Abstract

A modified Schwarzschild imaging spectrometer utilizing three nonconcentric aspheric mirrors and a plane grating is designed that can handle low F-number, long slit, and broad spectral range. Based on the geometrical aberration theory and Rowland circle condition, the astigmatism-correcting method of the Schwarzschild imaging spectrometer is analyzed. The design procedure of initial parameters is programmed using Matlab software. As an example, a modified Schwarzschild imaging spectrometer operating in 400–1000 nm waveband with F-number of 2.5 and slit length of 13 mm is designed, and good imaging quality is obtained.

© 2013 Optical Society of America

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References

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  1. H. A. Bender, P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design, performance and tolerancing of next-generation air borne imaging spectrometers,” Proc. SPIE 7812, 78120P (2010).
    [CrossRef]
  2. X. Prieto-Blanco, C. Montero-Orille, H. González-Núñez, M. D. Mouriz, E. L. Lago, and R. de la Fuente, “The Offner imaging spectrometer in quadrature,” Opt. Express 18, 12756–12769 (2010).
    [CrossRef]
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  4. D. R. Austin, T. Witting, and I. A. Walmsley, “Broadband astigmatism-free Czerny–Turner using spherical mirrors,” Appl. Opt. 48, 3846–3853 (2009).
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  5. S. H. Kim, H. J. Kong, H. Ku, and J. H. Lee, “Analytical design of a hyper-spectral imaging spectrometer utilizing a convex grating,” Proc. SPIE 8515, 85150V (2012).
    [CrossRef]
  6. X. Prieto-Blanco, C. Montero-Orille, B. Couce, and R. de la Fuente, “Analytical design of an Offner imaging spectrometer,” Opt. Express 14, 9156–9168 (2006).
    [CrossRef]
  7. M. D. Mouriz, E. L. Lago, X. Prieto-Blanco, H. González-Núñez, and R. de la Fuente, “Schwarzschild spectrometer,” Appl. Opt. 50, 2418–2424 (2011).
    [CrossRef]
  8. J. Fisher, J. Antoniades, C. Rollins, and L. Xiang, “A hyperspectral imaging sensor for the coastal environment,” Proc. SPIE 3115, 179–185 (2000).
  9. P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design of a coastal ocean imaging spectrometer,” Opt. Express 16, 9087–9096 (2008).
    [CrossRef]
  10. H. Beutler, “The theory of concave grating,” J. Opt. Soc. Am. 35, 311–350 (1945).
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  11. ZEMAX is a trademark of Zemax development Corporation, Bellevue, Washington 98004, USA.

2012 (1)

S. H. Kim, H. J. Kong, H. Ku, and J. H. Lee, “Analytical design of a hyper-spectral imaging spectrometer utilizing a convex grating,” Proc. SPIE 8515, 85150V (2012).
[CrossRef]

2011 (1)

2010 (2)

H. A. Bender, P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design, performance and tolerancing of next-generation air borne imaging spectrometers,” Proc. SPIE 7812, 78120P (2010).
[CrossRef]

X. Prieto-Blanco, C. Montero-Orille, H. González-Núñez, M. D. Mouriz, E. L. Lago, and R. de la Fuente, “The Offner imaging spectrometer in quadrature,” Opt. Express 18, 12756–12769 (2010).
[CrossRef]

2009 (2)

2008 (1)

2006 (1)

2000 (1)

J. Fisher, J. Antoniades, C. Rollins, and L. Xiang, “A hyperspectral imaging sensor for the coastal environment,” Proc. SPIE 3115, 179–185 (2000).

1945 (1)

Antoniades, J.

J. Fisher, J. Antoniades, C. Rollins, and L. Xiang, “A hyperspectral imaging sensor for the coastal environment,” Proc. SPIE 3115, 179–185 (2000).

Austin, D. R.

Bender, H. A.

H. A. Bender, P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design, performance and tolerancing of next-generation air borne imaging spectrometers,” Proc. SPIE 7812, 78120P (2010).
[CrossRef]

Beutler, H.

Couce, B.

de la Fuente, R.

Fisher, J.

J. Fisher, J. Antoniades, C. Rollins, and L. Xiang, “A hyperspectral imaging sensor for the coastal environment,” Proc. SPIE 3115, 179–185 (2000).

González-Núñez, H.

Green, R. O.

H. A. Bender, P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design, performance and tolerancing of next-generation air borne imaging spectrometers,” Proc. SPIE 7812, 78120P (2010).
[CrossRef]

P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design of a coastal ocean imaging spectrometer,” Opt. Express 16, 9087–9096 (2008).
[CrossRef]

Kim, S. H.

S. H. Kim, H. J. Kong, H. Ku, and J. H. Lee, “Analytical design of a hyper-spectral imaging spectrometer utilizing a convex grating,” Proc. SPIE 8515, 85150V (2012).
[CrossRef]

Kong, H. J.

S. H. Kim, H. J. Kong, H. Ku, and J. H. Lee, “Analytical design of a hyper-spectral imaging spectrometer utilizing a convex grating,” Proc. SPIE 8515, 85150V (2012).
[CrossRef]

Ku, H.

S. H. Kim, H. J. Kong, H. Ku, and J. H. Lee, “Analytical design of a hyper-spectral imaging spectrometer utilizing a convex grating,” Proc. SPIE 8515, 85150V (2012).
[CrossRef]

Lago, E. L.

Lee, J. H.

S. H. Kim, H. J. Kong, H. Ku, and J. H. Lee, “Analytical design of a hyper-spectral imaging spectrometer utilizing a convex grating,” Proc. SPIE 8515, 85150V (2012).
[CrossRef]

Lu, F.

Montero-Orille, C.

Mouriz, M. D.

Mouroulis, P.

H. A. Bender, P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design, performance and tolerancing of next-generation air borne imaging spectrometers,” Proc. SPIE 7812, 78120P (2010).
[CrossRef]

P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design of a coastal ocean imaging spectrometer,” Opt. Express 16, 9087–9096 (2008).
[CrossRef]

Prieto-Blanco, X.

Rollins, C.

J. Fisher, J. Antoniades, C. Rollins, and L. Xiang, “A hyperspectral imaging sensor for the coastal environment,” Proc. SPIE 3115, 179–185 (2000).

Walmsley, I. A.

Wang, S.

Wilson, D. W.

H. A. Bender, P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design, performance and tolerancing of next-generation air borne imaging spectrometers,” Proc. SPIE 7812, 78120P (2010).
[CrossRef]

P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design of a coastal ocean imaging spectrometer,” Opt. Express 16, 9087–9096 (2008).
[CrossRef]

Witting, T.

Xiang, L.

J. Fisher, J. Antoniades, C. Rollins, and L. Xiang, “A hyperspectral imaging sensor for the coastal environment,” Proc. SPIE 3115, 179–185 (2000).

Xue, Q.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Opt. Express (3)

Proc. SPIE (3)

H. A. Bender, P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design, performance and tolerancing of next-generation air borne imaging spectrometers,” Proc. SPIE 7812, 78120P (2010).
[CrossRef]

S. H. Kim, H. J. Kong, H. Ku, and J. H. Lee, “Analytical design of a hyper-spectral imaging spectrometer utilizing a convex grating,” Proc. SPIE 8515, 85150V (2012).
[CrossRef]

J. Fisher, J. Antoniades, C. Rollins, and L. Xiang, “A hyperspectral imaging sensor for the coastal environment,” Proc. SPIE 3115, 179–185 (2000).

Other (1)

ZEMAX is a trademark of Zemax development Corporation, Bellevue, Washington 98004, USA.

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagram of Rowland circle.

Fig. 2.
Fig. 2.

Schematic diagram of initial configuration for Schwarzschild spectral imaging system.

Fig. 3.
Fig. 3.

Program block diagram for calculating the initial structural parameters.

Fig. 4.
Fig. 4.

Program block diagram for calculating the initial structural parameters.

Fig. 5.
Fig. 5.

Layout of Schwarzschild spectral imaging system.

Fig. 6.
Fig. 6.

Spot diagram of Schwarzschild spectral imaging system.

Fig. 7.
Fig. 7.

RMS spot radius versus wavelength for (a) the modified Schwarzschild imaging spectrometer utilizing three nonconcentric aspheric mirrors and (b) the existing Schwarzschild imaging spectrometers utilizing three concentric spherical mirrors.

Fig. 8.
Fig. 8.

Total smile for different wavelengths.

Fig. 9.
Fig. 9.

Keystone for different object heights.

Tables (2)

Tables Icon

Table 1. Imaging Spectrometer Basic Parameters

Tables Icon

Table 2. Imaging Spectrometer Designed Parameters

Equations (24)

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cos2θr+cos2θrM=cosθ+cosθR,
1r+1rS=cosθ+cosθR,
sinθ+sinθ=mgλ,
1r+1rM=2Rcosθ,
1r+1rS=2cosθR.
rM=Rcosθ.
rS=Rcosθcos2θ,
Δl=rSrM=(1cos2θ1)Rcosθ.
r1=R1cosθ1,
Δl1=[1cos(2θ1)1]R1cosθ1.
rM2=(R2/2)cosθ2,
Δl2=(R2/2)[cosθ21cosθ2].
θ2=2θ1.
h=R1sinθ1.
Δl12=Δl1+Δl2=[1cos(2θ1)1]R1cosθ1+(R2/2)[cosθ21cosθ2].
R2=2R1sinθ1sinθ2=R1/cosθ1.
|C1E2|=R1sinθ1sinθ2=R2/2.
d1=R1R2/2=R1(2cosθ11)2cosθ1.
f=f1f2f1+f2d1,
f=R12cosθ1.
sinα+sinβ=mλg,
dβdλ=mgcosβ.
Δp=f·mgcosβ·(λ2λ1).
z=cr21+(1(1+ki)c2r2),

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