; move I1 to the right by a distance of one pixel each time, and calculate the absolute value e of the grayscale difference between I0 and I1; the value of e changes periodically with the moving distance, and the average periodic pixel number corresponding to the minimum value of e is the fringe period T of the interference fringes.

[0018] The steps for obtaining the fringe displacement N described in step (3) are preferably as follows: take the area in the phase-bending interference fringe image to be measured that is the same as the image variable I0 in the zero-phase bending interference fringe image, set it as the image variable I, move I to the right by a distance of one pixel each time, and calculate the absolute value e of the grayscale difference between I and I0. When the e value first reaches a minimum value, the corresponding I displacement is the interference fringe displacement N to be measured.

[0019] The application of the above-mentioned single-point quantitative phase extraction method of curved interference fringes in quantitative phase imaging of phase objects preferably includes the following steps: according to the above-mentioned single-point quantitative phase extraction method of curved interference fringes, the phase object is scanned point by point to obtain the phase value of each point of the phase object and reconstruct the phase distribution of the phase object or realize quantitative phase imaging of the phase object.

[0020] The working principle of the method of the present invention:

[0021] Figure 2 This is a schematic diagram of the principle of double-spot interference. The essence of double-spot interference is Young's interference. Figure 2 The F plane in the middle is the sample stage plane with coordinates (x0, y0), the distance between the double light spots S1 (reference light spot) and S2 (light spot to be measured) is S, L is the vertical distance from the double light spots to the plane I where the observation point P is located, the middle dotted line is the central axis, D is the distance from the observation point P to the central axis, the I plane is the plane where the receiving screen is located with coordinates (x, y), and c is the phase sample to be measured.

[0022] Assume that the complex amplitudes of the two spherical waves of the double-spot light in the interference field section are:

[0023]

[0024]

[0025] In formula (2), is the phase size of the phase object. For the convenience of discussion, let the coordinates of the two light spots be S1(-b,0,0) and S2(b,0,0), and examine the light intensity distribution on the receiving screen at a distance of z=L(L>0).

[0026]

[0027]

[0028] The light field in the interference field cross section is:

[0029]

[0030] In formula (5), Indicates the background light intensity. represents the amplitude, represents the phase difference between the two light points and the observation position, k is the wave number, and δ(x, y) and Represent the optical path difference and phase difference of the two light points respectively, then:

[0031]

[0032] From the analysis of formula (5), we can see that the interference fringes are modulated by the cosine function. It has nothing to do with the coordinates. Its size causes the directional movement of the whole stripe. The amount of movement is related to the phase value of the phase object. about; when When the period changes by 2π, the interference fringes move as a whole by one fringing period T. When the range of the interference fringe is [0,2π), let the fringe displacement be N, and the overall movement of the interference fringe N is is proportional to

[0033]

[0034] Arranged

[0035]

[0036] For a specific measurement system, It is a constant and is related to the degree of curvature of the interference fringes or the distance between the light source and the receiving plane, the wavelength, etc.

[0037] Therefore, for curved interference fringes, the phase magnitude at a certain point can be calculated by obtaining the interference displacement period T and its displacement N and substituting them into the formula:

[0038] The single-point phase extraction method includes the following steps:

[0039] [1] Input the collected interference fringe image.

[0040] [2] Preprocess the image input in step [1] by filtering to remove noise and improve contrast, and then perform binarization.

[0041] [3] Image tilt correction processing. Take the pixels in the middle row of the image and calculate the average period t of its grayscale change. Take the image as the fixed point and rotate it counterclockwise by a small angle σ°. Then calculate the average period t′ of the grayscale change of the pixels in the middle row of the image. Compare t and t′. If t′<t, continue to rotate counterclockwise by σ°. Repeat the above operation. After each rotation, compare the average period before and after the rotation until the minimum average period is obtained. If t′>t, rotate it clockwise by σ°. Repeat the same operation steps as before until the minimum average period is obtained. At this time, the image has been rotated to a horizontal state.

[0042] The coordinates of the center point will change after each rotation of the image. This is because after each rotation, Matlab will automatically fill the grayscale 0 pixels around the interference fringe image, increasing the number of pixels contained in the output image. If the coordinates of the center point taken after each rotation remain unchanged, the center point selected each time will not be the same pixel, causing rotation error. Therefore, in order to ensure that the center point selected each time is the same pixel, the size of the image should be calculated after each rotation of the image: the number of pixel rows is p, the number of columns is q, and (p / 2, q / 2) is used as the center point of the next rotation.

[0043] [4] Select the moving window. Take the [400:600, 400:600] area in the image corresponding matrix as the moving window.

[0044] [5] Calculate the displacement period. Take the zero-phase curved interference fringe image, select the moving window according to step [4], and set it as the image variable I0; take the same area of ​​the same image, set it as the image variable I1, move I1 to the right by one pixel each time, and calculate the absolute value e of the grayscale difference between I0 and I1. Since the interference fringes change periodically, the value of e also changes periodically. The coordinate corresponding to the minimum value of e is the number of pixels of the moving period at different positions. The average value of the period is taken as the average moving period T of the series of images.

[0045] [6] Calculate the interference fringe displacement N. Take the same area I in the interference fringe image as in the zero-phase image, move I to the right by one pixel each time, and calculate the absolute value e of the grayscale difference between I and I0. When the e value reaches a minimum value for the first time, the corresponding displacement is the interference fringe displacement N.

[0046] [7] Find the phase size of a phase object Substitute the fringe period T and the number of displacement pixels N obtained in steps [5] and [6] into the formula You can get the phase If the interference fringes are shifted to the left, the phase of the sample can be given by To obtain.

[0047] Compared with the prior art, the present invention has the following advantages and effects:

[0048] (1) The present invention can process both curved interference fringe and parallel straight fringe images, and has strong adaptability;

[0049] (2) The present invention can automatically rotate the inclined interference fringes to a horizontal position;

[0050] (3) The method of the present invention only needs to process the pixel points contained in the selected area (greater than two interference fringes), which greatly saves the processing time and improves the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of the present invention.

[0052] Figure 2 It is a schematic diagram of the double-spot interference principle of the present invention.

[0053] Figure 3 It is a schematic diagram of the experimental optical path of the present invention.

[0054] Figure 4 This is the image of the curved interference fringes of the holographic phase grating taken by the camera.

[0055] Figure 5 It is to repeatedly measure the phase distribution cross-section of a row of the holographic phase grating.

[0056] Figure 6 The phase distribution cross-section of a row of holographic phase grating with three different processing technologies.

[0057] Figure 7 This is a cross-sectional diagram of the phase distribution of a row of the holographic phase grating at different distances from the camera.

[0058] Figure 8 The present invention provides a three-dimensional reconstructed phase distribution diagram of holographic phase grating imaging by the method of the present invention. DETAILED DESCRIPTION

[0059] The present invention is further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0060] Example 1

[0061] Figure 3 The optical path diagram for shooting the interference fringe image of the present invention includes the following experimental process:

[0062] The light beam emitted by the semiconductor laser passes through an adjustable attenuation plate, a beam expander, a pinhole filter, and a collimating lens in sequence to form a plane light wave, which is then irradiated onto a one-dimensional grating. The light wave then passes through a Fourier transform lens to form a spectrum of the one-dimensional grating on the focal plane of the lens.

[0063] Use an aperture or slit to select two light spots with larger brightness on the spectrum (such as -1 level and 0 level) and let them pass. The light beams emitted by the two light spots will interfere in the overlap area to form interference fringes. Place a CMOS digital camera in the interference area and ensure that the interference fringes are not tilted to be visible to the naked eye. Collect the interference fringes image and store it on the computer connected to it. The distance between the two light spots and the camera determines whether the interference fringes are curved fringes or parallel fringes, that is, whether they meet the near-field diffraction or far-field diffraction conditions.

[0064] First, take an interference fringe image without adding the grating to be measured as a zero-phase curved interference fringe image; Figure 3 The sample in the grating is placed in the area where one of the light spots (the light spot to be measured) is located, and the other light spot (the reference light spot) does not pass through the grating. The two light waves in the area where the two light spots are located experience different phase modulation and interfere with each other. At this time, the image collected by the camera is the interference fringe image of the grating to be measured.

[0065] Scan the grating to be measured point by point in the horizontal direction, with the number of scanning points being 79 columns * 3 rows = 237, and record the interference fringe image, such as Figure 4 This is one of the images of curved interference fringes.

[0066] The following is a further explanation of the step-by-step pixel displacement method in combination with the quantitative measurement of the holographic phase grating, which includes the following process:

[0067] [1] Input the collected interference fringe image.

[0068] [2] Preprocess the image input in step [1] by filtering to remove noise and improve contrast, and then perform binarization.

[0069] [3] The image obtained after step [2] is rotated and corrected using a MATLAB program. The specific operation is as follows: take the pixels in the middle row of the image and calculate the average period t of its grayscale change. The image is rotated counterclockwise by 0.001° with its center point as the fixed point, and then the average period t′ of the grayscale change of the pixels in the middle row is calculated. Compare the sizes of t and t′. If t′<t, continue to rotate counterclockwise by 0.001°, and repeat the above operation. After each rotation, compare the average period of grayscale change before and after this rotation until the minimum average period is obtained; if t′>t, rotate 0.001° clockwise, and repeat the same operation steps as before until the minimum average period is obtained. At this time, the image has been rotated to a horizontal state. Since every time the image is rotated, MATLAB will automatically fill the grayscale 0 pixels around it, increasing the number of pixels contained in the image. If the pixels and fixed points in the middle row are not reselected, the statistical average period will not be the average period corresponding to the grayscale change of the pixels in the same row, and the fixed point of rotation will not be the center of the image, which will affect the accuracy of the phase solution. Therefore, after each rotation, the image size should be calculated first, the pixels in the middle row should be taken and the average period t should be calculated, and finally the center of the image should be used as the fixed point, rotated 0.001° and proceed to the subsequent steps.

[0070] [4] Select the moving window. Take the [400:600, 400:600] area in the image corresponding matrix as the moving window.

[0071] [5] Calculate the displacement period. Name the zero-phase curved interference fringe image without the grating as 0. According to step [4], take the pixel area [400:600,400:600] and name it I0 as the moving window; take the same area of ​​the same image and set it as the image variable I1. Each time I1 is moved to the right by one pixel, the absolute value e of the grayscale difference between I0 and I1 is calculated. Since the interference fringes are periodic, the value of e also changes periodically. The coordinate corresponding to the minimum value of e is the number of pixels of the moving period at different positions. The average value of the number of periodic pixels is taken as the average moving period T of the series of images.

[0072] [6] Calculate the interference fringe displacement N. Take the same area I in the interference fringe image as in the zero-phase image, move I to the right by one pixel each time, and calculate the absolute value e of the grayscale difference between I and I0. When the e value reaches a minimum value for the first time, the corresponding displacement is the interference fringe displacement N.

[0073] [7] Find the phase size of a phase object Substitute the fringe period T and the number of displacement pixels N obtained in steps [5] and [6] into the formula You can get the phase The value of .

[0074] [8] If the interference fringes are shifted to the left, then the phase of the sample can be given by To obtain.

[0075] Combine the following Figure 5-Figure 8 The single-point quantitative phase extraction method of the present invention is used to process the curved interference fringe image and the straight interference fringe image taken by the holographic phase grating, and the results are compared with the results of the processing using the classical double-point source quantitative phase scanning imaging technology.

[0076] Figure 5 The method provided by the present invention processes curved interference fringes to obtain a phase distribution cross-sectional diagram of a certain row in a certain area of ​​a holographic phase grating, indicating that the method has good repeatability, accuracy and stability of phase quantitative measurement.

[0077] Figure 6 The method provided by the present invention processes the image of curved interference fringes and the image of straight interference fringes, as well as the phase distribution cross-section of a certain row of a certain area of ​​the holographic phase grating obtained by using the classical double-point source quantitative phase scanning imaging technology. Among them, the maximum value of the grating phase obtained by processing the curved fringes formed by the grating using the method provided by the present invention is about 0.7901π, while the maximum value of the grating phase obtained by processing the straight fringes formed by the grating using the method is about 0.7865π; compared with the result of 0.8π obtained by processing with the classical double-point source quantitative phase scanning imaging technology, there are absolute errors of 0.0099π and 0.0135π, respectively, and the corresponding relative errors are 1.24% and 1.69%, respectively, indicating that the phase solved by the method of the present invention has a higher self-consistency and accuracy. Therefore, the method of the present invention is suitable for curved interference fringes and straight interference fringes, and the obtained phase distribution curve has a high degree of overlap with the curve of the processing result of the classical double-point source quantitative phase scanning imaging technology, indicating that the phase measurement results of the two technologies are very close.

[0078] There are two classical methods for extracting phase, namely the periodic fringe binary image algorithm (References 1-3) and the extreme value spacing algorithm (Reference 4). Among them, the periodic fringe binary image algorithm is the most commonly used. Its working principle is: first pre-process the straight, equally spaced interference fringe image collected by the CMOS digital camera to obtain a denoised, binary interference image, take one row of pixels for pixel count, that is, calculate the total number of pixels l and the total number of cycles n after removing the first and last incomplete cycles, and then obtain the average period of the fringe according to the formula T = l / n. The displacement size is calculated by a similar method. The number of displaced pixels of each interference fringe is calculated, and the number with the highest probability of occurrence is taken as the overall displacement N of the fringe. The extreme value spacing algorithm denoises and enhances the contrast of the interference fringe image, and adds the corresponding grayscale values ​​of each column of pixels to obtain a grayscale distribution matrix with a row number of 1, finds the corresponding coordinates of the maximum value in the matrix, and calculates the average value of its spacing as the average period T of the interference fringe. The method for solving the overall displacement of the stripes is similar to this: compare the interference stripe image with the maximum coordinates of the zero-phase interference stripe image to obtain the number of displacement pixels of each interference stripe, and take the displacement with the highest probability as the overall displacement N of the stripes. Finally, substitute T and N into formula (8) to extract the phase. For the curved interference stripe image, there is a large difference in the spacing between stripes of each level, and there is also a large difference in the spacing corresponding to different rows of the same level of stripes. The classical method of extracting the phase is based on the fact that the interference stripes are parallel and equally spaced. If the interference stripes are curved stripes with unequal spacing, the classical method of extracting the phase will result in a large error. Therefore, the classical method is not suitable for phase extraction of curved interference stripes. The method of the present invention does not need to count the movement of all interference stripes in the image, but only needs to process the area containing two stripes. It can be seen that the present invention has a wider range of applications and a faster processing speed.

[0079] Figure 7 It is a phase cross-section diagram of measuring the same row of the grating under the condition of changing the distance between the double light spots (phase object plane) and the camera. It can be seen from the figure that under different distance conditions, the phase value curve has a high degree of overlap, which shows that the method provided by the present invention has good adaptability.

[0080] Figure 8 The present invention provides a method for three-dimensionally reconstructing the phase distribution diagram of the holographic phase grating imaging, which can clearly observe the fluctuation of the phase and present the shape of the grating. In addition, the maximum reconstructed phase is 0.7901π, which is 0.0099π absolute error and 1.24% relative error compared with the maximum phase of 0.8π solved by the classical double-point source quantitative phase scanning imaging technology. It can be seen that this method has the ability to accurately measure and image the phase of an unknown phase object.

[0081] literature:

[0082] 1. Zuo-hua Huang, Feng-chao Chen. A New Method of Scanning Image for Phase Objects[J]. SPIE, 2006, 6150(30):1-5.

[0083] 2. Chen Fengchao, Huang Zuohua, Li Rong. Measurement of interference fringe period and its application in phase detection [J]. Laser Technology, 2007, 32(1):105-108.

[0084] 3. Chen Fengchao. Research on interferometry and scanning imaging technology of phase objects[D]. South China Normal University, 2007.

[0085] 4. Liu Yun, Wang Yan, Huang Zuohua. Improvement of phase object interferometry and scanning imaging system [C]. Proceedings of the 9th National Conference on Information Acquisition and Processing, 2011: 230-233.

[0086] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A single-point quantitative phase extraction method for curved interference fringes, characterized in that It includes the following steps: (1) When the phase object is not placed, in the region where the double - spot interference fringes are formed, capture an interference fringe image as the zero - phase bending interference fringe image; use a stepper motor to move the phase object so that the light spot serving as the measurement point hits the object, capture the measured - phase bending interference fringe image, and then pre - process the captured zero - phase bending interference fringe image and the measured - phase bending interference fringe image; (2) Perform tilt correction on the zero - phase bending interference fringe image and the measured - phase bending interference fringe image obtained after the processing in step (1) to make them in the horizontal direction; (3) Use the step - by - step pixel displacement algorithm to obtain the fringe period T of the zero - phase bending fringe image obtained after the processing in step (2); Obtain the fringe displacement amount N of the measured - phase bending interference fringe image obtained after the processing in step (2); (4) Substitute the fringe period T and fringe displacement N obtained in step (3) into the formula The corresponding single-point phase value or phase difference value can be obtained That is, the quantitative phase value of the phase object at the light point to be measured is obtained. If the interference fringes are moving to the left, the phase of the sample can be obtained by To obtain.

2. The single - point quantitative phase extraction method for bending interference fringes according to claim 1, wherein: The double light spots in step (1) are the reference light spot and the measured light spot; among them, the light spot where the measured - phase object is placed is the measured light spot, and the other light spot is the reference light spot; The capture in step (1) is performed using a digital camera.

3. The single - point quantitative phase extraction method for bending interference fringes according to claim 1, wherein: The pre - processing in step (1) is to filter out noise, improve contrast, and perform binarization processing.

4. The single - point quantitative phase extraction method for bending interference fringes according to claim 1, wherein: The tilt correction in step (2) is to first judge the correction direction of the interference fringe image of the zero - phase through a program, then automatically rotate it to the horizontal position, and calculate the rotation angle θ°. Other interference fringes in the same series only need to be rotated by θ° in the same direction to be corrected to the horizontal state.

5. The single - point quantitative phase extraction method for bending interference fringes according to claim 4, wherein: The program is a Matlab program.

6. The single - point quantitative phase extraction method for bending interference fringes according to claim 4, wherein: The specific steps of the program are as follows: Take the pixels in the middle row of the image, and obtain the average period t of the gray - scale change; make the image rotate counter - clockwise by a small angle σ° with its center point as the fixed point, then obtain the average period t' of the gray - scale change of the pixels in the middle row of the image, compare the sizes of t and t'. If t'<t, continue to rotate counter - clockwise by σ°, repeat the above operation, and compare the average period sizes before and after each rotation until the minimum average period is obtained; if t'>t, rotate clockwise by σ°, and perform the same operation steps as before until the minimum average period is obtained. At this time, the image has been rotated to the horizontal state; count the number of rotations n at this time, then the rotation angle of the interference fringe images in the same series is obtained by θ = n·σ; The center point is calculated in the following way: after each rotation of the image, the size of the image is calculated: the number of pixel rows is p, the number of columns is q, and As the center point for the next rotation.

7. The single - point quantitative phase extraction method for bending interference fringes according to claim 1, wherein: The steps for obtaining the fringe period T described in step (3) are as follows: take the interference fringe image with zero phase, and select a pixel area with a fringe number greater than 2 as a moving window, set as image variable I0; take the same area of ​​the same image, set as image variable I1; each time I1 is moved to the right by a distance of one pixel, and the absolute value e of the grayscale difference between I0 and I1 is calculated; the value of e changes periodically with the moving distance, and the average periodic pixel number corresponding to the minimum value of e is the fringe period T of the interference fringe.

8. The single-point quantitative phase extraction method of curved interference fringes according to claim 1, characterized in that: The steps for obtaining the fringe displacement N described in step (3) are as follows: for the same area I in the phase-bending interference fringe image to be measured as in the zero-phase bending interference fringe image, I is moved one pixel to the right each time, and the absolute value e of the grayscale difference between I and I0 is calculated. When the e value first reaches a minimum value, the corresponding I displacement is the interference fringe displacement N to be measured.

9. Application of the single-point quantitative phase extraction method of curved interference fringes as claimed in any one of claims 1 to 8 in quantitative phase imaging of phase objects.

10. The use according to claim 9, characterized in that The method comprises the following steps: scanning the phase object point by point according to the single-point quantitative phase extraction method of curved interference fringes as described in any one of claims 1 to 8, obtaining the phase value of each point of the phase object and reconstructing the phase distribution of the phase object or realizing quantitative phase imaging of the phase object.

Images