A lens focal length rapid measurement method and measurement system based on differential symmetry method

Abstract

The application discloses a kind of lens focal length fast measurement method and measurement system based on differential symmetry method, including obtaining the equivalence between multiple differential interference charts;Evaluate the correlation between focal length and multiple differential interference charts;Set focal length search range, calculate the evaluation function at each position in the range and determine the minimum value, the focal length corresponding to the minimum value is the focal length to be measured.The measurement method proposed in the application does not need to move the device repeatedly, eliminates the influence of initial position distance error, the range is not limited by the length of track, simplifies the measurement principle and analysis process, avoids the need for precise positioning of the measured lens to the horizontal distance of CCD in the experiment, and the symmetric interference chart acquisition solves the influence of experimental environment change on single experimental chart in the experiment, so that only the differential distance ΔL is controlled in the whole measurement process, and simple, efficient, high-precision and large-range measurement of the lens can be realized.

Description

TECHNICAL FIELD

[0001] The application relates to a lens focal length measurement method and a measurement system, in particular to a lens focal length fast measurement method and a measurement system based on a differential symmetry method. BACKGROUND

[0002] As the most basic optical element of an optical system, the measurement value of the focal length of a lens directly affects the debugging and use of the entire optical system. Therefore, it is of great practical significance to study a high-precision lens focal length measurement method.

[0003] Chinese Patent Publication No. CN102589854A discloses a reflective differential confocal lens focal length measurement method. The measurement process needs to determine the cat-eye and confocal positions by moving the reference plane multiple times, and uses a range finder to measure the distance between the cat-eye position and the confocal position, so as to realize the focal length measurement of the lens to be measured. In order to accurately obtain the cat-eye and confocal positions, the method needs to spend a lot of time for multiple scans, and the focal length measurement range is limited by the track length.

[0004] Chinese Patent Publication No. CN109459214A discloses a convex lens focal length measurement method and device. The convex lens back focal point position is determined by repeatedly adjusting the knife edge position, then the range finder measures the object distance and image distance, and then the convex lens focal length is calculated according to the imaging formula. In order to accurately obtain the convex lens back focal point position, the method needs to spend a lot of time to repeatedly move the knife edge position to determine the darkest position of the light spot, and the long focal length measurement is limited by the track length.

[0005] Chinese Patent Publication No. CN114061910A discloses a convex-concave lens focal length measurement device and method. The convex-concave lens focal length measurement device and method moves the frosted glass from left to right near the object and image of the lens to be measured, respectively, observes the position of the front surface of the frosted glass corresponding to the maximum scattered speckle of the image screen, records the positions of the object and image of the lens to be measured, respectively, and then calculates the convex lens focal length according to the imaging formula. The determination of the maximum scattering speckle is limited by the human eye parallax, and a lot of time is spent to move the frosted glass to obtain the positions of the object and image of the lens to be measured, and the long focal length measurement is limited by the track length.

[0006] Chinese Patent Publication No. CN112611548A discloses a lens focal length measurement device and method based on digital holography. The device changes the wave surface radius of the reference light through a beam expander, records the interference image of the reference wave surface and the test wave surface in the interference field through a charge coupled device, and then deduces the focal length measurement formula of the lens to be measured by analyzing the interference image information and the change amount of the reference light wave surface radius. The measurement system of the method needs to use more devices, has high debugging requirements, and cannot realize simple measurement of the lens focal length.

[0007] The lens focal length measurement method provided in the above invention patent has high measurement precision, but cannot realize long and short focal length high-precision measurement at the same time, and the measurement process is mostly complex in theory analysis or tedious in measurement process. Therefore, it has great practical significance to study a simple, efficient, high-precision and wide-range focal length measurement method. SUMMARY

[0008] Invention purposes: The purpose of the present application is to provide a lens focal length fast measurement method and measurement system based on differential symmetry method, so as to realize simple, efficient, high-precision and wide-range measurement of lens focal length.

[0009] Technical solutions: The present application comprises the following steps:

[0010] Step one, obtaining the equivalence relationship between multiple differential interference patterns;

[0011] Step two, evaluating the correlation degree between focal length and multiple differential interference patterns;

[0012] Step three, setting the focal length search range, calculating the evaluation function at each position in the range and determining the minimum value, and the focal length corresponding to the minimum value is the focal length to be measured.

[0013] The step one is specifically:

[0014] The incident angle α of the test light satisfies:

[0015]

[0016] In the formula, f is the focal length of the lens to be measured, (x, y) is the position coordinate of any point on the lens;

[0017] The refraction angle β of the test light satisfies:

[0018]

[0019] Wherein, n is the refractive index of the beam splitter material;

[0020] The normalized expression of the interference pattern is:

[0021]

[0022] In the formula, The phase introduced by the optical path difference of the reference light and the test light is k, the optical wave number is d, the size of the beam splitter is L, and the horizontal distance from the lens to be measured to the CCD target surface is L;

[0023] The parameters a and b are introduced to replace the complex parameter part:

[0024] I(x, y) = cos (a·L + b) (4)

[0025] wherein,

[0026] The central interference pattern of the differential interference pattern is denoted as:

[0027] I2(x,y)=cos(a·L+b) (5)

[0028] When the differential distance of ΔL is reduced on the basis of L, the normalized interference pattern expression at this time is I1(x,y):

[0029]

[0030] When the differential distance of ΔL is increased on the basis of L, the normalized interference pattern expression at this time is I3(x,y):

[0031]

[0032] Combining formula (5), formula (6) and formula (7), the following formula can be obtained:

[0033] I1(x,y)+I3(x,y)=2I2(x,y)cos(a·ΔL) (8)

[0034] The evaluation function for evaluating the correlation degree of the focal length with the plurality of differential interference patterns in the second step is as follows:

[0035] H(f;x,y)=I2(x,y)+I3(x,y)-2I1(x,y)cos(a·ΔL) (9)

[0036]

[0037]

[0038] wherein, (x,y) is the position coordinate of any point on the lens, k is the wave number, ΔL is the differential distance, I1(x,y) is the normalized interference pattern collected initially, I2(x,y) is the normalized interference pattern collected secondly, and I3(x,y) is the normalized interference pattern collected thirdly.

[0039] The third step is specifically setting the search range [F0,F1] of the focal length f, calculating H(f;x,y) about each focal length in the search range, and finding out the minimum value |H(f;x,y)| when the minimum value is obtained. min The focal length corresponding to |H(f;x,y)| is the measurement value of the lens to be measured.

[0040] The differential distance ΔL is in the range of [0,10mm].

[0041] The repetition accuracy of the differential distance ΔL is ≤0.1mm.

[0042] A measurement system for realizing a lens focal length fast measurement method based on a differential symmetry method, comprising a light source, a beam expanding collimation system, an interference system and a differential symmetry acquisition system, the interference system comprising a first beam splitter, a first plane mirror, a second plane mirror, a lens to be measured and a second beam splitter, the light emitted by the light source forms a collimated light beam through the beam expanding collimation system, after passing through the first beam splitter, one light beam is reflected by the first plane mirror to form a reference light, and the other light beam is reflected by the second plane mirror to form a test light through the lens to be measured, the test light and the reference light enter the differential symmetry acquisition system through the second beam splitter.

[0043] The differential symmetry acquisition system comprises a CCD and a motorized displacement table, the CCD is placed on the motorized displacement table, and the CCD is driven to move by controlling the two-dimensional motorized displacement table by computer, so that the interference pattern of the lens to be measured is differentially symmetrically acquired.

[0044] The target surface of the CCD is in the same height as the test light path and is coaxial.

[0045] The beam expanding collimation system comprises a concave lens and a convex lens arranged in sequence along the light path.

[0046] Beneficial effects: the measurement method provided by the application does not need to repeatedly move devices, eliminates the influence of initial position distance error, the measurement range is not limited by the length of the track, the measurement principle and analysis process are simplified, the horizontal distance of the lens to be measured to the CCD in the experiment is accurately positioned, the symmetric acquisition of the interference pattern solves the influence of the change of the experimental environment on a single experimental pattern in the experiment, so that only the differential distance Delta L is controlled in the whole measurement process, and simple, efficient, high-precision and large-range measurement of the lens can be realized. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 is a flowchart of the application;

[0048] Figure 2 is a measurement system diagram of the application;

[0049] Figure 3 is a differential symmetry diagram of the application;

[0050] Figure 4 is the measurement result of a 35mm standard lens in the embodiment: (a) is an interference pattern collected at the initial position, (b) is an interference pattern collected in front of the initial position, (c) is an interference pattern collected behind the initial position, and (d) is the minimum value distribution of |H(f;x,y)|

[0051] Figure 5The measurement results for a standard lens with a focal length of 175mm in the example are as follows: (a) is the interferogram acquired at the initial position, (b) is the interferogram acquired in front of the initial position, (c) is the interferogram acquired behind the initial position, and (d) is the minimum value distribution of |H(f;x,y)|. Detailed Implementation

[0052] The invention will now be further described with reference to the accompanying drawings.

[0053] like Figure 2 As shown, the measurement system of the present invention includes a light source 1, a beam expanding and collimating system, an interferometric system, and a differential symmetric acquisition system 11. The light source 1 is a helium-neon laser. The beam expanding and collimating system includes a concave lens 2 and a convex lens 3 arranged sequentially along the optical path. The interferometric system includes a first beam splitter 4, a first plane mirror 5, a second plane mirror 6, a lens under test 7, and a second beam splitter 8. The differential symmetric acquisition system 11 includes a CCD 9 and a two-dimensional electric displacement stage 10. The CCD 9 is placed on the two-dimensional electric displacement stage 10, and the two-dimensional electric displacement stage 10 controls the CCD 9 to move at equal intervals, and acquires the initial position and the position after two moves, for a total of three interferograms. The light emitted from light source 1 is collimated by a beam expander and collimator system. After passing through the first beam splitter 4, it forms two beams. One beam is reflected by the first plane mirror 5, placed at 45°, to form a reference beam. The other beam is reflected by the second plane mirror 6, placed at 45°, and passes through the lens under test 7 to form a test beam. The test beam and the reference beam enter the differential symmetric acquisition system 11 through the second beam splitter 8. The target surface of the CCD 9 in the differential symmetric acquisition system 11 is coaxial with the test beam path at the same height. Differential symmetric acquisition is achieved by controlling the CCD 9 to move once in front of and once behind the initial acquisition position symmetrically about the initial acquisition position using a two-dimensional electric displacement stage 10. Three interferograms are acquired at the initial position, in front of the initial position, and behind the initial position with equal differential distances. The differential distance ΔL is in the range of [0, 10 mm].

[0054] This invention uses a computer-controlled two-dimensional electric displacement stage 10 to move the CCD 9, thereby performing differential symmetrical acquisition of the interferogram of the lens 7 under test. The differential acquisition process is as follows: Figure 3 As shown, L1 is the initial acquisition position, L2 is the acquisition position in front of the initial acquisition position, and L3 is the acquisition position behind the initial acquisition position. The symmetrical differential distance is ΔL, and the repeatability of ΔL is ≤0.1mm.

[0055] like Figure 1 As shown, the measurement method of the present invention is based on a focal length extraction algorithm and specifically includes the following steps:

[0056] Step 1: Obtain the equivalence relationship between the three differential interferograms:

[0057] Through geometric theory derivation, it is known that the incident angle and the refraction angle of the test light entering the beam splitter have the same general formula, and α and β are the incident angle and the refraction angle of the test light entering the beam splitter, and the incident angle α of the test light satisfies:

[0058]

[0059] In the formula, f is the focal length of the lens to be tested, and (x, y) is the position coordinate of any point on the lens.

[0060] According to the refraction law and the trigonometric function conversion, it is known that the refraction angle β satisfies:

[0061]

[0062] In the formula, n is the refractive index of the beam splitter material.

[0063] The normalized expression of the interference pattern is:

[0064]

[0065] In the formula, is the phase introduced by the optical path difference between the reference light and the test light, k is the optical wave number, d is the size of the beam splitter, and L is the horizontal distance from the lens to be tested to the CCD target surface.

[0066] The parameters a and b are introduced to replace the complex parameter part:

[0067] I(x,y)=cos(a·L+b) (4)

[0068] In the formula,

[0069] The change of the normalized interference pattern is a cosine change about the distance L, and the central interference pattern of the three differential interference patterns is recorded as:

[0070] I2(x,y)=cos(a·L+b) (5)

[0071] When the differential distance ΔL is reduced on the basis of L, the normalized interference pattern expression at this time is I1(x,y):

[0072]

[0073] When the differential distance ΔL is increased on the basis of L, the normalized interference pattern expression at this time is I3(x,y):

[0074]

[0075] Combined with formula (5), formula (6) and formula (7), the following formula can be obtained:

[0076] I1(x,y) + I3(x,y) = 2I2(x,y)cos(a-AL) (8)

[0077] Step two, evaluate the correlation between focal length and three differential interference patterns:

[0078] The evaluation function of the correlation between focal length and three differential interference patterns is as follows:

[0079] H(f;x,y) = I2(x,y) + I3(x,y) - 2I1(x,y)cos(a-AL) (9)

[0080]

[0081]

[0082] where (x,y) is the position coordinate of any point on the lens, k is the wave number, AL is the differential distance, I1(x,y) is the normalized interference pattern collected initially, I2(x,y) is the normalized interference pattern collected secondly, and I3(x,y) is the normalized interference pattern collected thirdly.

[0083] Step three, set the search range of focal length, calculate the evaluation function at each position in the range, and determine the minimum value, which corresponds to the focal length to be measured. Specifically, set the search range [F0,F1] of focal length f, calculate H(f;x,y) about each focal length in the search range, find the minimum value |H(f;x,y)|, and the focal length corresponding to the minimum value |H(f;x,y)| is the measured value of the lens to be measured. min

[0084] Example 1

[0085] This example is an experimental example. The lens to be measured 7 is a standard convex lens with an aperture of 25.4 mm and a focal length of 35 mm; the first beam splitter 4 and the second beam splitter 8 are non-polarized beam splitting cubes with a size of 25.4 mm x 25.4 mm x 25.4 mm; the CCD 9 is selected to have a size of 3672 x 5496 pixels, and the pixel size is 2.4 μm x 2.4 μm; the two-dimensional electric displacement table 10 is selected to have a maximum stroke of 50 mm, a maximum speed of 40 mm / s, a minimum speed of 0.37 mm / s, a single-step precision of 3.125 x 10 -4 mm, and the differential distance AL is 5 mm. According to the three interference patterns collected by the differential symmetric system, the normalized preprocessed three normalized interference patterns are as shown in Figs. 4(a), 4(b), and 4(c), respectively. Figure 4 The minimum value of |H(f;x,y)| is as shown in Fig. 4(d) when the data of the three normalized interference patterns and AL = 5 mm are substituted into the relationship H(f;x,y). Figure 4 ​(d) as shown, the measurement result is 34.99 mm, and the time consumption is 7.2 s.

[0086] Embodiment 2

[0087] This embodiment is an experimental example. The to-be-measured lens 7 is replaced by a standard convex lens with a focal length of 175 mm, and other devices and parameters remain unchanged as in Embodiment 1. According to the three interference patterns collected by the differential symmetric system, the three normalized interference patterns are respectively Figure 5 (a), 5(b) and 5(c), after normalized preprocessing, the data of the three normalized interference patterns and ΔL=5 mm are substituted into the relationship H(f;x,y), and the minimum value of |H(f;x,y)| is as shown in Figure 5 (d), the measurement result is 174.93 mm, and the time consumption is 41.3 s.

[0088] The above two embodiments show that the present application solves the problem of needing to accurately position multiple distance parameters in experiments by a simple measurement system and method, without the need to move the to-be-measured lens multiple times, simplifying the measurement process, so that the entire measurement process can realize the large-range, fast and high-precision measurement of the to-be-measured lens through the computer control of the differential distance ΔL.

Claims

1. A rapid method for measuring the focal length of a lens based on differential symmetry, characterized in that, Includes the following steps: Step 1: Obtain the equivalence relationship between multiple differential interferograms, specifically: The incident angle α of the test light satisfies: (1) In the formula, f is the focal length of the lens under test, and (x, y) are the position coordinates of any point on the lens; The angle of refraction β of the test light satisfies: (2) Where n is the refractive index of the beam splitter material; The normalized expression for the interferogram is: (3) In the formula, φ(f; x, y) is the phase introduced by the optical path difference between the reference light and the test light, k is the wavenumber, d is the size of the beam splitter, and L is the horizontal distance from the lens under test to the CCD target surface. Introducing parameters a and b to replace the complex parameter parts: (4) in, , ; The central interferogram of the differential interferogram is denoted as: (5) When the differential distance ∆L is reduced from L, the normalized interferogram expression becomes I1(x, y): (6) When the differential distance ∆L is added to L, the normalized interferogram expression is I3(x, y): (7) Combining equations (5), (6), and (7), we can obtain: ；(8) Step 2: Evaluate the correlation between focal length and multiple differential interferograms. The evaluation function for evaluating the correlation between focal length and multiple differential interferograms is as follows: (9) Where (x, y) are the position coordinates of any point on the lens, k is the wave number, ∆L is the differential distance, I1(x, y) is the normalized interferogram of the initial acquisition, I2(x, y) is the normalized interferogram of the second acquisition, and I3(x, y) is the normalized interferogram of the third acquisition. Step 3: Set the focal length search range, calculate the evaluation function at each position within the range and determine the minimum value. The focal length corresponding to the minimum value is the focal length to be measured.

2. The method for rapid measurement of lens focal length based on differential symmetry according to claim 1, characterized in that, Step three specifically involves: setting the search range [F0, F1] for the focal length f, calculating H(f; x, y) for each focal length within the search range, and finding the minimum value |H(f; x, y)|. The minimum value is obtained when |H| is minimized. min The focal length corresponding to (f; x, y)| is the measured value of the lens under test.

3. The method for rapid measurement of lens focal length based on differential symmetry according to claim 1, characterized in that, The differential distance ∆L is in the range of [0, 10 mm].

4. The method for rapid measurement of lens focal length based on differential symmetry according to claim 1, characterized in that, The repeatability of the differential distance ∆L is ≤0.1mm.

5. A measurement system for implementing the rapid lens focal length measurement method based on differential symmetry as described in any one of claims 1 to 4, characterized in that, The system includes a light source, a beam expanding and collimating system, an interferometric system, and a differential symmetric acquisition system. The interferometric system includes a first beam splitter, a first plane mirror, a second plane mirror, a lens under test, and a second beam splitter. The light emitted from the light source is collimated by the beam expanding and collimating system. After passing through the first beam splitter, one beam is reflected by the first plane mirror to form a reference beam, and the other beam is reflected by the second plane mirror and passes through the lens under test to form a test beam. The test beam and the reference beam enter the differential symmetric acquisition system through the second beam splitter.

6. The measurement system for a rapid lens focal length measurement method based on differential symmetry as described in claim 5, characterized in that, The differential symmetric acquisition system includes a CCD and an electric displacement stage, with the CCD placed on the electric displacement stage.

7. The measurement system for a rapid lens focal length measurement method based on differential symmetry as described in claim 6, characterized in that, The target surface of the CCD is coaxial with the test optical path at the same height.

8. The measurement system for a rapid lens focal length measurement method based on differential symmetry as described in claim 5, characterized in that, The beam expanding and collimating system includes a concave lens and a convex lens arranged sequentially along the optical path.

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