Abstract

We aim to show that Dyson imaging spectrometers can be easily designed by applying the concept of the Rowland circle to refracting surfaces. This allows us to conceive an analytical procedure that is based on the removal of astigmatism at two wavelengths. Following this procedure, high-optical-quality spectrometers can be designed even for high speeds. Root-mean-square spot radii less than 2.5μm are obtained for speeds as high as f/1.5, slit lengths of 15mm, and wavelength ranges of 0.41.7μm. Design examples are presented for classical Dyson spectrometers in which the detector is glued to the glass plane surface and for spectrometers with an air gap between this surface and the image plane.

© 2011 Optical Society of America

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References

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  4. M. Kuester, J. McCorkel, B. Johnson, T. Kampe, P. Johnson, B. Good, K. Smith, and J. Lasnik, “A prototype airborne visible imaging spectrometer (PAVIS),” in Proceedings of the 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–7.
  5. P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design of a coastal ocean imaging spectrometer,” Opt. Express 16, 9087–9096 (2008).
    [CrossRef]
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    [CrossRef]
  7. R. Lucke and J. Fisher, “The Schmidt–Dyson: a fast space-borne wide field hyperspectral imager,” Proc. SPIE 7812, 78120M (2010).
    [CrossRef]
  8. C. Montero-Orille, X. Prieto-Blanco, H. González-Núñez, and R. de la Fuente, “Two-wavelength anastigmatic Dyson imaging spectrometers,” Opt. Lett. 35, 2379–2381(2010).
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  9. M. P. Chrisp, “Convex diffraction grating imaging spectrometer,” U.S. patent 5,880,834 (9 March 1999).
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    [CrossRef]
  17. D. R. Lobb, “Theory of concentric designs for grating spectrometers,” Appl. Opt. 33, 2648–2658 (1994).
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  18. R. Kingslake, “Who? Discovered Coddington’s equations?” Opt. Photon. News 5(8), 20–23 (1994).
    [CrossRef]

2010 (2)

R. Lucke and J. Fisher, “The Schmidt–Dyson: a fast space-borne wide field hyperspectral imager,” Proc. SPIE 7812, 78120M (2010).
[CrossRef]

C. Montero-Orille, X. Prieto-Blanco, H. González-Núñez, and R. de la Fuente, “Two-wavelength anastigmatic Dyson imaging spectrometers,” Opt. Lett. 35, 2379–2381(2010).
[CrossRef]

2008 (2)

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

D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high-performance infrared applications,” Opt. Eng. 47, 103601 (2008).
[CrossRef]

2006 (2)

2005 (1)

T. Martin, R. Brubaker, P. Dixon, M. A. Gagliardi, and T. Sudol, “640×512 InGaAs focal plane array camera for visible and SWIR imaging,” Proc. SPIE 5783, 12–20 (2005).
[CrossRef]

2000 (1)

N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000).
[CrossRef]

1994 (2)

D. R. Lobb, “Theory of concentric designs for grating spectrometers,” Appl. Opt. 33, 2648–2658 (1994).
[CrossRef]

R. Kingslake, “Who? Discovered Coddington’s equations?” Opt. Photon. News 5(8), 20–23 (1994).
[CrossRef]

1977 (1)

1959 (1)

1945 (1)

Beutler, H.

Brubaker, R.

T. Martin, R. Brubaker, P. Dixon, M. A. Gagliardi, and T. Sudol, “640×512 InGaAs focal plane array camera for visible and SWIR imaging,” Proc. SPIE 5783, 12–20 (2005).
[CrossRef]

Chrisp, M. P.

M. P. Chrisp, “Convex diffraction grating imaging spectrometer,” U.S. patent 5,880,834 (9 March 1999).

Couce, B.

de la Fuente, R.

Dixon, P.

T. Martin, R. Brubaker, P. Dixon, M. A. Gagliardi, and T. Sudol, “640×512 InGaAs focal plane array camera for visible and SWIR imaging,” Proc. SPIE 5783, 12–20 (2005).
[CrossRef]

Dyson, J.

Fisher, J.

R. Lucke and J. Fisher, “The Schmidt–Dyson: a fast space-borne wide field hyperspectral imager,” Proc. SPIE 7812, 78120M (2010).
[CrossRef]

Gagliardi, M. A.

T. Martin, R. Brubaker, P. Dixon, M. A. Gagliardi, and T. Sudol, “640×512 InGaAs focal plane array camera for visible and SWIR imaging,” Proc. SPIE 5783, 12–20 (2005).
[CrossRef]

Gat, N.

N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000).
[CrossRef]

González-Núñez, H.

Good, B.

M. Kuester, J. McCorkel, B. Johnson, T. Kampe, P. Johnson, B. Good, K. Smith, and J. Lasnik, “A prototype airborne visible imaging spectrometer (PAVIS),” in Proceedings of the 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–7.

Green, R. O.

Gutierrez, D. J.

D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high-performance infrared applications,” Opt. Eng. 47, 103601 (2008).
[CrossRef]

Johnson, B.

M. Kuester, J. McCorkel, B. Johnson, T. Kampe, P. Johnson, B. Good, K. Smith, and J. Lasnik, “A prototype airborne visible imaging spectrometer (PAVIS),” in Proceedings of the 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–7.

Johnson, P.

M. Kuester, J. McCorkel, B. Johnson, T. Kampe, P. Johnson, B. Good, K. Smith, and J. Lasnik, “A prototype airborne visible imaging spectrometer (PAVIS),” in Proceedings of the 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–7.

Kampe, T.

M. Kuester, J. McCorkel, B. Johnson, T. Kampe, P. Johnson, B. Good, K. Smith, and J. Lasnik, “A prototype airborne visible imaging spectrometer (PAVIS),” in Proceedings of the 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–7.

Keim, E. R.

D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high-performance infrared applications,” Opt. Eng. 47, 103601 (2008).
[CrossRef]

Kerekes, J.

J. Kerekes, “Imaging spectrometers go commercial,” Laser Focus World 42, 63–68 (2006).

Kingslake, R.

R. Kingslake, “Who? Discovered Coddington’s equations?” Opt. Photon. News 5(8), 20–23 (1994).
[CrossRef]

Kuester, M.

M. Kuester, J. McCorkel, B. Johnson, T. Kampe, P. Johnson, B. Good, K. Smith, and J. Lasnik, “A prototype airborne visible imaging spectrometer (PAVIS),” in Proceedings of the 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–7.

Lasnik, J.

M. Kuester, J. McCorkel, B. Johnson, T. Kampe, P. Johnson, B. Good, K. Smith, and J. Lasnik, “A prototype airborne visible imaging spectrometer (PAVIS),” in Proceedings of the 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–7.

Lobb, D. R.

Lucke, R.

R. Lucke and J. Fisher, “The Schmidt–Dyson: a fast space-borne wide field hyperspectral imager,” Proc. SPIE 7812, 78120M (2010).
[CrossRef]

Martin, T.

T. Martin, R. Brubaker, P. Dixon, M. A. Gagliardi, and T. Sudol, “640×512 InGaAs focal plane array camera for visible and SWIR imaging,” Proc. SPIE 5783, 12–20 (2005).
[CrossRef]

McCorkel, J.

M. Kuester, J. McCorkel, B. Johnson, T. Kampe, P. Johnson, B. Good, K. Smith, and J. Lasnik, “A prototype airborne visible imaging spectrometer (PAVIS),” in Proceedings of the 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–7.

Mertz, L.

Montero-Orille, C.

Mouroulis, P.

Prieto-Blanco, X.

Smith, K.

M. Kuester, J. McCorkel, B. Johnson, T. Kampe, P. Johnson, B. Good, K. Smith, and J. Lasnik, “A prototype airborne visible imaging spectrometer (PAVIS),” in Proceedings of the 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–7.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 1990).

Sudol, T.

T. Martin, R. Brubaker, P. Dixon, M. A. Gagliardi, and T. Sudol, “640×512 InGaAs focal plane array camera for visible and SWIR imaging,” Proc. SPIE 5783, 12–20 (2005).
[CrossRef]

Warren, D. W.

D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high-performance infrared applications,” Opt. Eng. 47, 103601 (2008).
[CrossRef]

Welford, W. T.

W. T. Welford, “Aberration theory of gratings and grating mountings,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1965), Vol.  IV, pp. 241–280.

Wilson, D. W.

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

Laser Focus World (1)

J. Kerekes, “Imaging spectrometers go commercial,” Laser Focus World 42, 63–68 (2006).

Opt. Eng. (1)

D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high-performance infrared applications,” Opt. Eng. 47, 103601 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Opt. Photon. News (1)

R. Kingslake, “Who? Discovered Coddington’s equations?” Opt. Photon. News 5(8), 20–23 (1994).
[CrossRef]

Proc. SPIE (3)

R. Lucke and J. Fisher, “The Schmidt–Dyson: a fast space-borne wide field hyperspectral imager,” Proc. SPIE 7812, 78120M (2010).
[CrossRef]

N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000).
[CrossRef]

T. Martin, R. Brubaker, P. Dixon, M. A. Gagliardi, and T. Sudol, “640×512 InGaAs focal plane array camera for visible and SWIR imaging,” Proc. SPIE 5783, 12–20 (2005).
[CrossRef]

Other (5)

M. Kuester, J. McCorkel, B. Johnson, T. Kampe, P. Johnson, B. Good, K. Smith, and J. Lasnik, “A prototype airborne visible imaging spectrometer (PAVIS),” in Proceedings of the 2007 IEEE Aerospace Conference (IEEE, 2007), pp. 1–7.

M. P. Chrisp, “Convex diffraction grating imaging spectrometer,” U.S. patent 5,880,834 (9 March 1999).

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 1990).

OSLO is a registered trademark of Lambda Research Corporation, 80 Taylor Street, P.O. Box 1400, Littleton, Mass., 01460.

W. T. Welford, “Aberration theory of gratings and grating mountings,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1965), Vol.  IV, pp. 241–280.

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Figures (10)

Fig. 1
Fig. 1

Rowland circle for the refraction on a spherical surface. The meridional images of point O on this circle, at two different wavelengths, are shown.

Fig. 2
Fig. 2

Dyson spectrometer: FO, foreoptics; S, slit; HL, hemispherical lens; G, diffraction grating; D, detector.

Fig. 3
Fig. 3

Optical path of the chief ray emerging from the slit center of a Dyson spectrometer for an arbitrary wavelength. Astigmatism has been intentionally overstated, and refraction at the plane surface of the hemispherical lens has not been drawn. Rowland circles are also shown for each refraction and for diffraction on the grating.

Fig. 4
Fig. 4

Relative difference of the paraxial ( ρ p ) and nonparaxial (ρ) radii ratio for spectrometer with gratings of different density.

Fig. 5
Fig. 5

Longitudinal astigmatism as a function of wavelength. Curves for different radii ratio are shown: (a)  r = 3.188 , (b)  r = 3.144 , and (c)  r = 3.11 . The groove density has been set to 100   lines / mm , and the glass material has been chosen to be fused silica.

Fig. 6
Fig. 6

Spot size and focal curve for a modified Dyson spectrometer with a lens shortened 3 mm in the image space.

Fig. 7
Fig. 7

RMS spot radius as a function of (a) object position for the minimum (solid curve), central (dashed curve), and maximum (dashed–dotted curve) wavelength and (b) wavelength for the on-axis (solid curve), 0.7 field (dashed curve), and full field (dash-dot curve) object point. The lens material is fused silica, and the specifications of the spectrometer are given in Table 1.

Fig. 8
Fig. 8

Worst RMS spot radius against clearance for the fused silica spectrometer whose specifications are given in Table 1; depth d removed from the lens is about 1.49 times larger than the clearance.

Fig. 9
Fig. 9

Image spot size as a function of the radii ratio (a) and groove density (b) modifications with respect to the design values given in Table 1 (left column).

Fig. 10
Fig. 10

Arbitrary meridional and chief rays refracted on a spherical surface.

Tables (1)

Tables Icon

Table 1 Specifications, Design Parameters, and Image Quality Results for a Broadband Dyson Spectrometer 0.4 1.7 μm

Equations (18)

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Δ r = R l sin θ l tan δ ,
Δ r = R l sin θ l tan δ 1 n l 2 sin 2 δ n l cos 2 δ .
δ = θ l θ g θ l = 0.
m λ g R g = R g sin θ g = R l sin θ l = n l R l sin θ l ,
ρ = sin θ l sin θ g = sin ( θ g + θ l ) sin θ g = cos ( θ l ) + sin θ l tan θ g = 1 ρ 2 sin 2 θ g n l 2 + ρ cos θ g n l
ρ = n l 1 2 n l cos θ g + n l 2 .
1 n a 2 2 cos θ g a ' n a = 1 n b 2 2 cos θ g b ' n b .
1 4 ( λ a 4 n a λ b 4 n b ) g 4 + ( λ a 2 n a λ b 2 n b ) g 2 + 1 n a 2 1 n b 2 2 ( 1 n a 1 n b ) = 0.
h R l [ sin θ l ( λ L ) sin θ l ( λ S ) ] .
h R g g [ λ L n L λ S n S ] R g g n ¯ ( Δ λ + λ ¯ Δ n n ¯ ) ,
t CLC = d n l ( 1 3 32 n l 2 1 n l 2 ( f / # ) 2 ) .
α = arctan ( t CLC ( λ S ) t CLC ( λ L ) h ) .
Λ = n 1 B O ¯ + n 2 B I ¯ ,
Λ = n 1 sgn ( z 0 ) U ( x , z ; x 0 , z 0 ) + n 2 sgn ( z i ) U ( x , z ; x i , z i ) ,
U ( x , z ; x , z ) = ( x x ) 2 + ( z z ) 2 .
d Λ d x | x = 0 = n 1 x o r o + n 2 x i r i = 0 n 1 sin θ 0 = n 2 sin θ i ,
d 2 Λ d x 2 | x = 0 = n 1 r o [ 1 z o R ( x o r o ) 2 ] + n 2 r i [ 1 z i R ( x i r i ) 2 ] = 0 n 1 ( cos 2 θ o r o cos θ o R ) = n 2 ( cos 2 θ i r i cos θ i R ) .
d 3 Λ d x 3 | x = 0 = n 1 3 x o r o 3 [ 1 z o R ( x o r o ) 2 ] + n 2 3 x i r i 3 [ 1 z i R ( x i r i ) 2 ] = 0 n 1 3 x o r o 2 ( cos 2 θ o r o cos θ o R ) = n 2 3 x i r i 2 ( cos 2 θ i r i cos θ i R ) .

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