Abstract

This is a proposal and description of a new configuration for an Offner imaging spectrometer based on the theory of aberrations of off-plane classical-ruled spherical diffraction gratings. This new spectrometer comprises a concave mirror used in double reflection and a convex reflection grating operating in quadrature, in a concentric layout. A very simple procedure obtains designs that are anastigmatic for a given point on the entrance slit and a given wavelength. Specific examples show that the performance of this type of system improves the performance of analogous conventional in-plane systems, when compactness and/or high spectral resolution is of fundamental importance.

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  1. D. R. Lobb, “Imaging spectrometer using concentric optics,” Proc. SPIE 3118, 339–347 (1997).
    [CrossRef]
  2. P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design of a coastal ocean imaging spectrometer,” Opt. Express 16(12), 9087–9096 (2008).
    [CrossRef] [PubMed]
  3. D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high performance infrared applications,” Opt. Eng. 47(10), 103061 (2008).
    [CrossRef]
  4. N. C. Das and M. V. R. K. Murty, ““Flat field spectrograph using convex holographic diffraction grating and concave mirror,” Pramäna-,” J. Phys. 27, 171–192 (1986).
  5. D. Kwo, G. Lawrence, and M. Chrisp, “Design of a grating spectrometer from a 1:1 Offner mirror system,” Proc. SPIE 818, 275–279 (1987).
  6. M. P. Chrisp, “Convex diffraction grating imaging spectrometer,” U.S. Patent nº 5,880,834 (1999).
  7. P. Mouroulis and M. M. McKerns, “Pushbroom imaging spectrometer with high spectroscopy data fidelity: experimental demonstration,” Opt. Eng. 39(3), 808–816 (2000).
    [CrossRef]
  8. C. Davis, J. Bowles, R. Leathers, D. Korwan, T. V. Downes, W. Snyder, W. Rhea, W. Chen, J. Fisher, P. Bissett, and R. A. Reisse, “Ocean PHILLS hyperspectral imager: design, characterization, and calibration,” Opt. Express 10(4), 210–221 (2002).
    [PubMed]
  9. X. Prieto-Blanco, C. Montero-Orille, B. Couce, and R. de la Fuente, “Analytical design of an Offner imaging spectrometer,” Opt. Express 14(20), 9156–9168 (2006).
    [CrossRef] [PubMed]
  10. P. Mouroulis, “Low-distortion imaging spectrometer design utilizing convex gratings,” Proc. SPIE 3482, 594–601 (1998).
    [CrossRef]
  11. C. Whyte, R. J. Leigh, D. Lobb, T. Williams, J. J. Remedios, M. Cutter, and P. S. Monks, “Assessment of the performance of a compact concentric spectrometer system for Atmospheric Differential Optical absorption Spectroscopy,” Atmos. Meas. Tech. 2(2), 789–800 (2009).
    [CrossRef]
  12. S. Kayser, B. Sang, J. Schubert, S. Hofer, and T. Stuffler, “Compact prism spectrometer of pushbroom type for Hyperspectral imaging,” Proc. SPIE 7100, 710014 (2008).
    [CrossRef]
  13. F. M. Reininger, “Imaging spectrometer/camera having convex grating,” U.S. Patent nº 6,100,974 (2000).
  14. R. L. Lucke, “Out-of-plane dispersion in an Offner spectrometer,” Opt. Eng. 46(7), 073004 (2007).
    [CrossRef]
  15. X. Prieto-Blanco, C. Montero-Orille, H. González-Núñez, M. D. Mouriz, E. López Lago, and R. de la Fuente, “Imaging with classical spherical diffraction gratings: the quadrature configuration,” J. Opt. Soc. Am. A 26(11), 2400–2409 (2009).
    [CrossRef]
  16. OSLO is a registered trademark of Lambda Research Corporation, 80 Taylor Street, P.O. Box 1400, Littleton, Mass. 01460.

2009 (2)

C. Whyte, R. J. Leigh, D. Lobb, T. Williams, J. J. Remedios, M. Cutter, and P. S. Monks, “Assessment of the performance of a compact concentric spectrometer system for Atmospheric Differential Optical absorption Spectroscopy,” Atmos. Meas. Tech. 2(2), 789–800 (2009).
[CrossRef]

X. Prieto-Blanco, C. Montero-Orille, H. González-Núñez, M. D. Mouriz, E. López Lago, and R. de la Fuente, “Imaging with classical spherical diffraction gratings: the quadrature configuration,” J. Opt. Soc. Am. A 26(11), 2400–2409 (2009).
[CrossRef]

2008 (3)

S. Kayser, B. Sang, J. Schubert, S. Hofer, and T. Stuffler, “Compact prism spectrometer of pushbroom type for Hyperspectral imaging,” Proc. SPIE 7100, 710014 (2008).
[CrossRef]

P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design of a coastal ocean imaging spectrometer,” Opt. Express 16(12), 9087–9096 (2008).
[CrossRef] [PubMed]

D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high performance infrared applications,” Opt. Eng. 47(10), 103061 (2008).
[CrossRef]

2007 (1)

R. L. Lucke, “Out-of-plane dispersion in an Offner spectrometer,” Opt. Eng. 46(7), 073004 (2007).
[CrossRef]

2006 (1)

2002 (1)

2000 (1)

P. Mouroulis and M. M. McKerns, “Pushbroom imaging spectrometer with high spectroscopy data fidelity: experimental demonstration,” Opt. Eng. 39(3), 808–816 (2000).
[CrossRef]

1998 (1)

P. Mouroulis, “Low-distortion imaging spectrometer design utilizing convex gratings,” Proc. SPIE 3482, 594–601 (1998).
[CrossRef]

1997 (1)

D. R. Lobb, “Imaging spectrometer using concentric optics,” Proc. SPIE 3118, 339–347 (1997).
[CrossRef]

1987 (1)

D. Kwo, G. Lawrence, and M. Chrisp, “Design of a grating spectrometer from a 1:1 Offner mirror system,” Proc. SPIE 818, 275–279 (1987).

1986 (1)

N. C. Das and M. V. R. K. Murty, ““Flat field spectrograph using convex holographic diffraction grating and concave mirror,” Pramäna-,” J. Phys. 27, 171–192 (1986).

Bissett, P.

Bowles, J.

Chen, W.

Chrisp, M.

D. Kwo, G. Lawrence, and M. Chrisp, “Design of a grating spectrometer from a 1:1 Offner mirror system,” Proc. SPIE 818, 275–279 (1987).

Couce, B.

Cutter, M.

C. Whyte, R. J. Leigh, D. Lobb, T. Williams, J. J. Remedios, M. Cutter, and P. S. Monks, “Assessment of the performance of a compact concentric spectrometer system for Atmospheric Differential Optical absorption Spectroscopy,” Atmos. Meas. Tech. 2(2), 789–800 (2009).
[CrossRef]

Das, N. C.

N. C. Das and M. V. R. K. Murty, ““Flat field spectrograph using convex holographic diffraction grating and concave mirror,” Pramäna-,” J. Phys. 27, 171–192 (1986).

Davis, C.

de la Fuente, R.

Downes, T. V.

Fisher, J.

González-Núñez, H.

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(10), 103061 (2008).
[CrossRef]

Hofer, S.

S. Kayser, B. Sang, J. Schubert, S. Hofer, and T. Stuffler, “Compact prism spectrometer of pushbroom type for Hyperspectral imaging,” Proc. SPIE 7100, 710014 (2008).
[CrossRef]

Kayser, S.

S. Kayser, B. Sang, J. Schubert, S. Hofer, and T. Stuffler, “Compact prism spectrometer of pushbroom type for Hyperspectral imaging,” Proc. SPIE 7100, 710014 (2008).
[CrossRef]

Keim, E. R.

D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high performance infrared applications,” Opt. Eng. 47(10), 103061 (2008).
[CrossRef]

Korwan, D.

Kwo, D.

D. Kwo, G. Lawrence, and M. Chrisp, “Design of a grating spectrometer from a 1:1 Offner mirror system,” Proc. SPIE 818, 275–279 (1987).

Lawrence, G.

D. Kwo, G. Lawrence, and M. Chrisp, “Design of a grating spectrometer from a 1:1 Offner mirror system,” Proc. SPIE 818, 275–279 (1987).

Leathers, R.

Leigh, R. J.

C. Whyte, R. J. Leigh, D. Lobb, T. Williams, J. J. Remedios, M. Cutter, and P. S. Monks, “Assessment of the performance of a compact concentric spectrometer system for Atmospheric Differential Optical absorption Spectroscopy,” Atmos. Meas. Tech. 2(2), 789–800 (2009).
[CrossRef]

Lobb, D.

C. Whyte, R. J. Leigh, D. Lobb, T. Williams, J. J. Remedios, M. Cutter, and P. S. Monks, “Assessment of the performance of a compact concentric spectrometer system for Atmospheric Differential Optical absorption Spectroscopy,” Atmos. Meas. Tech. 2(2), 789–800 (2009).
[CrossRef]

Lobb, D. R.

D. R. Lobb, “Imaging spectrometer using concentric optics,” Proc. SPIE 3118, 339–347 (1997).
[CrossRef]

López Lago, E.

Lucke, R. L.

R. L. Lucke, “Out-of-plane dispersion in an Offner spectrometer,” Opt. Eng. 46(7), 073004 (2007).
[CrossRef]

McKerns, M. M.

P. Mouroulis and M. M. McKerns, “Pushbroom imaging spectrometer with high spectroscopy data fidelity: experimental demonstration,” Opt. Eng. 39(3), 808–816 (2000).
[CrossRef]

Monks, P. S.

C. Whyte, R. J. Leigh, D. Lobb, T. Williams, J. J. Remedios, M. Cutter, and P. S. Monks, “Assessment of the performance of a compact concentric spectrometer system for Atmospheric Differential Optical absorption Spectroscopy,” Atmos. Meas. Tech. 2(2), 789–800 (2009).
[CrossRef]

Montero-Orille, C.

Mouriz, M. D.

Mouroulis, P.

P. Mouroulis, R. O. Green, and D. W. Wilson, “Optical design of a coastal ocean imaging spectrometer,” Opt. Express 16(12), 9087–9096 (2008).
[CrossRef] [PubMed]

P. Mouroulis and M. M. McKerns, “Pushbroom imaging spectrometer with high spectroscopy data fidelity: experimental demonstration,” Opt. Eng. 39(3), 808–816 (2000).
[CrossRef]

P. Mouroulis, “Low-distortion imaging spectrometer design utilizing convex gratings,” Proc. SPIE 3482, 594–601 (1998).
[CrossRef]

Murty, M. V. R. K.

N. C. Das and M. V. R. K. Murty, ““Flat field spectrograph using convex holographic diffraction grating and concave mirror,” Pramäna-,” J. Phys. 27, 171–192 (1986).

Prieto-Blanco, X.

Reisse, R. A.

Remedios, J. J.

C. Whyte, R. J. Leigh, D. Lobb, T. Williams, J. J. Remedios, M. Cutter, and P. S. Monks, “Assessment of the performance of a compact concentric spectrometer system for Atmospheric Differential Optical absorption Spectroscopy,” Atmos. Meas. Tech. 2(2), 789–800 (2009).
[CrossRef]

Rhea, W.

Sang, B.

S. Kayser, B. Sang, J. Schubert, S. Hofer, and T. Stuffler, “Compact prism spectrometer of pushbroom type for Hyperspectral imaging,” Proc. SPIE 7100, 710014 (2008).
[CrossRef]

Schubert, J.

S. Kayser, B. Sang, J. Schubert, S. Hofer, and T. Stuffler, “Compact prism spectrometer of pushbroom type for Hyperspectral imaging,” Proc. SPIE 7100, 710014 (2008).
[CrossRef]

Snyder, W.

Stuffler, T.

S. Kayser, B. Sang, J. Schubert, S. Hofer, and T. Stuffler, “Compact prism spectrometer of pushbroom type for Hyperspectral imaging,” Proc. SPIE 7100, 710014 (2008).
[CrossRef]

Warren, D. W.

D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high performance infrared applications,” Opt. Eng. 47(10), 103061 (2008).
[CrossRef]

Whyte, C.

C. Whyte, R. J. Leigh, D. Lobb, T. Williams, J. J. Remedios, M. Cutter, and P. S. Monks, “Assessment of the performance of a compact concentric spectrometer system for Atmospheric Differential Optical absorption Spectroscopy,” Atmos. Meas. Tech. 2(2), 789–800 (2009).
[CrossRef]

Williams, T.

C. Whyte, R. J. Leigh, D. Lobb, T. Williams, J. J. Remedios, M. Cutter, and P. S. Monks, “Assessment of the performance of a compact concentric spectrometer system for Atmospheric Differential Optical absorption Spectroscopy,” Atmos. Meas. Tech. 2(2), 789–800 (2009).
[CrossRef]

Wilson, D. W.

Atmos. Meas. Tech. (1)

C. Whyte, R. J. Leigh, D. Lobb, T. Williams, J. J. Remedios, M. Cutter, and P. S. Monks, “Assessment of the performance of a compact concentric spectrometer system for Atmospheric Differential Optical absorption Spectroscopy,” Atmos. Meas. Tech. 2(2), 789–800 (2009).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Phys. (1)

N. C. Das and M. V. R. K. Murty, ““Flat field spectrograph using convex holographic diffraction grating and concave mirror,” Pramäna-,” J. Phys. 27, 171–192 (1986).

Opt. Eng. (3)

P. Mouroulis and M. M. McKerns, “Pushbroom imaging spectrometer with high spectroscopy data fidelity: experimental demonstration,” Opt. Eng. 39(3), 808–816 (2000).
[CrossRef]

D. W. Warren, D. J. Gutierrez, and E. R. Keim, “Dyson spectrometers for high performance infrared applications,” Opt. Eng. 47(10), 103061 (2008).
[CrossRef]

R. L. Lucke, “Out-of-plane dispersion in an Offner spectrometer,” Opt. Eng. 46(7), 073004 (2007).
[CrossRef]

Opt. Express (3)

Proc. SPIE (4)

D. R. Lobb, “Imaging spectrometer using concentric optics,” Proc. SPIE 3118, 339–347 (1997).
[CrossRef]

D. Kwo, G. Lawrence, and M. Chrisp, “Design of a grating spectrometer from a 1:1 Offner mirror system,” Proc. SPIE 818, 275–279 (1987).

P. Mouroulis, “Low-distortion imaging spectrometer design utilizing convex gratings,” Proc. SPIE 3482, 594–601 (1998).
[CrossRef]

S. Kayser, B. Sang, J. Schubert, S. Hofer, and T. Stuffler, “Compact prism spectrometer of pushbroom type for Hyperspectral imaging,” Proc. SPIE 7100, 710014 (2008).
[CrossRef]

Other (3)

F. M. Reininger, “Imaging spectrometer/camera having convex grating,” U.S. Patent nº 6,100,974 (2000).

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

M. P. Chrisp, “Convex diffraction grating imaging spectrometer,” U.S. Patent nº 5,880,834 (1999).

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Figures (8)

Fig. 1
Fig. 1

View along the optical axis of three different configurations of the Offner imaging spectrometer. Each plot shows the diffraction grating (G), the concave mirror (M), the slit (S) and its spectral images. (a) The in-plane configuration. (b) The off-plane configuration included in [13,14]. This configuration can be obtained by rotating in configuration (a) the slit and grating grooves at an angle close to 90°. (c) The quadrature configuration. It can be obtained by rotating in configuration (a) the slit and grating grooves at an angle of 45°.

Fig. 2
Fig. 2

Scheme of the spherical diffraction grating. The diffraction grating surface is tangent to the XY plane at its vertex V. Light from the object point O is diffracted towards point I. The ray following the path O V I is the reference ray. The plane of incidence is defined as the plane containing the Z axis and the ray O V . It makes an angle α with the XZ plane. The plane of diffraction is defined as the plane containing the Z axis and the ray V I . It makes an angle α ' with the XZ plane.

Fig. 3
Fig. 3

Ray tracing in the quadrature configuration. Note that this figure is rotated with respect to Fig. 2. The projections of grating grooves on the XY plane are parallel to the Y axis. The X’Z plane is the plane of incidence and the Y’Z plane is the plane of diffraction. (a) The object distance from the grating vertex V is r a = R cos θ . Rays are shown converging on the image located at a distance r ' a = R / cos θ ' from the vertex. (b) The object distance from the grating vertex V is r b = R / cos θ . Rays are shown converging on the image located at a distance r ' b = R cos θ ' from the vertex.

Fig. 4
Fig. 4

Three different views of an Offner spectrometer in quadrature. (a) front view; (b) top view; (c) side view. C is the common center of curvature of the convex diffraction grating and concave mirror. O is the design point, O ' is its specular image and I the spectral image at order m for the design wavelength λ. V 1 , V 2 , V 3 are the vertices, i.e., the points of incidence of the reference ray on the reflectors. I 1 a , I 1 b , I 2 a and I 2 b are intermediate images.

Fig. 5
Fig. 5

Top view (a)-(c)-(e) and side view (b)-(d)-(f) of the Offner spectrometer in quadrature showing the path followed by the bundle of rays that depart from the design point O in the X’Z’ plane. (a) and (b) show the first reflection on the concave mirror; (c) and (d) show the reflection on the diffraction grating; (e) and (f) show the second reflection on the concave mirror.

Fig. 6
Fig. 6

Similar to Fig. 5 but showing the path followed by the bundle of rays departing from design point O on a plane parallel to the Y’Z’ plane.

Fig. 7
Fig. 7

Pixel size as a function of the slit length for the quadrature and in-plane spectrometers in example 3.

Fig. 8
Fig. 8

Geometrical spots diagrams for the imaging spectrometer in example 4 for three object height (0, 4.2 and 6 mm) and three wavelengths, (0.92, 1.12 and 1.32 μm). The design point is at 3.6 mm and the design wavelength is 1.256 μm

Tables (2)

Tables Icon

Table 1 Specifications and performance for the Offner imaging spectrometer in quadrature of example 1

Tables Icon

Table 2 Specifications and performance for the Offner imaging spectrometers in example 2

Equations (13)

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sin θ cos α + sin θ ' cos α ' = m λ d
sin θ sin α + sin θ ' sin α ' = 0
( 1 + cos 2 θ r + 1 + cos 2 θ ' r ' 2 cos θ + cos θ ' R ) 2 = ( sin 2 θ r sin 2 θ ' r ' ) 2 + 4 sin 2 θ sin 2 θ ' r r ' cos 2 ( α ' α )
cos 2 θ r + cos 2 θ ' r ' = cos θ + cos θ ' R ,
1 r + 1 r ' = cos θ + cos θ ' R
cos 2 θ r + 1 r ' = cos θ + cos θ ' R
1 r + cos 2 θ ' r ' = cos θ + cos θ ' R
sin θ ' = sin θ tan | α |
sin θ = m λ d cos α
sin ( 2 θ 1 ) = m λ q 2 d
C O = R 1 sin θ 1 = R 2 sin ( 2 θ 1 ) = C I
h = 2 C O Δ λ λ q
R 2 = h d Δ λ

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