Abstract

A conformal dome was designed and the aberration characteristics of the dome were analyzed using Zernike aberration theory. By deriving the equation used to correct Zernike aberrations, the phase coefficients and the phase orders of diffractive optical elements (DOEs) used to correct primary Zernike aberrations were obtained. DOEs were simulated to correct the aberrations of the conformal dome by using optical design software, and the aberrations of the conformal dome decreased dramatically. Finally, a complete cooled conformal optical system was designed. The results show that the number of the fixed corrector’s elements decreases by using DOEs, and the optical system has better imaging quality.

© 2013 Optical Society of America

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References

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    [CrossRef]
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2010 (1)

Y. M. Liu, J. Ma, H. P. Ma, and X. Z. Jiang, “Zernike aberration characteristics of precision conformal optical windows,” Proc. SPIE 7544, 75443W (2010).
[CrossRef]

2009 (2)

Y. Li, L. Li, Y. F. Huang, and J. G. Liu, “Conformal optical design with combination of static and dynamic aberration corrections,” Chin. Phys. B 18, 565–570 (2009).
[CrossRef]

J. Chang, L. P. Liu, D. W. Cheng, and N. Zhao, “Design of infrared optical system with special dome,” J. Infrared Millim. Waves 28, 204–206 (2009).
[CrossRef]

2008 (1)

D. X. Li, Z. W. Lu, Q. Sun, and Z. F. Lu, “Design of conformal optical system based on real ray tracing,” Infrared Laser Eng. 37, 834–838 (2008).

2007 (1)

J. X. Sun, Q. Sun, D. X. Li, and Z. W. Lu, “Conformal dome aberration correction with diffractive elements,” Acta Phys. Sin. 56, 3900–3905 (2007).

2001 (2)

P. A. Trotta, “Precision conformal optics technology program,” Proc. SPIE 4375, 96–107 (2001).
[CrossRef]

P. A. Trotta, “Precision conformal optics technology program,” Proc. SPIE 4375, 96–107 (2001).
[CrossRef]

2000 (1)

S. W. Sparrold, J. P. Mills, D. J. Knapp, K. S. Ellis, T. A. Mitchell, and P. K. Manhart, “Conformal dome correction with counter-rotating phase plates,” Opt. Eng. 39, 1822–1829 (2000).
[CrossRef]

1999 (2)

S. W. Sparrold, “Arch corrector for conformal optical systems,” Proc. SPIE 3705, 189–200 (1999).
[CrossRef]

S. W. Sparrold, D. J. Knapp, P. K. Manhart, and K. W. Elsberry, “Capabilities of an arch element for correcting conformal optical domes,” Proc. SPIE 3779, 434–444 (1999).

1998 (1)

B. G. Crowther, D. B. McKenney, and J. P. Mills, “Aberrations of optical domes,” Proc. SPIE 3482, 48–61 (1998).
[CrossRef]

1992 (1)

1989 (1)

1977 (2)

Buralli, D. A.

Chang, J.

J. Chang, L. P. Liu, D. W. Cheng, and N. Zhao, “Design of infrared optical system with special dome,” J. Infrared Millim. Waves 28, 204–206 (2009).
[CrossRef]

Cheng, D. W.

J. Chang, L. P. Liu, D. W. Cheng, and N. Zhao, “Design of infrared optical system with special dome,” J. Infrared Millim. Waves 28, 204–206 (2009).
[CrossRef]

Crowther, B. G.

B. G. Crowther, D. B. McKenney, and J. P. Mills, “Aberrations of optical domes,” Proc. SPIE 3482, 48–61 (1998).
[CrossRef]

Ellis, K. S.

S. W. Sparrold, J. P. Mills, D. J. Knapp, K. S. Ellis, T. A. Mitchell, and P. K. Manhart, “Conformal dome correction with counter-rotating phase plates,” Opt. Eng. 39, 1822–1829 (2000).
[CrossRef]

Elsberry, K. W.

S. W. Sparrold, D. J. Knapp, P. K. Manhart, and K. W. Elsberry, “Capabilities of an arch element for correcting conformal optical domes,” Proc. SPIE 3779, 434–444 (1999).

Huang, Y. F.

Y. Li, L. Li, Y. F. Huang, and J. G. Liu, “Conformal optical design with combination of static and dynamic aberration corrections,” Chin. Phys. B 18, 565–570 (2009).
[CrossRef]

Jiang, X. Z.

Y. M. Liu, J. Ma, H. P. Ma, and X. Z. Jiang, “Zernike aberration characteristics of precision conformal optical windows,” Proc. SPIE 7544, 75443W (2010).
[CrossRef]

Kleinhans, W. A.

Knapp, D. J.

S. W. Sparrold, J. P. Mills, D. J. Knapp, K. S. Ellis, T. A. Mitchell, and P. K. Manhart, “Conformal dome correction with counter-rotating phase plates,” Opt. Eng. 39, 1822–1829 (2000).
[CrossRef]

S. W. Sparrold, D. J. Knapp, P. K. Manhart, and K. W. Elsberry, “Capabilities of an arch element for correcting conformal optical domes,” Proc. SPIE 3779, 434–444 (1999).

Li, D. X.

D. X. Li, Z. W. Lu, Q. Sun, and Z. F. Lu, “Design of conformal optical system based on real ray tracing,” Infrared Laser Eng. 37, 834–838 (2008).

J. X. Sun, Q. Sun, D. X. Li, and Z. W. Lu, “Conformal dome aberration correction with diffractive elements,” Acta Phys. Sin. 56, 3900–3905 (2007).

Li, L.

Y. Li, L. Li, Y. F. Huang, and J. G. Liu, “Conformal optical design with combination of static and dynamic aberration corrections,” Chin. Phys. B 18, 565–570 (2009).
[CrossRef]

Li, Y.

Y. Li, L. Li, Y. F. Huang, and J. G. Liu, “Conformal optical design with combination of static and dynamic aberration corrections,” Chin. Phys. B 18, 565–570 (2009).
[CrossRef]

Liu, J. G.

Y. Li, L. Li, Y. F. Huang, and J. G. Liu, “Conformal optical design with combination of static and dynamic aberration corrections,” Chin. Phys. B 18, 565–570 (2009).
[CrossRef]

Liu, L. P.

J. Chang, L. P. Liu, D. W. Cheng, and N. Zhao, “Design of infrared optical system with special dome,” J. Infrared Millim. Waves 28, 204–206 (2009).
[CrossRef]

Liu, Y. M.

Y. M. Liu, J. Ma, H. P. Ma, and X. Z. Jiang, “Zernike aberration characteristics of precision conformal optical windows,” Proc. SPIE 7544, 75443W (2010).
[CrossRef]

Lu, Z. F.

D. X. Li, Z. W. Lu, Q. Sun, and Z. F. Lu, “Design of conformal optical system based on real ray tracing,” Infrared Laser Eng. 37, 834–838 (2008).

Lu, Z. W.

D. X. Li, Z. W. Lu, Q. Sun, and Z. F. Lu, “Design of conformal optical system based on real ray tracing,” Infrared Laser Eng. 37, 834–838 (2008).

J. X. Sun, Q. Sun, D. X. Li, and Z. W. Lu, “Conformal dome aberration correction with diffractive elements,” Acta Phys. Sin. 56, 3900–3905 (2007).

Ma, H. P.

Y. M. Liu, J. Ma, H. P. Ma, and X. Z. Jiang, “Zernike aberration characteristics of precision conformal optical windows,” Proc. SPIE 7544, 75443W (2010).
[CrossRef]

Ma, J.

Y. M. Liu, J. Ma, H. P. Ma, and X. Z. Jiang, “Zernike aberration characteristics of precision conformal optical windows,” Proc. SPIE 7544, 75443W (2010).
[CrossRef]

Manhart, P. K.

S. W. Sparrold, J. P. Mills, D. J. Knapp, K. S. Ellis, T. A. Mitchell, and P. K. Manhart, “Conformal dome correction with counter-rotating phase plates,” Opt. Eng. 39, 1822–1829 (2000).
[CrossRef]

S. W. Sparrold, D. J. Knapp, P. K. Manhart, and K. W. Elsberry, “Capabilities of an arch element for correcting conformal optical domes,” Proc. SPIE 3779, 434–444 (1999).

McKenney, D. B.

B. G. Crowther, D. B. McKenney, and J. P. Mills, “Aberrations of optical domes,” Proc. SPIE 3482, 48–61 (1998).
[CrossRef]

Mills, J. P.

S. W. Sparrold, J. P. Mills, D. J. Knapp, K. S. Ellis, T. A. Mitchell, and P. K. Manhart, “Conformal dome correction with counter-rotating phase plates,” Opt. Eng. 39, 1822–1829 (2000).
[CrossRef]

B. G. Crowther, D. B. McKenney, and J. P. Mills, “Aberrations of optical domes,” Proc. SPIE 3482, 48–61 (1998).
[CrossRef]

Mitchell, T. A.

S. W. Sparrold, J. P. Mills, D. J. Knapp, K. S. Ellis, T. A. Mitchell, and P. K. Manhart, “Conformal dome correction with counter-rotating phase plates,” Opt. Eng. 39, 1822–1829 (2000).
[CrossRef]

Morris, G. M.

Sparrold, S. W.

S. W. Sparrold, J. P. Mills, D. J. Knapp, K. S. Ellis, T. A. Mitchell, and P. K. Manhart, “Conformal dome correction with counter-rotating phase plates,” Opt. Eng. 39, 1822–1829 (2000).
[CrossRef]

S. W. Sparrold, “Arch corrector for conformal optical systems,” Proc. SPIE 3705, 189–200 (1999).
[CrossRef]

S. W. Sparrold, D. J. Knapp, P. K. Manhart, and K. W. Elsberry, “Capabilities of an arch element for correcting conformal optical domes,” Proc. SPIE 3779, 434–444 (1999).

Sun, J. X.

J. X. Sun, Q. Sun, D. X. Li, and Z. W. Lu, “Conformal dome aberration correction with diffractive elements,” Acta Phys. Sin. 56, 3900–3905 (2007).

Sun, Q.

D. X. Li, Z. W. Lu, Q. Sun, and Z. F. Lu, “Design of conformal optical system based on real ray tracing,” Infrared Laser Eng. 37, 834–838 (2008).

J. X. Sun, Q. Sun, D. X. Li, and Z. W. Lu, “Conformal dome aberration correction with diffractive elements,” Acta Phys. Sin. 56, 3900–3905 (2007).

Sweatt, W. C.

Trotta, P. A.

P. A. Trotta, “Precision conformal optics technology program,” Proc. SPIE 4375, 96–107 (2001).
[CrossRef]

P. A. Trotta, “Precision conformal optics technology program,” Proc. SPIE 4375, 96–107 (2001).
[CrossRef]

Zhao, N.

J. Chang, L. P. Liu, D. W. Cheng, and N. Zhao, “Design of infrared optical system with special dome,” J. Infrared Millim. Waves 28, 204–206 (2009).
[CrossRef]

Acta Phys. Sin. (1)

J. X. Sun, Q. Sun, D. X. Li, and Z. W. Lu, “Conformal dome aberration correction with diffractive elements,” Acta Phys. Sin. 56, 3900–3905 (2007).

Appl. Opt. (3)

Chin. Phys. B (1)

Y. Li, L. Li, Y. F. Huang, and J. G. Liu, “Conformal optical design with combination of static and dynamic aberration corrections,” Chin. Phys. B 18, 565–570 (2009).
[CrossRef]

Infrared Laser Eng. (1)

D. X. Li, Z. W. Lu, Q. Sun, and Z. F. Lu, “Design of conformal optical system based on real ray tracing,” Infrared Laser Eng. 37, 834–838 (2008).

J. Infrared Millim. Waves (1)

J. Chang, L. P. Liu, D. W. Cheng, and N. Zhao, “Design of infrared optical system with special dome,” J. Infrared Millim. Waves 28, 204–206 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

S. W. Sparrold, J. P. Mills, D. J. Knapp, K. S. Ellis, T. A. Mitchell, and P. K. Manhart, “Conformal dome correction with counter-rotating phase plates,” Opt. Eng. 39, 1822–1829 (2000).
[CrossRef]

Proc. SPIE (6)

P. A. Trotta, “Precision conformal optics technology program,” Proc. SPIE 4375, 96–107 (2001).
[CrossRef]

P. A. Trotta, “Precision conformal optics technology program,” Proc. SPIE 4375, 96–107 (2001).
[CrossRef]

S. W. Sparrold, D. J. Knapp, P. K. Manhart, and K. W. Elsberry, “Capabilities of an arch element for correcting conformal optical domes,” Proc. SPIE 3779, 434–444 (1999).

B. G. Crowther, D. B. McKenney, and J. P. Mills, “Aberrations of optical domes,” Proc. SPIE 3482, 48–61 (1998).
[CrossRef]

S. W. Sparrold, “Arch corrector for conformal optical systems,” Proc. SPIE 3705, 189–200 (1999).
[CrossRef]

Y. M. Liu, J. Ma, H. P. Ma, and X. Z. Jiang, “Zernike aberration characteristics of precision conformal optical windows,” Proc. SPIE 7544, 75443W (2010).
[CrossRef]

Other (1)

CODE V Reference Manual, ORA (Optical Research Associates).

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Figures (6)

Fig. 1.
Fig. 1.

Schematic of a seeker with an ellipsoidal dome.

Fig. 2.
Fig. 2.

Aberration characteristics of an ellipsoidal dome at different FOR.

Fig. 3.
Fig. 3.

Conformal optical system with fixed correctors.

Fig. 4.
Fig. 4.

Aberration characteristics of conformal optical system after optimization.

Fig. 5.
Fig. 5.

Schematic of a cooled conformal optical system.

Fig. 6.
Fig. 6.

Modulation transfer function (MTF) of conformal optical system with FOR (a) 0°, (b) 10°, (c) 20°, and (d) 30°.

Tables (4)

Tables Icon

Table 1. Zernike Aberration Polynomial

Tables Icon

Table 2. Parameters of an Ellipsoidal Dome

Tables Icon

Table 3. Zernike Aberrations and their Corresponding Diffractive Phase Coefficients

Tables Icon

Table 4. Phase Coefficients of Diffractive Elements

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

F = L D ,
r = D 4 F ,
k = 1 4 F 2 1 ,
ϕ ( x , y ) = 2 π λ n , m a n m x n y m ,
OPD ( r , θ ) = 2 π n , m a n m r n + m ( cos θ ) n ( sin θ ) m .
OPD ( r , θ ) = A 00 + 1 2 n = 2 A n 0 R n 0 + n = 1 m = 1 A n m R n m ( r ) ( cos m θ + sin m θ ) ,
R n m ( r ) = 1 [ ( n m ) / 2 ] ! r m [ d d ( r 2 ) ] ( n m ) / 2 × [ ( r 2 ) ( n + m ) / 2 ( r 2 1 ) ( n m ) / 2 ] .
2 π n , m a n m r n + m ( cos θ ) n ( sin θ ) m = A 00 + 1 2 n = 2 A n 0 R n 0 + n = 1 m = 1 R n m ( r ) ( cos m θ + sin m θ ) .
OPD ( r , θ ) = A r 2 cos 2 θ .

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