• Infrared and Laser Engineering
  • Vol. 49, Issue 7, 20190519 (2020)

Abstract

The zoom fish-eye lens had the characteristics of much larger field-of-view angle, much larger relative aperture, and much larger anti-far ratio. In the work described in this paper, the initial structure of a fish-eye lens with fixed focal length was firstly designed using the theory of a plane symmetric optical system. And then the initial structure components of the fish-eye lens were divided into two groups, the former-group and the rear-group, and then the entire zoom fish-eye lens system was optimized using Gaussian optical theory. Finally, a zoom fish-eye lens system with good imaging quality was obtained. This fish-eye lens system had a field-of-view angle of 180° with an 8 mm short focal length and a field-of-view angle of 90° with a 16 mm long focal length. Its relative aperture was 1/3.5. The design results show that the modulation transfer function of this zoom lens system at different focal lengths is no less than 0.45 when the spatial frequency is 50 lp/mm. This zoom fish-eye photographic objective lens had higher imaging quality than other zoom fish-eye lenses.
$ \mathop \sum \limits_{i = 1}^{{2}}\Delta {L_{{i}}} = \left( {{{{L}}_1} - {{L}}_1^{{'}}} \right) + \left( {{{{L}}_2} - {{L}}_2^{{'}}} \right) = 0 $ (1)

View in Article

$ {L_{{\rm{min}}}} = 4{{f}}' $ (2)

View in Article

$\mathop \sum \limits_{i = 1}^{{n}} \frac{{1 - m_i^2}}{{m_i^2}}f_i^{{'}}{\rm{d}}{m_i} = 0$ (3)

View in Article

$s = {r_2}\left( {1 + \frac{{\sin \left( {{\theta _2} - {\omega _2}} \right)}}{{\sin {\omega _2}}}} \right)$ (4)

View in Article

$ \sin \theta = \frac{{{h_2}}}{{{r_2}}} \equiv k $ (5)

View in Article

$ \sin {\alpha _{{\rm{i}} + 1}} = \frac{{{r_{i + 1}} + {d_i} - {r_i}}}{{{\rho _{i + 1}}}}\sin {\omega _i} + \frac{{{\rho _i}}}{{{\rho _{i + 1}}}}\sin {\beta _i} $ (6)

View in Article

$ {\omega _{\rm{i}}} = {\omega _{i - 1}} + {\beta _i} - {\alpha _i} = {\omega _0} + \sum\limits_{i = 1}^i {\left( {{\beta _i} - {\alpha _i}} \right)} $ (7)

View in Article

$ {\beta _j} = \arcsin \left( {\frac{{{n_{i - 1}}}}{{{n_i}}}\sin {\alpha _i}} \right) $ (8)

View in Article

$ {{{S}}_{\rm{I}}} = \sum\limits_{i = 1}^k {h_i^4} \varphi _i^3{P_i} $ (9)

View in Article

$ {{{S}}_{{\rm{II}}}} = \sum\limits_{i = 1}^k {h_i^3} {h_{pi}}\varphi _i^3{P_i} - J\sum\limits_{i = 1}^k {h_i^3} \varphi _i^2{W_i} $ (10)

View in Article

$ {{{S}}_{{\rm{III}}}} = \sum\limits_{i = 1}^k {h_i^2} h_{{{pi}}}^2\varphi _i^3{P_i} - 2J\sum\limits_{i = 1}^k {{h_i}} {h_{pi}}\varphi _i^2{W_i} + {J^2}\sum\limits_{i = 1}^k {{\varphi _i}} $ (11)

View in Article

$ {{{S}}_{{V}}} = \sum\limits_{i = 1}^k {{h_i}} h_{{{pi}}}^3\varphi _i^3{P_i} - 3J\sum\limits_{i = 1}^k {h_{pi}^2} \varphi _i^2{W_i} + {J^2}\sum\limits_{i = 1}^k {\frac{{{h_{pi}}}}{{{h_i}}}} (3 + \mu ){\varphi _i} $ (12)

View in Article

$ \mu = \dfrac{{\displaystyle \sum\limits_{i = 1}^k {\dfrac{{{\phi _i}}}{{{n_i}}}} }}{{\displaystyle \sum\limits_{i = 1}^k {{\phi _i}} }} \approx 0.6 - 0.65 $ (13)

View in Article

$ {P_i} = P_i^\infty + {u_i}\left( {4{W}_i^\infty - 1} \right) + u_i^2(3 + 2\mu ) $ (14)

View in Article

$ {W_i} = W_i^\infty + (2 + \mu ){u_i} $ (15)

View in Article

$ {u_i} = {u_i}/{h_i}{\varphi _i} = f_i^\prime /{l_i} $ (16)

View in Article