Focal length measuring system

Abstract

The invention provides a focal length measuring system, and relates to the technical field of optical measurement, the focal length measuring system comprises a light source module, a beam expanding module, a diffraction screen, a lens module and an imaging module which are arranged in sequence, the diffraction screen is of a porous structure with a complex aperture, and light emitted by the light source module is subjected to beam expanding through the beam expanding module and then diffracted through the diffraction screen; imaging on a 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 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 focal length of the lens module is measured based on the diffraction pattern of the complex aperture diffraction screen, the experimental device and operation steps are simplified, the measurement result is accurate, the error is small, the operation is simple and rapid, the requirement on experimental equipment and the measurement environment is low, the dependence on the experimental equipment and the measurement environment is small, the precision and the stability are high, and an accurate and reliable result is provided 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 the performance evaluation of optical systems and related research. How to accurately and quickly obtain focal length data in the system is a very basic and important issue. There are many means to accurately obtain focal length. Traditional focal length measurement methods include displacement method, magnification method, Gaussian formula method, autocollimation method, etc., and emerging methods include interference method, diffraction method, holographic method, etc. For more complex or special focal length measurement needs, methods such as Talber-Mohr interferometry technology can also be used to accurately determine the focal length of the lens.

[0003] However, the above measurement methods have limited scope of application and certain limitations: the measurement results of the displacement method are easily affected by the experimental conditions, resulting in unsatisfactory repeatability; the magnification method is complicated to operate; the Gaussian formula method is not easy to accurately define the position of the object image, which makes the measurement accuracy low. The emerging methods are often more complicated and not simple enough, and have high requirements for experimental instruments and experimental environment, which limits their use in certain specific scenarios. For example, in university physics experimental teaching, the mainstream methods of 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 the focal length, and the method is simple and easy to operate.

[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 arranged in sequence, wherein the diffraction screen is a porous structure with a complex aperture, and the light emitted by the light source module is expanded by the beam expansion module, then diffracted by the diffraction screen, and imaged on a 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 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.

[0006] Optionally, 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.

[0007] 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.

[0008] 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.

[0009] Optionally, the multiple holes of the diffraction screen are located in the same plane along a direction perpendicular to the optical axis.

[0010] Optionally, the thickness of the diffraction screen along the optical axis direction is 0.1 mm to 1 mm.

[0011] Optionally, the lens module includes a lens, and the lens has at least one convex surface along the optical axis direction.

[0012] Optionally, the lens includes at least a plano-convex lens, a concave-convex lens and a biconvex lens.

[0013] Optionally, the lens module is a lens group, and the lens group includes two or more lenses.

[0014] Optionally, the light source module includes at least a laser.

[0015] The focal length measurement system provided in the embodiment of the present application measures the focal length of the lens module based on the diffraction pattern of the diffraction screen with a complex aperture, and realizes accurate and fast measurement of the focal length of the lens module through simplified experimental equipment and operation steps. The measurement results are accurate, the error is small, and the operation is simple and fast. The requirements and dependence on experimental equipment and measurement environment are low, and high accuracy and stability are shown in the measurement of multiple lenses, which can provide accurate and reliable results for the focal length measurement of common lenses and lens groups. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. 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 related drawings can be obtained based on these drawings without paying creative work.

[0017] Figure 1 is a schematic diagram of the structure of the focal length measurement system provided in this embodiment; Figure 2 is a dark field image of the diffraction screen provided in this embodiment in an optical microscope; Figure 3 is a scanning electron microscope image of the diffraction screen provided in this embodiment; Figure 4 is a simplified schematic diagram of imaging of a single convex lens system provided in this embodiment; Figure 5 is an image when diffraction fringes exist during imaging by the focal length measurement system provided by this embodiment; Figure 6 is the image when the diffraction fringes disappear during imaging by the focal length measurement system provided by this embodiment; Figure 7 is an image obtained when the focal length measurement system provided in 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 z0; Figure 8 is the image of the imaging module at z0 when the focal length measurement system provided in this embodiment uses a convex lens with a nominal focal length of 19.00 cm for imaging; Fig. 9 yes Figure 8 A magnified image of the box at z0 with the frame moved forward 0.2 cm along the z axis; Fig.10 yes Figure 8 The enlarged image framed at z0; Fig.11 yes Figure 8 A magnified image of the box at z0 with the frame shifted 0.2 cm back along the z axis; Fig.12 is a relationship diagram between an ideal value and a measured value of a lens with a focal length of 19.00 cm in the focal length measurement system provided in this embodiment; Fig.13 is a relationship diagram between an ideal value and a measured value of a lens with a focal length of 15.00 cm in the focal length measurement system provided in this embodiment; Fig.14 is a relationship diagram between an ideal value and a measured value of a lens with a focal length of 10.00 cm in the focal length measurement system provided in this embodiment; Fig.15 is a relationship diagram between an ideal value and a measured value of a lens with a focal length of 7.00 cm in the focal length measurement system provided in this embodiment; Fig.16 is a relationship diagram between an ideal value and a measured value of a lens with a focal length of 5.00 cm in the focal length measurement system provided in this embodiment; Fig.17 is a relationship diagram between an ideal value and a measured value of a lens with a focal length of 4.50 cm in the focal length measurement system provided in this embodiment; Fig.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; Fig.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; Fig. 20 is the third measured value of the focal length of the lens before and after correction by the focal length measurement system provided in this embodiment; Fig.21 is the fourth measured value of the focal length of the lens before and after correction by the focal length measurement system provided in this embodiment; Fig. 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; Fig.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; Fig.24 is one of the relative deviation diagrams of the focal length measurement value f after correction and the focal length nominal value F of the focal length measurement system provided in this embodiment; Fig.25 is a 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 the present embodiment; Fig.26 is a third 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 the present embodiment; Fig. 27 FIG4 is a 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 in this embodiment; Fig.28 is a fifth 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 in this embodiment; Fig.29 is a sixth 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 in this embodiment; Fig.30 This is a schematic diagram of lens spherical aberration.

[0018] 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

[0019] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0020] In the description of this application, it should be noted that the terms "inside", "outside", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the application is usually placed when in use, which is only for the convenience of describing this application and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on this application. In addition, the terms "first", "second", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0021] It should also be noted that, unless otherwise clearly specified and limited, the terms "disposed" and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection, or an indirect connection through an intermediate medium, or it can be the internal communication of two elements. For ordinary technicians in this field, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0022] Please refer to Figure 1 As shown, the 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 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 a plurality of holes, and the apertures of the plurality of holes are different, the light emitted by the light source module 101 is expanded by the beam expansion module 102, then diffracted by the diffraction screen 103, and imaged on the receiving surface of the imaging module 105 after passing through the lens module 104; The focal length of the lens module 104 satisfies f=1 / (1 / z1+1 / z2) (1); 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 .

[0023] 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 bi-convex 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, and 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.

[0024] 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 .

[0025] The center distance z1 from the object plane 106 to the center of the lens module 104 refers to the distance from the aperture surface of the diffraction screen 103 to the center of the lens module 104 (hereinafter referred to as the object distance) in the experiment. The distance z2 from the image plane 107 to the plane of the lens module 104 refers to the distance from the CCD receiving surface to the center of the lens module 104 (hereinafter referred to as the image distance) in the experiment.

[0026] The present application utilizes the diffraction pattern of the diffraction screen 103 with complex aperture to accurately and quickly measure the focal length of the lens module 104. Therefore, the diffraction screen 103 of the present application is a porous structure with a certain thickness, and 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, and the thickness of the diffraction screen 103 along the direction of 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.

[0027] The following illustrates the derivation process of equation (1) based on the Fourier optics principle: Based on the theoretical analysis of the imaging properties of lenses, we first theoretically verify the phenomenon in the above imaging process and the conclusion that the object distance, the inverse of the image distance and the approximate inverse of the lens focal length. Figure 4 As shown, taking the lens module 104 as a convex lens as an example, considering 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 z axis is used as the vertical coordinate axis to establish the system according to the right-hand system. Assume that parallel light passes through the object plane 106 (the horizontal axis of this plane is marked as , the vertical axis is marked as , the 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.

[0028] Calculating the impulse response of the system, the scalar diffraction theory can be written as The field distribution of the emitted light wave reaching the lens surface , which can be expressed paraxially as: (1-1); In formula (1-1): is the wave vector, is the wavelength, is a unit imaginary number.

[0029] Let the pupil function be , then the light field distribution after lens modulation is for: (1-2); The light field distribution of the point light source on the image plane 107 can be written using the Fresnel diffraction integral formula: (1-3); make , , lateral magnification , and order for (1-4); Then formula (1-3) can be simplified as: (1-5); 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: (1-6); make , when z1 and z2 satisfy the following relationship: (1-7); 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: (1-8); At this time, the light intensity distribution of the image plane 107 for: (1-9); 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.

[0030] Taking into account the influence of the diffraction effect caused by the lens aperture on the result, equation (1-8) becomes: (1-10); In formula (1-10) represents the convolution operator, in formula (1-10) is the Fraunhofer diffraction pattern of the lens aperture. The diffraction pattern at this point can no longer be regarded as an accurate reproduction of the aperture pattern, but rather as a deformed image of the aperture. The smaller the aperture, the more severe the deformation, which results in measurement errors. Therefore, in order to ensure the accuracy of the measurement results, the aperture of the convex lens to be measured should not be too small.

[0031] Therefore, the formula (1) can be obtained through the above formula (1-7).

[0032] For example, in one embodiment, the laser wavelength is 632.8 nm, and the spot radius after expansion by the 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, according to 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).

[0033] The focal length measurement system provided in the embodiment of the present application measures the focal length of the lens module 104 based on the diffraction pattern of the diffraction screen 103 with a complex aperture, and realizes accurate and rapid measurement of the focal length of the lens module 104 through simplified experimental equipment and operation steps. The measurement result is accurate, the error is small, and the operation is simple and rapid. The requirements and dependence on experimental equipment and measurement environment are low, and high accuracy and stability are shown in the measurement of multiple lenses, and accurate and reliable results can be provided for the focal length measurement of common lenses and lens groups.

[0034] 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 5As shown, obvious stripes will appear on the receiving surface of the CCD camera. The lens module 104 can be moved 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 then "disappear" and transform into many holes with clear boundaries. The experimental phenomenon in this process is 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.

[0035] Further, Figure 7 to Figure 11 is the image captured using a convex lens with a nominal focal length of 19.00 cm, Figure 7 This is the image taken by the CCD at 0.2 cm in front of z0. Figure 8 The 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 bright spots with clear boundaries, that is, Figure 7 becomes Figure 8 To explore the effect of image distance change on the image, a series of images were taken at intervals of 0.1 cm with z0 as the base point. Fig. 9 , Fig.10 , Fig.11 The following are the enlarged 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. Fig. 9 , Fig.10 , Fig.11 They are Figure 8 The enlarged image in the dotted box. As can be seen from the figure, the image after the CCD position deviates from z0 has diffraction interference fringes, and the image at the CCD position z0 has no diffraction interference fringes, that is, the image distance only changes by 0.2 cm, and the image has produced a resolvable change, which shows that the position of z0 can be determined more accurately.

[0036] 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 to make the image a restored image. At this time, the distance (image distance) z2=z0, and the image distance was measured and recorded. The image distance corresponding to each object distance was measured five times independently to reduce random errors and increase the reliability of the experimental data.

[0037] 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. Figure 12 to Figure 17The ideal value (calculated using the Gaussian formula) and measured value of lenses with different focal lengths are shown. The deviation between the two sets of data in each figure shows that there is a certain difference between the focal length of the lens calculated directly using the Gaussian imaging formula and the actual focal length.

[0038] On this basis, in order to explore the reasons for the deviation between experimental data and theoretical calculations and make corrections, taking into account the influence of lens thickness and primary spherical aberration of the lens, the focal length formula is corrected to: f=1 / (1 / z1+1 / z2)-△f1-△f2(2); in, ; ; ; ; 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.

[0039] The specific value of the correction term in the above formula (2) can be conveniently and accurately measured from the experiment. After respectively measuring the object distance and image distance at the restored image, the data previously measured according to formula (1) can be corrected according to formula (2) to obtain a more accurate result. The result corrects the deviation caused by lens thickness and spherical aberration and has higher accuracy.

[0040] In order to verify the effectiveness of the correction method and explore the accuracy of the lens focal length measurement method based on complex aperture diffraction patterns, 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 Figure 2. Figure 18 to Figure 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 ratio of object distance to focal length), without unit.

[0041] 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 Figure 24 to Figure 29 shown. Figure 18 to Figure 23 It shows that the corrected measurement result is closer to the nominal focal length value than the uncorrected one, that is, the measurement result is more accurate. Figure 24 to Figure 29 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.

[0042] According to the above derivation, we can get formula (1). When the distance (image distance) z2=z0, the measured object distance and image distance 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 situations, 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 measurement deviation caused by the actual lens thickness and aberration is the main factor that affects the measurement results and can be corrected more conveniently. 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.

[0043] The thickness of the lens makes the object principal point and image principal point of the lens not coincide with the center of the lens, and 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' object principal point z at this time. L1 and the image side principal point position z L2 Assume that the lens width is d, the aperture size is D, and the radius of curvature is R1=-R2=R, from which the object principal point position z can be written L1 and the image side principal point position z L2 for: (2-1); Then the spacing z C for: (2-2); 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: (2-3); Consider the effect of the spherical aberration of the lens on the focal length measurement. Fig.30 As shown, after the light beams from different regions converge, they are no longer concentric beams. Their focus (here refers to the position where the light beams from different regions converge on the optical axis) Fig.30 2, 3, 4, and 5 represent different focal positions respectively) and the deviation from 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 in the measurement. At this time, the image width is the smallest and the image distance is at Fig.30 The focus position is between 4 and 3 in the image. 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.

[0044] First calculate the maximum axial spherical aberration δLm 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: (2-4); in is the refractive index, and is the aperture angle, S i is the spherical aberration distribution coefficient on the i-th surface. Combining the lens parameters, let h = D / 2, the maximum axial spherical aberration of this lens is δL m for: (2-5); When the image width is the smallest, it is located at Calculate, 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: (2-6); According to the above discussion, considering the influence of lens thickness and primary spherical aberration of lens, equation (1) should be corrected as follows: (2); The specific values ​​of the above correction items can also be conveniently and accurately measured from experiments. After respectively measuring the object distance and image distance at the restored image, the previously measured data can be corrected according to formula (2) to correct the deviation caused by lens thickness and spherical aberration to obtain a more accurate result.

[0045] In summary, the present application is based on the principle of Fourier optics and uses the change of the diffraction pattern of a complex aperture to accurately and quickly measure the focal length of a single convex lens. Starting from the experimental phenomenon, the object distance and image distance when the restored image appears are measured by utilizing the characteristic that the restored image phenomenon (i.e., the disappearance of diffraction fringes) is more sensitive to the change of image distance, and the focal length of the lens is calculated according to the Gaussian formula. The analysis results of the experimental data show that the changing trend of the reciprocal of the object distance and the image distance is consistent with the calculation results of the Gaussian formula. Furthermore, through theoretical analysis and formula correction, the focal length value measurement results of convex lenses with different nominal focal lengths are made more accurate.

[0046] The lens focal length measurement method based on complex aperture diffraction patterns has accurate measurement results, small errors, simple and fast operation, and low requirements for experimental equipment and measurement environment. This measurement method will provide a reliable means for accurate measurement of lens focal length required in teaching and experiments.

[0047] The above are only embodiments of the present application and are not intended to limit the scope of protection of the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in 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 arranged in sequence, wherein the diffraction screen is a porous structure with a complex aperture, and the light emitted by the light source module is expanded by the beam expansion module, then diffracted by the diffraction screen, and then formed 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 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.

2. The focal length measurement system according to claim 1, characterized in that: 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 or 2, characterized in that: 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 does not have a restored image of diffraction fringes.

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

5. The focal length measurement system according to claim 1 or 2, characterized in that: The multiple holes of the diffraction screen are located in the same plane along a direction perpendicular to the optical axis.

6. The focal length measurement system according to claim 1 or 2, characterized in that: The thickness of the diffraction screen along the optical axis direction is 0.1 mm to 1 mm.

7. 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 direction.

8. The focal length measurement system according to claim 7, characterized in that: The lens at least includes a plano-convex lens, a concave-convex lens and a biconvex lens.

9. 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.

10. 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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