CN116819768B - Design method and device for single lens system with large depth of field - Google Patents

Design method and device for single lens system with large depth of field Download PDF

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CN116819768B
CN116819768B CN202310842313.0A CN202310842313A CN116819768B CN 116819768 B CN116819768 B CN 116819768B CN 202310842313 A CN202310842313 A CN 202310842313A CN 116819768 B CN116819768 B CN 116819768B
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single lens
depth
aperture
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CN116819768A (en
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谭凡教
孙再武
侯晴宇
李宗岭
杨昌健
张荣帅
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Harbin Institute of Technology
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    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012Optical design, e.g. procedures, algorithms, optimisation routines
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0025Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for optical correction, e.g. distorsion, aberration
    • GPHYSICS
    • G02OPTICS
    • G02BOPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B3/00Simple or compound lenses

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Abstract

The invention discloses a design method and a device of a large-depth-of-field single lens system, comprising the following steps: s1, primarily optimizing a single lens by taking an aberration index as a constraint; s2, evaluating aberration correction capacities of different apertures of the primarily optimized single lens, and dividing the primarily optimized single lens aperture into areas with different aberration correction capacities; and S3, setting different imaging quality constraints on the divided aperture areas, and optimizing to obtain the large-depth single lens system with unchanged and clear point spread function depth. By adopting the technical scheme of the invention, the single lens imaging system with large depth of field can be designed, and certain performance requirements are met.

Description

Design method and device for single lens system with large depth of field
Technical Field
The invention belongs to the technical field of optical computing imaging, and particularly relates to a design method and device of a large-depth-of-field single lens system.
Background
In the optical system, the depth of field is inversely proportional to the square of the relative aperture, and the depth of field of the optical system with smaller relative aperture is larger, but the light quantity entering the optical system is insufficient, the imaging quality is damaged, and the depth of field is reduced when the relative aperture is increased. Compared with a small-aperture system, in a system with a larger aperture, light rays in a complete aperture area cannot be completely converged into an ideal image point by means of optimization, object point imaging with different depths shows the characteristics of divergence and different degrees of divergence, and as a result, imaging at the depth where imaging is clear becomes fuzzy, so that the depth of field of an optical system is difficult to promote.
Compared with a complex lens group, the single-lens imaging system has the advantages of small volume, light weight, simple design and the like. However, in view of the problems faced by the depth-of-field extension, it is difficult to obtain a single-lens imaging system with a large depth of field by using a conventional design method.
Disclosure of Invention
The invention aims to solve the technical problem of providing a design method and a device for a large-depth-of-field single lens system so as to solve the problem that a large-depth-of-field single lens optical system is difficult to design.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a design method of a large-depth-of-field single lens system comprises the following steps:
s1, primarily optimizing a single lens by taking an aberration index as a constraint;
s2, evaluating aberration correction capacities of different apertures of the primarily optimized single lens, and dividing the primarily optimized single lens aperture into areas with different aberration correction capacities;
and S3, setting different imaging quality constraints on the divided aperture areas, and optimizing to obtain the large-depth single lens system with unchanged and clear point spread function depth.
Preferably, in the step S1, a single lens imaging model is built based on geometric ray tracing, uniformly spaced sampling object points are set, coordinates of sampling rays from the sampling object points on an image plane after passing through the single lens are calculated, aberration indexes are used as constraints, and aberrations of the single lens for imaging different object distances are initially optimized to solve single lens parameters with minimum aberration indexes.
Preferably, in step S2, spot radii corresponding to different apertures of the primarily optimized single lens are obtained, and are used for evaluating aberration correction capabilities of the different apertures, and the apertures are divided into areas with different aberration correction capabilities according to the evaluation result.
Preferably, in step S3, discrete imaging quality constraints are applied to regions of different aberration correction capabilities; wherein, for the area with high aberration correction capability, an aberration index is used as a constraint; the area with low image correction capability adopts contrast and consistency constraint; wherein the discrete imaging quality constraint optimizes the single lens parameters to obtain a large-depth single lens system with unchanged point spread function depth and clear imaging
The invention provides a design device of a large-depth-of-field single lens system, which comprises:
the first optimization module is used for primarily optimizing the single lens by taking the aberration index as a constraint;
the dividing module is used for dividing the primarily optimized single lens aperture into areas with different aberration correction capacities;
and the second optimization module is used for setting different imaging quality constraints on the divided aperture areas and optimizing to obtain a large-depth single lens system with unchanged and clear point spread function depth.
Preferably, the first optimization module is configured to establish a single lens imaging model based on geometric ray tracing, set uniformly spaced sampling object points, calculate coordinates of sampling rays from the sampling object points on an image plane after the sampling rays pass through the single lens, and preliminarily optimize aberrations of the single lens for imaging different object distances with respect to aberration indexes as constraints, so as to solve single lens parameters with minimum aberration indexes.
Preferably, the dividing module is configured to evaluate aberration correction capabilities of different apertures of the initially optimized single lens according to the spot radii corresponding to the different apertures, and divide the apertures into areas with different aberration correction capabilities according to the evaluation result.
Preferably, the second optimization module is used for adopting discrete imaging quality constraints on areas with different aberration correction capacities; wherein, for the area with high aberration correction capability, an aberration index is used as a constraint; contrast and consistency constraints are applied to areas with low aberration correction capability; the discrete imaging quality constraints optimize the single lens parameters to obtain a large-depth single lens system with unchanged point spread function depth and clear imaging.
The invention has the following technical effects:
(1) According to the invention, the single lens is initially optimized by taking the traditional aberration index as a constraint, and the evaluation index is calculated by the initially optimized single lens system, so that the aberration correction capability of different aperture positions in the imaging process of the object point with a large depth of field can be evaluated.
(2) The invention combines aberration characteristics of different aperture areas, provides an aperture discrete optimization strategy for restricting different imaging quality of different aperture areas, and solves the problem that in the design of a large-depth single lens, the integral aperture aberration is difficult to correct.
(3) The invention combines imaging characteristics of the single lens at different object distances, provides a contrast ratio and consistency constraint, can realize the unchanged and clear imaging of the point spread function depth of the optimized single lens system in a large depth of field range, can meet the design requirement of the large depth of field single lens optical system, and forms a new single lens depth of field extension thought.
Drawings
For a clearer description of the technical solutions of the present invention, the drawings that are required to be used in the embodiments are briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that, without inventive effort, other drawings may be obtained by those skilled in the art according to the drawings:
FIG. 1 is a flow chart of a design method of a large depth of field single lens system according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a single lens ray trace in an embodiment of the invention;
FIG. 3 is a graph showing the variation of the aberration correction capability index of the single lens system with the aperture value after preliminary optimization according to the embodiment of the present invention;
FIG. 4 shows point spread functions and simulated images of a single lens optical system designed according to an embodiment of the present invention at different depths.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Example 1:
as shown in fig. 1, an embodiment of the present invention provides a method for designing a large depth of field single lens system, including:
s1, primarily optimizing a single lens by taking an aberration index as a constraint;
s2, evaluating aberration correction capacities of different apertures of the primarily optimized single lens, and dividing the primarily optimized single lens aperture into areas with different aberration correction capacities;
and S3, setting different imaging quality constraints on the divided aperture areas, and optimizing to obtain the large-depth single lens system with unchanged and clear point spread function depth.
In step S1, a single lens imaging model is built based on geometric ray tracing, N sampling object points with uniform intervals are set, coordinates of sampling rays from the sampling object points on an image plane after passing through the single lens are calculated, and aberrations of the single lens for imaging different object distances are initially optimized with a conventional aberration index as a constraint, so as to solve a single lens parameter θ which minimizes the conventional aberration index. The object distance of the kth sampling object point is denoted as l k The conventional aberration index defines a loss function of L (θ, L) k ) The optimization procedure is expressed as:
in step S1, the above-mentioned optimization process may be accomplished by using a gradient descent method.
As one implementation of the embodiment of the present invention, in step S2, an aberration correction capability evaluation index I (R) is defined for evaluating the aberration correction capability of the single lens at an aperture having a radius R.
Wherein,indicated at kthThe light emitted by the object point position is sampled, and the distance between the falling point of the image surface and the center of the image surface is passed through the aperture position with the radius of R.
As one implementation of the embodiment of the present invention, in step S2, the single lens aperture is divided into regions having different aberration correction capabilities by setting a threshold value for the aberration correction capability evaluation index. The aperture range on the aperture stop for I (R) to be smaller than the set threshold is defined as Ω c Radius R epsilon omega on aperture diaphragm c The pore size range of (2) is defined as omega IC The corresponding area has high aberration correction capability, and the upper radius of the aperture diaphragm is adjustedIs in the range of omega OC The corresponding region has low aberration correction capability, emits the kth sampling object point, passes through the aperture range omega OC The point spread function obtained for the light of (2) is defined as +.>
As one implementation manner of the embodiment of the present invention, in step S3, discrete imaging quality constraints are set for regions with different aberration correction capabilities, and for regions with high aberration correction capabilities, conventional aberration indexes are used as constraints; a contrast and consistency constraint is put on a region with low aberration correction capability, so that the point spread function of the region has low contrast and consistency in a large depth of field.
The contrast constraint can be expressed as:
wherein θ 1 Representing the single lens parameters that satisfy the minimum contrast for all sample object points as a result of imaging the lens region.
The consistency constraint may be expressed as the following optimization problem:
wherein E {.cndot }' represents averaging over different sample object points,mean value theta of point spread function corresponding to different sampling object points 2 Representing the single lens parameters that minimize the difference in PSF of the aperture range between the sample object points.
Further, a discrete aperture loss function is proposed, which can be expressed as:
wherein,for the kth sample point, passing through the radius range omega IC Root mean square radius of the ray at the image plane landing point. Alpha, beta and gamma are weights.
And optimizing the single lens parameters by taking the minimum loss function as an optimization target to obtain the large-depth single lens system with unchanged point spread function depth and clear imaging.
Example 2:
the embodiment of the invention also provides a design method of the single lens system with large depth of field, which comprises the following specific implementation steps:
and S1, primarily optimizing the single lens by taking the aberration index as a constraint.
And establishing a single lens imaging model based on geometric ray tracing, setting N sampling object points at uniform intervals, and calculating coordinates of sampling rays from the sampling object points on an image plane after passing through the single lens. The optical system in the embodiment is a plano-convex even aspheric single lens optical system, and the ray tracing diagram is shown in fig. 2, wherein the thickness of the lens is 2.65mm, the focal length f=39 mm, the radius of curvature r=19.15 mm, the material is PMMA, and the parameters to be optimized are 4, 6, 8, 10, 12, 14, 16-order even aspheric surfaces of the rear surfaceFace coefficient, defined as θ= (a) 4 ,a 6 ,a 8 ,a 10 ,a 12 ,a 14 ,a 16 ) The initial values are all 0.
Taking 64×64 sampling points in the aperture range on the front surface of the single lens, and representing the spatial coordinates of the sampling points as P 0 =(x 0 ,y 0 ,z 0 ) R is used 0 Representing the distance of the sampling point from the optical axis.
The ray from the sample object point to the aperture sample point is the incident ray on the front surface, and the propagation direction of the refracted ray on the front surface is calculated according to the refraction law.
Since the rear surface of the lens is an even aspheric surface and contains a high-order even aspheric coefficient, the equation of intersection of the ray and the curved surface cannot be solved and the partial derivative of the aspheric surface is very complex, an iterative approximation method is adopted in the embodiment to calculate the intersection of the ray and the rear surface of the lens, the propagation distance t of the ray between the front surface and the rear surface is defined as an unknown quantity, and the iterative equation is as follows:
wherein Δz t For the Z-axis coordinate of the falling point and the axial distance of the rear surface after the light ray propagates by t distance, delta Z is defined t+h The Z-axis coordinate of the falling point and the axial distance of the rear surface after the light propagation distance t+h are the iteration parameters, and the falling point Z-axis coordinate and the axial distance of the rear surface are attenuated along with the iteration times, and the falling point Z-axis coordinate is equal to the axial distance of the rear surface t Less than the set threshold 10 -7 mm, stop the iteration. Obtaining an approximate solution of the intersection point of the light ray and the rear surface of the lens, and representing the intersection point of the light ray and the rear surface as P 1 =(x 1 ,y 1 ,z 1 )。
Calculating refraction angle of light ray on back surface by using refraction law, obtaining light ray on image plane by using intersection point and refraction angle of light ray on back surface and using simple geometric relationshipDrop point on, denoted P 2 =(x 2 ,y 2 )。
Six object points are uniformly taken within the distance range of 1000mm to 2000mm in the object space, and the object distances of the sampled object points are 1000mm,1200mm,1400mm,160 mm, 1500mm and 2000mm respectively. Taking the sum of root mean square radii of the sampling object point imaging as constraint, performing preliminary optimization on the single lens system to solve the single lens parameter theta minimizing the loss function 0 . The object distance of the kth sampling object point is denoted as l k The conventional aberration index defines a loss function of L (θ, L) k ) The optimization procedure is expressed as:
based on Pytorch deep learning framework, the optical system is initially optimized by using an Adam optimizer, the learning rate is set to be 0.005, and after 200 periods of optimization, the obtained initial optimized single lens has 4-16-order aspheric coefficients of-5.345E-5, 1.7885E-7, 1.1335 XE-8, 1.4495E-10, 2.642E-12, 1.655E-13 and 2.989E-16 on the rear surface.
And S2, evaluating aberration correction capacities of different apertures of the primarily optimized single lens, and dividing the primarily optimized single lens aperture into areas with different aberration correction capacities. Uniformly taking 500 sampling aperture values on the front surface of the single lens, calculating the falling point coordinates of light rays passing through the front surface sampling points from all sampling object points on the image plane, and calculating an aberration correction capability evaluation index I (R):
fig. 3 is a graph showing a variation of aberration correction capability index with aperture value in a single lens system after preliminary optimization according to an embodiment of the present invention.
Setting the image plane pixel size to 0.0125mm, in the embodiment, setting the single pixel size as the threshold value of the aberration correction capability evaluation index, and passing the single lens hole through the threshold valueThe diameter is divided into areas of different aberration correction capabilities. The aperture range on the aperture stop for I (R) to be smaller than the set threshold is defined as Ω c Radius R epsilon omega on aperture diaphragm c The pore size range of (2) is defined as omega IC The corresponding area has high aberration correction capability, and the upper radius of the aperture diaphragm is adjustedIs in the range of omega OC The corresponding region has a low aberration correction capability.
Omega after division according to threshold IC Is [0,2.85 ]],Ω OC Is (2.85,5)]Namely, the light with the aperture value smaller than 2.85mm on the aperture has strong aberration correction capability, the light is easy to be converged into an ideal image point in the optimization process, the light with the aperture value larger than 2.85mm has weak aberration correction capability, and the light is difficult to be converged into the ideal image point in the optimization process.
And S3, setting different imaging quality constraints on the divided aperture areas, and optimizing to obtain the large-depth single lens system with unchanged and clear point spread function depth.
For areas with high aberration correction capability, the sum of root mean square radii of all depth-sampled image points is used as a loss function, so that the optimized optical system can meet the condition of a large depth of field, and the aberration of the aperture range is minimized. A contrast and consistency constraint is placed on areas with low aberration correction capability in order to allow the optimized optical system to have a consistent point spread function at the sampling point for high quality imaging of the full aperture.
Calculating the aperture range of the sampling point on the front surface to be omega IC The coordinates of the falling points of the light rays on the image plane are calculated, and the root mean square radius of the falling points is calculated; calculating the aperture range of the sampling point on the front surface to be omega OC The coordinates of the falling point of the light ray on the image plane are obtained as the point spread functionUse->Representing the average of the point spread functions corresponding to all the sample object points.
The contrast constraint can be expressed as:
wherein θ 1 Representing the single lens parameters that satisfy the minimum contrast for all sample object points, the lens region imaging result, the contrast constraint can be expressed as:
wherein θ 2 Representing the single lens parameters that minimize the difference in PSF of the aperture range between the sample object points.
The constraint weighted sum is used for calculating the total loss function:
wherein α, β and γ are weights of different parts of the loss function, 1,0.01,1 respectively.
Based on Pytorch deep learning framework, the optical system is further optimized by using an Adam optimizer, the learning rate is 0.005, the loss function is not reduced after 200 periods of optimization, the optimal surface shape parameters are considered to be obtained, and the 4-16-order even aspherical coefficients of the rear surface of the single lens after optimization are respectively-9.70E-6, 1.937E-5, -1.789E-7, -1.128E-7, -3.838E-9, -5.988E-10 and-2.458E-11.
The first row and the third row of fig. 4 sequentially show the optimized optical system, the ideal image point and the point spread function of imaging the object point at the positions of 2000mm, 1750mm, 1500mm, 1250mm and 1000mm, the second row and the fourth row show the original clear image, the simulation image and the partial enlarged image of the image at the corresponding object distance, and as can be seen from fig. 4, the optical system designed by the method can realize clear imaging in a large depth range.
Example 3:
the invention provides a design device of a large-depth-of-field single lens system, which comprises:
the first optimization module is used for primarily optimizing the single lens by taking the aberration index as a constraint;
the dividing module is used for dividing the primarily optimized single lens aperture into areas with different aberration correction capacities;
and the second optimization module is used for setting different imaging quality constraints on the divided aperture areas and optimizing to obtain a large-depth single lens system with unchanged and clear point spread function depth.
As an implementation manner of the embodiment of the present invention, a first optimization module is configured to establish a single lens imaging model based on geometric ray tracing, set uniformly spaced sampling object points, calculate coordinates on an image plane of a sampling ray from the sampling object points after passing through a single lens, and primarily optimize aberrations of the single lens for imaging different object distances with respect to an aberration index as a constraint, so as to solve a single lens parameter that minimizes the aberration index.
As an implementation manner of the embodiment of the present invention, the dividing module is configured to evaluate aberration correction capabilities of different apertures of the initially optimized single lens according to spot radii corresponding to the different apertures, and divide the apertures into areas with different aberration correction capabilities according to the evaluation result.
As an implementation manner of the embodiment of the present invention, the second optimization module is configured to apply discrete imaging quality constraints to areas with different aberration correction capabilities; wherein, for the area with high aberration correction capability, an aberration index is used as a constraint; contrast and consistency constraints are applied to areas with low aberration correction capability; the discrete imaging quality constraints optimize the single lens parameters to obtain a large-depth single lens system with unchanged point spread function depth and clear imaging.
The above embodiments are merely illustrative of the preferred embodiments of the present invention, and the scope of the present invention is not limited thereto, but various modifications and improvements made by those skilled in the art to which the present invention pertains are made without departing from the spirit of the present invention, and all modifications and improvements fall within the scope of the present invention as defined in the appended claims.

Claims (4)

1. The design method of the large-depth-of-field single lens system is characterized by comprising the following steps of:
s1, primarily optimizing a single lens by taking an aberration index as a constraint;
s2, evaluating aberration correction capacities of different apertures of the primarily optimized single lens, and dividing the primarily optimized single lens aperture into areas with different aberration correction capacities;
s3, setting different imaging quality constraints on the divided aperture areas, and optimizing to obtain a large-depth single lens system with unchanged point spread function depth and clear imaging;
in step S2, the single lens aperture is divided into regions having different aberration correction capabilities by setting a threshold value for the aberration correction capability evaluation index, and an aperture range on the aperture stop in which I (R) is smaller than the set threshold value is defined as Ω c Radius R epsilon omega on aperture diaphragm c The pore size range of (2) is defined as omega IC The corresponding area has high aberration correction capability, and the upper radius of the aperture diaphragm is adjustedIs in the range of omega OC The corresponding region has low aberration correction capability, emits the kth sampling object point, passes through the aperture range omega OC The point spread function obtained for the light of (2) is defined as +.>
In step S3, discrete imaging quality constraints are adopted for regions with different aberration correction capabilities; wherein, for the area with high aberration correction capability, an aberration index is used as a constraint; contrast and consistency constraints are applied to areas with low aberration correction capability; the discrete imaging quality constraint optimizes the single lens parameters to obtain a large-depth single lens system with unchanged point spread function depth and clear imaging; the method comprises the following steps:
the contrast constraint is expressed as:
wherein θ 1 Representing single lens parameters meeting the minimum contrast of imaging results of all sampling object points of the lens region;
the consistency constraint is expressed as the following optimization problem:
wherein E {.cndot }' represents averaging over different sample object points,mean value theta of point spread function corresponding to different sampling object points 2 A single lens parameter representing the smallest difference between the PSFs of the aperture range and the sample object point;
the discrete aperture loss function is designed, expressed as:
wherein,for the kth sample point, passing through the radius range omega IC The root mean square radius of the light rays at the falling point of the image plane, and alpha, beta and gamma are weights;
and optimizing the single lens parameters by taking the minimum loss function as an optimization target to obtain the large-depth single lens system with unchanged point spread function depth and clear imaging.
2. The method of designing a large depth of field single lens system according to claim 1, wherein in the step S1, a single lens imaging model is built based on geometric ray tracing, uniformly spaced sampling object points are set, coordinates on an image plane of a sampling ray from the sampling object points after passing through the single lens are calculated, aberration indexes are used as constraints, aberrations of the single lens for imaging different object distances are initially optimized, and single lens parameters minimizing the aberration indexes are solved.
3. A large depth of field single lens system designing apparatus that realizes the large depth of field single lens system designing method of any one of claims 1 to 2, characterized by comprising:
the first optimization module is used for primarily optimizing the single lens by taking the aberration index as a constraint;
the dividing module is used for dividing the primarily optimized single lens aperture into areas with different aberration correction capacities;
and the second optimization module is used for setting different imaging quality constraints on the divided aperture areas and optimizing to obtain a large-depth single lens system with unchanged and clear point spread function depth.
4. The large depth of field single lens system design apparatus of claim 3, wherein the first optimizing module is configured to establish a single lens imaging model based on geometric ray tracing, set uniformly spaced sampling object points, calculate coordinates on an image plane of a sampling ray from the sampling object points after passing through the single lens, and preliminarily optimize aberrations of the single lens for imaging different object distances with respect to an aberration index as a constraint, so as to solve for single lens parameters minimizing the aberration index.
CN202310842313.0A 2023-07-11 2023-07-11 Design method and device for single lens system with large depth of field Active CN116819768B (en)

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KR20140077068A (en) * 2012-12-13 2014-06-23 한국항공대학교산학협력단 Apparatus and method for correcting lens distortion
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