A lens focal length measurement method based on vortex light interference

Abstract

This invention discloses a lens focal length measurement method based on vortex light interferometry, comprising the following steps: constructing a measurement system for vortex light and spherical wave interference; acquiring the interferogram I1(x,y) of the vortex light and spherical wave interference, the interferogram I2(x,y) for center positioning, the parallel light spot pattern I3(x,y), and the converging light spot pattern I4(x,y); obtaining the center coordinates (x0,y0) of the effective image of the interferogram I2(x,y), and cropping the effective image region I from the interferogram I1(x,y) based on the center coordinates. R (x,y); Get I R The maximum light intensity point distribution map I5(x,y) is obtained by transforming I5(x,y) to the polar coordinate system, resulting in the maximum light intensity point distribution map I6(θ,r) in the polar coordinate system. Periodic reconstruction of I6(θ,r) yields the maximum light intensity point distribution map I... m (θ,r), and for I m The points in (θ,r) are fitted to obtain the fitting result a; the acquired parallel light spot image I3(x,y) and converging light spot image I4(x,y) are binarized to obtain the binarized images I'3 and I'4, and the ratio β of their spot sizes is calculated; the focal length f = βa of the lens under test is calculated from the fitting result a and the ratio β of the spot sizes. The measurement optical path structure of this invention is simple, the measurement error is small, and the measurement accuracy is high.

Description

Technical Field

[0001] This invention relates to a method for measuring the focal length of a lens, and more particularly to a method for measuring the focal length of a lens based on vortex optical interferometry. Background Technology

[0002] Lenses, as a core component of optical devices, play a crucial role in many industries, particularly in optical instrument manufacturing, medical imaging, photography, and astronomy. The focal length of a lens is one of the important indicators for measuring its optical properties. The accuracy of the focal length directly affects the lens's performance in imaging, magnification, and focusing. Therefore, developing a high-precision, stable, and reliable method for measuring lens focal length has significant scientific research and practical application value.

[0003] Chinese Patent Publication No. CN216978325U discloses a convex lens focal length measuring device, comprising: a slide rail, a bracket, a light source, a reflector, a convex lens, a screen, a laser rangefinder sensor, a power supply, a microcontroller, and a display. By adjusting the distance between the screen and the lens, the light from the light source is focused onto the screen. Then, a laser rangefinder mounted on the screen measures the distance from the screen to the lens; this distance is the focal length of the lens under test. While this method is fast and systematic, spherical aberration of the lens often prevents the light beam from converging to an ideal point, and the judgment of the degree of convergence is subjective and prone to error. Furthermore, it requires measuring the distance from the lens to the screen.

[0004] Chinese Patent Publication No. CN114061910A discloses a device and method for measuring the focal length of a convex or concave lens, including an optical guide rail, a laser source, a short focal length convex lens, a lens under test, a connecting body, a frosted glass, and an image screen. By moving the frosted glass, the positions corresponding to the front surface of the frosted glass when the speckle on the image screen is at its maximum are the positions of the object and image of the lens under test. Then, the object distance and image distance are measured, and the focal length of the lens under test is calculated using the lens imaging formula. This method is simple to operate and requires few measuring devices, but the judgment of speckle size is somewhat subjective, and the object distance and image distance need to be obtained through the scale on the optical guide rail, which introduces a certain degree of error. The measurement range is limited by the length of the guide rail.

[0005] Chinese Patent Publication No. CN112611548A discloses a lens focal length measurement device and method based on digital holography. The device includes a laser, a beam splitter, an optical mirror, a beam expander, a pinhole filter, a collimating lens, a concave lens under test, a charge-coupled device (CCD), and a computer. This method causes the object light wave passing through the lens under test to interfere with a reference light wave, changing the wavefront radius of the reference light. An interference image is recorded in the interference field using the CCD, and the focal length of the lens under test is measured by analyzing the interference image information and the change in the wavefront radius of the reference light wave. While this method eliminates subjective human factors, it still requires measuring the distance between the lens and the CCD, making measurement errors unavoidable. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to propose a lens focal length measurement method based on vortex optical interferometry. While ensuring measurement accuracy, the required optical path structure is simple, the measurement error is small, and there is no need to measure the distance between the components. It can measure the focal length of convex and concave lenses and reduce the impact of lens spherical aberration on measurement accuracy.

[0007] Technical solution: This invention includes the following steps:

[0008] S1. Construct a measurement system for the interference of vortex light and spherical waves;

[0009] S2. Acquire the interference pattern I1(x,y) of the interference between vortex light and spherical wave, the interference image I2(x,y) for center positioning, the parallel light spot pattern I3(x,y) and the converging light spot pattern I4(x,y).

[0010] S3. Obtain the center coordinates (x0, y0) of the effective image of the interferogram I2(x,y), and extract the effective image region I from the interferogram I1(x,y) based on these center coordinates. R (x,y);

[0011] S4, Get I R The maximum light intensity point distribution map I5(x,y) is obtained by transforming I5(x,y) to the polar coordinate system, resulting in the maximum light intensity point distribution map I6(θ,r) in the polar coordinate system. Periodic reconstruction of I6(θ,r) yields the maximum light intensity point distribution map I... m (θ,r), and for I m The points in (θ,r) are fitted to obtain the fitting result a;

[0012] S5. Perform binarization on the acquired parallel light spot image I3(x,y) and converging light spot image I4(x,y) to obtain the binarized images I3' and I'4, and calculate the ratio β of their spot sizes.

[0013] S6. Calculate the focal length f = βa of the lens under test from the ratio of the fitting result a to the size of the light spot β.

[0014] The data acquisition steps in S2 include:

[0015] S21: After placing the lens to be tested, adjust the vortex wave plate, move the distance between the dark spot at the center of the vortex light and the center of the spherical wave interference ring, rotate the linear polarizer to improve the contrast of the interference fringes, and collect the interference pattern I1(x,y) between the vortex light and the spherical wave at this time.

[0016] S22: Adjust the vortex waveplate to move the center of the vortex light away, generating the interference image that appears when the spherical wave and the plane wave interfere, and acquire the interference image I2(x,y);

[0017] S23: Block the light path of the lens under test and collect the image at this time as parallel light spot I3(x,y). Block the light path of the vortex light and obtain the converging light spot I4(x,y).

[0018] The center coordinates (x0, y0) are obtained using a circle center positioning algorithm.

[0019] The circle center localization algorithm is as follows: Gaussian filtering is applied to the interference image I2(x,y) to obtain the filtered Newton's rings interference image I'2(x,y), and I'2 is processed to obtain the center coordinates (x0,y0) of the effective image.

[0020] The Hough transform algorithm is used when processing I'2, specifically including:

[0021] 1) Extract the ring (xa) 2 +(yb) 2 =r 2 , where (a,b) are the center coordinates (x0,y0) of the effective image, r is the radius of the extracted ring, and (x,y) are the coordinates of any point on the extracted ring in the xoy coordinate system;

[0022] 2) Extract all points (x) on the annulus. i ,y i (i = 1, 2, 3, ..., n), any point of which, after undergoing a Hough transformation to the parameter space coordinate system, becomes a conical surface. The expression for the conical surface in parameter space is:

[0023] (ax i ) 2 +(by i ) 2 =r 2

[0024] Among them, (x i ,y iLet (i, b, r) be the coordinates of the i-th point on the annulus extracted in the xoy coordinate system, and let a, b, r be the variables in the parameter space coordinate system that satisfy the conical expression. By finding the cumulative maximum value in the parameter space, the coordinates (a, b, r) are obtained, where (a, b) is the center coordinate (x0, y0) of the effective image, and r is the radius of the extracted annulus.

[0025] The maximum light intensity point distribution map I5(x,y) is obtained by analyzing the effective region I of the interferogram. R (x,y) is obtained through filtering and extreme value search algorithms.

[0026] The I m The method for obtaining (θ,r) is as follows: In the polar coordinate system, arrange all the points with the maximum light intensity in I6(θ,r) in ascending order of polar radius r to obtain I'6(θ,r). Then, iterate through all the points with the maximum light intensity in I'6. If the previous point (θ,r) is... i ,r i ) of θ i Greater than the next point (θ) i+1 ,r i+1 ) of θ i+1 Then the next point (θ) i+1 ,r i+1 ) becomes (θ i+1 +2nπ,r i+1 Stored in a new matrix I m The corresponding position of (θ,r), where n is the number of times the magnitude is reversed, and finally I m (θ,r) stores the maximum light intensity point data after the θ range is expanded.

[0027] The fitting method in S4 is as follows: I is fitted in polar coordinates. m The data points in (θ,r) are fitted using the following formula:

[0028]

[0029] In the formula, k is the wave vector 2π / λ, f is the focal length of the lens under test, L is the distance from the lens under test to the CCD imaging plane, C is a constant term, and finally the fitting result fL is obtained. Let it be a, that is, a=fL.

[0030] The periodic recovery in S4 is a 2π periodic recovery.

[0031] The specific calculation method for the ratio β of the light spot size is as follows:

[0032] Image binarization is performed on the parallel light spot image I3(x,y) and the converging light spot image I4(x,y) to obtain two binarized images I3' and I'4. Then, each row in the image matrix is ​​traversed, and the sum of gray values ​​in each row is counted. The number of pixels corresponding to the diameter of the spot in the two spot images is obtained from the sum of gray values ​​in each row. Assuming that the number of pixels corresponding to the diameter of the parallel light spot is D2 and the number of pixels corresponding to the diameter of the converging light spot is D1, the spot size β = D2 / D1 is calculated.

[0033] Beneficial effects: The measurement method of the present invention requires a simple optical path structure, the measurement process is easy to operate, the measurement error is small, and there is no need to measure the distance between the components. It can simultaneously measure the focal length of convex and concave lenses, and can also greatly reduce the influence of lens spherical aberration on measurement accuracy, resulting in high measurement accuracy. Attached Figure Description

[0034] Figure 1 This is a flowchart of the present invention;

[0035] Figure 2 This is the optical path diagram of the measurement system of the present invention;

[0036] Figure 3 (a) is the interferogram obtained after effective region cropping and Gaussian filtering; (b) is the distribution map of the maximum light intensity point in the coordinate system; (c) is the curve fitted according to the fitting formula in the polar coordinate system; (d) is the relationship between the sum of the gray values ​​of each row of pixels and the number of rows after binarization of the parallel light spot map and the converging light spot map.

[0037] Figure 4 (a) is the interferogram obtained after effective region cropping and Gaussian filtering; (b) is the distribution map of the maximum light intensity point in polar coordinates; (c) is the curve fitted according to the fitting formula in polar coordinates; (d) is the relationship between the sum of the gray values ​​of each row of pixels and the number of columns after binarization of the parallel light spot map and the converging light spot map. Detailed Implementation

[0038] The invention will now be further described with reference to the accompanying drawings.

[0039] like Figure 1 As shown, the lens focal length measurement method based on vortex optical interferometry of the present invention includes the following steps:

[0040] S1, Build as follows Figure 2The measurement system for interference between vortex light and spherical waves shown includes a laser 1, a beam expander 2, a linear polarizer 3, a first beam splitter prism 4, a first reflecting mirror 5, a circular polarizer 6, a vortex waveplate 7, a second beam splitter prism 8, a second reflecting mirror 9, a lens under test 10, and a CCD 11. The beam expander 2 contains two biconvex lenses, I and II, and the topological charge m of the vortex waveplate 7 is 1. The laser emitted from the laser 1 is converted to linear polarization by the linear polarizer 3 after passing through the beam expander 2. It is then split into two paths by the first beam splitter prism 4. The transmitted beam is reflected by the first reflecting mirror 5, becomes circularly polarized by the circular polarizer 6, and then becomes a vortex beam by the first-order vortex waveplate 7. The other beam is reflected by the second reflecting mirror 9, passes through the lens under test 10, and becomes a converging spherical wave. This spherical wave is then combined with the vortex wave by the second beam splitter prism 8, producing interference fringes on the CCD surface, which are then received by the CCD 11.

[0041] S2. Acquire the interference pattern I1(x,y) of the interference between the vortex light and the spherical wave, the interference image I2(x,y) for center positioning, and the parallel light spot pattern I3(x,y) and the converging light spot pattern I4(x,y); the specific acquisition steps include:

[0042] S21: After placing the lens to be tested, adjust the two-dimensional adjuster on the vortex wave plate mounting bracket, move the distance from the center dark spot of the vortex light to the center of the spherical wave interference ring, rotate the linear polarizer to improve the contrast of the interference fringes, and collect the interference pattern I1(x,y) of the vortex light and the spherical wave at this time.

[0043] S22: After acquiring the interferogram, adjust the two-dimensional adjuster on the vortex wave plate mounting bracket to move the center of the vortex light away, generating a Newton's rings-like interferogram that appears when spherical waves and plane waves interfere, and acquire the interferogram I2(x,y);

[0044] S23: Use a light shield to block the light path of the lens under test and collect the image at this time as parallel light spot image I3(x,y). Block the light path of the vortex light path and obtain the converging light spot image I4(x,y).

[0045] S3. Using a circle center positioning algorithm, obtain the effective image center coordinates (x0, y0) of the acquired interferometric image I2(x,y). Based on these center coordinates, extract the effective image region I from the interferogram I1(x,y) of the interference between the vortex light and the spherical wave. R (x,y); where the circle center positioning algorithm is specifically as follows:

[0046] Gaussian filtering is applied to the interferometric image I2(x,y) to obtain the filtered Newton's rings interferometric image I'2(x,y). The Hough transform algorithm is then used to process I'2 to obtain the center coordinates (x0,y0) of the effective image. The principle of the Hough transform method for locating the center of a circle is as follows:

[0047] 1) Extract the ring (xa) 2 +(yb) 2 =r 2 , where (a,b) are the center coordinates (x0,y0) of the effective image, r is the radius of the extracted ring, and (x,y) are the coordinates of any point on the extracted ring in the xoy coordinate system;

[0048] 2) Extract all points (x) on the annulus. i ,y i (i = 1, 2, 3, ..., n), any point of which, after undergoing a Hough transformation to the parameter space coordinate system, becomes a conical surface. The expression for the conical surface in parameter space is:

[0049] (ax i ) 2 +(by i ) 2 =r 2

[0050] Among them, (x i ,y i Let be the coordinates of the i-th point on the annulus extracted in the xoy coordinate system, and let a, b, and r be variables in the parameter space coordinate system that satisfy the conical expression.

[0051] For the n points extracted on the ring, n corresponding cones will be formed in the parameter space, and all n cones will intersect at a point. By finding the cumulative maximum value in the parameter space, the coordinates (a,b,r) are obtained, where (a,b) is the center coordinate (x0,y0) of the effective image, and r is the radius of the extracted ring.

[0052] S4. For the effective region I of the interferogram R The maximum light intensity point distribution map I5(x,y) is obtained by filtering and extreme value search algorithms on (x,y). The points in I5(x,y) are transformed into polar coordinates to obtain the maximum light intensity point distribution map I6(θ,r) in polar coordinates. I6 is then subjected to 2π periodic recovery to obtain I... m (θ,r), using the fitting formula for I m We fit the points in (θ,r) to obtain the fitting result fL, and let it be a, that is, a=fL;

[0053] The extraction of the point of maximum light intensity and the polar coordinate transformation specifically include:

[0054] S41: Effective image region I in the interference diagram of the extracted vortex light and spherical wave interference. R (x,y) is processed by Gaussian filtering to obtain I' R(x,y), the maximum light intensity point is extracted using the extreme value search method. The principle of the extreme value search method is to traverse the entire image with a matrix of a certain size. The extreme value that appears in the small matrix is ​​the extreme value of this small part of the image. After using this method, an image I5(x,y) with only the maximum light intensity point can be obtained.

[0055] S42: Transform the points in I5(x,y), i.e., the points of maximum light intensity, from Cartesian coordinates to polar coordinates using the four-quadrant arctangent function to obtain I6(θ,r). Since the four-quadrant arctangent function produces periodic results, i.e., θ is always in [-π,π], it is necessary to expand the range of θ. The method adopted is: arrange all the points of maximum light intensity in I6(θ,r) in the polar coordinate system according to the size of the polar radius r from smallest to largest to obtain I'6(θ,r). Traverse all the points of maximum light intensity in I'6. If the previous point (θ i ,r i ) of θ i Greater than the next point (θ) i+1 ,r i+1 ) of θ i+1 Then the next point (θ) i+1 ,r i+1 ) becomes (θ i+1 +2nπ,r i+1 Stored in a new matrix I m The corresponding positions of (θ,r), where n is the number of times the order of magnitude is reversed. Finally, I m (θ,r) stores the maximum light intensity point data after the θ range is expanded.

[0056] The method for fitting the maximum light intensity point is as follows: In the polar coordinate system, for I... m The data points in (θ,r) are fitted using the following formula:

[0057]

[0058] In the formula, k is the wave vector 2π / λ, f is the focal length of the lens under test, L is the distance from the lens under test to the CCD imaging plane, C is a constant term that has no effect on the result, and the fitting method is the least squares method to obtain the fitting result fL. Let it be a, that is, a=fL.

[0059] S5. Perform binarization on the acquired parallel light spot image I3(x,y) and converging light spot image I4(x,y) to obtain two binarized images I3' and I'4, and calculate the ratio β of their spot sizes; the specific calculation method is as follows:

[0060] By binarizing the parallel light spot image I3(x,y) and the converging light spot image I4(x,y), two binarized images I3' and I'4 can be obtained. Then, by traversing each row of the image matrix and counting the sum of the gray values ​​in each row, the number of pixels corresponding to the diameter of the spot in the two spot images can be obtained from the sum of the gray values ​​in each row. Assuming that the number of pixels corresponding to the diameter of the parallel light spot is D2 and the number of pixels corresponding to the diameter of the converging light spot is D1, the spot size β = D2 / D1 can be calculated.

[0061] S6. Calculate the focal length f = βa of the lens under test from the ratio of the fitting result a to the spot size β.

[0062] Example 2

[0063] This embodiment is an experimental example. The lens under test is a biconvex lens with a nominal effective focal length f = 200 mm and a nominal error of ±1%. The laser wavelength used is λ = 632.8 nm. The specific measurement process is as follows:

[0064] (1) Constructing a measurement system for the interference of vortex light and spherical waves: The system used for measurement is as follows Figure 2 As shown, the laser emitted from the He-Ne laser is converted into linearly polarized light by a linear polarizer after passing through a beam expander system. Then, it is split into two paths by a first beam splitter prism. The transmitted beam is reflected by a mirror and becomes circularly polarized light after passing through a circular polarizer. It then becomes a vortex beam after passing through a first-order vortex plate. The other beam is reflected by a mirror and passes through the lens under test, becoming a converging spherical wave. After being combined with the vortex beam by a second beam splitter prism, it produces interference fringes on the CCD surface and is received by the CCD.

[0065] (2) Acquisition of interferograms:

[0066] Step 1: After placing the lens to be tested, adjust the two-dimensional adjuster on the vortex wave plate mounting bracket, move the dark spot at the center of the vortex light to the center of the spherical wave, rotate the linear polarizer to improve the contrast of the interference fringes, and collect the interference pattern I1(x,y) of the vortex light and the spherical wave at this time.

[0067] Step 2: After acquiring the interferogram, adjust the two-dimensional adjuster on the vortex wave plate mounting bracket to move the center of the vortex light away, generating a Newton's rings-like interference image that appears when spherical waves and plane waves interfere, and acquire this interference image I2(x,y);

[0068] Step 3: Use a light shield to block the light path of the lens under test and collect the image at this time as parallel light spot pattern I3(x,y). Block the light path of the vortex light path to obtain the converging light spot pattern I4(x,y).

[0069] (3) Apply the Hough transform algorithm to the acquired center positioning image I2(x,y) to obtain the effective image center coordinates (x0,y0), and extract the effective image region I from the interference diagram I1(x,y) of the interference between the vortex light and the spherical wave based on these center coordinates. R (x,y), such as Figure 3 As shown in (a).

[0070] (4) For the effective region I of the interferogram R The maximum light intensity point distribution map I5(x,y) is obtained by filtering and extreme value search algorithms on (x,y). The points in I5x(,y) are transformed into polar coordinates to obtain the maximum light intensity point distribution map I6(θ,r) in polar coordinates. The maximum light intensity points in I6 are then periodically recovered using 2π to obtain I... m (θ,r), such as Figure 3 As shown in (b), the fitting formula is used to fit I. m We fit the points in (θ,r) to obtain the fitting result fL, let it be a, i.e., a = fL. The fitted curve is as follows. Figure 3 As shown in (c).

[0071] (5) Calculation of spot size ratio: Binarize the parallel light spot image I3(x,y) and the converging light spot image I4(x,y) to obtain two binarized images, I3' and I'4. Then, traverse each row of the image matrix and count the sum of gray values ​​in each row. The number of pixels corresponding to the diameter of the spot in each image can be obtained from the gray value sum curve. The gray value sum curve is shown below. Figure 3 As shown in (d), assuming that the diameter of the parallel light spot corresponds to the number of pixels D2 and the diameter of the converging light spot corresponds to the number of pixels D1, the light spot ratio β = D2 / D1 is calculated.

[0072] (6) Calculation of the focal length f of the lens under test: Based on the above steps, the result of fitting the maximum light intensity point is a = fL, and the ratio of the light spot size is β = D2 / D1. Then the final focal length of the lens under test is f = βa = 200.7299 mm, with an error of 0.36%.

[0073] Example 3

[0074] This embodiment is an experimental example. The lens under test is a biconcave lens with a nominal effective focal length f = -100mm and a nominal error of ±1%. The laser wavelength used is λ = 632.8nm. The specific measurement process is as follows:

[0075] The original interferogram acquired, after being cropped and processed by Gaussian filtering, is shown below. Figure 4 As shown in (a), the distribution of the maximum light intensity point in the polar coordinate system after transforming the Cartesian coordinate system to the polar coordinate system is as follows. Figure 4As shown in (b), the data point is fitted according to the given formula to obtain fL = a, and the fitted image is as follows. Figure 4 As shown in (c). Next, parallel light spot images and divergent light spot images are acquired, binarized, and then each row of the image matrix is ​​traversed. The sum of the gray values ​​in each column is calculated, and the relationship between the sum of the gray values ​​in each column and the column number can be obtained through a graph, such as... Figure 4 (d) Then obtain the ratio β of the number of pixels corresponding to the diameter of the parallel light spot D2 and the number of pixels corresponding to the diameter of the divergent light spot D1. Finally, calculate the focal length of the lens under test f = βa = -99.9822 mm, with an error of 0.01776%.

Claims

1. A method for measuring the focal length of a lens based on the interference of vortex light, characterized in that, Includes the following steps: S1. Construct a measurement system for interference between vortex beams and spherical waves: The laser emitted from the laser passes through a beam expander and is converted into linearly polarized light by a linear polarizer. It is then split into two paths by the first beam splitter. The transmitted beam is reflected by a mirror and becomes circularly polarized light by a circular polarizer. It then becomes a vortex beam by a first-order vortex wave plate. The other beam is reflected by a mirror and passes through the lens under test, becoming a converging spherical wave. After being combined with the vortex beam by the second beam splitter, interference fringes are generated on the CCD surface and received by the CCD. S2. Collect the interference pattern of vortex light and spherical wave interference. Interferometric images used for center positioning Parallel light spot diagram and converged light spot pattern Specifically: S21: After inserting the lens to be tested, adjust the vortex wave plate, move the distance between the dark spot at the center of the vortex beam and the center of the spherical wave interference ring, rotate the linear polarizer to improve the contrast of the interference fringes, and collect the interference pattern of the vortex beam and the spherical wave at this time. ; S22: Adjust the vortex plate to move the center of the vortex light away, generating an interference image that appears when spherical waves and plane waves interfere. Acquire this interference image. ; S23: Block the light path through the lens under test, and acquire the image at this time as a parallel light spot pattern. By blocking the optical path of the vortex light, a converged light spot pattern is obtained. ; S3. Acquire the interference image Center coordinates of the effective image Interferograms are extracted based on the coordinates of the center. Effective image region ; S4, Obtain Maximum light intensity point distribution map ,Will Transforming to polar coordinates yields the distribution map of the maximum light intensity points in polar coordinates. ,right Periodic recovery is achieved and to Fit the points in the data to obtain the fitting result. ; S5. Collect parallel light spot images. and converged light spot pattern Perform a binarization operation to obtain the binarized image. and And calculate the ratio of its spot size. ; S6. From the fitting results The ratio of the size of the light spot Calculate the focal length of the lens under test .

2. The lens focal length measurement method based on vortex optical interferometry according to claim 1, characterized in that, The center coordinates The center of the circle is located using a circle positioning algorithm.

3. The lens focal length measurement method based on vortex optical interferometry according to claim 2, characterized in that, The circle center localization algorithm specifically involves: analyzing the interference image... Gaussian filtering is performed to obtain the filtered Newton's rings interferometric image. ,right The center coordinates of the effective image are obtained through processing. .

4. The lens focal length measurement method based on vortex optical interferometry according to claim 3, characterized in that, The pair The Hough transform algorithm is used during processing, specifically including: 1) Extract the ring Where (a, b) are the center coordinates of the effective image. r is the radius of the extracted annulus, and (x, y) are the coordinates of any point on the extracted annulus in the xoy coordinate system. 2) Extract all points (x i , y i ) (i=1,2,3,…,n) on the circle, any point of which becomes a conical surface after Hough transformation to the parameter space coordinate system. The expression of the conical surface in the parameter space is: Among them, (x i , y i Let (a, b, r) be the coordinates of the i-th point on the annulus extracted in the xoy coordinate system, and let a, b, and r be variables in the parameter space coordinate system that satisfy the conical expression. The coordinates (a, b, r) are obtained by finding the cumulative maximum value in the parameter space, where (a, b) are the center coordinates of the effective image. , where r is the radius of the extracted annulus.

5. The lens focal length measurement method based on vortex optical interferometry according to claim 1, characterized in that, The maximum light intensity point distribution map By analyzing the effective region of the interferogram Filtering and extreme value search algorithms are used to obtain the results.

6. The lens focal length measurement method based on vortex optical interferometry according to claim 1, characterized in that, The The method for obtaining it is as follows: in the polar coordinate system, according to the polar radius Arranged from smallest to largest Find all the points with the highest light intensity and obtain ,exist Iterate through all points with the highest light intensity, if the previous point of Greater than the next point of Then the next point Become Stored in a new matrix The corresponding position, among which The final number of times the size is reversed. What is stored is Maximum light intensity point data after range expansion.

7. The lens focal length measurement method based on vortex optical interferometry according to claim 6, characterized in that, The fitting method in S4 is as follows: In the polar coordinate system... The data points in the data are fitted using the following formula: In the formula, wave vector , That is, the focal length of the lens to be tested. The distance from the lens under test to the CCD imaging plane is denoted as . As a constant term, the final fitting result is obtained. , to make him ,Right now .

8. The lens focal length measurement method based on vortex optical interferometry according to claim 7, characterized in that, The periodic recovery in S4 is as follows: Periodic recovery.

9. The lens focal length measurement method based on vortex optical interferometry according to claim 1, characterized in that, The ratio of the size of the light spot The specific calculation method is as follows: Parallel light spot pattern and converged light spot pattern Image binarization is performed to obtain two binarized images of the light spots. and Then, iterate through each row of the image matrix, summing the gray values ​​in each row. Using the gray value sum curve for each row, obtain the number of pixels corresponding to the diameter of the light spot in the two light spot images. Assume the number of pixels corresponding to the diameter of the parallel light spot is... The diameter of the converged light spot corresponds to the number of pixels. The size of the light spot was calculated. .

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