Researching

Journals
  • Advanced Photonics
  • Photonics Insights
  • Advanced Photonics Nexus
  • Photonics Research
  • Advanced Imaging
  • View All Journals
  • Chinese Optics Letters
  • High Power Laser Science and Engineering
    • Articles
  • Optics
  • Physics
  • Geography
  • View All Subjects
    • Conferences
  • CIOP
  • HPLSE
  • AP
  • View All Events
    • News
    About CLP
    Search by keywords or author
    Journals >Infrared and Laser Engineering >Volume 50 >Issue 6 >Page 20200505 > Article
    • Infrared and Laser Engineering
    • Vol. 50, Issue 6, 20200505 (2021)
    Fish-eye lens system design based on sixth-order wave aberration theory
    Guozhu Hou1、2, Lijun Lv2, and Yiqing Cao3
    Author Affiliations
  • 1Industrial Technology Center, Shanghai Dianji University, Shanghai 201306, China
  • 2Department of Precision Mechanical Engineering, Shanghai University, Shanghai 200444, China
  • 3School of Mechanical and Electrical Engineering, Putian University, Putian 351100, China
    • show less
    DOI: 10.3788/IRLA20200505 Cite this Article
    Guozhu Hou, Lijun Lv, Yiqing Cao. Fish-eye lens system design based on sixth-order wave aberration theory[J]. Infrared and Laser Engineering, 2021, 50(6): 20200505 Copy Citation Text show less

    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.

    Keywords

    $ \Delta {x}_{01}^{{{'}}}=- {\Delta }{x}_{2}^{*} $ (1)

    View in Article

    $ \Delta {y}_{01}^{{{'}}}= {\Delta }{y}_{2}^{*} $ (2)

    View in Article

    $ \begin{split} \Delta {x}_{01}^{{{'}}}=&-({d}_{200\left(2\right)}^{{{'}}}{x}_{2}^{2}+{d}_{020\left(2\right)}^{{{'}}}{y}_{2}^{2}+{d}_{300\left(2\right)}^{{{'}}}{x}_{2}^{3}+{d}_{120\left(2\right)}^{{{'}}}{{x}_{2}y}_{2}^{2}+\\ & {d}_{400\left(2\right)}^{{{'}}}{x}_{2}^{4}+{d}_{220\left(2\right)}^{{{'}}}{x}_{2}^{2}{y}_{2}^{2}+{d}_{040\left(2\right)}^{{{'}}}{y}_{2}^{4}+{d}_{500\left(2\right)}^{{{'}}}{x}_{2}^{5}+\\ & {d}_{320\left(2\right)}^{{{'}}}{x}_{2}^{3}{y}_{2}^{2}+{d}_{140\left(2\right)}^{{{'}}}{x}_{2}{y}_{2}^{4}) \end{split}$(3)

    View in Article

    $ \begin{split} \Delta {y}_{01}^{{{'}}}=&\left({h}_{110\left(2\right)}^{{{'}}}{x}_{2}{y}_{2}+{h}_{210\left(2\right)}^{{{'}}}{x}_{2}^{2}{y}_{2}+{h}_{030\left(2\right)}^{{{'}}}{y}_{2}^{3}+{h}_{310\left(2\right)}^{{{'}}}{x}_{2}^{3}{y}_{2}+\right.\\ & \left.{h}_{130\left(2\right)}^{{{'}}}{x}_{2}{y}_{2}^{3}+{h}_{410\left(2\right)}^{{{'}}}{x}_{2}^{4}{y}_{2}+{h}_{230\left(2\right)}^{{{'}}}{x}_{2}^{2}{y}_{2}^{3}+{h}_{050\left(2\right)}^{{{'}}}{y}_{2}^{5}\right) \end{split} $(4)

    View in Article

    $ {\Delta x}_{1}=\frac{{\Delta x}_{01}^{{{'}}}}{{\cos}{\beta }_{1}} $(5)

    View in Article

    $ {\Delta y}_{1}={\Delta y}_{01}^{{{'}}} $(6)

    View in Article

    $ \begin{split} &{x_1} = {A_1}{x_2} + {A_1}{\varGamma _{R\left( 1 \right)}}x_2^2 + {A_1}{\varGamma _{\rho \left( 1 \right)}}y_2^2\\ & {y_1} = {B_1}{y_2} + {B_1}{\varGamma _{12\left( 1 \right)}}{x_2}{y_2} \end{split} $ (7)

    View in Article

    $ {\varGamma _{R\left( k \right)}} = {A_k}{c_{2,0\left( k \right)}}\tan {\beta _k} - {c_{2,0\left( {k + 1} \right)}}\tan {\alpha _{k + 1}} + \frac{{\sin \left( {{\alpha _{k + 1}} - {\beta _k}} \right)}}{{{r_{m\left( {k + 1} \right)}}\cos {\beta _k}}} $ (8)

    View in Article

    $ {\varGamma _{\rho \left( k \right)}} = \frac{{B_k^2{c_{0,2\left( k \right)}}\tan {\beta _k}}}{{{A_k}}} - {c_{0,2\left( {k + 1} \right)}}\tan {\alpha _{k + 1}} $ (9)

    View in Article

    $ {\varGamma _{12\left( k \right)}} = \frac{{\sin {\alpha _{k + 1}}}}{{{r_{s\left( {k + 1} \right)}}}} - \frac{{{A_k}\sin {\beta _k}}}{{{{r'}_{s\left( k \right)}}}} $ (10)

    View in Article

    $ {A}_{k}={r}_{m\left(k\right)}^{{'}}\cos{\alpha }_{k+1}/\left({r}_{m\left(k+1\right)}\cos{\beta }_{k}\right) $ (11)

    View in Article

    $ {B}_{k}=-{r}_{s\left(k\right)}^{{'}}/{r}_{s\left(k+1\right)} $(12)

    View in Article

    $\begin{split} {W_1} =& {w_{120\left( 1 \right)}}\left( {{x_1} + \Delta {x_1}} \right){\left( {{y_1} + \Delta {y_1}} \right)^2} + {w_{300\left( 1 \right)}}{\left( {{x_1} + \Delta {x_1}} \right)^3}\; + \\ & {w_{400\left( 1 \right)}}{\left( {{x_1} + \Delta {x_1}} \right)^4} + {w_{220\left( 1 \right)}}{\left( {{x_1} + \Delta {x_1}} \right)^2}{\left( {{y_1} + \Delta {y_1}} \right)^2}\; + \\ & {w_{040\left( 1 \right)}}{\left( {{y_1} + \Delta {y_1}} \right)^4} + {w_{500\left( 1 \right)}}{\left( {{x_1} + \Delta {x_1}} \right)^5} + \\ & {w_{140\left( 1 \right)}}\left( {{x_1} + \Delta {x_1}} \right){\left( {{y_1} + \Delta {y_1}} \right)^4} + \\ & {w_{320\left( 1 \right)}}{\left( {{x_1} + \Delta {x_1}} \right)^3}{\left( {{y_1} + \Delta {y_1}} \right)^2}\; + \\ & {w_{600\left( 1 \right)}}{\left( {{x_1} + \Delta {x_1}} \right)^6} + {w_{240\left( 1 \right)}}{\left( {{x_1} + \Delta {x_1}} \right)^2}{\left( {{y_1} + \Delta {y_1}} \right)^4} + \\ & {w_{420\left( 1 \right)}}{\left( {{x_1} + \Delta {x_1}} \right)^4}{\left( {{y_1} + \Delta {y_1}} \right)^2} + {w_{060\left( 1 \right)}}{\left( {{y_1} + \Delta {y_1}} \right)^6} \end{split} $ (13)

    View in Article

    $ w_{400}^{\left( S \right)} = 3\overline {w_{300}^{\varPsi 1}} $ (14)

    View in Article

    $ w_{220}^{\left( S \right)} = 3\overline {w_{300}^{\varPsi 2}} + \overline {w_{120}^{\varPsi 1}} + 2\overline {w_{120}^{\varPsi 3}} $ (15)

    View in Article

    $ w_{040}^{\left( S \right)} = \overline {w_{120}^{\varPsi 2}} $ (16)

    View in Article

    $ w_{500}^{\left( S \right)} = 4\overline {w_{400}^{\varPsi 1}} $ (17)

    View in Article

    $ w_{140}^{\left( S \right)} = 2\overline {w_{220}^{\varPsi 2}} + 4\overline {w_{040}^{\varPsi 3}} $ (18)

    View in Article

    $ w_{320}^{\left( S \right)} = 2\overline {w_{220}^{\varPsi 1}} + 2\overline {w_{220}^{\varPsi 3}} + 4\overline {w_{400}^{\varPsi 2}} $ (19)

    View in Article

    $ w_{600}^{\left( S \right)} = 5\overline {w_{500}^{\varPsi 1}} $ (20)

    View in Article

    $ w_{240}^{\left( S \right)} = \overline {w_{140}^{\varPsi 1}} + 4\overline {w_{140}^{\varPsi 3}} + 3\overline {w_{320}^{\varPsi 2}} $ (21)

    View in Article

    $ w_{420}^{\left( S \right)} = 5\overline {w_{500}^{\varPsi 2}} + 3\overline {w_{320}^{\varPsi 1}} + 2\overline {w_{320}^{\varPsi 3}} $ (22)

    View in Article

    $ w_{060}^{\left( S \right)} = \overline {w_{140}^{\varPsi 2}} $ (23)

    View in Article

    $ \overline {w_{ij0}^{\varPsi n}} = \sum\limits_{l = 1}^{g - 1} {A_{l|g}^i} B_{l|g}^j{\varPsi _{n\left( l \right)}}{w_{ij0\left( l \right)}}\;\;\left( {n = 1{,}\;2{,}\;3} \right) $ (24)

    View in Article

    $ {\varPsi _{1\left( i \right)}} = \sum\limits_{l = i}^{g - 1} {{A_{l + 1|g}}{\varGamma _{R\left( l \right)}}} $ (25)

    View in Article

    $ {\varPsi _{2\left( i \right)}} = \sum\limits_{l = i}^{g - 1} {\frac{{B_{l + 1|g}^2}}{{{A_{l + 1|g}}}}} {\varGamma _{\rho \left( l \right)}} $ (26)

    View in Article

    $ {\varPsi _{3\left( i \right)}} = \sum\limits_{l = i}^{g - 1} {{A_{l + 1|g}}} {\varGamma _{12\left( l \right)}} $ (27)

    View in Article

    $ {A_{k|g}} = \frac{{{x_k}}}{{{x_g}}} = \frac{{{{r'}_{m\left( k \right)}}{{r'}_{m\left( {k + 1} \right)}} \cdots {{r'}_{m\left( {g - 1} \right)}}\cos {\alpha _{k + 1}}\cos {\alpha _{k + 2}} \cdots \cos {\alpha _g}}}{{{r_{m\left( {k + 1} \right)}}{r_{m\left( {k + 2} \right)}} \cdots {r_{m\left( g \right)}}\cos {\beta _k}\cos {\beta _{k + 1}} \cdots \cos {\beta _{g - 1}}}} $ (28)

    View in Article

    $ {B_{k|g}} = \frac{{{y_k}}}{{{y_g}}} = {\left( { - 1} \right)^{g - k}} \cdot \frac{{{{r'}_{s\left( k \right)}}{{r'}_{s\left( {k + 1} \right)}} \cdots {{r'}_{s\left( {g - 1} \right)}}}}{{{r_{s\left( {k + 1} \right)}}{r_{s\left( {k + 2} \right)}} \cdots {r_{s\left( g \right)}}}} $ (29)

    View in Article

    $ {w_{ij0\left( T \right)}}{\rm{ = }}{\bar w_{ij0}} + w_{ij0}^{\left( E \right)} + w_{ij0}^{\left( S \right)} $ (30)

    View in Article

    Full Text
    Get PDF
    Figures&Tables (9)
    Equations (30)
    References (15)
    Get Citation
    Copy Citation Text
    Guozhu Hou, Lijun Lv, Yiqing Cao. Fish-eye lens system design based on sixth-order wave aberration theory[J]. Infrared and Laser Engineering, 2021, 50(6): 20200505
    Download Citation
    EndNote(RIS)
    BibTex
    Plain Text
    Tools
    Share
    Save the article for my favorites
    Paper Information
    Recommended Topics
    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology