Lens astigmatism correction method, device, terminal and storage medium

Abstract

The present application provides a lens astigmatism correction method, device, terminal, and storage medium. The method is applied to a Qiming lens, which consists of a front surface and a back surface, wherein the front surface is aspherical and the back surface is spherical. The method includes: obtaining lens parameters and object point parameters; performing primary astigmatism correction and primary coma correction on the lens based on the lens parameters and object point parameters to obtain the lens center thickness, the front surface vertex curvature radius, the back surface curvature radius, and image point parameters; based on the Fermat principle, performing spherical aberration correction on the lens according to the lens refractive index, the lens center thickness, the distance between the front surface vertex and the object plane where the object point is located, the distance between the back surface spherical vertex and the image plane where the image point is located, and the back surface curvature radius, to obtain aspheric surface discrete points; and obtaining aspheric lens coefficients based on the aspheric surface discrete points. The present application can achieve lens astigmatism correction, improve the optical properties and applicability of the lens, and is simple and convenient to operate.

Description

Technical Field

[0001] The present application relates to the field of lens improvement technology, and in particular to a lens astigmatism correction method, device, terminal and storage medium. Background Art

[0002] In LiDAR applications, the performance of optical lenses has a significant impact on the overall performance of the LiDAR. A high-performance transmitting lens helps reduce the divergence angle of laser detection, improves emission efficiency, and reduces the impact of stray light. A high-performance receiving lens can improve optical gain and receiving efficiency, reduce the detector receiving area, and help reduce the impact of stray light, thereby improving the system's signal-to-noise ratio and overall performance. Due to the narrow wavelength range of lasers, the impact of chromatic aberration is usually not considered in optical design applications. On the premise of meeting the corresponding optical index requirements, in order to reduce system volume and reduce the difficulty of system assembly, people usually use aspheric lens technology to replace multiple spherical lens groups with a single lens.

[0003] The design of the Qiming lens primarily corrects for spherical aberration by introducing an aspheric lens surface to correct for spherical aberration, based on a structure that corrects primary spherical aberration and primary coma in the paraxial region. This often fails to eliminate lens astigmatism, resulting in poor imaging uniformity across different fields of view and in different directions (meridional and sagittal planes), and significant differences in aberration characteristics. Since the detector's photosensitive surface is typically circular, the lens characteristics do not match the detector surface well. Furthermore, as the field of view increases, the astigmatism effect on the lens' optical performance becomes increasingly pronounced, exacerbating off-axis aberrations and limiting improvements in the field of view. Summary of the Invention

[0004] The present application provides a lens astigmatism correction method, device, terminal and storage medium to solve the problem in the prior art that transparent astigmatism cannot be eliminated during the correction process of a Qiming lens.

[0005] In a first aspect, the present application provides a lens astigmatism correction method, the method being applied to a Qiming lens, the Qiming lens comprising a front surface and a back surface, the front surface being aspherical, and the back surface being spherical, the method comprising:

[0006] Obtaining lens parameters and object point parameters, wherein the lens parameters include the lens refractive index and the lens focal length, and the object point parameters include the distance between the front surface vertex and the object plane where the object point is located and the height of the object point;

[0007] performing primary astigmatism correction and primary coma correction on the lens based on the lens parameters and the object point parameters to obtain a lens center thickness, a front surface vertex curvature radius, a back surface curvature radius, and image point parameters, wherein the image point parameters include a distance between a back surface spherical vertex and an image plane where the image point is located, and an image point height;

[0008] Based on the Fermat principle, the lens is corrected for spherical aberration according to the refractive index of the lens, the center thickness of the lens, the distance between the vertex of the front surface and the object plane where the object point is located, the distance between the vertex of the spherical surface of the rear surface and the image plane where the image point is located, and the curvature radius of the rear surface, to obtain discrete points of the aspherical surface type;

[0009] According to the aspheric surface discrete points, the aspheric lens coefficients are obtained.

[0010] In a second aspect, the present application provides a lens astigmatism correction device, the device being applied to a Qiming lens, the Qiming lens comprising a front surface and a rear surface, the front surface being aspherical, and the rear surface being spherical, the device comprising:

[0011] an acquisition module, configured to acquire lens parameters and object point parameters, wherein the lens parameters include the lens refractive index and the lens focal length, and the object point parameters include the distance between the front surface vertex and the object plane where the object point is located and the height of the object point;

[0012] a first correction module, configured to perform primary astigmatism correction and primary coma correction on the lens based on the lens parameters and the object point parameters, to obtain a lens center thickness, a front surface vertex curvature radius, a back surface curvature radius, and image point parameters, wherein the image point parameters include a distance between a back surface spherical vertex and an image plane where the image point is located, and an image point height;

[0013] a second correction module, configured to perform spherical aberration correction on the lens based on the Fermat principle and according to the lens refractive index, the center thickness of the lens, the distance between the front surface vertex and the object plane where the object point is located, the distance between the back surface spherical vertex and the image plane where the image point is located, and the back surface curvature radius, to obtain aspheric surface discrete points;

[0014] The determination module is used to obtain the aspheric lens coefficient according to the aspheric surface discrete points.

[0015] In a third aspect, the present application provides a terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the method described in the first aspect or any possible implementation of the first aspect are implemented.

[0016] In a fourth aspect, the present application provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the method described in the first aspect or any possible implementation of the first aspect.

[0017] The present application provides a lens astigmatism correction method, device, terminal, and storage medium. The present application corrects lens astigmatism by first correcting primary astigmatism and primary coma, and then correcting spherical aberration. This corrects lens astigmatism, thereby solving the problem of imaging balance in small-angle fields of view and different directions (meridian and sagittal planes), improving the optical properties and applicability of the lens. Furthermore, by solving the aspheric lens coefficients through discrete points of the aspheric surface shape, the professional requirements for designers can be greatly reduced, and the operation is simple and convenient. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments or descriptions of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0019] Figure 1 Schematic diagram of the structure of the Qiming lens provided in an embodiment of the present application;

[0020] Figure 2 This is a flowchart of the lens astigmatism correction method provided in an embodiment of the present application;

[0021] Figure 3 Schematic diagram of parameters of the Qiming lens provided in an embodiment of the present application;

[0022] Figure 4 Schematic diagram of parameters for correcting primary astigmatism provided in an embodiment of the present application;

[0023] Figure 5 is a list of primary aberration coefficients and a lens profile diagram of the optical software provided in the embodiments of the present application;

[0024] Figure 6 The point diagram, wavefront diagram and aberration curve diagram of the simulated lens provided in the embodiment of the present application are shown;

[0025] Figure 7 This is the lens outline of the Thorlabs lens library number A375;

[0026] Figure 8 is a lens profile diagram provided in an embodiment of the present application;

[0027] Figure 9 Here are the point diagram, energy bracketing diagram, and aberration curve diagram of the A375 lens;

[0028] Figure 10 The point diagram, energy bracket diagram, and aberration curve diagram of the lens provided in the embodiments of the present application are shown in FIG.

[0029] Figure 11is a structural schematic diagram of a lens astigmatism correction device provided in an embodiment of the present application;

[0030] Figure 12 It is a schematic diagram of a terminal provided in an embodiment of the present application. DETAILED DESCRIPTION

[0031] In the following description, specific details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0032] In order to make the purpose, technical solutions and advantages of this application clearer, specific embodiments will be described below with reference to the accompanying drawings.

[0033] Figure 1 This is a schematic diagram of the structure of the Qiming lens provided in the embodiment of the present application. Figure 1 As shown, the Qiming lens consists of a front surface 1 and a rear surface 2. The front surface 1 is an aspherical surface or a free-form surface, and the front surface coincides with the aperture surface. The rear surface 2 is a spherical surface.

[0034] In the present application, a Qiming lens that is a combination of a spherical surface and an aspheric surface is used to correct lens astigmatism. Since the Qiming lens has a small F number, diffraction-limited imaging can be achieved within a small angle range.

[0035] See also Figure 2 , which shows a flowchart of the implementation of the lens astigmatism correction method provided by the embodiment of the present application, and is described in detail as follows:

[0036] In step 201 , lens parameters and object point parameters are obtained. The lens parameters include the lens refractive index and the lens focal length. The object point parameters include the distance between the front surface vertex and the object plane where the object point is located and the height of the object point.

[0037] See also Figure 3 , the object point parameters include: the distance l between the front surface vertex and the object plane where the object point P is located a , object point height y a , l a with y a is based on Figure 3 Known parameters; lens parameters include: lens refractive index n and lens focal length f are both known parameters, which are determined by the lens material.

[0038] Among them, for l a and y aThe sign of is stipulated as follows: Since the object point P is on the left side of the vertex o on the front surface of the lens (negative z axis), then l a is a negative value, or, since the object point P is to the right of the vertex o on the front surface of the lens (z positive axis), then l a is a positive value; since the off-axis object point Q is on the upper side of the vertex o on the front surface of the lens (positive y axis), y a is a positive value, or, since the off-axis object point Q is below the vertex o on the front surface of the lens (y negative axis), then y a Negative value. Figure 3 , l a is a negative value, y a Is a positive value.

[0039] In step 202, primary astigmatism correction and primary coma correction are performed on the lens based on the lens parameters and the object point parameters to obtain the lens center thickness, the front surface vertex curvature radius, the back surface curvature radius and the image point parameters. The image point parameters include the distance between the back surface spherical vertex and the image plane where the image point is located, and the image point height.

[0040] According to n, f, l obtained in step 201 a and y a , perform primary astigmatism correction and primary coma correction on the lens, and obtain the center thickness of the lens, the curvature radius of the front surface vertex, the curvature radius of the back surface, the distance between the vertex of the back surface spherical surface and the image plane where the image point is located, and the image point height.

[0041] See also Figure 3 The center thickness of the lens is d, the radius of curvature of the front surface vertex is r1, the radius of curvature of the back surface is r2, and the distance between the vertex of the back surface spherical surface and the image plane where the image point P' is located is l b , the image point height is y b .

[0042] Among them, the positive and negative signs of the above parameters are stipulated as follows: Since the image point P' is on the right side of the vertex of the rear surface of the lens (z positive axis), then l b is a positive value, or, since the image point P' is on the left side of the vertex of the rear surface of the lens (negative z axis), then l b is a negative value; since the off-axis image point Q' is on the upper side of the vertex o on the front surface of the lens (positive y axis), y b is a positive value, or, since the off-axis image point Q' is below the vertex o on the front surface of the lens (y negative axis), then y b is a negative value; if the center of the circle corresponding to r1 is to the right of the vertex o on the front surface of the lens, then r1 is a positive value, or, if the center of the circle corresponding to r1 is to the left of the vertex o on the front surface of the lens, then r1 is a negative value; if the center of the circle corresponding to r2 is to the right of the vertex on the back surface of the lens, then r2 is a positive value, or, if the center of the circle corresponding to r2 is to the left of the vertex on the back surface of the lens, then r2 is a negative value. Figure 3 , lb is a positive value, y b is a negative value, r1 is a positive value, and r2 is a negative value.

[0043] The present application eliminates the primary astigmatism of the lens under the condition of constraining the primary coma, solves the problem of imaging balance in small-angle fields of view and different directions (meridian and sagittal planes), and improves the optical properties and applicability of the lens.

[0044] In a possible implementation, step 202 may specifically include:

[0045] Based on the primary coma calculation formula, lens parameters and object point parameters, the primary coma correction of the lens is performed to obtain the value range of the front surface vertex curvature radius and the center thickness of the lens. The primary coma calculation formula is derived from the focal length calculation formula and primary aberration theory.

[0046] Calculate the back surface curvature radius and image point parameters based on the range of the front surface vertex curvature radius and the center thickness of the lens;

[0047] The focal length calculation formula is:

[0048]

[0049] Where f is the focal length, n is the refractive index of the lens, r1 is the radius of curvature of the front surface vertex, r2 is the radius of curvature of the back surface, and d is the center thickness of the lens;

[0050] The formula for calculating primary coma is:

[0051] S II =α4(n,r1,f,l a )d 4 +α3(n,r1,f,l a )d 3 +α2(n,r1,f,l a )d 2 +α1(n,r1,f,l a )d+α0(n,r1,f,l a )=0

[0052] Among them, α4(n,r1,f,l a )=(l a -nl a +r1) 3 (f-nf+nr1) 2 (f-nf+n 2 r1);

[0053]

[0054]

[0055]

[0056]

[0057] Among them, S II To correct the primary coma coefficient, l a is the distance between the vertex of the front surface and the object plane where the object point is located, α0 is the first coefficient, α1 is the second coefficient, α2 is the third coefficient, α3 is the fourth coefficient, and α4 is the fifth coefficient.

[0058] In the embodiment of the present application, when the focal length of the lens is f, the focal length calculation formula is:

[0059]

[0060] According to the above focal length calculation formula, the following relationship is satisfied: According to the primary aberration theory, when the stop surface of the lens front surface coincides, S II With n, r1, r2, l a 、y a , lens radius hole height h, d and l b Related, and S II ∝y a , S II ∝h 3 , so that the calculation formula of primary coma can correct the primary coma, that is, solve S II = 0 to correct the primary coma, which is equivalent to solving Φ(n,r1,r2,l a ,d,l b )=0. According to the Gaussian formula of the object image position, l b It can be expressed as n,r1,r2,l a ,d,l b function, and according to the focal length calculation formula, r2 can be expressed as a function of n, r1, la, d, so Φ(n, r1, r2, l a ,d,l b )=0 can be transformed into Φ(n,r1,f,l a ,d)=0, and after solving and simplifying, we can get the primary coma calculation formula.

[0061] For the above parameters n, r1, f and l a , once the lens material is determined, n is known, f and l a It is given by the lens parameters and the object distance, where the radius of curvature of the front surface vertex is a range of values. Under the primary coma calculation formula, according to the range of the radius of curvature of the front surface vertex and d, r2 and l are calculated.b and y b .

[0062] In one possible implementation, the two endpoints of the range of the front surface vertex curvature radius are the minimum front surface vertex curvature radius and the maximum front surface vertex curvature radius; and calculating the back surface curvature radius and image point parameters based on the range of the front surface vertex curvature radius and the center thickness of the lens may include:

[0063] Calculating a first primary astigmatism coefficient for the maximum front surface vertex curvature radius, and calculating a second primary astigmatism coefficient for the minimum front surface vertex curvature radius;

[0064] determining whether a product of the first primary astigmatism coefficient and the second primary astigmatism coefficient is less than 0;

[0065] If the product of the first primary astigmatism coefficient and the second primary astigmatism coefficient is less than 0, a bisection method is used to narrow the value range of the radius of curvature of the vertex of the front surface;

[0066] calculating a third primary astigmatism coefficient for all curvature radii within a value range of the reduced front surface vertex curvature radius;

[0067] If the absolute value of the third primary astigmatism coefficient corresponding to a curvature radius in the reduced value range of the front surface vertex curvature radius is greater than the preset value, the process returns to the step of reducing the value range of the front surface vertex curvature radius using the dichotomy method and continues until the absolute values of the third primary astigmatism coefficients corresponding to all curvature radii in the reduced value range of the front surface vertex curvature radius are no greater than the preset value, and any curvature radius in the current reduced value range of the front surface vertex curvature radius is used as the target curvature radius;

[0068] If the product of the first primary astigmatism coefficient and the second primary astigmatism coefficient is not less than 0, calculating the fourth primary astigmatism coefficient for all curvature radii within the value range of the front surface vertex curvature radius, and selecting the minimum value among the absolute values of the fourth primary astigmatism coefficients corresponding to all curvature radii as the target curvature radius;

[0069] Input the target curvature radius and the center thickness of the lens into the first formula to calculate the back surface curvature radius and image point parameters;

[0070] The first formula is:

[0071]

[0072] Where r2 is the radius of curvature of the rear surface, l b is the distance between the vertex of the back surface sphere and the image plane where the image point is located, y b is the image point height.

[0073] Since the equation for correcting primary astigmatism is relatively complex to solve and calculate, and it is relatively easy to calculate primary astigmatism through lens parameters, in the embodiment of the present application, a numerical calculation method is used to obtain the primary astigmatism coefficient as 0, and then the primary coma calculation formula is solved to remove inappropriate solutions, and d is calculated. Combining the parameters n, r1, and f, r2 can be calculated, and then l is calculated by the Gaussian formula. b , thus completing the calculation of the primary parameters for correcting primary coma and primary astigmatism. Since r1 corresponding to the correction of primary astigmatism cannot be predicted, it is necessary to initially set the value range of the front surface vertex curvature radius according to the parameters. The two endpoints of the value range are the minimum front surface vertex curvature radius r min and the maximum front surface vertex curvature radius r max , that is, the range of the curvature radius of the front surface vertex is [r min ,f max ].

[0074] The process of solving the curvature radius of the front surface vertex is:

[0075] Step 1: According to [r min ,r max ], for r max Calculate the first primary astigmatism coefficient S III (r max ), for r min Calculate the second primary astigmatism coefficient S III (r mib );

[0076] Step 2: Calculate S III (r min )·S III (r max ), and judge S III (r min )·S III (r max ) is less than 0:

[0077] Step 3: If S III (r min )·S III (r max ) is less than 0, the bisection method is used to further narrow the value range of the front surface vertex curvature radius, and the third primary astigmatism coefficient S′ is calculated for all curvature radii in the narrowed value range of the front surface vertex curvature radius. III (r1), and for S′ III (r1) takes the absolute value, i.e. |S′ III (r1)|;

[0078] Step 4: Determine |S′ III(r1)| is greater than the preset value? If so, return to step 3 and continue until |S′ III (r1)| is not greater than a preset value, and any curvature radius within the value range of the curvature radius of the vertex of the front surface after the current reduction is used as the target curvature radius, where the target curvature radius is a value range. Since after the bisection method is used, any curvature radius that meets the requirements can be used as the target curvature radius, any one can be selected when using it;

[0079] Step 5: If S III (r min )·S III (r max ) is not less than 0, then [r min ,r max ] calculate the fourth primary astigmatism coefficient S″ III (r1), and for S″ III (r1) takes the absolute value, i.e. |S″ III (r1)|, and select |S″ III The smallest value in (r1)|, namely |S″ III (r1)| min , change |S″ III (r1)| min The corresponding curvature radius is used as the target curvature radius, that is, the target curvature radius r1.

[0080] After calculating the target curvature radius r1 and d, combined with n, f, l a and y a , according to the first formula, calculate r2, l b and y b .

[0081] In step 203, based on the Fermat principle, the lens is corrected for spherical aberration according to the lens refractive index, the center thickness of the lens, the distance between the front surface vertex and the object plane where the object point is located, the distance between the back surface spherical vertex and the image plane where the image point is located, and the back surface curvature radius to obtain discrete points of the aspheric surface.

[0082] According to n, l a ,d,l b and r2, and under the constraints of primary coma correction and primary astigmatism correction, the spherical aberration of the lens is corrected using the Fermat principle, that is, the path of the object point P on the optical axis of the lens transmitted to the image point P' through the front and back surfaces of the lens satisfies the Fermat principle so that the on-axis point aberration is completely corrected, and the aspheric surface discrete point is obtained.

[0083] In a possible implementation, the aspherical surface discrete points include the aspherical surface discrete point coordinates (z pi ,h pi); where z pi h is the distance between the first intersection point corresponding to each discrete angle and the y-axis in the yoz coordinate system, pi is the distance between the first intersection point corresponding to each discrete angle and the optical axis; where the yoz coordinate system is established with the optical axis of the lens as the z-axis, the vertex of the front surface of the lens as the origin o, and the straight line passing through the origin o and parallel to the line connecting the object point and the off-axis object point as the y-axis;

[0084] Step 203 may specifically include:

[0085] Discretize the angle between the line connecting the second intersection point and the center of the back surface and the optical axis into N discrete angles, where the second intersection point is the intersection point of the light incident from the object point and the back surface;

[0086] Input the lens refractive index, lens center thickness, distance between the front surface vertex and the object plane where the object point is located, distance between the back surface spherical vertex and the image plane where the image point is located, and back surface curvature radius into the Fermat principle formula to obtain the distance between the first intersection point corresponding to each discrete angle and the optical axis and the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis direction;

[0087] Calculate the distance between the first intersection point corresponding to each discrete angle and the y-axis based on the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis;

[0088] The Fermat principle formula is:

[0089]

[0090] Among them, l a is the distance between the vertex of the front surface and the object plane where the object point is located, n is the refractive index of the lens, d is the center thickness of the lens, l b is the distance between the vertex of the spherical surface of the back surface and the image plane where the image point is located, r2 is the radius of curvature of the back surface, h pi is the distance between the first intersection point corresponding to each discrete angle and the optical axis, L 0i is the distance between the second intersection point and the image point corresponding to each discrete angle, L 1i is the distance between the first intersection point and the second intersection point corresponding to each discrete angle, L 2i is the distance between the object point and the first intersection point corresponding to each discrete angle, α i is the angle between the incident light from the object point and the optical axis after passing through the front surface, θ i is the i-th discrete angle, u i is the angle between the direction of the outgoing light beam and the optical axis after the incident light from the object point is refracted by the rear surface, corresponding to each discrete angle, z 1iis the projection distance along the optical axis of the line segment composed of the second intersection point corresponding to each discrete angle and the image point, z 2i is the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis, and i is any one of the N discrete angles.

[0091] According to see Figure 3 From the yoz coordinate system, we can know that the coordinates of discrete points on the aspherical surface (z pi ,h pi ), z pi For each discrete angle θ i The distance between the corresponding first intersection point A and the y-axis, h pi is the distance between the first intersection point A and the optical axis (z axis) corresponding to each discrete angle, where h pi This is consistent with the lens radius hole height h in step 202 .

[0092] Discretize the angle between the line connecting the second intersection point B and the center of the back surface and the optical axis into N discrete angles θ i , according to the Fermat principle formula, and combined with n, d, l a 、l b and r2, calculate h pi The projection distance z of the line segment formed by the first intersection point A corresponding to each discrete angle and the image point P' along the optical axis 2i , and according to z 2i Calculate z pi .

[0093] In one possible implementation, calculating the distance between the first intersection point corresponding to each discrete angle and the y-axis based on the projection distance from the first intersection point corresponding to each discrete angle to the image point along the optical axis may include:

[0094] The projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis, the distance between the vertex of the rear surface spherical surface and the image plane where the image point is located, and the center thickness of the lens are input into the second formula to calculate the distance between the first intersection point corresponding to each discrete angle and the y-axis. The second formula is:

[0095] z pi = b +- 2i (=1…N)

[0096] Among them, z pi is the distance between the first intersection point and the y-axis corresponding to each discrete angle, l b is the distance between the vertex of the spherical surface of the back surface and the image plane where the image point is located, d is the center thickness of the lens, z 2iis the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis, N is the number of discrete angles, and i is any one of the N discrete angles.

[0097] According to z 2i 、l b and d, calculate z by the second formula pi , by z pi and h pi Together they form the coordinates of discrete points on the aspherical surface (z pi ,h pi ).

[0098] In step 204, the aspheric lens coefficients are obtained according to the aspheric surface discrete points.

[0099] According to the discrete point coordinates (z pi ,h pi ), calculate the aspheric lens coefficients.

[0100] In a possible implementation, step 204 may specifically include:

[0101] Based on the curvature radius of the front surface vertex, the aspheric surface discrete points are converted into a first data group and a second data group. The first data group includes the first data, and the second data group includes the second data. The calculation formula of the first data is:

[0102]

[0103] Among them, y pi is the first data corresponding to the i-th discrete angle, and N is the number of discrete angles;

[0104] The calculation formula for the second data is:

[0105]

[0106] Among them, x pi is the second data;

[0107] Taking the first data as the dependent variable and the second data as the independent variable, a linear fit is performed, and the cone coefficient is obtained based on the coefficient in the linear fit formula;

[0108] calculating a first constant based on the cone coefficient and the radius of curvature of the front surface vertex;

[0109] Calculating the distance between the first intersection point corresponding to each discrete angle and the y-axis based on the first data after a linear fit, and obtaining the distance between the first intersection point corresponding to each discrete angle and the y-axis after fitting;

[0110] The distance between the first intersection point corresponding to each discrete angle and the optical axis is used as the independent variable, and the distance between the first intersection point corresponding to each discrete angle after fitting and the y-axis is used as the dependent variable. The linear least squares method is used to perform even-order polynomial fitting, and in the process of even-order polynomial fitting, the constant in the even-order polynomial fitting formula is limited to the first constant to obtain the polynomial coefficients in the even-order polynomial fitting formula, and the polynomial coefficients in the even-order polynomial fitting formula are used as the aspheric lens coefficients.

[0111] In the embodiment of the present application, r1 is used to convert the coordinates of the discrete points on the aspherical surface (z pi ,h pi ) is converted into a first data group and a second data group, wherein the first data group includes the first data y pi ,Right now The second data group includes second data x pi ,Right now y pi As the dependent variable, x pi As an independent variable, input into the first fitting formula to obtain the cone coefficient k, where the first fitting formula is:

[0112] y pi =(k+1)x pi (i=1…N).

[0113] Calculate the first constant from k and r1 According to the y after a fitting pi Calculate the distance z' between the first intersection point A and the y-axis corresponding to each discrete angle after fitting pi After that, h pj As the independent variable, z' pi As the dependent variable, the linear least square method is used to fit the even-order polynomial, and the constant in the even-order polynomial fitting formula is limited to the first constant, and the polynomial coefficients a4, a6, a8, a in the even-order polynomial fitting formula are obtained. 10 、a 12 、a 14 The polynomial coefficients in the even-order polynomial fitting formula are used as the aspheric lens coefficients, namely the first aspheric lens coefficient a4, the second aspheric lens coefficient a6, the third aspheric lens coefficient a8, the fourth aspheric lens coefficient a 10 , the fifth aspheric lens coefficient a 12 , the sixth aspheric lens coefficient a 14 .

[0114] In one possible implementation, the even-order polynomial fitting formula is:

[0115]

[0116] in, is the first constant, a4 is the first aspheric lens coefficient, a6 is the second aspheric lens coefficient, a8 is the third aspheric lens coefficient, a 10 is the fourth aspheric lens coefficient, a 12 is the fifth aspheric lens coefficient, a 14 is the sixth aspheric lens coefficient.

[0117] In the embodiment of the present application, according to the even-order polynomial fitting formula, Take the minimum value to solve the even-order polynomial fitting formula. The specific solution process is as follows:

[0118] Convert the even-order polynomial fitting formula into the linear least squares method to solve M N×6 a 6×1 -z pN×1 The minimum value of the weighted average sum is obtained to obtain the coefficient matrix, that is, the aspheric lens coefficient.

[0119] Among them, the linear matrix is:

[0120]

[0121] The coefficient matrix is:

[0122] a 6×1 =[a4 a6 a8 a 10 a 12 a 14 ] T

[0123] The vector is:

[0124] z pN×1 =[z p1 z p2 …z pN ] T

[0125] From the linear matrix, coefficient matrix and vector, we can get:

[0126] a 6×1 =(M N×6 T M N×6 ) -1 M N×6 T z pN×1

[0127] Where T is the transpose of the matrix.

[0128] According to the polynomial coefficients a4, a6, a8, a 10 、a 12 、a 14, can be selected according to the error value of numerical calculation. When the fitting surface error is 100nm, the predetermined accuracy can be achieved and the fitting order can be reduced, that is, the highest polynomial coefficient is a 14 Reduced to a 12 Or lower; when the fitting surface error does not meet the accuracy requirements, the fitting order can be increased and the highest order term can be changed to a 16 Or higher.

[0129] This application provides a method for correcting lens astigmatism. This method corrects lens astigmatism by first correcting primary astigmatism and primary coma, and then correcting spherical aberration. This method solves the problems of imaging balance in small-angle fields of view and in different directions (meridian and sagittal planes), improves the optical properties and applicability of the lens, and solves the aspheric lens coefficients by using discrete points of the aspheric surface shape, which greatly reduces the professional requirements for designers and is simple and convenient to operate.

[0130] The above lens astigmatism correction method is described below through an embodiment.

[0131] Take a Qiming lens used for receiving as an example to illustrate the above lens astigmatism correction method. When the laser operating wavelength is 670.0nm, H-LAK54_MOLD glass is selected as the lens material, and the corresponding n is 1.7235, only f = 12.00mm, h = 3.30mm, l a =500.00mm,y a =8.82mm, then we can start the calculation.

[0132] See also Figure 4 , the initial setting of the front surface vertex curvature radius range is [-533.60mm, -112.00mm], and the corresponding primary astigmatism coefficient is calculated to meet S III (r min )·S III (r max )<0, then continuously narrow the calculation range of r1 from range 1, range 2, range 3, to range 4, solve the range and constrain the absolute value of the calculated primary astigmatism coefficient to the preset value ε=10 -9 In, so that |S III (r1)|≤ε, we get r1=-183.60, and the corresponding d=8.45, l b =12.52 and y b =-0.21. In the entire calculation range, the primary coma coefficient S II It is always 0, indicating that the above process is carried out under the constraint of correcting the primary coma, and the results are in line with expectations.

[0133] After calculation based on the above initial parameters, the aspheric lens coefficients are obtained by combining the Fermat principle with the law of refraction and numerical fitting, as shown in Table 1.

[0134] Table 1 Parameters of the Qiming lens obtained in the embodiment of this application

[0135]

[0136] In order to verify the transparent performance of the Qiming lens designed according to the lens astigmatism correction method described above, the optical simulation software was used to model and evaluate the transparent performance of the Qiming lens parameters in Table 1 obtained from this application. The primary aberration coefficient calculated by the optical simulation shows that S II and S III Both are 0, that is, the primary coma and primary astigmatism are corrected, while the primary spherical aberration is left. The spherical aberration is then completely corrected by the aspheric surface, rather than being corrected under the spherical aberration constraint, which is different from the ordinary Qiming lens. Figure 5 The lens has a meniscus shape, which is similar to the shape of a commonly used landscape lens, but the lens has better performance and can achieve ideal imaging of different fields of view within a larger relative aperture range. Figure 6 The simulation results show that the geometric radius distribution of the point diagram at different fields of view or object point heights of 0.00mm, 6.00mm, and 8.82mm is 0.53, 0.52, and 0.49, respectively. The image points are distributed in a uniform circular pattern, and all the image points are within the Airy radius, indicating that the lens meets the diffraction limit conditions in all three fields of view. The wavefront aberration in different fields of view is less than 1 / 4 wavelength, achieving ideal imaging. The aberration curves in the meridian and sagittal planes are all within 0.60, and due to the elimination of primary astigmatism, the characteristics of the meridian and sagittal planes are quite consistent, with no obvious differences. The marginal rays are slightly blocked, and its actual relative aperture is slightly smaller, with an F-number close to 2.25.

[0137] The effectiveness and applicability of the above lens astigmatism correction method are demonstrated by comparing it with a lens from the lens library of lens supplier Thorlabs. The selected single lens is numbered A375, with an f value of 7.49mm, an h value of 4.50mm, and a lens material of H-LAK54_MOLD glass. The laser operating wavelength is 810.00nm, corresponding to n = 1.7179. The rear surface of the lens is spherical, and the object plane is at infinity. The corresponding field of view angles are: 0.0°, 1.0°, 2.0°, and 3.0°. The front surface is aspherical and coincides with the aperture surface. The lens parameters are shown in Table 2.

[0138] Table 2 Lens parameters for commercial model A375 in the Thorlabs lens library

[0139]

[0140] According to this application, f and h are set, as well as the material and operating wavelength are the same as A375, and the following parameters are obtained: f = 7.49, h = 2.25, l a =10 10 mm, the corresponding field of view angles are: 0.0°, 1.0°, 2.0°, 3.0°, and the corresponding primary astigmatism coefficient is calculated by selecting the front surface vertex curvature radius range, which does not meet the S III (r min )· III (r max )<0, within the selected range, when r1=137.70, the absolute value of the primary astigmatism coefficient is the smallest, making |S III (r1)|=2.5×10 -5 , the primary astigmatism is well corrected, and the following lens parameters are calculated, as shown in Table 3.

[0141] Table 3 Lens parameters for comparing A375 lens performance

[0142]

[0143] The two lenses have similar shapes, both exhibiting meniscus lens characteristics. The F-number, which measures relative aperture, is the same, both being 1.66. However, the curvature direction is different. The A375 is curved toward the image plane and has a certain primary astigmatism with an astigmatism coefficient of 1.6×10 -3 , and the lens in the embodiment of the present application is curved toward the object plane, see Figure 7 and Figure 8 .

[0144] Figure 9 and Figure 10The spot diagram, energy bracketing diagram, and aberration curves of the two lenses are shown. Simulations show that both lenses achieve diffraction-limited imaging at relatively small fields of view (FOV) of 0.0° and 1.0°. The energy bracketing diagram distribution is essentially concentrated within the Airy radius, and the aberration curves in the meridional and sagittal planes are relatively balanced and consistent. As the FOV increases to 2.0°, the aberration of the A375 increases rapidly, and the geometric radius of the spot diagram exceeds the Airy radius, reaching 5.45. Furthermore, the aberration curves in the meridional and sagittal planes show significant differences, with the meridional aberration being greater than the sagittal aberration. When the FOV continues to increase to 3.0°, the geometric radius of the spot diagram reaches 11.49, and the meridional aberration is nearly twice as large as the sagittal aberration. However, when the FOV of the lens of the embodiment of the present application increases to 2.0°, the geometric radius of the spot diagram is still less than the Airy radius, at 0.65. The energy bracketing diagram shows that all energies fall within the Airy radius, and the aberration curves in the meridional and sagittal planes remain balanced and consistent. When the field of view continues to increase to 3.0°, the geometric radius of the point diagram is 1.39, which is still smaller than the Airy radius. Differences begin to appear between the meridional aberration and the sagittal aberration, indicating that higher-order astigmatism begins to take effect. The overall off-axis aberration characteristics of its performance are better than those of A375, and ideal imaging can be achieved within the field of view of 0.0° to 3.0°.

[0145] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0146] The following are device embodiments of the present application. For details not fully described therein, please refer to the corresponding method embodiments described above.

[0147] Figure 11 A schematic diagram of the structure of a lens astigmatism correction device provided in an embodiment of the present application is shown. For ease of explanation, only the parts related to the embodiment of the present application are shown, which are detailed as follows:

[0148] like Figure 11 As shown, the lens astigmatism correction device 11 includes:

[0149] An acquisition module 111 is configured to acquire lens parameters and object point parameters, wherein the lens parameters include the lens refractive index and the lens focal length, and the object point parameters include the distance between the front surface vertex and the object plane where the object point is located and the height of the object point;

[0150] A first correction module 112 is configured to perform primary astigmatism correction and primary coma correction on the lens based on the lens parameters and the object point parameters, and obtain the lens center thickness, the front surface vertex curvature radius, the back surface curvature radius, and image point parameters. The image point parameters include the distance between the back surface spherical vertex and the image plane where the image point is located, and the image point height.

[0151] The second correction module 113 is configured to correct the spherical aberration of the lens based on the Fermat principle and the lens refractive index, the center thickness of the lens, the distance between the front surface vertex and the object plane where the object point is located, the distance between the back surface spherical vertex and the image plane where the image point is located, and the back surface curvature radius to obtain discrete points of the aspherical surface shape;

[0152] The determination module 114 is configured to obtain aspheric lens coefficients according to the aspheric surface discrete points.

[0153] The present application provides a lens astigmatism correction device. This device corrects lens astigmatism by first correcting primary astigmatism and primary coma, and then correcting spherical aberration. This corrects lens astigmatism, thereby addressing issues of imaging balance in small-angle fields of view and in different directions (meridian and sagittal planes), improving the optical properties and applicability of the lens. Furthermore, by solving the aspheric lens coefficients using discrete points of the aspheric surface, the device significantly reduces the professional requirements for designers, and provides simple and convenient operation.

[0154] In a possible implementation, the first correction module may be specifically configured to:

[0155] Based on the primary coma calculation formula, lens parameters and object point parameters, the primary coma correction of the lens is performed to obtain the value range of the front surface vertex curvature radius and the center thickness of the lens. The primary coma calculation formula is derived from the focal length calculation formula and primary aberration theory.

[0156] Calculate the back surface curvature radius and image point parameters based on the range of the front surface vertex curvature radius and the center thickness of the lens;

[0157] The focal length calculation formula is:

[0158]

[0159] Where f is the focal length, n is the refractive index of the lens, r1 is the radius of curvature of the front surface vertex, r2 is the radius of curvature of the back surface, and d is the center thickness of the lens;

[0160] The formula for calculating primary coma is:

[0161] S II =α4(n,r1,, a )d 4 +α3(n,r1,, a )d 3 +α2(n,r1,, a )d 2 +α1(n,r1,, a )d

[0162] +α0(n,r1,, a )=0

[0163] Among them, α4(n,r1,, a )=(l a -l a +1) 3 (f-nf+nr1) 2 (f-nf+n 2 r1);

[0164]

[0165]

[0166]

[0167]

[0168] Among them, S II To correct the primary coma coefficient, l a is the distance between the vertex of the front surface and the object plane where the object point is located, α0 is the first coefficient, α1 is the second coefficient, α2 is the third coefficient, α3 is the fourth coefficient, and α4 is the fifth coefficient.

[0169] In a possible implementation, two endpoints of the value range of the front surface vertex curvature radius are a minimum front surface vertex curvature radius and a maximum front surface vertex curvature radius; the first correction module may further be used to:

[0170] Calculating a first primary astigmatism coefficient for the maximum front surface vertex curvature radius, and calculating a second primary astigmatism coefficient for the minimum front surface vertex curvature radius;

[0171] determining whether a product of the first primary astigmatism coefficient and the second primary astigmatism coefficient is less than 0;

[0172] If the product of the first primary astigmatism coefficient and the second primary astigmatism coefficient is less than 0, a bisection method is used to narrow the value range of the radius of curvature of the vertex of the front surface;

[0173] calculating a third primary astigmatism coefficient for all curvature radii within a value range of the reduced front surface vertex curvature radius;

[0174] If the absolute value of the third primary astigmatism coefficient corresponding to a curvature radius in the reduced value range of the front surface vertex curvature radius is greater than the preset value, the process returns to the step of reducing the value range of the front surface vertex curvature radius using the dichotomy method and continues until the absolute values of the third primary astigmatism coefficients corresponding to all curvature radii in the reduced value range of the front surface vertex curvature radius are no greater than the preset value, and any curvature radius in the current reduced value range of the front surface vertex curvature radius is used as the target curvature radius;

[0175] If the product of the first primary astigmatism coefficient and the second primary astigmatism coefficient is not less than 0, calculating the fourth primary astigmatism coefficient for all curvature radii within the value range of the front surface vertex curvature radius, and selecting the minimum value among the absolute values of the fourth primary astigmatism coefficients corresponding to all curvature radii as the target curvature radius;

[0176] Input the target curvature radius and the center thickness of the lens into the first formula to calculate the back surface curvature radius and image point parameters;

[0177] The first formula is:

[0178]

[0179] Where r2 is the radius of curvature of the rear surface, l b is the distance between the vertex of the back surface sphere and the image plane where the image point is located, y b is the image point height.

[0180] In a possible implementation, the aspherical surface discrete points include the aspherical surface discrete point coordinates (z pi ,h pi ); where z pi h is the distance between the first intersection point corresponding to each discrete angle and the y-axis in the yoz coordinate system, pi is the distance between the first intersection point corresponding to each discrete angle and the optical axis; where the yoz coordinate system is established with the optical axis of the lens as the z-axis, the vertex of the front surface of the lens as the origin o, and the straight line passing through the origin o and parallel to the line connecting the object point and the off-axis object point as the y-axis;

[0181] The second correction module can be specifically used for:

[0182] Discretize the angle between the line connecting the second intersection point and the center of the back surface and the optical axis into N discrete angles, where the second intersection point is the intersection point of the light incident from the object point and the back surface;

[0183] Input the lens refractive index, lens center thickness, distance between the front surface vertex and the object plane where the object point is located, distance between the back surface spherical vertex and the image plane where the image point is located, and back surface curvature radius into the Fermat principle formula to obtain the distance between the first intersection point corresponding to each discrete angle and the optical axis and the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis direction;

[0184] Calculate the distance between the first intersection point corresponding to each discrete angle and the y-axis based on the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis;

[0185] The Fermat principle formula is:

[0186]

[0187] Among them, l a is the distance between the vertex of the front surface and the object plane where the object point is located, n is the refractive index of the lens, d is the center thickness of the lens, l b is the distance between the vertex of the spherical surface of the back surface and the image plane where the image point is located, r2 is the radius of curvature of the back surface, h pi is the distance between the first intersection point corresponding to each discrete angle and the optical axis, L 0i is the distance between the second intersection point and the image point corresponding to each discrete angle, L 1i is the distance between the first intersection point and the second intersection point corresponding to each discrete angle, L 2i is the distance between the object point and the first intersection point corresponding to each discrete angle, α i is the angle between the incident light from the object point and the optical axis after passing through the front surface, θ i is the i-th discrete angle, u i is the angle between the direction of the outgoing light beam and the optical axis after the incident light from the object point is refracted by the rear surface, corresponding to each discrete angle, z 1i is the projection distance along the optical axis of the line segment composed of the second intersection point corresponding to each discrete angle and the image point, z 2i is the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis, and i is any one of the N discrete angles.

[0188] In a possible implementation, the second correction module may also be used to:

[0189] The projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis, the distance between the vertex of the rear surface spherical surface and the image plane where the image point is located, and the center thickness of the lens are input into the second formula to calculate the distance between the first intersection point corresponding to each discrete angle and the y-axis. The second formula is:

[0190] z pi = b +- 2i (=1…N)

[0191] Among them, z pi is the distance between the first intersection point and the y-axis corresponding to each discrete angle, l b is the distance between the vertex of the spherical surface of the back surface and the image plane where the image point is located, d is the center thickness of the lens, z 2i is the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis, N is the number of discrete angles, and i is any one of the N discrete angles.

[0192] In a possible implementation, the determination module may be specifically used to:

[0193] Based on the curvature radius of the front surface vertex, the aspheric surface discrete points are converted into a first data group and a second data group. The first data group includes the first data, and the second data group includes the second data. The calculation formula of the first data is:

[0194]

[0195] Among them, y pi is the first data corresponding to the i-th discrete angle, and N is the number of discrete angles;

[0196] The calculation formula for the second data is:

[0197]

[0198] Among them, x pi is the second data;

[0199] Taking the first data as the dependent variable and the second data as the independent variable, a linear fit is performed, and the cone coefficient is obtained based on the coefficient in the linear fit formula;

[0200] calculating a first constant based on the cone coefficient and the radius of curvature of the front surface vertex;

[0201] Calculating the distance between the first intersection point corresponding to each discrete angle and the y-axis based on the first data after a linear fit, and obtaining the distance between the first intersection point corresponding to each discrete angle and the y-axis after fitting;

[0202] The distance between the first intersection point corresponding to each discrete angle and the optical axis is used as the independent variable, and the distance between the first intersection point corresponding to each discrete angle after fitting and the y-axis is used as the dependent variable. The linear least squares method is used to perform even-order polynomial fitting, and in the process of even-order polynomial fitting, the constant in the even-order polynomial fitting formula is limited to the first constant to obtain the polynomial coefficients in the even-order polynomial fitting formula, and the polynomial coefficients in the even-order polynomial fitting formula are used as the aspheric lens coefficients.

[0203] In one possible implementation, the even-order polynomial fitting formula is:

[0204]

[0205] in, is the first constant, a4 is the first aspheric lens coefficient, a6 is the second aspheric lens coefficient, a8 is the third aspheric lens coefficient, a 10 is the fourth aspheric lens coefficient, a 12 is the fifth aspheric lens coefficient, a 14 is the sixth aspheric lens coefficient.

[0206] Figure 12Schematic diagram of the terminal provided in the embodiment of the present application. Figure 12 As shown, the terminal 12 of this embodiment includes: a processor 120, a memory 121, and a computer program 122 stored in the memory 121 and executable on the processor 120. When the processor 120 executes the computer program 122, the steps in the above-mentioned lens astigmatism correction method embodiments are implemented, for example Figure 2 Alternatively, when the processor 120 executes the computer program 122, the functions of the modules / units in the above-mentioned device embodiments are realized, for example, Figure 11 Functions of modules 111 to 114 are shown.

[0207] For example, the computer program 122 may be divided into one or more modules, which are stored in the memory 121 and executed by the processor 120 to complete the present application. The one or more modules may be a series of computer program instruction segments that can complete specific functions, and the instruction segments are used to describe the execution process of the computer program 122 in the terminal 12. For example, the computer program 122 may be divided into Figure 11 Modules 111 to 114 are shown.

[0208] The terminal 12 may be a computing device such as a desktop computer, a notebook, a PDA, or a cloud server. The terminal 12 may include, but is not limited to, a processor 120 and a memory 121. Those skilled in the art will understand that Figure 12 It is only an example of the terminal 12 and does not constitute a limitation on the terminal 12. The terminal may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the terminal may also include input and output devices, network access devices, buses, etc.

[0209] The processor 120 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0210] The memory 121 may be an internal storage unit of the terminal 12, such as a hard disk or memory of the terminal 12. The memory 121 may also be an external storage device of the terminal 12, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the terminal 12. Furthermore, the memory 121 may include both an internal storage unit of the terminal 12 and an external storage device. The memory 121 is used to store the computer program and other programs and data required by the terminal. The memory 121 may also be used to temporarily store data that has been output or is about to be output.

[0211] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In actual applications, the above-mentioned functions can be distributed and completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0212] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0213] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0214] In the embodiments provided in this application, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For example, the division of the modules or units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0215] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0216] In addition, the functional units in the various embodiments of the present application may be integrated into a single processing unit, or each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0217] If the integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present application implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of the above-mentioned lens astigmatism correction method embodiments. The computer program includes computer program code, which can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal and software distribution medium. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practices in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practices, computer-readable media does not include electrical carrier signals and telecommunication signals.

[0218] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A method for correcting lens astigmatism, characterized in that: The method is applied to a Qiming lens, which consists of a front surface and a back surface, wherein the front surface is aspherical and the back surface is spherical. The method includes: Obtaining lens parameters and object point parameters, wherein the lens parameters include the lens refractive index and the lens focal length, and the object point parameters include the distance between the front surface vertex and the object plane where the object point is located and the height of the object point; Performing primary astigmatism correction and primary coma correction on the lens based on the lens parameters and the object point parameters to obtain the lens center thickness, the front surface vertex curvature radius, the back surface curvature radius and image point parameters, wherein the image point parameters include the distance between the back surface spherical vertex and the image plane where the image point is located and the image point height; wherein, performing primary coma correction on the lens based on the primary coma calculation formula, the lens parameters and the object point parameters to obtain the value range of the front surface vertex curvature radius and the lens center thickness; using a dichotomy method, calculating the primary astigmatism coefficient based on the two endpoints of the value range of the front surface vertex curvature radius, narrowing the value range of the front surface vertex curvature radius to obtain a target curvature radius, and calculating the back surface curvature radius and the image point parameters based on the target curvature radius and the lens center thickness; Based on the Fermat principle, the lens is corrected for spherical aberration according to the refractive index of the lens, the center thickness of the lens, the distance between the vertex of the front surface and the object plane where the object point is located, the distance between the vertex of the spherical surface of the rear surface and the image plane where the image point is located, and the curvature radius of the rear surface, to obtain discrete points of the aspherical surface type; According to the aspheric surface discrete points, the aspheric lens coefficients are obtained.

2. The lens astigmatism correction method according to claim 1, wherein: The primary coma calculation formula is derived from the focal length calculation formula and the primary aberration theory. The focal length calculation formula is: Wherein, f is the focal length, n is the refractive index of the lens, r1 is the radius of curvature of the front surface vertex, r2 is the radius of curvature of the back surface, and d is the center thickness of the lens; The primary coma calculation formula is: S II =α4(n,r1,f,l a )d 4 +α3(n,r1,f,l a )d 3 +α2(n,r1,f,l a )d 2 +α1(n,r1,f,l a )d+α0(n,r1,f,l a )=0 Among them, α4(n,r1,f,l a )=(l a -nl a +r1) 3 (f-nf+nr1) 2 (f-nf+n 2 r1); Among them, S II To correct the primary coma coefficient, l a is the distance between the vertex of the front surface and the object plane where the object point is located, α0 is the first coefficient, α1 is the second coefficient, α2 is the third coefficient, α3 is the fourth coefficient, and α4 is the fifth coefficient.

3. The lens astigmatism correction method according to claim 2, wherein: The two endpoints of the value range of the front surface vertex curvature radius are the minimum front surface vertex curvature radius and the maximum front surface vertex curvature radius; the primary astigmatism coefficient includes a first primary astigmatism coefficient and a second primary astigmatism coefficient, and the bisection method is used to calculate the primary astigmatism coefficient according to the two endpoints of the value range of the front surface vertex curvature radius, narrow the value range of the front surface vertex curvature radius to obtain a target curvature radius, and calculate the back surface curvature radius and image point parameters according to the target curvature radius and the center thickness of the lens, including: Calculating the first primary astigmatism coefficient for the maximum front surface vertex curvature radius, and calculating the second primary astigmatism coefficient for the minimum front surface vertex curvature radius; determining whether a product of the first primary astigmatism coefficient and the second primary astigmatism coefficient is less than 0; If the product of the first primary astigmatism coefficient and the second primary astigmatism coefficient is less than 0, a bisection method is used to narrow the value range of the curvature radius of the front surface vertex; calculating a third primary astigmatism coefficient for all curvature radii within the reduced value range of the vertex curvature radius of the front surface; If the absolute value of the third primary astigmatism coefficient corresponding to a curvature radius in the reduced value range of the front surface vertex curvature radius is greater than a preset value, returning to the step of reducing the value range of the front surface vertex curvature radius using the bisection method and continuing until the absolute values of the third primary astigmatism coefficients corresponding to all curvature radii in the reduced value range of the front surface vertex curvature radius are no greater than the preset value, and taking any curvature radius in the current reduced value range of the front surface vertex curvature radius as the target curvature radius; If the product of the first primary astigmatism coefficient and the second primary astigmatism coefficient is not less than 0, calculating a fourth primary astigmatism coefficient for all curvature radii within a value range of the front surface vertex curvature radius, and selecting a minimum value among the absolute values of the fourth primary astigmatism coefficients corresponding to all curvature radii as a target curvature radius; Inputting the target curvature radius and the center thickness of the lens into a first formula to calculate the back surface curvature radius and image point parameters; The first formula is: Wherein, r2 is the radius of curvature of the rear surface, l b is the distance between the vertex of the spherical surface of the back surface and the image plane where the image point is located, y b is the image point height.

4. The lens astigmatism correction method according to claim 1, wherein: The aspheric surface discrete points include the aspheric surface discrete point coordinates (z pi ,h pi ); where z pi h is the distance between the first intersection point corresponding to each discrete angle and the y-axis in the yoz coordinate system, pi is the distance between the first intersection point corresponding to each discrete angle and the optical axis; wherein the yoz coordinate system is established with the optical axis of the lens as the z-axis, the vertex of the front surface of the lens as the origin o, and the straight line passing through the origin o and parallel to the line connecting the object point and the off-axis object point as the y-axis; The method of performing spherical aberration correction on the lens based on the Fermat principle according to the lens refractive index, the center thickness of the lens, the distance between the front surface vertex and the object plane where the object point is located, the distance between the back surface spherical vertex and the image plane where the image point is located, and the back surface curvature radius to obtain aspheric surface discrete points includes: Discretize the angle between the line connecting the second intersection point and the center of the back surface and the optical axis into N discrete angles, where the second intersection point is the intersection point of the light incident from the object point and the back surface; Inputting the lens refractive index, the lens center thickness, the distance between the front surface vertex and the object plane where the object point is located, the distance between the back surface spherical vertex and the image plane where the image point is located, and the back surface curvature radius into the Fermat principle formula, the distance between the first intersection point corresponding to each discrete angle and the optical axis and the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis are obtained; Calculate the distance between the first intersection point corresponding to each discrete angle and the y-axis based on the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis; The Fermat principle formula is: Among them, l a is the distance between the vertex of the front surface and the object plane where the object point is located, n is the refractive index of the lens, d is the center thickness of the lens, l b is the distance between the vertex of the spherical surface of the back surface and the image plane where the image point is located, r2 is the radius of curvature of the back surface, h pi is the distance between the first intersection point corresponding to each discrete angle and the optical axis, L 0i is the distance between the second intersection point and the image point corresponding to each discrete angle, L 1i is the distance between the first intersection point and the second intersection point corresponding to each discrete angle, L 2i is the distance between the object point and the first intersection point corresponding to each discrete angle, α i is the angle between the incident light from the object point and the optical axis after passing through the front surface, θ i is the i-th discrete angle, u i is the angle between the direction of the outgoing light beam and the optical axis after the incident light from the object point is refracted by the rear surface, corresponding to each discrete angle, z 1i is the projection distance along the optical axis of the line segment composed of the second intersection point corresponding to each discrete angle and the image point, z 2i is the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis, and i is any one of the N discrete angles.

5. The lens astigmatism correction method according to claim 4, wherein: The calculating the distance between the first intersection point corresponding to each discrete angle and the y-axis based on the projection distance from the first intersection point corresponding to each discrete angle to the image point along the optical axis includes: The projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis, the distance between the vertex of the spherical surface of the rear surface and the image plane where the image point is located, and the center thickness of the lens are input into a second formula to calculate the distance between the first intersection point corresponding to each discrete angle and the y-axis. The second formula is: z pi =l b +d-z 2i (i=1…N) Among them, z pi is the distance between the first intersection point corresponding to each discrete angle and the y-axis, l b is the distance between the vertex of the spherical surface of the rear surface and the image plane where the image point is located, d is the center thickness of the lens, z 2i is the projection distance of the line segment formed by the first intersection point corresponding to each discrete angle and the image point along the optical axis direction, N is the number of discrete angles, and i is any one of the N discrete angles.

6. The lens astigmatism correction method according to claim 4, wherein: The aspheric lens coefficients are obtained according to the aspheric surface discrete points, including: The aspheric surface discrete points are converted into a first data group and a second data group based on the front surface vertex curvature radius, wherein the first data group includes first data, and the second data group includes second data. The calculation formula of the first data is: Among them, y pi is the first data corresponding to the i-th discrete angle, and N is the number of discrete angles; The calculation formula of the second data is: Among them, x pi is the second data; Performing a linear fit using the first data as a dependent variable and the second data as an independent variable, and obtaining a cone coefficient based on the coefficients in the linear fit formula; Calculating a first constant based on the cone coefficient and the front surface vertex curvature radius; Calculating the distance between the first intersection point corresponding to each discrete angle and the y-axis based on the first data after a linear fit, and obtaining the distance between the first intersection point corresponding to each discrete angle and the y-axis after fitting; The distance between the first intersection point corresponding to each discrete angle and the optical axis is used as the independent variable, and the distance between the first intersection point corresponding to each discrete angle after fitting and the y-axis is used as the dependent variable. The linear least squares method is used to perform even-order polynomial fitting, and during the even-order polynomial fitting process, the constant in the even-order polynomial fitting formula is limited to the first constant to obtain the polynomial coefficients in the even-order polynomial fitting formula, and the polynomial coefficients in the even-order polynomial fitting formula are used as the aspheric lens coefficients.

7. The lens astigmatism correction method according to claim 6, wherein: The even-order polynomial fitting formula is: in, is the first constant, a4 is the first aspheric lens coefficient, a6 is the second aspheric lens coefficient, a8 is the third aspheric lens coefficient, a 10 is the fourth aspheric lens coefficient, a 12 is the fifth aspheric lens coefficient, a 14 is the sixth aspheric lens coefficient.

8. A lens astigmatism correction device, characterized in that: The device is applied to a Qiming lens, which is composed of a front surface and a rear surface, wherein the front surface is aspherical and the rear surface is spherical. The device includes: an acquisition module, configured to acquire lens parameters and object point parameters, wherein the lens parameters include the lens refractive index and the lens focal length, and the object point parameters include the distance between the front surface vertex and the object plane where the object point is located and the height of the object point; a first correction module, configured to perform primary astigmatism correction and primary coma correction on the lens based on the lens parameters and the object point parameters, to obtain a lens center thickness, a front surface vertex curvature radius, a back surface curvature radius, and image point parameters, wherein the image point parameters include a distance between a back surface spherical vertex and an image plane where the image point is located, and an image point height; wherein, based on a primary coma calculation formula, the lens parameters, and the object point parameters, the lens is subjected to primary coma correction to obtain a value range of the front surface vertex curvature radius and a lens center thickness; a bisection method is used to calculate a primary astigmatism coefficient based on two endpoints of the value range of the front surface vertex curvature radius, the value range of the front surface vertex curvature radius is narrowed to obtain a target curvature radius, and the back surface curvature radius and the image point parameters are calculated based on the target curvature radius and the lens center thickness; a second correction module, configured to perform spherical aberration correction on the lens based on the Fermat principle and according to the lens refractive index, the center thickness of the lens, the distance between the front surface vertex and the object plane where the object point is located, the distance between the back surface spherical vertex and the image plane where the image point is located, and the back surface curvature radius, to obtain aspheric surface discrete points; The determination module is used to obtain the aspheric lens coefficient according to the aspheric surface discrete points.

9. A terminal comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the lens astigmatism correction method according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the lens astigmatism correction method according to any one of claims 1 to 7 are implemented.

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