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The fish-eye lens system designed is a lens in the visible-light band with the F number that no more than 3.5, with the focal length no less than 5 mm when the system FOV angle is 180°. The modulation-transfer-function (MTF) requirement is that, when the space frequency is 60 lp/mm, the modulus of the optical transfer function (OTF) is no less than 0.5. The size of the image plane is approximately 18 mm, and the aspect ratio of the image plane is 4:3. The design specifications of the fish-eye lens system are listed in Tab.1.
Parameter Value Focal length/mm ≥5 F number ≤3.5 FOV/(°) 180 Design spectrum Visible light (F, D, C) Maximum lens clear aperture/mm ≤100 Object location At infinity Table 1. Design specifications
Generally, fish-eye lens consists of several negative meniscus lenses for compressed FOV in the former group and several objective lenses in the latter group. The design idea is firstly to determine the parameters of the former group optical system according to the design constraints, and then select the structure and parameters of the latter group objective lenses according to the space field angle and aberration distribution of the former group optical system. The reason for adopting the above strategy is that the parameters of the former group optical system should be used to meet the relevant constraints. For example, the small radius of the negative meniscus lens should meet the requirements of the lateral and longitudinal size limits of the fish-eye lens. At the same time, some aberrations (mainly field curvature) of the lens should be controlled. According to the structure of the lens, many parameters can be used to optimize the system aberration.
The wave aberrations of the field curvature, axial chromatic aberration and vertical chromatic aberration of the former optical group are calculated by using the wave aberration theory of the plane symmetric optical system. According to the wave aberration balance condition of the former and the latter optical groups[10], the optical power and optical spacing of each lens of the latter optical group objective lens (i.e. the first-order optical parameters) are calculated. The flow chart of fish-eye lens system design using the sixth-order wave aberration theory is shown in Fig.3.
By using the sixth-order wave aberration theory, a large aperture imaging simulation of a fish-eye lens optical system is carried out, and the simulation results are compared with the numerical results of ZEMAX ray tracing. The optical parameters of the fish-eye lens system are shown in Tab.2. The monochromatic aberration distribution of visible light at five field angles of 0°, 27°, 45°, 63° and 90° is calculated respectively. It is assumed that the F-number of the fish-eye lens system is 3.2. The distance between the object point and the first optical plane is infinite at different field angles. The fish-eye lens optical system with maximum field of view angle of 180° is designed. The Optical path diagram of the optical system is shown in Fig.4.
Surface
No.Radius of
curvature/mmThickness/
mmGlass Clear diameter/
mmObject Infinity Infinity − − 1 133 20 − 193.2188 2 113.6006 24 H-LAF52 133.5434 3 21.2604 21.3598 − 42.5158 4 212.5634 14.9998 H-LAF6LA 40.4013 5 18.6054 8.6801 − 24.5525 6 −23.3482 7.9816 H-ZK7 24.3792 7 −151.8651 10.7462 H-ZF3 27.5062 8 −61.2174 0.2868 − 30.2412 9 −67.4453 9.5701 H-ZF6 30.3071 10 −47.9643 3.2664 − 32.6737 11 127.1637 15.0004 H-LAF3B 32.2762 12 −83.7291 35.0010 − 30.4971 13 (STO) Infinite 0.1976 − 10.0882 14 448.1495 1.9986 H-ZK14 10.2155 15 −42.4732 0.1993 − 10.7582 16 54.5847 8.6472 H-QK3L 11.0715 17 −17.1825 1.9988 H-ZF6 12.4013 18 −51.6904 0.3922 − 13.1415 19 563.3054 10.0301 H-KF6 13.3806 20 −17.1944 0.1988 − 14.8488 21 −18.5197 5.8883 H-LAFL5 14.7652 22 21.2408 8.3961 H-QK3L 16.9785 23 −26.0496 1.5939 − 19.2195 24 90.2547 11.9746 H-ZF6 20.5244 25 −40.54 10 − 21.3152 Image Infinity − − 18.0099 Table 2. Optical parameters of fish-eye lens system
In order to improve the accuracy of aberration calculation, it is necessary to consider the sixth-order wave aberration and more accurate pupil coordinate transfer processing. Through the calculation and analysis of this fish-eye lens systems similar to the above cases, the results show that the wave aberrations correction including higher-order aberrations and the second-order accuracy of pupil coordinates significantly improves the accuracy of aberrations calculation[11], which is related to the specific design of the system.
It is also an auxiliary method to verify the wave aberration theory to analyze whether the simplified results of aberration expression in processing paraxial optical system are consistent with the previous results. In the sixth-order wave aberration theory, if
$ \alpha ={180}^{ \circ } $ ,$\; \beta ={0}^{ \circ }, $ and the optical surface is a sphere, it represents the aberration of the object point on the axis of the axisymmetric optical system. As a result, the fourth-order intrinsic wave aberration coefficient is the same as that of Seidel, the third-order and fifth-order are zero, the sixth-order intrinsic wave aberration coefficient is the same as that of w060 reported in reference[13]. Moreover, the expression of the aberration in the direction of meridian and sagittal also becomes the same, which conforms to the geometric symmetry with axial symmetry optical system.
Fish-eye lens system design based on sixth-order wave aberration theory
doi: 10.3788/IRLA20200505
- Received Date: 2020-12-22
- Rev Recd Date: 2021-02-05
- Publish Date: 2021-06-30
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Key words:
- fish-eye lens /
- sixth-order wave aberration /
- aberration balance /
- the former optical group /
- the latter optical group
Abstract: The fish-eye lens system has the characteristics of plane symmetry, large field of view and large aperture imaging. That makes fish-eye lens design very complicated. Wave aberration theory is an important means to study optical system. Because the fish-eye lens system has the imaging characteristics of plane symmetry, Seidel primary aberration and higher-order aberration theory based on axisymmetric optical system are no longer suitable for aberration analysis and design of the fish-eye lens systems. The theory of sixth-order wave aberration was introduced, including the sixth-order intrinsic wave aberrations, the fifth-order aberration, transverse aberrations and the influence of the second-order accuracy of the aperture ray on the wave aberration. The flow chart of fish-eye lens system design based on sixth-order wave aberration theory was given. The former optical group of fish eye lens was designed based on sixth-order wave aberration theory, and the latter optical group design was obtained by balancing the aberrations of former group and latter group. Finally, a fish-eye lens system with good imaging quality was obtained. Its focal length is 5.989 mm, its field of view angle (FOV) is 180°, and its relative aperture is 1/3.2. The design results show that the modulation transfer function (MTF) of the fish-eye lens system is no less than 0.56 when the spatial frequency is 60 lp/mm. This fish-eye lens system has better imaging quality.