Optimal design method of tilt term coefficients of alvarez lens

Abstract

The application discloses a kind of optimal tilt term coefficient design methods of Alvarez lens. Including according to preliminary optical design, the surface form coefficient of vertical axis zoom lens and effective light range are determined;The vertical axis zoom lens is composed of two pieces of Alvarez lens, two pieces of lens have a free surface and a plane respectively, the free surface surface form of the two pieces of lens is same;According to surface form coefficient and light range requirement, the sag of effective surface form range is calculated by discrete sampling, the sag difference of the highest point and the lowest point of surface form is calculated;Change the first tilt term of vertical axis moving direction in surface form coefficient;Repeat the above process until the maximum and minimum value difference of surface form sag obtained is greater than or equal to the value obtained in last iteration, the tilt term coefficient value at this time is optimal tilt term coefficient value.The application effectively reduces the surface form sag change of vertical axis zoom lens, reduces the air gap in assembly stage, improves the compact structure, realizes the image quality improvement of imaging system.

Description

Technical Field

[0001] This invention relates to vertical axis zoom imaging systems, and more specifically to a method for designing the optimal tilt term coefficient of an Alvarez lens. Background Technology

[0002] In 1967, Luis W. Alvarez proposed a lens assembly with variable optical power, comprising two freeform lenses. Each lens has one freeform surface and one flat surface, and the freeform surfaces are identical. In a Cartesian coordinate system, with the z-axis as the optical axis, the surface elevation z is a function of x and y, expressed by the formula:

[0003]

[0004] Where A is the surface profile coefficient. Therefore, the thicknesses t1 and t2 of the two lenses can be expressed as follows:

[0005] t1(x,y)=C1+z(x,y), t2(x,y)=C2-z(x,y)

[0006] Where C1 and C2 are the center thicknesses of the two lenses, respectively. Therefore, the superimposed thickness T of the two lenses is:

[0007] T(x,y)=t1(x,y)+t2(x,y)

[0008] When the two lenses are displaced by d and -d perpendicularly in the x-direction respectively, the superimposed thickness T of the two lenses becomes:

[0009] T(x,y)=t1(xd,y)+t2(x+d,y)

[0010] If this lens combination is considered as a thin lens, the focal length f of the transverse zoom lens group is:

[0011]

[0012] Where A is the aspect ratio, d is the transverse displacement, and n is the refractive index of the lens material. This lens combination, which uses transverse axis movement to change optical power, is now also known as an Alvarez lens. This method allows for a wider focal length tuning range and reduces the overall length of the zoom imaging system.

[0013] A transverse zoom imaging system can be achieved by using two sets of Alvarez lenses, one as the zoom group and the other as the compensation group. Since the basic surface in this system is a cubic surface, increasing the aperture will cause a sharp increase in the surface sagitta. Therefore, in order to prevent the lenses from rubbing against each other during bidirectional transverse movement, the lens spacing must be increased or the surface sagitta change must be reduced.

[0014] To ensure system compactness and image quality, a tilt term is typically added to the lens to reduce the change in surface profile sagitta, i.e.:

[0015]

[0016] In this way, the stacking thickness T remains constant, reducing the change in surface height without altering the paraxial approximate optical power of the lens group. However, the optimal coefficient E cannot be obtained through optical simulation software optimization and must be calculated.

[0017] One current method for calculating the coefficient E involves performing a definite integral over the elevation of the surface within a quarter of the effective range (x>0, y>0) based on the surface symmetry, until the integral value is zero, and then determining the relationship between coefficient E and coefficient A. However, this method does not guarantee that the difference between the maximum and minimum elevation values ​​for the entire effective surface is minimized, and the integral calculation is extremely complex for Alvarez lenses with special contours other than square or circular shapes. Summary of the Invention

[0018] The purpose of this invention is to address the shortcomings of existing technologies by providing an optimal surface shape coefficient design method for vertical axis zoom lenses. By using known surface shape coefficients and light transmission range conditions, the optimal first tilt term coefficient of the Alvarez lens in the optical system is obtained, effectively reducing the range of surface shape elevation variation.

[0019] The purpose of this invention is achieved through the following technical solution: an iterative design method for the optimal surface coefficient of a vertical zoom lens, comprising the following steps: (1) determining the surface coefficient and effective light transmission range of the vertical zoom lens based on the preliminary optical design; the vertical zoom lens is composed of two Alvarez lenses, each of which has a freeform surface and a flat surface, and the freeform surfaces of the two lenses have the same surface shape;

[0020] (2) Based on the surface shape coefficient and the effective light transmission range requirements, the sag within the effective surface shape range is calculated by discrete sampling, and the sag difference between the highest and lowest points of the surface shape is calculated.

[0021] (3) The first tilt term in the surface coefficient that changes the direction of vertical axis movement;

[0022] (4) Repeat steps (2) and (3) until the difference between the maximum and minimum values ​​of the surface elevation is greater than or equal to the value obtained in the previous iteration. The value of the tilt term coefficient at this time is the optimal tilt term coefficient value.

[0023] Further, step (1) specifically includes:

[0024] (1.1) Add a vertical zoom system containing an Alvarez lens group in the optical simulation software, set the surface coefficient A, add the vertical axis eccentricity value required by the design target to the plane of the Alvarez lens group, and record the semi-aperture value of the major axis in the plane as L; if the Alvarez lens group is displaced vertically in the x direction, then 2L is the effective light transmission length of the Alvarez lens group in the x direction.

[0025] (1.2) Add a standard plane before and after the coordinate breakpoint of the Alvarez lens group, and record the minor axis semi-aperture value of the two planes as R. Then 2R is the effective light transmission aperture of the Alvarez lens group.

[0026] (1.3) Based on the short axis semi-aperture value R obtained in step (1.1) and the long axis semi-aperture value L obtained in step (1.2), the effective light-transmitting aperture of the Alvarez lens group is determined to be a region with a width of 2R in the y direction, a distance of 2L between the two vertices in the x direction, and a semi-circle with a radius of R on both sides. That is, this region is the effective light-transmitting aperture of the Alvarez lens group.

[0027] Furthermore, the optical simulation software includes Zemax and CODE V.

[0028] Furthermore, step (2) specifically includes:

[0029] (2.1) Input the surface profile coefficient A, the major axis semi-diameter value L, and the minor axis semi-diameter value R;

[0030] (2.2) Set the sampling calculation precision according to the effective light transmission range, and combine it with the basic surface shape function to obtain the vector height matrix of each sampling point of the surface shape;

[0031] (2.3) Set a binary matrix with sampling points within the effective light transmission range as 1 and sampling points outside the effective light transmission range as 0, i.e., the light transmission mask matrix;

[0032] (2.4) Multiply the sag value matrix and the light transmission mask matrix by the point to obtain the surface sag within the effective aperture, and obtain the difference between the maximum and minimum values.

[0033] Further, in step (2.2), the basic surface type function is:

[0034] In step (3), the tilt term that changes the direction of vertical axis movement is called the first tilt term, and the surface shape function at this time is:

[0035]

[0036] Where n is the number of iterations and e is the step size.

[0037] Furthermore, the formula for the tilt term coefficient E is:

[0038] E = (n-1)e.

[0039] Furthermore, the optimal tilt term coefficient value is used to improve imaging quality.

[0040] The beneficial effects of this invention are:

[0041] 1. Reduced the surface profile sagitta of the vertical zoom lens;

[0042] 2. Reduced air gap during assembly, improving compactness;

[0043] 3. Reduce the degradation of image quality caused by changes in surface shape and air gaps. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a schematic diagram of the overall process of the method of the present invention;

[0046] Figure 2 Schematic diagram of effective aperture;

[0047] Figure 3 A flowchart illustrating the process of obtaining the difference in elevation between the highest and lowest points;

[0048] Figure 4 This is a schematic diagram of the zoom group and compensation group of a vertical axis zoom imaging system, showing the structure of the lens group before and after optimization under three optical power conditions: short focal length, medium focal length, and long focal length.

[0049] Figure 5 A schematic diagram comparing the dot plots obtained in simulation software before and after optimization of the short focal length structure of the vertical axis zoom imaging system;

[0050] Figure 6 This is a schematic diagram comparing the dot plots obtained in simulation software before and after optimization of the focal structure in a vertical axis zoom imaging system.

[0051] Figure 7 This is a schematic diagram comparing the dot plots obtained in simulation software before and after optimizing the telephoto structure of the vertical axis zoom imaging system. Detailed Implementation

[0052] The present invention will now be described in detail with reference to the accompanying drawings. Unless otherwise specified, the features of the following embodiments and implementations can be combined with each other.

[0053] This invention provides a method for designing the optimal tilt term coefficient of an Alvarez lens, such as... Figure 1 The diagram shown illustrates the process flow of the method of the present invention, which includes the following steps:

[0054] (1) Based on the preliminary optical design, determine the surface shape coefficient and effective light transmission range of the vertical axis zoom lens; the vertical axis zoom lens is composed of two Alvarez lenses, each of which has a freeform surface and a flat surface, and the freeform surfaces have the same surface shape.

[0055] (1.1) Add a vertical zoom system containing the Alvarez lens group in optical simulation software such as Zemax and CODE V (or you can program the simulation yourself), set the surface coefficient A, add the vertical axis eccentricity value required by the design target to the plane of the Alvarez lens group, and record the half-aperture value of the major axis in the plane as L; if the Alvarez lens is displaced vertically in the x direction, then 2L is the effective light transmission length of the Alvarez lens group in the x direction.

[0056] (1.2) Add a standard plane before and after the coordinate breakpoint of the Alvarez lens group, and record the semi-aperture value of the minor axis of the two planes as R. Then 2R is the effective light transmission aperture of the lens group.

[0057] (1.3) such as Figure 2 As shown, based on parameters L and R, the effective aperture of this lens group can be determined to be an effective aperture with a width of 2R in the y direction, a distance of 2L between the two vertices in the x direction, and two semicircles with a radius of R on each side, i.e., an oval shape.

[0058] (2) Based on the surface shape coefficient and the effective light transmission range requirements, the sag within the effective surface shape range is calculated by discrete sampling, and the sag difference between the highest and lowest points of the surface shape is calculated.

[0059] like Figure 3 As shown, step (2) specifically involves:

[0060] (2.1) Input the surface profile coefficient A, the major axis semi-diameter value L, and the minor axis semi-diameter value R;

[0061] (2.2) Set the sampling calculation accuracy according to the effective light transmission range, and combine it with the basic surface function. Find the vector height matrix of each sampling point of the surface shape.

[0062] (2.3) Set a binary matrix with sampling points within the effective light transmission range as 1 and sampling points outside the effective light transmission range as 0, i.e., mask matrix.

[0063] (2.4) Multiply the sag value matrix and the light transmission mask matrix by the point to obtain the surface sag within the effective aperture, and obtain the difference between the maximum and minimum values.

[0064] (3) The first-order tilt term of the vertical axis movement direction in the surface shape coefficient is changed according to the iteration number n and the step size e. At this time, the surface shape function is:

[0065]

[0066] (4) Repeat steps (2) and (3) until the difference between the maximum and minimum values ​​of the surface elevation is greater than or equal to the value obtained in the previous iteration. At this point, E = (n-1)e is the optimal tilt term coefficient value under the current surface shape, aperture, and calculation accuracy.

[0067] Table 1 lists the values ​​of A = 1.2 × 10⁻⁶. -3 Under the conditions of L=14, R=9 and sampling calculation accuracy of 0.01mm, the difference between the maximum and minimum values ​​of the sagitta within the effective surface area is calculated using three methods: without the first-order tilt term coefficient, adding a sagitta integral of 0, and the method described in this paper.

[0068] Table 1: Difference between maximum and minimum sagittal heights within the effective surface area under three conditions

[0069]

[0070] It is evident that this method yields a better slant term coefficient E.

[0071] like Figure 4 As shown, in a zoom imaging system employing two sets of Alvarez lenses, a certain air gap needs to be maintained between the lenses. Before optimization (E=0), the lens surface profile sag varies greatly. To prevent lens scratching during movement towards each other along the perpendicular axis, a large air gap is maintained. This air gap further increases during movement away from the perpendicular axis, reducing image quality. After optimization using this method, the lens surface profile sag values ​​are consistent in both the -x and +x directions. This effectively prevents lens scratching during both movement towards and away from the perpendicular axis, while maintaining a small air gap and good image quality.

[0072] Table 2 lists the overall simulation results, such as Figures 5-7 As shown, specifically, the RMS radius values ​​of the point array diagram at the five edge fields of view and the central field of view of the imaging system under three optical powers (long, medium, and short) before and after optimization.

[0073] Table 2: RMS radius of the point plots before and after optimization in three cases

[0074]

[0075] It is evident that this method effectively improves image quality.

[0076] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0077] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

[0078] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only.

[0079] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope.

Claims

1. A method for designing optimal tilt term coefficients of an Alvarez lens, characterized in that, The method comprises the following steps: (1) determining the surface profile coefficient and effective aperture range of the vertical zoom lens according to the preliminary optical design; the vertical zoom lens is composed of two Alvarez lenses, each of which has one free surface and one plane, and the free surfaces of the two lenses have the same surface profile; (2) calculating the sag of each sampling point in the effective surface profile range according to the surface profile coefficient and the effective aperture range requirement, and calculating the sag difference between the maximum and minimum points of the surface profile; (3) changing the first tilt term of the surface profile coefficient in the vertical movement direction; (4) repeating steps (2) and (3) until the maximum and minimum value difference of the surface profile sag reaches the minimum value, and the tilt term coefficient value at this time is the optimal tilt term coefficient value.

2. The method of claim 1, wherein the optimal coefficients of the Alvarez lens are determined by the following equation: ###0001### where, a is the coefficient of the Alvarez lens, n is the refractive index of the lens, d is the thickness of the lens, and f is the focal length of the lens. The step (1) is specifically: (1.1) adding a vertical zoom system containing an Alvarez lens group in an optical simulation software, setting the surface profile coefficient A, adding the required vertical eccentricity value of the plane of the Alvarez lens group to the design target, and recording the long axis half aperture value L in the plane; if the Alvarez lens group is vertically displaced in the x direction, then 2L is the effective aperture length of the Alvarez lens group in the x direction; (1.2) adding a standard surface before and after the coordinate breakpoint of the Alvarez lens group, and recording the short axis half aperture value R of the two surfaces, then 2R is the effective aperture of the Alvarez lens group; (1.3) determining the effective aperture of the Alvarez lens group according to the long axis half aperture value L obtained in step (1.1) and the short axis half aperture value R obtained in step (1.2), which is a semicircle with a radius R on both sides of the x direction with a distance of 2L between the two vertices, i.e. the area is the effective aperture of the Alvarez lens group.

3. The method of claim 2, wherein the optimal tilt term coefficient of an Alvarez lens is designed by, The optical simulation software includes Zemax and CODE V.

4. The method of claim 1, wherein the optimal tilt term coefficient design method of an Alvarez lens is characterized by, The step (2) is specifically: (2.1) inputting the surface profile coefficient A, the long axis half aperture value L and the short axis half aperture value R; (2.2) setting the sampling calculation precision according to the effective aperture range, and combining the basic surface profile function to obtain the sag value matrix of each sampling point of the surface profile; (2.3) setting the sampling points in the effective aperture range as 1 and the sampling points outside the effective aperture range as 0 in the binary matrix, i.e. the aperture mask matrix; (2.4) multiplying the sag value matrix and the aperture mask matrix to obtain the surface profile sag in the effective aperture, and obtaining the difference between the maximum and minimum values.

5. The method of claim 4, wherein the optimal tilt term coefficient of an Alvarez lens is designed by, In the step (2.2), the basic surface function is .

6. The method of claim 1, wherein the optimal coefficients of the Alvarez lens are determined by the following equation: ###0002### where, A is the optimal coefficients of the Alvarez lens, and B is the coefficients of the Alvarez lens. In the step (3), the first tilt term in the vertical movement direction is changed, and the surface profile function at this time is: ； wherein n is the iteration number and e is the step length.

7. The method of claim 1, wherein the optimal coefficients of the Alvarez lens are determined by the following equation: ###0002### where, A is the optimal coefficients of the Alvarez lens, and B is the coefficients of the Alvarez lens. The formula of the tilt term coefficient value E is: ； wherein n is the iteration number and e is the step length.

8. The method of claim 1, wherein the optimal tilt term coefficient design method of an Alvarez lens is characterized by, The optimal tilt term coefficient value is used to improve the imaging quality.

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