Abstract

We describe the modeling of the generic spatial heterodyne spectrometer. This instrument resembles a somewhat modified Michelson interferometer, in which the power spectrum of the input source is determined by performing a one-dimensional Fourier transform on the output intensity profile. Code has been developed to analyze the performance of this type of spectrometer by determining the dependence of both spectral resolution and throughput on parameters such as aperture and field of view. An example of a heterodyne spectrometer is developed to illustrate the techniques employed in the modeling and a comparison undertaken between its performance and that of a conventional spectrometer. Unlike the traditional Fourier transform infrared system, the heterodyne spectrometer has the very desirable feature of having no moving components.

© 2006 Optical Society of America

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References

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    [CrossRef] [PubMed]

2002 (2)

1999 (1)

S. Milligan, J. Howard, B. Laubscher, B. Smith, R. Berggren, and J. Harlander, "Optical design of an imaging spatial heterodyne infrared spectrometer," in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik Scholl, eds., Proc. SPIE 3698, 869-881 (1999).
[CrossRef]

1996 (1)

1995 (1)

1992 (2)

M.-L. Juntilla, "Stationary Fourier-transform spectrometer," Appl. Opt. 31, 4106-4112 (1992).
[CrossRef]

J. Harlander, R. J. Reynolds, and F. L. Roesler, "Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths," Astrophys. J. 396, 730-740 (1992).
[CrossRef]

1969 (1)

1968 (1)

Berggren, R.

S. Milligan, J. Howard, B. Laubscher, B. Smith, R. Berggren, and J. Harlander, "Optical design of an imaging spatial heterodyne infrared spectrometer," in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik Scholl, eds., Proc. SPIE 3698, 869-881 (1999).
[CrossRef]

Bradley, C. F.

Cardon, J. G.

Conway, R. R.

Courtial, J.

Englert, C. R.

Harlander, J.

S. Milligan, J. Howard, B. Laubscher, B. Smith, R. Berggren, and J. Harlander, "Optical design of an imaging spatial heterodyne infrared spectrometer," in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik Scholl, eds., Proc. SPIE 3698, 869-881 (1999).
[CrossRef]

J. Harlander, R. J. Reynolds, and F. L. Roesler, "Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths," Astrophys. J. 396, 730-740 (1992).
[CrossRef]

Harlander, J. M.

Harvey, A. R.

Hochheimer, B. F.

Howard, J.

S. Milligan, J. Howard, B. Laubscher, B. Smith, R. Berggren, and J. Harlander, "Optical design of an imaging spatial heterodyne infrared spectrometer," in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik Scholl, eds., Proc. SPIE 3698, 869-881 (1999).
[CrossRef]

Johnston, W. D.

Juntilla, M.-L.

Kauppinen, J. K.

Laubscher, B.

S. Milligan, J. Howard, B. Laubscher, B. Smith, R. Berggren, and J. Harlander, "Optical design of an imaging spatial heterodyne infrared spectrometer," in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik Scholl, eds., Proc. SPIE 3698, 869-881 (1999).
[CrossRef]

Milligan, S.

S. Milligan, J. Howard, B. Laubscher, B. Smith, R. Berggren, and J. Harlander, "Optical design of an imaging spatial heterodyne infrared spectrometer," in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik Scholl, eds., Proc. SPIE 3698, 869-881 (1999).
[CrossRef]

Padgett, M. J.

Patterson, B. A.

Reynolds, R. J.

J. Harlander, R. J. Reynolds, and F. L. Roesler, "Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths," Astrophys. J. 396, 730-740 (1992).
[CrossRef]

Roesler, F. L.

J. M. Harlander, F. L. Roesler, J. G. Cardon, C. R. Englert, and R. R. Conway, "SHIMMER: a spatial heterodyne spectrometer for remote sensing of Earth's middle atmosphere," Appl. Opt. 41, 1343-1352 (2002).
[CrossRef] [PubMed]

J. Harlander, R. J. Reynolds, and F. L. Roesler, "Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths," Astrophys. J. 396, 730-740 (1992).
[CrossRef]

Salomaa, I. K.

Salonen, K. I.

Sibbett, W.

Smith, B.

S. Milligan, J. Howard, B. Laubscher, B. Smith, R. Berggren, and J. Harlander, "Optical design of an imaging spatial heterodyne infrared spectrometer," in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik Scholl, eds., Proc. SPIE 3698, 869-881 (1999).
[CrossRef]

Zhan, G.

Appl. Opt. (7)

Astrophys. J. (1)

J. Harlander, R. J. Reynolds, and F. L. Roesler, "Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths," Astrophys. J. 396, 730-740 (1992).
[CrossRef]

Proc. SPIE (1)

S. Milligan, J. Howard, B. Laubscher, B. Smith, R. Berggren, and J. Harlander, "Optical design of an imaging spatial heterodyne infrared spectrometer," in Infrared Technology and Applications XXV, B. F. Andresen and M. Strojnik Scholl, eds., Proc. SPIE 3698, 869-881 (1999).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

(Color online) Beam incident on grating at Littrow angle.

Fig. 2
Fig. 2

(Color online) Interference between wavefronts from two arms of interferometer.

Fig. 3
Fig. 3

Optical path length perturbation.

Fig. 4
Fig. 4

Phase map of monochromatic ( λ = 525   nm ) point on axis.

Fig. 5
Fig. 5

(Color online) Intensity distribution and energy spectrum for 1.2   mm diameter source at reference plane conjugate with diffraction gratings.

Fig. 6
Fig. 6

(Color online) Intensity distribution and energy spectrum for a 12 μ m diameter source at interference plane moved to a more accessible location.

Fig. 7
Fig. 7

(Color online) Schematic of a heterodyne spectrometer with relay optics.

Fig. 8
Fig. 8

(Color online) Intensity distribution and energy spectrum for a 1.2   mm diameter source for heterodyne spectrometer with relay optics.

Fig. 9
Fig. 9

(Color online) Schematic of an anamorphic spatial heterodyne spectrometer.

Fig. 10
Fig. 10

(Color online) Schematic of a simple conventional spectrometer.

Fig. 11
Fig. 11

(Color online) PSFs associated with conventional spectrometer for 50   nm bandwidth.

Fig. 12
Fig. 12

(Color online) PSFs associated with conventional spectrometer for 100   nm bandwidth.

Tables (1)

Tables Icon

Table 1 Performance Comparison of Conventional and Heterodyne Spectrometers

Equations (16)

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μ Λ [ sin ( θ ) + sin ( θ + β ) ] = m λ ,
R = λ / Δ λ ,
Δ θ / Δ λ = m / [ μ Λ   cos ( θ ) ] .
Δ θ min = λ / [ μ W   cos ( θ ) ] ,
R = 2 μ W   sin ( θ ) / λ ,
f ( λ ) = 2 μ m   sin ( β ) / λ .
f ( λ ) 2 μ m ( λ λ 0 ) cos ( θ ) λ ,
I ( x ) = 0 B ( λ ) { 1 + cos [ 2 π f ( λ ) ] } d λ ,
Δ ( opd ) = 4 μ W   sin ( θ ) [ cos ( β ) cos ( β + y ) ] ,
Δ ( opd ) = 2 μ W   sin ( θ ) γ ( γ + 2 β ) .
γ = β + 2 ( β 2 + λ 2 μ W   sin ( θ ) ) 1 / 2 .
γ / Δ θ min = β + 2 ( β 2 + λ 2 μ W   sin ( θ ) ) 1 / 2 λ μ W   cos ( θ ) .
e = ( L 1 + L 2 ) ( X 1 X 2 ) + ( M 1 + M 2 ) ( Y 1 Y 2 ) + ( N 1 + N 2 ) ( Z 1 Z 2 ) 1 + L 1 L 2 + M 1 M 2 + N 1 N 2 ,
I ( X , Y ) = 1 / 2 { 1 + cos [ 2 π / λ Δ ( o p d ( X , Y ) ) ] } .
β = sin - 1 [ m ( λ λ 0 ) μ Λ   cos ( θ ) ] θ .
Δ ξ min = λ / [ 2 μ   sin ( θ ) ] .

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