Construction method of axially asymmetric lenses

Akira Yabe

doi:10.1364/AO.50.003369

Applied Optics
Vol. 50,
Issue 19,
pp. 3369-3374
(2011)
•https://doi.org/10.1364/AO.50.003369

Construction method of axially asymmetric lenses

Akira Yabe

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Akira Yabe, "Construction method of axially asymmetric lenses," Appl. Opt. 50, 3369-3374 (2011)

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Abstract

A method to find the optimal position of tilt surfaces to construct axially asymmetric lens systems is proposed. The tilt surface number is extended to the real number and included in the independent variables of the optimization.

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a. Singlet without tilt
Surface Curvature		Distance	Index	Tilt
1	C1	D1	N1	0
2	C2	D2	1	0
b. Tilt at the front surface
Surface Curvature		Distance	Index	Tilt
1	C1	D1	N1	T
2	C2	D2	1	0
c. Tilt at the rear surface
Surface Curvature		Distance	Index	Tilt
1	C1	D1	N1	0
2	C2	D2	1	$- T$
d. Addition of a thin layer of glass before the front surface
Surface Curvature		Distance	Index	Tilt
1	C1	0	N1	0
a	C1	0	1	0
b	C1	D1	N1	T
2	C2	D2	1	0
e. Addition of a thin layer of glass after the rear surface
Surface Curvature		Distance	Index	Tilt
1	C1	D1	N1	0
a	C2	0	1	$- T$
b	C2	0	N1	0
2	C2	D2	1	0
f. Intermediate state with interpolation ratio 1:3
Surface Curvature		Distance	Index	Tilt
1	C1	$D 1 / 4$	N1	0
a	$(C 1^{*} 3 + C 2) / 4$	0	1	$- T / 4$
b	$(C 1^{*} 3 + C 2) / 4$	$D 1^{*} 3 / 4$	N1	$T^{*} 3 / 4$
2	C2	D2	1	0
g. Intermediate state with interpolation ratio of 2:2
Surface Curvature		Distance	Index	Tilt
1	C1	$D 1 / 2$	N1	0
a	$(C 1 + C 2) / 2$	0	1	$- T / 2$
b	$(C 1 + C 2) / 2$	$D 1 / 2$	N1	$T / 2$
2	C2	D2	1	0
h. Intermediate state with interpolation ratio of 3:1
Surface Curvature		Distance	Index	Tilt
1	C1	$D 1^{*} 3 / 4$	N1	0
a	$(C 1 + C 2^{*} 3) / 4$	0	1	$- T^{*} 3 / 4$
b	$(C 1 + C 2^{*} 3) / 4$	$D 1 / 4$	N1	$T / 4$
2	C2	D2	1	0

Surface Curvature		Distance	Index	Tilt
a. Doublet without tilt
1	0	D1	N1	0
2	C2	D2	1	0
3	C3	D3	N3	0
4	0	D4	1	0
b. Tilt at the rear surface of the first lens
1	0	D1	N1	0
2	C2	D2	1	$- T$
3	C3	D3	N3	0
4	0	D4	1	0
c. Tilt at the front surface of the second lens
1	0	D1	N1	0
2	C2	D2	1	0
3	C3	D3	N3	T
4	0	D4	1	0
d. Addition of a thin layer of air before the rear surface of the first lens
1	0	D1	N1	0
2	C2	0	1	0
c	C2	0	N1	0
d	C2	D2	1	$- T$
3	C3	D3	N3	0
4	0	D4	1	0
e. Addition of a thin layer of air after the front surface of the second lens
1	0	D1	N1	0
2	C2	D2	1	0
c	C3	0	N3	T
d	C3	0	1	0
3	C3	D3	N3	0
4	0	D4	1	0
f. Intermediate state with interpolation ratio of 1:3
1	0	D1	N1	0
2	C2	$D 2 / 4$	1	0
$c^{'}$	$(C 2^{*} 3 + C 3) / 4$	0	$(N 1^{*} 3 + N 3) / 4$	$T / 4$
$d^{'}$	$(C 2^{*} 3 + C 3) / 4$	$D 2^{*} 3 / 4$	1	$- T^{*} 3 / 4$
3	C3	D3	N3	0
4	0	D4	1	0
g. Intermediate state with interpolation ratio of 2:2
1	0	D1	N1	0
2	C2	$D 2 / 2$	1	0
$c^{'}$	$(C 2 + C 3) / 2$	0	$(N 1 + N 3) / 2$	$T / 2$
$d^{'}$	$(C 2 + C 3) / 2$	$D 2 / 2$	1	$- T / 2$
3	C3	D3	N3	0
4	0	D4	1	0
h. Intermediate state with interpolation ratio of 3:1
1	0	D1	N1	0
2	C2	$D 2^{*} 3 / 4$	1	0
$c^{'}$	$(C 2 + C 3^{*} 3) / 4$	0	$(N 1 + {N 3}^{*} 3) / 4$	$T^{*} 3 / 4$
$d^{'}$	$(C 2 + C 3^{*} 3) / 4$	$D 2 / 4$	1	$- T / 4$
3	C3	D3	N3	0
4	0	D4	1	0

a. Another definition of the intermediate state of the singlet
Surface Curvature		Distance	Index	Tilt
1	C1	D1	N1	$T / 2$
2	C2	D2	1	$- T / 2$
b. Another definition of the intermediate state of the doublet
Surface Curvature		Distance	Index	Tilt
1	0	D1	N1	0
2	C2	D2	1	$- T / 2$
3	C3	D3	N3	$T / 2$
4	0	D4	1	0

Surface	Tilt (deg)
4	19.0390791
5	4.3986189
9	$- 6.9849731$
10	$- 6.2928789$
21	$- 0.0009493$
23	0.5493747

a. Singlet without tilt
Surface Curvature		Distance	Index	Tilt
1	C1	D1	N1	0
2	C2	D2	1	0
b. Tilt at the front surface
Surface Curvature		Distance	Index	Tilt
1	C1	D1	N1	T
2	C2	D2	1	0
c. Tilt at the rear surface
Surface Curvature		Distance	Index	Tilt
1	C1	D1	N1	0
2	C2	D2	1	$- T$
d. Addition of a thin layer of glass before the front surface
Surface Curvature		Distance	Index	Tilt
1	C1	0	N1	0
a	C1	0	1	0
b	C1	D1	N1	T
2	C2	D2	1	0
e. Addition of a thin layer of glass after the rear surface
Surface Curvature		Distance	Index	Tilt
1	C1	D1	N1	0
a	C2	0	1	$- T$
b	C2	0	N1	0
2	C2	D2	1	0
f. Intermediate state with interpolation ratio 1:3
Surface Curvature		Distance	Index	Tilt
1	C1	$D 1 / 4$	N1	0
a	$(C 1^{*} 3 + C 2) / 4$	0	1	$- T / 4$
b	$(C 1^{*} 3 + C 2) / 4$	$D 1^{*} 3 / 4$	N1	$T^{*} 3 / 4$
2	C2	D2	1	0
g. Intermediate state with interpolation ratio of 2:2
Surface Curvature		Distance	Index	Tilt
1	C1	$D 1 / 2$	N1	0
a	$(C 1 + C 2) / 2$	0	1	$- T / 2$
b	$(C 1 + C 2) / 2$	$D 1 / 2$	N1	$T / 2$
2	C2	D2	1	0
h. Intermediate state with interpolation ratio of 3:1
Surface Curvature		Distance	Index	Tilt
1	C1	$D 1^{*} 3 / 4$	N1	0
a	$(C 1 + C 2^{*} 3) / 4$	0	1	$- T^{*} 3 / 4$
b	$(C 1 + C 2^{*} 3) / 4$	$D 1 / 4$	N1	$T / 4$
2	C2	D2	1	0

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Applied Optics