A method for optimizing the design of vertical axis zoom lens assembly based on phase residual term

Abstract

The present invention discloses an optimization design method for a vertical axis zoom lens group based on a phase residual term. First, the initial surface shape of the free-form surface in the vertical axis zoom lens group is determined; then, a phase expression of the initial surface shape is constructed; then, the difference between the phase expression of the initial surface shape and the phase expression of the ideal imaging condition is calculated and obtained and recorded as a phase residual term; then, a high-order XY polynomial corresponding to the initial surface shape is selected and then a corrected surface shape is constructed, and a phase change expression corresponding to the corrected surface shape is established; finally, in the clear aperture area, the XY polynomial coefficients of the corrected surface shape are optimized and solved by the least square method based on the phase residual term to obtain the corrected surface shape after the solution, and the initial surface shape of the free-form surface and the corrected surface shape obtained by the solution together constitute the optimized surface shape of the free-form surface. The present invention corrects aberrations by introducing additional XY terms on the basis of not changing the original zoom capability of the free-form surface, thereby improving the imaging quality of the vertical axis zoom lens group.

Description

Technical Field

[0001] The present invention relates to a vertical axis zoom lens group optimization design method in the field of optical zoom imaging technology, and in particular to a vertical axis zoom lens group optimization design method based on a phase residual term. Background Art

[0002] Optical zoom technology switches the magnification of the system by changing the focal length of the system. It has important applications in the fields of civil photography, security monitoring and virtual reality. It is also an important development direction in the fields of aerospace and extraterrestrial exploration imaging. As a key component of the zoom system, the zoom lens group has a significant impact on the performance of the zoom system.

[0003] The mainstream optical zoom technology mainly changes the overall optical power of the optical system by changing the position of a specific lens group along the optical axis in the optical system. The calculation formula for the optical power Φ of the optical system is as follows:

[0004] Φ=Φ1+Φ2-dΦ1Φ2

[0005] Where Φ is the overall focal length of the optical system, Φ1 is the focal length of the front lens group, Φ2 is the focal length of the rear lens group, and d is the distance between the front and rear lens groups.

[0006] However, this zooming method that moves along the optical axis requires a large axial displacement and involves a relatively complex zooming movement mechanical structure, so its application in certain special fields is limited.

[0007] In 1967, Luis W Alvarez proposed a zoom method for a free-form surface lens with variable focal power based on an XY third-order polynomial. This method can achieve the zoom function through the relative movement of two free-form surfaces along the direction perpendicular to the optical axis. The surface expression of the free-form surface is as follows:

[0008]

[0009] Among them, z is the surface height along the optical axis, x, y are the plane coordinates perpendicular to the optical axis, and A is the surface coefficient.

[0010] This optical zoom method has a compact structure and has unique advantages in the application of aerospace. However, although the XY third-order polynomial free-form surface proposed by Alvarez can realize the zoom function, it will inevitably produce large aberrations, and the aberrations produced by this zoom lens combination will change with the displacement during the movement perpendicular to the optical axis. For this problem, the current method mainly relies on optical design software such as ZEMAX and CODEV to optimize the design of the zoom lens group by adding other XY high-order polynomials. However, these methods have problems such as few optimization variables, many restrictions and slow optimization speed, and the zoom ability of the zoom lens group will be lost during the optimization process. Summary of the invention

[0011] The purpose of the present invention is to provide a method for optimizing the design of a vertical axis zoom lens group based on a phase residual term in view of the deficiencies in the prior art. The present invention converts the aberration of the zoom lens group that changes with the offset during the movement of the zoom lens group perpendicular to the optical axis into a phase residual term for description, and can simultaneously add multiple XY high-order polynomial optimization variables to compensate for the aberration, and the optimization speed is fast, and the image quality after optimization is high, thereby comprehensively improving the optimization performance of the vertical axis zoom lens group.

[0012] In order to achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0013] Step 1: Determine the initial surface shape of the free-form surface in the vertical axis zoom lens assembly;

[0014] Step 2: construct a phase expression of the initial surface shape based on the initial surface shape of the free-form surface in the vertical axis zoom lens group;

[0015] Step 3: According to the phase expression of the initial surface shape, the difference between the phase expression of the initial surface shape and the phase expression of the ideal imaging condition is calculated and obtained and recorded as the phase residual term;

[0016] Step 4: After selecting the high-order XY polynomial corresponding to the initial surface shape, construct the modified surface shape and establish the phase change expression corresponding to the modified surface shape;

[0017] Step 5: Determine the clear aperture area of ​​the vertical axis zoom lens group. In the clear aperture area, optimize and solve the XY polynomial coefficients corresponding to the corrected surface shape using the least squares method based on the phase residual term to obtain the corrected surface shape after solution. The optimized surface shape of the free-form surface in the vertical axis zoom lens group is composed of the initial surface shape of the free-form surface in the vertical axis zoom lens group and the corrected surface shape obtained by solution.

[0018] In step 2, the phase expression of the initial surface shape is The formula is as follows:

[0019]

[0020] Among them, x and y represent the two position coordinates of the light when it propagates in the mirror group, and n λ represents the material refractive index corresponding to the design wavelength λ, λ represents the design wavelength, δ represents the lateral displacement, (t1(x+δ,y) represents the thickness of the element after the first free-form surface lens is displaced δ distance along the positive direction of the x-axis, t2(x-δ,y) represents the thickness of the element after the second free-form surface lens is displaced δ distance along the negative direction of the x-axis.

[0021] The step 3 is specifically as follows:

[0022] First, extract (x 2 +y 2 ) term, and then determine the equivalent focal length f corresponding to different lateral displacements δ, and then construct the phase distribution expression under ideal imaging conditions based on the equivalent focal length f Finally, the phase distribution expression under ideal imaging condition is The difference between the phase expression of the initial surface shape is recorded as the phase residual term

[0023] In step 4, the order of each monomial in the modified surface shape is at least one order greater than that of each monomial in the initial surface shape.

[0024] In step 5, the phase residual term mean square error W is calculated based on the phase residual term and the phase change expression corresponding to the corrected surface type. residual And the phase mean square error W after introducing the modified surface shape revised , the phase mean square error W after the modified surface shape is introduced revised Denoted as the evaluation function, the formula is as follows:

[0025]

[0026]

[0027] Where M is the number of horizontal grids in the light aperture area, N is the number of vertical grids in the light aperture area, m is the horizontal grid number, and n is the vertical grid number. is the phase residual term at the grid point (m,n) in the clear aperture region, The phase change expression corresponding to the modified surface shape in the grid point (m,n) of the clear aperture area is expressed;

[0028] Under the preset constraints, the evaluation function is minimized by using the least square method, and then the coefficients of the modified XY polynomial are obtained;

[0029] The formula of the preset constraint condition is as follows:

[0030]

[0031] Among them, l x Indicates the length of the vertical axis zoom lens group along the x-axis, l y Indicates the length of the vertical axis zoom lens group along the y-axis direction, C ij Represents the polynomial x i y j The corresponding coefficient, A is the initial surface coefficient.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] (1) The present invention converts the aberration of the zoom lens group that changes with the offset during the movement perpendicular to the optical axis into a phase residual term for representation, which can quantitatively describe the aberration change under different lateral displacement amounts.

[0034] (2) The present invention can simultaneously add multiple XY high-order polynomial optimization variables to compensate for aberrations by compensating for phase residual terms. The upper limit of variables that can be optimized is higher than that of the prior art, and the image quality can be better improved.

[0035] (3) The present invention can effectively correct the aberrations produced under different offset conditions and has a fast optimization speed. The image quality after optimization is high, and the optimization performance of the vertical axis zoom lens group is comprehensively improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of a flow chart of a method for optimizing the design of a vertical-axis zoom lens assembly based on a phase residual term in the present invention;

[0037] Figure 2 Schematic diagram of the initial structure of the fifth-order polynomial free-form surface of the vertical axis zoom lens assembly XY in an embodiment of the present invention;

[0038] Figure 3 Schematic diagram of the phase expression of the initial surface shape in an embodiment of the present invention;

[0039] Figure 4 Schematic diagram of phase expression of ideal imaging conditions in an embodiment of the present invention;

[0040] Figure 5 This is a schematic diagram of the phase residual item in an embodiment of the present invention;

[0041] Figure 6 is a phase distribution change curve diagram of the phase residual term in the XoY plane according to an embodiment of the present invention;

[0042] Figure 7 A curve diagram showing the change of the modified surface phase distribution introduced in the embodiment of the present invention;

[0043] Figure 8A phase distribution variation curve diagram of the modified surface profile for correcting aberrations in the XoY plane introduced in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0045] like Figure 1 As shown, the present invention comprises the following steps:

[0046] Step 1: Determine the initial surface shape of the free-form surface in the vertical axis zoom lens group; the vertical axis zoom lens group includes a first free-form surface lens and a second free-form surface lens, and the initial surface shape of the free-form surface is an XY polynomial. For each monomial c in different XY polynomials ij x i y j The coefficient c ij A certain proportional relationship is satisfied between them, so that after a lateral offset occurs between the first free-form surface lens and the second free-form surface lens, the lens group has an equivalent optical focal length.

[0047] In the specific implementation, an optimization description is given based on an example of a zoom surface shape based on an XY fifth-order polynomial free-form surface. The corresponding expression of the XY fifth-order polynomial free-form surface is as follows:

[0048] z(x,y)=A(x 5 +10x 3 y 2 +5xy 4 )

[0049] Among them, z is the surface height along the optical axis, x, y are the plane coordinates perpendicular to the optical axis, and A is the surface coefficient.

[0050] The two lenses have one free-form surface and one flat surface respectively, and the free-form surface has the same surface expression, and the shape is as follows Figure 2 As shown. The thicknesses t1(x,y) and t2(x,y) of the two lenses can be expressed as:

[0051] t1(x,y)=C1+z(x,y)=C1+A(x 5 +10x 3 y 2 +5xy 4 )

[0052] t2(x,y)=C2-z(x,y)=C2-A(x5 +10x 3 y 2 +5xy 4 )

[0053] Among them, C1 and C2 are the center thickness of the two lenses respectively.

[0054] Step 2: construct a phase expression of the initial surface shape based on the initial surface shape of the free-form surface in the vertical axis zoom lens group, which is recorded as the actual phase expression;

[0055] In step 2, the vector height distribution equation t(x, y) of different regions of the mirror group is written according to the determined surface expression. When the lateral displacement is δ, the phase distribution of the light after passing through the mirror group is constructed according to the vector height function. Phase expression of initial surface shape The formula is as follows:

[0056]

[0057] Among them, x and y represent the two position coordinates of the light when it propagates in the mirror group, and n λ represents the material refractive index corresponding to the design wavelength λ, λ represents the design wavelength, δ represents the lateral displacement, (t1(x+δ,y) represents the thickness of the element after the first free-form surface lens is displaced δ distance along the positive direction of the x-axis, t2(x-δ,y) represents the thickness of the element after the second free-form surface lens is displaced δ distance along the negative direction of the x-axis.

[0058] In specific implementation, Figure 3 As shown, the phase expression of the initial surface shape is The formula is as follows:

[0059]

[0060] Step 3: According to the phase expression of the initial surface shape, the difference between the phase expression of the initial surface shape and the phase expression of the ideal imaging condition is calculated and obtained and recorded as a phase residual term, thereby causing the aberration of the zoom lens group;

[0061] Step 3 is as follows:

[0062] First, extract (x 2 +y 2 ) term, and then determine the equivalent focal length f corresponding to different lateral displacements δ, and then construct the phase distribution expression under ideal imaging conditions based on the equivalent focal length f Finally, the phase distribution expression under ideal imaging condition is Phase expression with initial surface shape The difference between them is recorded as the phase residual term In specific implementation, The formula is as follows:

[0063]

[0064] In a specific implementation, the equivalent focal length f is expressed as follows:

[0065]

[0066] The expression is as follows, and its distribution is as follows Figure 4 As shown:

[0067]

[0068] The expression of the phase residual term is as follows, and its distribution is as follows Figure 5 As shown, its cross-sectional distribution along the X-axis and Y-axis directions is as follows Figure 6 As shown, Figure 6 (a) and (b) are the phase distribution change curves along the X-axis and along the Y-axis respectively:

[0069]

[0070] Step 4: Select the high-order XY polynomial corresponding to the initial surface shape and record it as the modified surface shape, and establish the phase change expression corresponding to the modified surface shape The formula is as follows:

[0071]

[0072] Wherein, t′1() represents the thickness of the element after the first piece of corrected free-form surface lens is displaced by a distance δ along the positive direction of the x-axis, and t′2(x-δ,y) represents the thickness of the element after the first piece of corrected free-form surface lens is displaced by a distance δ along the negative direction of the x-axis. ;

[0073] In specific implementation, the formula for correcting the surface shape z(x,y) is as follows:

[0074] z(x,y)=c 70 x 7 +c 52 x 5 y 2 +c 34 x 3 y 4 +c 16 xy 6

[0075] Among them, c 70 、c 52 、c 34 、c 16 x 7 、x5 y 2 、x 3 y 4 and xy 6 The coefficient of .

[0076] The distribution of Figure 7 As shown, its cross-sectional distribution along the X-axis and Y-axis directions is as follows Figure 8 As shown, Figure 8 (a) and (b) are the phase distribution change curves along the X-axis and along the Y-axis, respectively. The expressions are as follows:

[0077]

[0078] In step 4, the order of each monomial in the modified surface shape is at least one order greater than that of each monomial in the initial surface shape, and two orders higher than that of the initial surface shape can well correct aberrations. The orders of each monomial in the modified surface shape can be the same or different.

[0079] Step 5: Determine the clear aperture area of ​​the vertical axis zoom lens group. In the clear aperture area, optimize and solve the optimization variables (i.e., various coefficients) introduced in the phase change expression corresponding to the corrected surface shape based on the phase residual term using the least squares method to obtain the corrected surface shape after solution. The initial surface shape of the free-form surface in the vertical axis zoom lens group and the corrected surface shape obtained by solution together form the optimized surface shape of the free-form surface, thereby improving the image quality of the zoom lens group.

[0080] In step 5, the aperture size of the vertical axis zoom lens group is determined according to the actual situation, and then the aperture area is divided into an M×N grid. The mean square error W of the phase residual term corresponding to the M×N grid point (m, n) is calculated based on the phase residual term and the phase change expression corresponding to the correction surface type. residual And the phase mean square error W after introducing the modified surface shape revised , the phase mean square error W after the modified surface shape is introduced revised Denoted as the evaluation function, the formula is as follows:

[0081]

[0082]

[0083] Where M is the number of horizontal grids in the light aperture area, N is the number of vertical grids in the light aperture area, m is the horizontal grid number, and n is the vertical grid number. is the phase residual term at the grid point (m,n) in the clear aperture region, The phase change expression corresponding to the modified surface shape in the grid point (m,n) of the clear aperture area is expressed;

[0084] Under the preset constraints, the least squares method is used to minimize the evaluation function, that is, min(W revised ), determine the optimal first-fourth correction coefficient c 70 、c 52 、c 34 、c 16 , and then obtain the coefficients of the modified XY polynomial after solution;

[0085] The formula for the preset constraints is as follows:

[0086]

[0087] Among them, l x represents the length of the free-form surface element in the vertical axis zoom lens group along the x-axis direction, l y represents the length of the free-form surface element in the vertical axis zoom lens group along the y-axis direction, C ij Represents the polynomial x i y j The corresponding coefficient, A is the initial surface coefficient.

Claims

1. A method for optimizing the design of a vertical axis zoom lens assembly based on a phase residual term, characterized in that: The steps include: Step 1: Determine the initial surface shape of the free-form surface in the vertical axis zoom lens assembly; Step 2: construct a phase expression of the initial surface shape based on the initial surface shape of the free-form surface in the vertical axis zoom lens group; Step 3: According to the phase expression of the initial surface shape, the difference between the phase expression of the initial surface shape and the phase expression of the ideal imaging condition is calculated and obtained and recorded as the phase residual term; Step 4: Select the high-order XY polynomial corresponding to the initial surface shape and then construct the modified surface shape, and establish the phase change expression corresponding to the modified surface shape; Step 5: Determine the clear aperture area of ​​the vertical axis zoom lens group. In the clear aperture area, optimize and solve the XY polynomial coefficients corresponding to the corrected surface shape using the least squares method based on the phase residual term to obtain the corrected surface shape after solution. The optimized surface shape of the free-form surface in the vertical axis zoom lens group is composed of the initial surface shape of the free-form surface in the vertical axis zoom lens group and the corrected surface shape obtained by solution.

2. The method for optimizing the design of a vertical axis zoom lens assembly based on a phase residual term according to claim 1, characterized in that: In step 2, the phase expression of the initial surface shape is The formula is as follows: Among them, x and y represent the two position coordinates of the light when it propagates in the mirror group, and n λ It represents the material refractive index corresponding to the design wavelength λ, λ represents the design wavelength, δ represents the lateral displacement, t1(x+δ,y) represents the thickness of the element after the first free-form surface lens is displaced δ along the positive direction of the x-axis, and t2(x-δ,y) represents the thickness of the element after the second free-form surface lens is displaced δ along the negative direction of the x-axis.

3. The method for optimizing the design of a vertical axis zoom lens assembly based on a phase residual term according to claim 1, characterized in that: The step 3 is specifically as follows: First, extract (x 2 +y 2 ) term, and then determine the equivalent focal length f corresponding to different lateral displacements δ, and then construct the phase distribution expression under ideal imaging conditions based on the equivalent focal length f Finally, the phase distribution expression under ideal imaging condition is The difference between the phase expression of the initial surface shape is recorded as the phase residual term x and y represent the two position coordinate values ​​of the light when it propagates in the mirror group.

4. The method for optimizing the design of a vertical axis zoom lens assembly based on a phase residual term according to claim 1, characterized in that: In step 4, the order of each monomial in the modified surface shape is at least one order greater than that of each monomial in the initial surface shape.

5. The method for optimizing the design of a vertical axis zoom lens assembly based on a phase residual term according to claim 1, characterized in that: In step 5, the phase residual term mean square error W is calculated based on the phase residual term and the phase change expression corresponding to the corrected surface type. residual And the phase mean square error W after introducing the modified surface shape revised , the phase mean square error W after the modified surface shape is introduced revised Denoted as the evaluation function, the formula is as follows: Where M is the number of horizontal grids in the light aperture area, N is the number of vertical grids in the light aperture area, m is the horizontal grid number, and n is the vertical grid number. is the phase residual term at the grid point (m,n) in the clear aperture region, represents the phase change expression corresponding to the modified surface shape in the grid point (m,n) of the clear aperture area; δ represents the lateral displacement; Under the preset constraints, the evaluation function is minimized by using the least square method, and then the coefficients of the modified XY polynomial are obtained; The formula of the preset constraint condition is as follows: Among them, l x Indicates the length of the vertical axis zoom lens group along the x-axis, l y Indicates the length of the vertical axis zoom lens group along the y-axis direction, C ij Represents the polynomial x i y j The corresponding coefficient, A is the initial surface coefficient.

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