Abstract

The throughput of a tilted Fourier-transform spectrometer (FTS) with collimation is calculated. It is shown that the maximum off-axis angle that is acceptable in the interferometer is inversely proportional to the distance between the detector and the location where the tilt is applied to the wave fronts and is also inversely proportional to the tilt angle. This effect leads to tilt sensitivity in a scanning FTS and to the loss of the throughput advantage in a FTS with no moving part in which a tilt between two collimated beams is used to disperse the interferogram spatially. Experimental verification confirms the throughput condition with tilt angle.

© 1998 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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1995 (2)

1992 (1)

1991 (1)

1985 (1)

1984 (1)

1965 (1)

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965).
[CrossRef]

1961 (1)

J. Connes, “Recherches sur la spectroscopie par la transformation de Fourier,” Rev. Opt. Theor. Exper. 40, 41–79, 116–140, 171–190, 231–265 (1961).

1955 (1)

Aryamanya-Mugisha, H.

Blatt, J. H.

Brault, J. W.

J. W. Brault, “Fourier transform spectrometry,” in High Resolution in Astronomy, A. O. Benz, M. C. E. Huber, M. Mayor, eds., Proceedings of the 15th Advanced Course of the Swiss Society of Astronomy and Astrophysics (Swiss Society of Astronomy and Astrophysics, Saas-Fee, Switzerland, 1985), pp. 1–61.

Bruce, J. R.

L. J. I. Otten, R. G. Sellar, J. R. Bruce, “Measured performance of an airborne Fourier transform hyperspectral imager,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 291–299 (1996).
[CrossRef]

Budney, C.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” in Imaging Spectrometry of the Terrestial Environment, G. Vane, ed., Proc. SPIE1937, 130–141 (1993).
[CrossRef]

Butler, E. W.

A. D. Meigs, E. W. Butler, B. A. Jones, L. J. Otten, R. G. Sellar, J. B. Rafert, “Airborne visible hyperspectral imaging spectrometer: optical and system level description,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 278–284 (1996).
[CrossRef]

Connes, J.

J. Connes, “Recherches sur la spectroscopie par la transformation de Fourier,” Rev. Opt. Theor. Exper. 40, 41–79, 116–140, 171–190, 231–265 (1961).

Funkhouser, A. T.

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965).
[CrossRef]

Girard, A.

A. Girard, “Devices for multiplex stellar spectroscopy,” in Proceedings of the Aspen International Conference on Fourier Transform Spectroscopy (ICOFTS 1), G. A. Vanasse, A. T. Stais, D. J. Barker, eds., AFCRL-0019-71 (Air Force Cambridge Research Laboratory, Bedford, Mass., 1971), pp. 425–428.

Hinck, K.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” in Imaging Spectrometry of the Terrestial Environment, G. Vane, ed., Proc. SPIE1937, 130–141 (1993).
[CrossRef]

Horton, K.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” in Imaging Spectrometry of the Terrestial Environment, G. Vane, ed., Proc. SPIE1937, 130–141 (1993).
[CrossRef]

Horton, R. F.

R. F. Horton, “Optical design for a high étendue imaging Fourier transform spectrometer,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 300–315 (1996).
[CrossRef]

Ikonen, E.

Jones, B. A.

A. D. Meigs, E. W. Butler, B. A. Jones, L. J. Otten, R. G. Sellar, J. B. Rafert, “Airborne visible hyperspectral imaging spectrometer: optical and system level description,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 278–284 (1996).
[CrossRef]

Junttila, M.-L.

Kauppinen, J.

Kawata, S.

Lucey, P. G.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” in Imaging Spectrometry of the Terrestial Environment, G. Vane, ed., Proc. SPIE1937, 130–141 (1993).
[CrossRef]

Meigs, A. D.

A. D. Meigs, E. W. Butler, B. A. Jones, L. J. Otten, R. G. Sellar, J. B. Rafert, “Airborne visible hyperspectral imaging spectrometer: optical and system level description,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 278–284 (1996).
[CrossRef]

Minami, S.

Möller, K.

Okamoto, T.

Otten, L. J.

A. D. Meigs, E. W. Butler, B. A. Jones, L. J. Otten, R. G. Sellar, J. B. Rafert, “Airborne visible hyperspectral imaging spectrometer: optical and system level description,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 278–284 (1996).
[CrossRef]

Otten, L. J. I.

L. J. I. Otten, R. G. Sellar, J. R. Bruce, “Measured performance of an airborne Fourier transform hyperspectral imager,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 291–299 (1996).
[CrossRef]

Peck, E. R.

Rafert, J. B.

J. B. Rafert, R. Sellar, J. H. Blatt, “Monolithic Fourier-transform imaging spectrometer,” Appl. Opt. 34, 7228–7230 (1995).
[CrossRef] [PubMed]

A. D. Meigs, E. W. Butler, B. A. Jones, L. J. Otten, R. G. Sellar, J. B. Rafert, “Airborne visible hyperspectral imaging spectrometer: optical and system level description,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 278–284 (1996).
[CrossRef]

Sellar, R.

Sellar, R. G.

L. J. I. Otten, R. G. Sellar, J. R. Bruce, “Measured performance of an airborne Fourier transform hyperspectral imager,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 291–299 (1996).
[CrossRef]

A. D. Meigs, E. W. Butler, B. A. Jones, L. J. Otten, R. G. Sellar, J. B. Rafert, “Airborne visible hyperspectral imaging spectrometer: optical and system level description,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 278–284 (1996).
[CrossRef]

Stroke, G. W.

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965).
[CrossRef]

Williams, R.

Williams, T.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” in Imaging Spectrometry of the Terrestial Environment, G. Vane, ed., Proc. SPIE1937, 130–141 (1993).
[CrossRef]

Appl. Opt. (4)

Appl. Spectrosc. (1)

J. Opt. Soc. Am. (1)

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

Phys. Lett. (1)

G. W. Stroke, A. T. Funkhouser, “Fourier-transform spectroscopy using holographic imaging without computing and with stationary interferometers,” Phys. Lett. 16, 272–274 (1965).
[CrossRef]

Rev. Opt. Theor. Exper. (1)

J. Connes, “Recherches sur la spectroscopie par la transformation de Fourier,” Rev. Opt. Theor. Exper. 40, 41–79, 116–140, 171–190, 231–265 (1961).

Other (6)

J. W. Brault, “Fourier transform spectrometry,” in High Resolution in Astronomy, A. O. Benz, M. C. E. Huber, M. Mayor, eds., Proceedings of the 15th Advanced Course of the Swiss Society of Astronomy and Astrophysics (Swiss Society of Astronomy and Astrophysics, Saas-Fee, Switzerland, 1985), pp. 1–61.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” in Imaging Spectrometry of the Terrestial Environment, G. Vane, ed., Proc. SPIE1937, 130–141 (1993).
[CrossRef]

A. D. Meigs, E. W. Butler, B. A. Jones, L. J. Otten, R. G. Sellar, J. B. Rafert, “Airborne visible hyperspectral imaging spectrometer: optical and system level description,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 278–284 (1996).
[CrossRef]

L. J. I. Otten, R. G. Sellar, J. R. Bruce, “Measured performance of an airborne Fourier transform hyperspectral imager,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 291–299 (1996).
[CrossRef]

A. Girard, “Devices for multiplex stellar spectroscopy,” in Proceedings of the Aspen International Conference on Fourier Transform Spectroscopy (ICOFTS 1), G. A. Vanasse, A. T. Stais, D. J. Barker, eds., AFCRL-0019-71 (Air Force Cambridge Research Laboratory, Bedford, Mass., 1971), pp. 425–428.

R. F. Horton, “Optical design for a high étendue imaging Fourier transform spectrometer,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 300–315 (1996).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Tilted Michelson interferometer: FOV, field of view.

Fig. 2
Fig. 2

Beam incident at an angle upon a tilted mirror pair.

Fig. 3
Fig. 3

Schematic of the experimental setup.

Fig. 4
Fig. 4

Visibility as a function of tilt angle.

Tables (1)

Tables Icon

Table 1 Values of the Parameters Needed To Predict Visibility

Equations (7)

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E 1 = E o 1 exp - jk cos 2 α + θ z - sin 2 α + θ y , E 2 = E o 2 exp - jk cos 2 α - θ z + sin 2 α - θ y ,
E 1 + E 2 = E o exp - jk cos 2 α + θ z - sin 2 α + θ y + exp - jk cos 2 α - θ z + sin 2 α - θ y .
P θ = 2 E o 2 cos 2 k cos 2 α - θ - cos 2 α + θ 2 z + sin 2 α - θ + sin 2 α + θ 2 y .
P θ = 0 = 2 E o 2 cos 2 k   sin 2 α y ,
P = - θ max θ max   2 E o 2 cos 2 k 2 α θ z + y d θ .
P = 2 E o 2 θ max 1 + cos 4 α ky sin 4 α k θ max z 4 α k θ max z .
θ max < π 8 α kz .

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