Abstract

This paper presents an efficient approach to designing a Schmidt–Cassegrain objective for a remote sensing satellite. The objective is required to have multispectral operational bands, with three spectral channels distributed along the range (0.5 to 0.9μm), as well as a panchromatic channel; 4° field of view; distortion smaller than 0.3%; and a modulation transfer function, at 50  lines/mm spatial frequency, better than 0.5 and 0.35 at the center and edge of the field of view. The proposed design approach is based on Slyusarev’s theory of aberrations and optical design. An image quality index is formulated as a function of optical system component powers and axial distances. For each combination of parameters, there exists a possible solution that can be realized into a thin lens system by solving Seidel sum equations. The final design is then reached by a simple and quick optimization step. The best three designs are compared in terms of initial values of optical system parameters and final design specifications. The best system image quality is thoroughly analyzed. All three presented designs meet and exceed the required design specifications.

© 2009 Optical Society of America

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References

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  1. M. Laikin, Lens Design, 3rd ed. (Marcel Dekker, 2001).
  2. W. J. Smith, Modern Lens Design, 2nd ed. (McGraw-Hill, 2005).
  3. G. G. Slyusarev, Aberration and Optical Design Theory, 2nd ed. (Institute of Physics, 1997).
  4. B. G. Boone, Signal Processing Using Optics (Oxford U. Press, 1998).

Boone, B. G.

B. G. Boone, Signal Processing Using Optics (Oxford U. Press, 1998).

Laikin, M.

M. Laikin, Lens Design, 3rd ed. (Marcel Dekker, 2001).

Slyusarev, G. G.

G. G. Slyusarev, Aberration and Optical Design Theory, 2nd ed. (Institute of Physics, 1997).

Smith, W. J.

W. J. Smith, Modern Lens Design, 2nd ed. (McGraw-Hill, 2005).

Other

M. Laikin, Lens Design, 3rd ed. (Marcel Dekker, 2001).

W. J. Smith, Modern Lens Design, 2nd ed. (McGraw-Hill, 2005).

G. G. Slyusarev, Aberration and Optical Design Theory, 2nd ed. (Institute of Physics, 1997).

B. G. Boone, Signal Processing Using Optics (Oxford U. Press, 1998).

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Figures (13)

Fig. 1
Fig. 1

Schematic of Schmidt–Cassegrain objective.

Fig. 2
Fig. 2

Geometric construction for calculating the MTF, due to a diffraction-limited and centrally obscured optical system that is under incoherent illumination conditions.

Fig. 3
Fig. 3

MTF of a Schmidt–Cassegrain configuration at different k.

Fig. 4
Fig. 4

Axial ray is traced along a thin lens system.

Fig. 5
Fig. 5

(a) Steepness versus angle α 3 C 1 has two minima; (b) each diagram corresponds to a solution.

Fig. 6
Fig. 6

Vignetting introduced by optical baffles and central screening at FOV = (a)  2 ° , (b)  1.3 ° , (c)  1 ° , and (d)  0 ° .

Fig. 7
Fig. 7

Axial (a) transverse and (b) longitudinal spherical aberrations.

Fig. 8
Fig. 8

Off-axis aberrations. Fan of y tangential off-axis rays at inclination angles (a)  2 ° , (b)  1.3 ° , (c)  1 ° , and (d)  0 ° .

Fig. 9
Fig. 9

Aberrations due to fan of off-axis rays in the sagittal y plane, at inclination angles (a)  2 ° , (b)  1.3 ° , (c)  1 ° , and (d)  0 ° .

Fig. 10
Fig. 10

Aberrations due to fan of rays in the x sagittal plane, at inclination angles (a)  2 ° , (b)  1.3 ° , (c)  1 ° , and (d)  0 ° .

Fig. 11
Fig. 11

Chromatic aberrations: (a) magnification chromatism and (b) position chromatism.

Fig. 12
Fig. 12

Off-axis spot diagram.

Fig. 13
Fig. 13

Axial MTF compared to aberration-free MTF at spectral channels (a) I, (b) II, and (c) III.

Tables (3)

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Table 1 Design Specifications of the Best Three Solutions

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Table 2 Variation of Initial System Parameters After Conducting Optimization

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Table 3 Third-Order Aberrations of Initial Solution A and Final System

Equations (41)

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S I = i h i P i ,
S I I = i y i P i J i W i
S I I I = i y i 2 h i P i 2 J i y i h i W i + J 2 t ϕ t ,
S I V = t ϕ t n t ,
S V = i y i 3 h i 2 P i 3 J i y i 2 h i 2 W i + J 2 i y t h t φ t ( 3 + 1 n t ) ,
S I chromatic = t h t 2 ϕ t v t = t h t C t = t h t 2 ϕ t v t ,
S I I chromatic = 1 J i y i C i = 1 J t y t h t C t = t y t h t ϕ t v t ,
P = i ( α i + 1 α i 1 n i + 1 1 n i ) 2 ( α i + 1 n i + 1 α i n i ) ,
W = i ( α i + 1 α i 1 n i + 1 1 n i ) ( α i + 1 n i + 1 α i n i ) ,
C = i ( α i + 1 α i 1 n i + 1 1 n i ) ( 1 ( 1 / n i + 1 ) v i + 1 1 ( 1 / n i ) v i ) ,
MTF ( υ , ν ) = | OTF ( υ , ν ) | = | P ( λ z υ , λ z ν ) P ( λ z ( υ υ ) , λ z ( ν ν ) ) d υ d ν P 2 ( λ z υ , λ z ν ) d υ d ν | ,
MTF = ( 2 / π ( 1 k 2 ) ) ( A ( θ ) k 2 ( π + A ( β ) ) ) ; ( 1 k ) NA λ v > 0 = ( 2 / π ( 1 k 2 ) ) ( A ( θ ) A ( γ ) + k 2 ( A ( β ) A ( ϕ ) ) ) ; 2 k NA λ v > ( 1 k ) NA λ = ( 2 / π ( 1 k 2 ) ) ( A ( θ ) A ( γ ) k 2 A ( ϕ ) ) ; ( 1 + k ) NA λ v > 2 k NA λ = ( 2 / π ( 1 k 2 ) ) A ( θ ) ; 2 k NA λ v > ( 1 + k ) NA λ ,
A ( ξ ) = ξ cos ( ξ ) sin ( ξ ) , θ = cos 1 ( λ v 2 NA ) , γ = cos 1 ( λ v 2 NA + ( 1 k 2 ) NA 2 λ v ) , β = 1 ; k = 0 = cos 1 ( λ v 2 NA · k ) ; k 0 , ϕ = 1 ; k = 0 = cos 1 ( λ v 2 k · NA ( 1 k 2 ) NA 2 k λ v ) ; k 0 ,
α k + 1 = α k + h k ϕ k .
α 2 = ϕ 1 ,
h 2 = 1 d ϕ 1 ,
α 3 = k + d ϕ 1 1 d ,
α 6 = 1 , h 6 = 0 h 5 = δ ,
α 5 = 1 δ ϕ 22 ,
h 4 = δ + d 2 ( 1 δ ϕ 22 ) ,
α 4 = 1 δ ϕ 22 ϕ 21 ( δ + d 2 ( 1 δ ϕ 22 ) ) .
k = δ + d 1 ( 1 δ ϕ 22 ( d 2 ( 1 δ ϕ 22 ) + δ ) ϕ 21 ) + d 2 ( 1 δ ϕ 22 ) ,
L = d 1 + d 2 + δ .
β k + 1 = β k n k n k + 1 + y k n k + 1 n k n k + 1 R k ,
y 2 = d ,
y 3 = 2 d ( 1 + d f R m 1 ) ,
y 4 = d 1 ( ψ + 2 d f R m 2 ) 2 d ( 1 + d f R m 1 ) ,
y 5 = d 2 ( 2 d f R m 2 + ψ ) ( 1 d 2 ϕ 22 ) · ( 2 d ( 1 + d f R m 1 ) + d 1 ( ψ + 2 d f R m 2 ) ) .
R m 1 = 2 f d 1 ( 1 d 1 ϕ 1 ) k 1 2 d 1 ϕ 1 ,
R m 2 = 2 f k d 1 2 k 1 L + d 1 ( 1 + ϕ 1 ) ,
R 1 C 1 = f n 1 C 1 1 n 1 C 1 α 2 C 1 ,
R 2 C 1 = f 1 n 1 C 1 α 3 C 1 n 1 C 1 α 2 C 1 ,
R 3 C 1 = f n 2 C 1 1 n 2 C 1 α 4 C 1 α 3 C 1 ,
R 4 C 1 = f 1 n 2 C 1 ϕ 1 n 2 C 1 α 4 C 1 ,
2 α 2 C 1 = α 3 C 1 ( 2 n + 1 ) n + 2 ( n 1 ) W 1 α 3 C 1 ( n + 1 ) P 1 ( n 2 1 ) W 1 n ( 2 + n ) ,
2 α 4 C 1 = α 3 C 1 ( 2 n + 1 ) n + 2 + ( n 1 ) W 1 α 3 C 1 ( n + 1 ) P 1 ( n 2 1 ) W 1 n ( 2 + n ) ,
S = ( α 2 c 1 ) 2 + ( α 3 c 1 α 2 c 1 ) 2 + ( α 4 c 1 α 3 c 1 ) 2 + ( α 4 c 1 ) 2 .
R 1 C 2 = f ( δ + d 2 σ ) ( n 1 C 2 1 ) n 1 C 2 α 2 C 2 ( σ ϕ 21 ( δ + d 2 σ ) ) ,
R 2 C 2 = f ( δ + d 2 σ ) ( 1 n 1 C 2 ) σ n 1 C 2 α 2 C 2 ,
R 3 C 2 = f δ ( n 2 C 2 1 ) n 2 C 2 α 4 C 2 σ ,
R 4 C 2 = f δ ( 1 n 2 C 2 ) 1 n 2 C 2 α 4 C 2 ,

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