A focal length measurement system

Abstract

The present application provides a focal length measurement system, relating to the field of optical measurement technology. The system comprises a light source module, a beam expansion module, a diffraction screen, a lens module, and an imaging module, which are sequentially arranged. The diffraction screen is a porous structure with a complex aperture. Light emitted from the light source module is expanded by the beam expansion module, diffracted by the diffraction screen, and formed into an image on the receiving surface of the imaging module after passing through the lens module. The focal length of the lens module satisfies f = 1 / (1 / z1 + 1 / z2); z1 is the center-to-center distance between the diffraction screen and the lens module, and z2 is the distance between the lens module and the receiving surface of the imaging module. The system measures the focal length of the lens module based on the diffraction pattern of the complex-aperture diffraction screen, simplifies the experimental apparatus and operating procedures, and provides accurate measurement results with low errors. The system is simple and fast to operate, has low requirements and dependence on experimental equipment and the measurement environment, and has high precision and stability, thus providing accurate and reliable results for focal length measurement.

Description

Technical Field

[0001] The present application relates to the field of optical measurement technology, and in particular to a focal length measurement system. Background Art

[0002] In the field of optical imaging, accurate measurement of lens focal length is crucial for optical system performance evaluation and related research. Accurately and quickly acquiring focal length data within a system is a fundamental and crucial issue. Numerous methods exist for accurately determining focal length. Traditional focal length measurement methods include displacement, magnification, Gaussian equations, and autocollimation. Emerging methods include interferometry, diffraction, and holography. For more complex or specialized focal length measurement requirements, methods such as Talber-Mohr interferometry can also be used to accurately determine lens focal length.

[0003] However, the aforementioned measurement methods have limited applicability and certain limitations: the displacement method's measurement results are easily affected by experimental conditions, resulting in suboptimal repeatability; the magnification method is complex to operate; and the Gaussian formula method makes it difficult to accurately define the position of the object image, resulting in low measurement accuracy. Emerging methods are often more complex and less convenient, and have high requirements for experimental instruments and environments, which limits their use in certain specific scenarios. For example, in university physics experimental teaching, the mainstream methods for measuring focal length are mostly based on the principles of geometric optics, which cannot achieve accurate and simple measurements. Summary of the Invention

[0004] The purpose of the embodiments of the present application is to provide a focal length measurement system that can accurately and quickly measure focal length with a simple method and easy operation.

[0005] In one aspect of an embodiment of the present application, a focal length measurement system is provided, comprising a light source module, a beam expansion module, a diffraction screen, a lens module, and an imaging module, which are sequentially arranged. The diffraction screen is a porous structure with a complex aperture. Light emitted from the light source module is expanded by the beam expansion module, then diffracted by the diffraction screen, and finally imaged by the lens module on a receiving surface of the imaging module.

[0006] The focal length of the lens module satisfies f=1 / (1 / z1+1 / z2); z1 is the center distance between the diffraction screen and the lens module, and z2 is the distance between the lens module and the receiving surface of the imaging module.

[0007] Optionally, the focal length of the lens module satisfies f=1 / (1 / z1+1 / z2)-Δf1-Δf2;

[0008] in, ; ;

[0009] ; ; d is the width of the lens module, R is the radius of curvature of the lens module, n0 is the refractive index of the lens module, and D is the aperture of the lens module.

[0010] Optionally, the distance z2 between the lens and the receiving surface of the imaging module is z0, where z0 is the distance between the lens module and the receiving surface of the imaging module when the image received by the receiving surface of the imaging module is a restored image without diffraction fringes.

[0011] Optionally, the lens module is movably arranged along the optical axis direction so that the receiving surface of the imaging module is located at an image restoration position.

[0012] Optionally, the multiple holes of the diffraction screen are located in the same plane along a direction perpendicular to the optical axis.

[0013] Optionally, the diffraction screen has a thickness along the optical axis of 0.1 mm to 1 mm.

[0014] Optionally, the lens module includes a lens, and the lens has at least one convex surface along the optical axis.

[0015] Optionally, the lens includes at least a plano-convex lens, a concave-convex lens and a biconvex lens.

[0016] Optionally, the lens module is a lens group, and the lens group includes two or more lenses.

[0017] Optionally, the light source module includes at least a laser.

[0018] The focal length measurement system provided in the embodiments of the present application measures the focal length of a lens module based on the diffraction pattern of a diffraction screen with a complex aperture. Through simplified experimental setup and operation steps, it achieves accurate and rapid measurement of the focal length of a lens module. The system achieves accurate measurement results with minimal error, simple and rapid operation, and low requirements and dependence on experimental equipment and measurement environment. It also demonstrates high precision and stability in measuring multiple lenses, providing accurate and reliable results for focal length measurements of common lenses and lens groups. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments of the present application. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0020] Figure 1is a schematic structural diagram of a focal length measurement system provided in this embodiment;

[0021] Figure 2 is a dark field image of the diffraction screen provided in this embodiment under an optical microscope;

[0022] Figure 3 is a scanning electron microscope image of the diffraction screen provided in this embodiment;

[0023] Figure 4 1 is a simplified schematic diagram of imaging of a single convex lens system provided in this embodiment;

[0024] Figure 5 is an image when diffraction fringes exist during imaging by the focal length measurement system provided by this embodiment;

[0025] Figure 6 is the image when the diffraction fringes disappear during imaging by the focal length measurement system provided by this embodiment;

[0026] Figure 7 The image is generated when the focal length measurement system provided by this embodiment uses a convex lens with a nominal focal length of 19.00 cm to form an image, and the imaging module is moved forward 0.2 cm along the z-axis at position z0;

[0027] Figure 8 is the image of the imaging module at z0 when the focal length measurement system provided by this embodiment uses a convex lens with a nominal focal length of 19.00 cm for imaging;

[0028] Figure 9 yes Figure 8 A magnified image with the box at z0 moved forward 0.2 cm along the z axis;

[0029] Figure 10 yes Figure 8 The enlarged image framed at z0;

[0030] Figure 11 yes Figure 8 A magnified image with the box at z0 shifted 0.2 cm back along the z axis;

[0031] Figure 12 is a relationship diagram between the ideal value and the measured value of a lens with a focal length of 19.00 cm in the focal length measurement system provided in this embodiment;

[0032] Figure 13 is a relationship diagram between the ideal value and the measured value of a lens with a focal length of 15.00 cm in the focal length measurement system provided in this embodiment;

[0033] Figure 14 is a relationship diagram between the ideal value and the measured value of a lens with a focal length of 10.00 cm in the focal length measurement system provided in this embodiment;

[0034] Figure 15 is a relationship diagram between the ideal value and the measured value of a lens with a focal length of 7.00 cm in the focal length measurement system provided in this embodiment;

[0035] Figure 16 is a relationship diagram between the ideal value and the measured value of a lens with a focal length of 5.00 cm in the focal length measurement system provided in this embodiment;

[0036] Figure 17 is a relationship diagram between the ideal value and the measured value of a lens with a focal length of 4.50 cm in the focal length measurement system provided in this embodiment;

[0037] Figure 18 is one of the measured values ​​of the focal length of the lens before and after correction by the focal length measurement system provided in this embodiment;

[0038] Figure 19 is the second of the measured values ​​of the focal length of the lens before and after correction by the focal length measurement system provided in this embodiment;

[0039] Figure 20 is the third of the measured values ​​of the focal length of the lens before and after correction by the focal length measurement system provided in this embodiment;

[0040] Figure 21 is one of the fourth measured values ​​of the focal length of the lens before and after correction by the focal length measurement system provided in this embodiment;

[0041] Figure 22 is the fifth of the measured values ​​of the focal length of the lens before and after correction by the focal length measurement system provided in this embodiment;

[0042] Figure 23 is the sixth of the measured values ​​of the focal length of the lens before and after correction by the focal length measurement system provided in this embodiment;

[0043] Figure 24 This is one of the relative deviation diagrams of the corrected focal length measurement value f and the nominal focal length value F of the focal length measurement system provided in this embodiment;

[0044] Figure 25 This is the second relative deviation diagram of the focal length measurement value f after correction and the focal length nominal value F of the focal length measurement system provided by this embodiment;

[0045] Figure 26 This is the third diagram of the relative deviation between the corrected focal length measurement value f and the nominal focal length value F of the focal length measurement system provided by this embodiment;

[0046] Figure 27 This is the fourth diagram of the relative deviation between the corrected focal length measurement value f and the nominal focal length value F of the focal length measurement system provided by this embodiment;

[0047] Figure 28This is the fifth diagram of the relative deviation between the corrected focal length measurement value f and the nominal focal length value F of the focal length measurement system provided by this embodiment;

[0048] Figure 29 This is the sixth graph of relative deviation between the corrected focal length measurement value f and the nominal focal length value F of the focal length measurement system provided by this embodiment;

[0049] Figure 30 This is a schematic diagram of lens spherical aberration.

[0050] Icons: 1-Gaussian image point; 101-light source module; 102-beam expansion module; 103-diffraction screen; 104-lens module; 105-imaging module; 106-object plane; 107-image plane; z1-center distance; z2-distance. DETAILED DESCRIPTION

[0051] The technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application.

[0052] In the description of this application, it should be noted that the terms "inner" and "outer" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, or the orientations or positional relationships in which the product of this application is typically placed when in use. These terms are intended solely to facilitate the description of this application and simplify the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on this application. Furthermore, the terms "first" and "second" and the like are used solely for distinction and should not be construed as indicating or implying relative importance.

[0053] It should also be noted that, unless otherwise expressly specified or limited, the terms "disposed" and "connected" should be understood broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to direct connections, indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art will understand the specific meanings of these terms in this application based on the specific circumstances.

[0054] Please refer to Figure 1 As shown, an embodiment of the present application provides a focal length measurement system, comprising: a light source module 101, a beam expansion module 102, a diffraction screen 103, a lens module 104, and an imaging module 105, which are arranged in sequence. The diffraction screen 103 is a porous structure with a complex aperture. The complex aperture means that the diffraction screen 103 has multiple holes with different apertures. Light emitted from the light source module 101 is expanded by the beam expansion module 102, then diffracted by the diffraction screen 103, and formed into an image on the receiving surface of the imaging module 105 after passing through the lens module 104.

[0055] The focal length of the lens module 104 satisfies f=1 / (1 / z1+1 / z2) (1);

[0056] z1 is the center distance between the diffraction screen 103 and the lens module 104 , and z2 is the distance between the lens module 104 and the receiving surface of the imaging module 105 .

[0057] Among them, the light source module 101 is generally a laser source, the imaging module 105 can be a CCD camera, and the lens module 104 can be a single lens, and the single lens has at least one convex surface along the optical axis direction (i.e., the z-axis direction), such as a plano-convex lens, a biconvex lens, a concave-convex lens, etc.; the lens module 104 can also be a lens group, and the lens group includes two or more lenses. The surface shapes of the two or more lenses can be the same or different, as long as the entire lens group can converge the light beam to form a focal length.

[0058] During measurement, the laser emitted by the light source module 101 is expanded into a parallel light wave by the beam expansion module 102 , diffracted by the aperture surface of the diffraction screen 103 with a complex aperture, and imaged at the receiving surface of the imaging module 105 after being modulated by the lens module 104 .

[0059] The center distance z1 between object plane 106 and the center of lens module 104 refers to the distance between the aperture surface of diffraction screen 103 and the center of lens module 104 (hereinafter referred to as the object distance). The distance z2 between image plane 107 and the plane of lens module 104 refers to the distance between the CCD receiving surface and the center of lens module 104 (hereinafter referred to as the image distance).

[0060] This application utilizes the diffraction pattern of a diffraction screen 103 with a complex aperture to accurately and quickly measure the focal length of the lens module 104. Therefore, the diffraction screen 103 of this application is a porous structure with a certain thickness. The multiple holes of the diffraction screen 103 penetrate the thickness of the diffraction screen 103. The multiple holes of the diffraction screen 103 are located in the same plane along the direction perpendicular to the optical axis. The thickness of the diffraction screen 103 is the dimension in the direction of the optical axis. The thickness of the diffraction screen 103 along the optical axis is 0.1mm to 1mm. For example Figure 2 、 Figure 3 As shown, Figure 2 is the dark field image of the diffraction screen 103 under an optical microscope, Figure 3 This is a scanning electron microscope image of the diffraction screen 103. Figure 3 The structural morphology of the diffraction screen 103 is shown. Figure 3 Scanning was performed using a scanning electron microscope model "S4800" with an acceleration voltage of 5.0 kV, a working distance (the distance between the sample surface and the objective lens observation surface) of 8.0 mm, a magnification of 50 times, a working mode of "SE(M)", and a scale of 1.0 mm.

[0061] The following illustrates the derivation process of formula (1) based on the Fourier optics principle:

[0062] Based on the theoretical analysis of the imaging properties of the lens, we first theoretically verify the phenomenon in the above imaging process and the conclusion that the object distance and the inverse of the image distance are approximately the inverse of the lens focal length. Figure 4 As shown, taking the lens module 104 as a convex lens as an example, consider an imaging system composed of a single thin convex lens. A rectangular coordinate system O-xyz is established at the center of the convex lens and the z-axis is made to coincide with the optical axis of the convex lens. That is, the system is established according to the right-hand system with the z-axis as the vertical coordinate axis. Assume that parallel light passes through the object plane 106 (the horizontal coordinate axis of this plane is marked as , the vertical axis is marked The horizontal and vertical coordinates of any point on this plane are marked as , this set of parameters characterizes the two-dimensional spatial information of the light field) and the light field distribution (complex amplitude distribution) is , the object distance is the center distance z1, and the light field distribution after passing through the convex lens is U l (x, y), the light field distribution at the image plane 107 (the horizontal and vertical coordinates of this plane are marked as (u, v)) is U i (u, v), the image distance is distance z2, and the focal length of the lens is f.

[0063] Calculate the impulse response of the system. From the scalar diffraction theory, we can write The field distribution of the emitted light wave reaching the lens surface , which can be expressed as follows according to the paraxial approximation:

[0064] (1-1);

[0065] In formula (1-1): is the wave vector, is the wavelength, is a unit imaginary number.

[0066] Let the pupil function be , then the light field distribution after lens modulation is for:

[0067] (1-2);

[0068] The light field distribution of the point light source on the image plane 107 can be expressed using the Fresnel diffraction integral formula:

[0069] (1-3);

[0070] make , , lateral magnification , and order for (1-4);

[0071] Then formula (1-3) can be simplified to:

[0072] (1-5);

[0073] The above formula (1-5) is the impulse response of the system , we can write the light field distribution of the image plane 107 when parallel light enters the system .make , ,but:

[0074] (1-6);

[0075] make , when z1 and z2 satisfy the following relationship:

[0076] (1-7);

[0077] That is, when the Gaussian formula is satisfied, substituting equation (1-7) into equation (1-6), the output light field distribution U3 at this time can be obtained as:

[0078] (1-8);

[0079] At this time, the light intensity distribution of the image plane 107 is for:

[0080] (1-9);

[0081] The last digit in formula (1-9) Indicates taking conjugate, the diffraction pattern at this time can be regarded as an accurate reproduction of the object pattern, and the pattern size becomes M times the original, and the light intensity becomes times.

[0082] Taking into account the influence of the diffraction effect caused by the lens aperture on the result, equation (1-8) becomes: (1-10);

[0083] In formula (1-10) Represents the convolution operator, in formula (1-10) This is the Fraunhofer diffraction pattern of the lens aperture. At this point, the diffraction pattern can no longer be considered an exact reproduction of the aperture pattern, but rather a distorted image of it. The smaller the aperture, the more severe the distortion, leading to measurement error. Therefore, to ensure accurate measurement results, the aperture of the convex lens being measured should not be too small.

[0084] Therefore, the above formula (1-7) can be used to obtain formula (1).

[0085] For example, in one embodiment, the laser wavelength is 632.8 nm, and the spot radius after expansion by the beam expansion module 102 is 3.00 cm. The lens module 104 is a convex lens with a nominal focal length F of 19.00 cm, made of BK-17, with a corresponding refractive index n0=1.515 and an aperture D=3.20 cm. The diffraction screen 103 with a complex aperture surface used in the experiment is a porous structure with a certain thickness. The average aperture diameter of the diffraction screen 103 with a complex aperture is 59.95 um, the maximum aperture is 249.54 um, and the minimum aperture is 8.62 um. Compared with the wavelength of the laser light source, the aperture size of the diffraction screen 103 meets the diffraction condition. Figure 1 As shown, all components are placed on the optical axis of the optical rail, z1 and z2 are obtained by measurement, and the focal length f of the lens module 104 can be calculated according to formula (1).

[0086] The focal length measurement system provided in the embodiments of the present application measures the focal length of a lens module 104 based on the diffraction pattern of a complex-aperture diffraction screen 103. Through simplified experimental setup and operating procedures, it achieves accurate and rapid measurement of the focal length of the lens module 104. The measurement results are accurate, with minimal error, and the operation is simple and rapid. The system has low requirements and minimal reliance on experimental equipment and the measurement environment, and demonstrates high precision and stability in measuring multiple lenses, providing accurate and reliable results for the focal length measurement of common lenses and lens groups.

[0087] Furthermore, in the experiment of observing the diffraction pattern of the diffraction screen 103 with complex aperture, the image usually observed is as follows: Figure 5 As shown, obvious stripes will appear on the receiving surface of the CCD camera. The lens module 104 is movable along the optical axis. When the CCD camera is adjusted to a certain position, the diffraction stripes in the received image will shrink toward the center and "disappear" and transform into many clear-cut, sharp holes. The experimental phenomenon in this process is explained by Figure 5 becomes Figure 6 .definition Figure 6 The image shown is the restored image. Assume that the distance from the receiving surface of the CCD camera to the center of the lens is z0.

[0088] Furthermore, Figures 7 to 11 is an image taken using a convex lens with a nominal focal length of 19.00 cm, Figure 7 This is the image captured by the CCD at 0.2 cm in front of z0. Figure 8The image is taken by the CCD at z0. The experiment found that as the CCD approaches z0, some stripes in the image gradually shrink into many spots with blurred boundaries, and the remaining stripes surround these spots. When the CCD is moved to the restored image, the stripes in the image shrink into spots with clear boundaries and bright colors, that is, Figure 7 becomes Figure 8 To explore the effect of image distance change on the image, a series of images were taken with z0 as the base point at intervals of 0.1 cm. Figure 9 、 Figure 10 、 Figure 11 The following are the magnified images of the same area of ​​the image obtained when the CCD is located at the restored image and when it is moved 0.2 cm forward and backward. Figure 9 、 Figure 10 、 Figure 11 They are Figure 8 The enlarged image in the dotted box shows that the image after the CCD position deviates from z0 has diffraction interference fringes, while the image at the CCD position z0 has no diffraction interference fringes. This means that a discernible change in the image occurs with only a 0.2 cm change in image distance, indicating that the position of z0 can be determined relatively accurately.

[0089] In order to quantitatively analyze the accuracy of this method, specific data were measured for verification: the object distance was adjusted to the set value, and the CCD position was adjusted so that the image was restored. At this time, the distance (image distance) z2=z0, and the image distance was measured and recorded. Five independent measurements were performed for each object distance corresponding to the image distance to reduce random errors and increase the reliability of the experimental data.

[0090] Analyzing the experimental data, we found that the reciprocal of the object distance (1 / z1) and the reciprocal of the image distance (1 / z2) in each set of data are inversely proportional. Figures 12 to 17 The figure shows the ideal value (calculated using the Gaussian formula) and the measured value of lenses with different focal lengths. The deviation between the two sets of data in each figure indicates that there is a certain difference between the lens focal length calculated directly according to the Gaussian imaging formula and the actual focal length.

[0091] On this basis, in order to explore the reasons for the deviation between experimental data and theoretical calculations and to correct them, taking into account the influence of lens thickness and primary spherical aberration of the lens, the focal length formula is corrected to:

[0092] f=1 / (1 / z1+1 / z2)-△f1-△f2(2);

[0093] in, ; ;

[0094] ; ; d is the width of the lens module 104, R is the radius of curvature of the lens module 104, n0 is the refractive index of the lens module 104, and D is the aperture of the lens module 104.

[0095] The specific value of the correction term in equation (2) can be easily and accurately measured experimentally. After measuring the object distance and image distance at the restored image, the data previously measured according to equation (1) can be corrected according to equation (2) to obtain a more accurate result. This result corrects for the deviation caused by lens thickness and spherical aberration, and has higher accuracy.

[0096] To verify the effectiveness of the correction method, the accuracy of the lens focal length measurement method based on complex aperture diffraction patterns was explored. Six lenses with nominal focal lengths F of 19.00 cm, 15.00 cm, 10.00 cm, 7.00 cm, 5.00 cm, and 4.50 cm were measured. The measured data were substituted into the formula (1) before correction and the formula (2) after correction to obtain two sets of measurement values. The results are shown in the figure below. Figures 18 to 23 In the figure, the ordinate f is the focal length measurement value, in cm, and the abscissa k is the ratio of the set object distance to the nominal focal length (abbreviated as the object distance to focal length ratio), without unit.

[0097] Assume that the relative deviation between the corrected focal length measurement value and the nominal focal length value is δ c , the relative deviation of the measured values ​​of each lens is as follows Figures 24 to 29 shown. Figures 18 to 23 It shows that the corrected measurement results are closer to the nominal focal length value than the uncorrected ones, that is, the measurement results are more accurate. Figures 24 to 29 Among them, except for the lens with a nominal focal length of 5.00 cm, the relative deviation between the average value of the corrected lens focal length measurement and the nominal focal length value is less than 0.47%, showing a high measurement accuracy.

[0098] According to the above derivation, we can obtain formula (1). When the distance (image distance) z2=z0, the object distance and image distance measured satisfy the Gaussian formula. However, previous experimental results show that there is a certain deviation between the focal length value calculated according to formula (1) and the actual focal length value. Part of the deviation comes from the fact that the above derivation and analysis are all ideal conditions, and the results cannot fully and accurately describe the actual situation, resulting in a certain deviation. Another part of the deviation comes from the systematic error caused by the experimental device. After consulting the data and analyzing it, it is found that the main influence on the measurement results and the measurement deviation caused by the actual lens thickness and aberration is relatively easy to correct. Therefore, this paper mainly considers the influence of the lens thickness and the primary spherical aberration of the lens on the measurement results, and corrects formula (1) accordingly.

[0099] The thickness of the lens makes the object side principal point and the image side principal point of the lens not coincide with the center of the lens. The object distance and image distance discussed previously are all based on the center of the lens as the reference point. To do this, we need to calculate the position of the lens's object side principal point z at this time. L1 and the image side principal point position z L2 Assuming the lens width is d, the aperture size is D, and the curvature radius is R1=-R2=R, we can write the object side principal point position z L1 and the image side principal point position z L2 for:

[0100] (2-1);

[0101] Then the spacing z C for:

[0102] (2-2);

[0103] After correction, the object distance value becomes z1+z C / 2, the image distance becomes z2+z C / 2, and the deviation from formula (1-7) is:

[0104] (2-3);

[0105] Consider the influence of lens spherical aberration on focal length measurement. Figure 30 As shown, the light beams from different areas are no longer concentric beams after converging, and their focus (here refers to the position where the light beams from different areas converge on the optical axis, Figure 30 The deviation between 2, 3, 4, and 5 (where 2, 3, 4, and 5 represent different focal positions) and the Gaussian image point 1 is the axial spherical aberration of the lens, and the maximum value corresponds to the outermost beam. For the case of this application, the position where the diffraction pattern is closest to the aperture pattern (with the highest similarity) is taken as the restored image position. At this time, the image width is the smallest and the image distance is at Figure 30 The focus position is between 4 and 3. However, formula (1) is only suitable for the case where the minimum image width coincides with Gaussian image point 1, so it is necessary to make some corrections to formula (1) to better meet the specific experimental conditions.

[0106] First calculate the maximum axial spherical aberration δL m According to the knowledge of engineering optics, the axial spherical aberration of an optical system composed of n surfaces can be written as Distributed as:

[0107] (2-4);

[0108] in is the refractive index, and is the aperture angle, S iis the spherical aberration distribution coefficient on the i-th surface. Combined with the lens parameters, let h=D / 2, the maximum axial spherical aberration of this lens is δL m for:

[0109] (2-5);

[0110] When the image width is minimum, Calculation, the image distance value of the lens to be measured should be , so the deviation △f2 relative to the result calculated by formula (1) is:

[0111] (2-6);

[0112] According to the above discussion, considering the influence of lens thickness and primary spherical aberration of the lens, equation (1) should be modified as follows:

[0113] (2);

[0114] The specific values ​​of the above correction terms can also be easily and accurately measured from experiments. After measuring the object distance and image distance at the restored image, the previously measured data can be corrected according to formula (2) to correct for deviations caused by lens thickness and spherical aberration, thereby obtaining more accurate results.

[0115] In summary, this application presents a new method based on the principles of Fourier optics, utilizing changes in the diffraction pattern of a complex aperture to accurately and quickly measure the focal length of a single convex lens. Starting from experimental phenomena and taking advantage of the sensitivity of the restored image phenomenon (i.e., the disappearance of diffraction fringes) to changes in image distance, the object distance and image distance at the time of the restored image are measured, and the focal length of the lens is calculated using the Gaussian formula. Analysis of the experimental data shows that the changing trends of the reciprocals of the object distance and image distance are consistent with the results calculated using the Gaussian formula. Furthermore, through theoretical analysis and formula correction, the focal length measurements of convex lenses with different nominal focal lengths are more accurate.

[0116] This lens focal length measurement method, based on complex aperture diffraction patterns, offers accurate results with minimal error, is simple and fast to operate, and requires minimal experimental equipment and measurement environment. This method will provide a reliable means for accurately measuring lens focal lengths in teaching and experiments.

[0117] The above are merely examples of the present application and are not intended to limit the scope of protection of the present application. Those skilled in the art will appreciate that various modifications and variations are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

Claims

1. A focal length measurement system, characterized in that: include: A light source module, a beam expansion module, a diffraction screen, a lens module, and an imaging module are sequentially arranged. The diffraction screen is a porous structure with a complex aperture. Light emitted from the light source module is expanded by the beam expansion module to form parallel light waves, which are then diffracted by the diffraction screen and imaged on the receiving surface of the imaging module after passing through the lens module. The multiple holes in the diffraction screen extend through the thickness of the diffraction screen and are located in the same plane perpendicular to the optical axis. The thickness of the diffraction screen along the optical axis is 0.1 mm to 1 mm. The aperture of the diffraction screen with a complex aperture is 8.62 μm to 249.54 μm. The aperture size of the diffraction screen meets the diffraction condition. The focal length of the lens module satisfies f=1 / (1 / z1+1 / z2); z1 is the center distance between the diffraction screen and the lens module, and z2 is the distance between the lens module and the receiving surface of the imaging module; The distance z2 between the lens and the receiving surface of the imaging module is z0, where z0 is the distance between the lens module and the receiving surface of the imaging module when the image received by the receiving surface of the imaging module has no restored image of diffraction fringes.

2. The focal length measurement system according to claim 1, wherein: The focal length of the lens module satisfies f=1 / (1 / z1+1 / z2)-Δf1-Δf2; in, , ; ； ;d is the width of the lens module, R is the radius of curvature of the lens module, n0 is the refractive index of the lens module, and D is the aperture of the lens module.

3. The focal length measurement system according to claim 1, wherein: The lens module is movably arranged along the optical axis so that the receiving surface of the imaging module is located at the imaging restoration position.

4. The focal length measurement system according to claim 1 or 2, characterized in that: The lens module includes a lens, and the lens has at least one convex surface along the optical axis.

5. The focal length measurement system according to claim 4, wherein: The lenses at least include a plano-convex lens, a meniscus lens and a biconvex lens.

6. The focal length measurement system according to claim 1 or 2, characterized in that: The lens module is a lens group, and the lens group includes two or more lenses.

7. The focal length measurement system according to claim 1 or 2, characterized in that: The light source module at least includes a laser.

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