Abstract

Wave propagation equations in the stationary-phase approximation have been used to identify the theoretical bounds of a miniature holographic Fourier-transform spectrometer (HFTS). It is demonstrated that the HFTS throughput can be larger than for a scanning Fourier-transform spectrometer. Given room- or a higher-temperature constraint, a small HFTS has the potential to outperform a small multichannel dispersive spectrograph with the same resolving power because of the size dependence of the signal-to-noise ratio. These predictions are used to analyze the performance of a miniature HFTS made from simple optical components covering a broad spectral range from the UV to the near IR. The importance of specific primary aberrations in limiting the HFTS performance has been both identified and verified.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. I. P. Petrov, B. N. Grechushnikov, “Photographic method of recording in Fourier spectrometry,” Opt. Spectrosc. 19, 82–83 (1965).
  2. 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]
  3. K. Yoshihara, A. Kitade, “Holographic spectra using a triangle path interferometer,” Jpn. J. Appl. Phys. 6, 116 (1967).
    [CrossRef]
  4. K. Kamiya, K. Yoshihara, K. Okada, “Holographic spectra obtained with a Lloyd’s mirror,” Jpn. J. Appl. Phys. 7, 1129 (1968).
    [CrossRef]
  5. K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach-Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
    [CrossRef]
  6. J. W. Cooley, J. W. Tukey, “An algorithm for machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
    [CrossRef]
  7. P. Fellgett, “A propos de la theorie du spectrometre interferentiel multiplex,” J. Phys. Radium 19, 187–191 (1958).
    [CrossRef]
  8. J. D. Strong, G. A. Vanasse, “Interferometric spectroscopy in the far infrared,” J. Opt. Soc. Am. 49, 844–850 (1959).
    [CrossRef]
  9. P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 268–312 (1960).
    [CrossRef]
  10. L. Genzel, “Aperiodic and periodic interference modulation for spectrographic purposes,” J. Mol. Spectrosc. 4, 241–261 (1960).
    [CrossRef]
  11. P. L. Richards, “High-resolution Fourier transform spectroscopy in the far-infrared,” J. Opt. Soc. Am. 54, 1474–1484 (1964).
    [CrossRef]
  12. I. G. Nolt, A. J. Sievers, “Stress induced frequency shift of a lattice resonant mode,” Phys. Rev. Lett. 16, 1103–1105 (1966).
    [CrossRef]
  13. H. D. Drew, A. J. Sievers, “Far-infrared absorption in superconducting and normal lead,” Phys. Rev. Lett. 19, 697–699 (1967).
    [CrossRef]
  14. L. Genzel, K. Sakai, “Interferometry from 1950 to present,” J. Opt. Soc. Am. 67, 871–879 (1977).
    [CrossRef]
  15. T. Okamoto, S. Kawata, S. Minami, “Fourier transform spectrometer with a self-scanning photodiode array,” Appl. Opt. 23, 269–273 (1984).
    [CrossRef] [PubMed]
  16. T. H. Barnes, “Photodiode array Fourier transform spectrometer with improved dynamic range,” Appl. Opt. 24, 3702–3706 (1985).
    [CrossRef] [PubMed]
  17. L. V. Egorova, I. E. Leshcheva, B. N. Popov, A. Y. Stroganova, “Static fast response Fourier spectrometer having a linear CCD image forming system,” J. Opt. Technol. 56, 220–221 (1989).
  18. J. V. Sweedler, M. B. Denton, “Spatially encoded Fourier transform spectroscopy in the ultraviolet to the near infrared,” Appl. Spectrosc. 43, 1378–1384 (1989).
    [CrossRef]
  19. W. H. Smith, W. V. Schempp, “Digital array scanned interferometers for astronomy,” Exp. Astron. 1, 389–405 (1991).
    [CrossRef]
  20. M.-L. Junttila, “Stationary Fourier-transform spectrometer,” Appl. Opt. 31, 4106–4112 (1992).
    [CrossRef] [PubMed]
  21. S. Takahashi, J. S. Ahn, S. Asaka, T. Kitagawa, “Multichannel Fourier transform spectroscopy using two-dimensional detection of the interferogram and its application to Raman spectroscopy,” Appl. Spectrosc. 47, 863–868 (1993).
    [CrossRef]
  22. P. G. Lucey, K. Horton, T. Williams, K. Hinck, C. Budney, J. B. Rafert, T. B. Rusk, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” in Imaging Spectrometry of the Terrestrial Environment, G. Vane, ed., Proc. SPIE1937, 130–141 (1993).
    [CrossRef]
  23. M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse, Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
    [CrossRef] [PubMed]
  24. W. H. Smith, “Digital array scanned interferometer: sensor and results,” Appl. Opt. 35, 2902–2909 (1996).
    [CrossRef] [PubMed]
  25. M. Hashimoto, H. Hamaguchi, “Construction of a multichannel Fourier transform infrared spectrometer for single-event time-resolved spectroscopy,” Appl. Spectrosc. 50, 1030–1033 (1996).
    [CrossRef]
  26. B. A. Patterson, J. P. Lenney, W. Sibbett, B. Hirst, N. K. Hedges, M. J. Padgett, “Detection of benzene and other gases with an open-path, static Fourier-transform UV spectrometer,” Appl. Opt. 37, 3172–3175 (1998).
    [CrossRef]
  27. J. T. Daly, E. A. Johnson, A. Bodkin, W. A. Stevenson, D. A. White, “Recent advances in miniaturization of infrared spectrometers,” in Silicon-based Optoelectronics II, D. J. Robbins, D. C. Houghton, eds., Proc. SPIE3953, 70–87 (2000).
    [CrossRef]
  28. J. P. Ferguson, S. Schoenfelder, “Micromoulded spectrometers produced by the LIGA process,” in Proceedings of IEEE Colloquium on Microengineering in Optics and Optoelectronics (Institute of Electrical and Electronics Engineers, London, UK, 1999), pp. 11/11–11/10.
  29. H. J. Caulfield, “Spectroscopy,” in Handbook of Optical Holography, H. J. Caulfield, ed. (Academic, New York, 1979), pp. 587–594.
  30. A. Walther, The Ray and Wave Theory of Lenses, Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, UK, 1995).
  31. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).
  32. R. F. Horton, “Optical design for a high-etendue imaging Fourier transform spectrometer,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 300–315 (1996).
    [CrossRef]
  33. K. Dohlen, “Interferometric spectrometer for liquid mirror survey telescopes,” in Optical Telescopes of Today and Tomorrow: Following in the Direction of Tycho Brahe, A. Ardeberg, ed., Proc. SPIE2871, 1359–1364 (1996).
    [CrossRef]
  34. F. D. Kahn, “The signal: noise ratio of a suggested spectral analyzer,” Astrophys. J. 129, 518–521 (1959).
    [CrossRef]
  35. M. H. Tai, M. Harwit, “Fourier and Hadamard transform spectrometers: a limited comparison,” Appl. Opt. 15, 2664–2666 (1976).
    [CrossRef] [PubMed]
  36. R. R. Treffers, “Signal-to-noise ratio in Fourier spectroscopy,” Appl. Opt. 16, 3103–3106 (1977).
    [CrossRef] [PubMed]
  37. J. Zhao, R. L. McCreery, “Multichannel FT-Raman spectroscopy: noise analysis and performance assesment,” Appl. Spectrosc. 51, 1687–1697 (1997).
    [CrossRef]
  38. F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362 (2001).
    [CrossRef]
  39. S. P. Davis, M. C. Abrams, J. W. Brault, Fourier Transform Spectrometry (Academic, San Diego, Calif., 2001).
  40. K. Ito, ed., Encyclopedic Dictionary of Mathematics, 2nd ed. (MIT, Cambridge, Mass., 1987), Vol. 2.
  41. R. G. Sellar, J. B. Rafert, “Effects of aberrations on spatially modulated Fourier transform spectrometers,” Opt. Eng. 33, 3087–3092 (1994).
    [CrossRef]
  42. W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, UK, 1986).
  43. R. R. Shannon, The Art and Science of Optical Design (Cambridge U. Press, Cambridge, UK, 1997).
    [CrossRef]
  44. M. Born, E. Wolf, Principles of Optics, 2nd ed. (Pergamon, New York, 1964).

2001 (1)

F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362 (2001).
[CrossRef]

1998 (1)

1997 (1)

1996 (2)

1994 (2)

M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse, Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
[CrossRef] [PubMed]

R. G. Sellar, J. B. Rafert, “Effects of aberrations on spatially modulated Fourier transform spectrometers,” Opt. Eng. 33, 3087–3092 (1994).
[CrossRef]

1993 (1)

1992 (1)

1991 (1)

W. H. Smith, W. V. Schempp, “Digital array scanned interferometers for astronomy,” Exp. Astron. 1, 389–405 (1991).
[CrossRef]

1989 (2)

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A. Y. Stroganova, “Static fast response Fourier spectrometer having a linear CCD image forming system,” J. Opt. Technol. 56, 220–221 (1989).

J. V. Sweedler, M. B. Denton, “Spatially encoded Fourier transform spectroscopy in the ultraviolet to the near infrared,” Appl. Spectrosc. 43, 1378–1384 (1989).
[CrossRef]

1985 (1)

1984 (1)

1977 (2)

1976 (2)

M. H. Tai, M. Harwit, “Fourier and Hadamard transform spectrometers: a limited comparison,” Appl. Opt. 15, 2664–2666 (1976).
[CrossRef] [PubMed]

K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach-Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
[CrossRef]

1968 (1)

K. Kamiya, K. Yoshihara, K. Okada, “Holographic spectra obtained with a Lloyd’s mirror,” Jpn. J. Appl. Phys. 7, 1129 (1968).
[CrossRef]

1967 (2)

K. Yoshihara, A. Kitade, “Holographic spectra using a triangle path interferometer,” Jpn. J. Appl. Phys. 6, 116 (1967).
[CrossRef]

H. D. Drew, A. J. Sievers, “Far-infrared absorption in superconducting and normal lead,” Phys. Rev. Lett. 19, 697–699 (1967).
[CrossRef]

1966 (1)

I. G. Nolt, A. J. Sievers, “Stress induced frequency shift of a lattice resonant mode,” Phys. Rev. Lett. 16, 1103–1105 (1966).
[CrossRef]

1965 (3)

I. P. Petrov, B. N. Grechushnikov, “Photographic method of recording in Fourier spectrometry,” Opt. Spectrosc. 19, 82–83 (1965).

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]

J. W. Cooley, J. W. Tukey, “An algorithm for machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

1964 (1)

1960 (2)

P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 268–312 (1960).
[CrossRef]

L. Genzel, “Aperiodic and periodic interference modulation for spectrographic purposes,” J. Mol. Spectrosc. 4, 241–261 (1960).
[CrossRef]

1959 (2)

J. D. Strong, G. A. Vanasse, “Interferometric spectroscopy in the far infrared,” J. Opt. Soc. Am. 49, 844–850 (1959).
[CrossRef]

F. D. Kahn, “The signal: noise ratio of a suggested spectral analyzer,” Astrophys. J. 129, 518–521 (1959).
[CrossRef]

1958 (1)

P. Fellgett, “A propos de la theorie du spectrometre interferentiel multiplex,” J. Phys. Radium 19, 187–191 (1958).
[CrossRef]

Abrams, M. C.

S. P. Davis, M. C. Abrams, J. W. Brault, Fourier Transform Spectrometry (Academic, San Diego, Calif., 2001).

Ahn, J. S.

Asaka, S.

Barnes, T. H.

Bell, R. J.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).

Bodkin, A.

J. T. Daly, E. A. Johnson, A. Bodkin, W. A. Stevenson, D. A. White, “Recent advances in miniaturization of infrared spectrometers,” in Silicon-based Optoelectronics II, D. J. Robbins, D. C. Houghton, eds., Proc. SPIE3953, 70–87 (2000).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 2nd ed. (Pergamon, New York, 1964).

Brault, J. W.

S. P. Davis, M. C. Abrams, J. W. Brault, Fourier Transform Spectrometry (Academic, San Diego, Calif., 2001).

Budney, C.

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

Caulfield, H. J.

H. J. Caulfield, “Spectroscopy,” in Handbook of Optical Holography, H. J. Caulfield, ed. (Academic, New York, 1979), pp. 587–594.

Cooley, J. W.

J. W. Cooley, J. W. Tukey, “An algorithm for machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

Daly, J. T.

J. T. Daly, E. A. Johnson, A. Bodkin, W. A. Stevenson, D. A. White, “Recent advances in miniaturization of infrared spectrometers,” in Silicon-based Optoelectronics II, D. J. Robbins, D. C. Houghton, eds., Proc. SPIE3953, 70–87 (2000).
[CrossRef]

Davis, S. P.

S. P. Davis, M. C. Abrams, J. W. Brault, Fourier Transform Spectrometry (Academic, San Diego, Calif., 2001).

Denton, M. B.

Dohlen, K.

K. Dohlen, “Interferometric spectrometer for liquid mirror survey telescopes,” in Optical Telescopes of Today and Tomorrow: Following in the Direction of Tycho Brahe, A. Ardeberg, ed., Proc. SPIE2871, 1359–1364 (1996).
[CrossRef]

Drew, H. D.

H. D. Drew, A. J. Sievers, “Far-infrared absorption in superconducting and normal lead,” Phys. Rev. Lett. 19, 697–699 (1967).
[CrossRef]

Duncan, A. J.

Egorova, L. V.

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A. Y. Stroganova, “Static fast response Fourier spectrometer having a linear CCD image forming system,” J. Opt. Technol. 56, 220–221 (1989).

Fellgett, P.

P. Fellgett, “A propos de la theorie du spectrometre interferentiel multiplex,” J. Phys. Radium 19, 187–191 (1958).
[CrossRef]

Ferguson, J. P.

J. P. Ferguson, S. Schoenfelder, “Micromoulded spectrometers produced by the LIGA process,” in Proceedings of IEEE Colloquium on Microengineering in Optics and Optoelectronics (Institute of Electrical and Electronics Engineers, London, UK, 1999), pp. 11/11–11/10.

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]

Genzel, L.

L. Genzel, K. Sakai, “Interferometry from 1950 to present,” J. Opt. Soc. Am. 67, 871–879 (1977).
[CrossRef]

L. Genzel, “Aperiodic and periodic interference modulation for spectrographic purposes,” J. Mol. Spectrosc. 4, 241–261 (1960).
[CrossRef]

Grechushnikov, B. N.

I. P. Petrov, B. N. Grechushnikov, “Photographic method of recording in Fourier spectrometry,” Opt. Spectrosc. 19, 82–83 (1965).

Hamaguchi, H.

Harvey, A. R.

Harwit, M.

Hashimoto, M.

Hedges, N. K.

Higuchi, M.

K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach-Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
[CrossRef]

Hinck, K.

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

Hirst, B.

Horton, K.

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

Horton, R. F.

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

Jacquinot, P.

P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 268–312 (1960).
[CrossRef]

Johnson, E. A.

J. T. Daly, E. A. Johnson, A. Bodkin, W. A. Stevenson, D. A. White, “Recent advances in miniaturization of infrared spectrometers,” in Silicon-based Optoelectronics II, D. J. Robbins, D. C. Houghton, eds., Proc. SPIE3953, 70–87 (2000).
[CrossRef]

Junttila, M.-L.

Kahn, F. D.

F. D. Kahn, “The signal: noise ratio of a suggested spectral analyzer,” Astrophys. J. 129, 518–521 (1959).
[CrossRef]

Kamiya, K.

K. Kamiya, K. Yoshihara, K. Okada, “Holographic spectra obtained with a Lloyd’s mirror,” Jpn. J. Appl. Phys. 7, 1129 (1968).
[CrossRef]

Kawata, S.

Kitade, A.

K. Yoshihara, A. Kitade, “Holographic spectra using a triangle path interferometer,” Jpn. J. Appl. Phys. 6, 116 (1967).
[CrossRef]

Kitagawa, T.

Lenney, J. P.

Leshcheva, I. E.

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A. Y. Stroganova, “Static fast response Fourier spectrometer having a linear CCD image forming system,” J. Opt. Technol. 56, 220–221 (1989).

Lucey, P. G.

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

McCreery, R. L.

Minami, S.

Nakashima, K.

K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach-Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
[CrossRef]

Nolt, I. G.

I. G. Nolt, A. J. Sievers, “Stress induced frequency shift of a lattice resonant mode,” Phys. Rev. Lett. 16, 1103–1105 (1966).
[CrossRef]

Okada, K.

K. Kamiya, K. Yoshihara, K. Okada, “Holographic spectra obtained with a Lloyd’s mirror,” Jpn. J. Appl. Phys. 7, 1129 (1968).
[CrossRef]

Okamoto, T.

Padgett, M. J.

Patterson, B. A.

Petrov, I. P.

I. P. Petrov, B. N. Grechushnikov, “Photographic method of recording in Fourier spectrometry,” Opt. Spectrosc. 19, 82–83 (1965).

Popov, B. N.

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A. Y. Stroganova, “Static fast response Fourier spectrometer having a linear CCD image forming system,” J. Opt. Technol. 56, 220–221 (1989).

Rafert, J. B.

R. G. Sellar, J. B. Rafert, “Effects of aberrations on spatially modulated Fourier transform spectrometers,” Opt. Eng. 33, 3087–3092 (1994).
[CrossRef]

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

Reininger, F. M.

F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362 (2001).
[CrossRef]

Richards, P. L.

Rusk, T. B.

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

Sakai, K.

Schempp, W. V.

W. H. Smith, W. V. Schempp, “Digital array scanned interferometers for astronomy,” Exp. Astron. 1, 389–405 (1991).
[CrossRef]

Schoenfelder, S.

J. P. Ferguson, S. Schoenfelder, “Micromoulded spectrometers produced by the LIGA process,” in Proceedings of IEEE Colloquium on Microengineering in Optics and Optoelectronics (Institute of Electrical and Electronics Engineers, London, UK, 1999), pp. 11/11–11/10.

Sellar, R. G.

R. G. Sellar, J. B. Rafert, “Effects of aberrations on spatially modulated Fourier transform spectrometers,” Opt. Eng. 33, 3087–3092 (1994).
[CrossRef]

Shannon, R. R.

R. R. Shannon, The Art and Science of Optical Design (Cambridge U. Press, Cambridge, UK, 1997).
[CrossRef]

Sibbett, W.

Sievers, A. J.

H. D. Drew, A. J. Sievers, “Far-infrared absorption in superconducting and normal lead,” Phys. Rev. Lett. 19, 697–699 (1967).
[CrossRef]

I. G. Nolt, A. J. Sievers, “Stress induced frequency shift of a lattice resonant mode,” Phys. Rev. Lett. 16, 1103–1105 (1966).
[CrossRef]

Smith, W. H.

W. H. Smith, “Digital array scanned interferometer: sensor and results,” Appl. Opt. 35, 2902–2909 (1996).
[CrossRef] [PubMed]

W. H. Smith, W. V. Schempp, “Digital array scanned interferometers for astronomy,” Exp. Astron. 1, 389–405 (1991).
[CrossRef]

Stevenson, W. A.

J. T. Daly, E. A. Johnson, A. Bodkin, W. A. Stevenson, D. A. White, “Recent advances in miniaturization of infrared spectrometers,” in Silicon-based Optoelectronics II, D. J. Robbins, D. C. Houghton, eds., Proc. SPIE3953, 70–87 (2000).
[CrossRef]

Stroganova, A. Y.

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A. Y. Stroganova, “Static fast response Fourier spectrometer having a linear CCD image forming system,” J. Opt. Technol. 56, 220–221 (1989).

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]

Strong, J. D.

Sweedler, J. V.

Tai, M. H.

Takahashi, S.

Treffers, R. R.

Tukey, J. W.

J. W. Cooley, J. W. Tukey, “An algorithm for machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

Vanasse, G. A.

Walther, A.

A. Walther, The Ray and Wave Theory of Lenses, Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, UK, 1995).

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, UK, 1986).

White, D. A.

J. T. Daly, E. A. Johnson, A. Bodkin, W. A. Stevenson, D. A. White, “Recent advances in miniaturization of infrared spectrometers,” in Silicon-based Optoelectronics II, D. J. Robbins, D. C. Houghton, eds., Proc. SPIE3953, 70–87 (2000).
[CrossRef]

Williams, T.

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

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 2nd ed. (Pergamon, New York, 1964).

Yoshihara, K.

K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach-Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
[CrossRef]

K. Kamiya, K. Yoshihara, K. Okada, “Holographic spectra obtained with a Lloyd’s mirror,” Jpn. J. Appl. Phys. 7, 1129 (1968).
[CrossRef]

K. Yoshihara, A. Kitade, “Holographic spectra using a triangle path interferometer,” Jpn. J. Appl. Phys. 6, 116 (1967).
[CrossRef]

Zhao, J.

Appl. Opt. (8)

Appl. Spectrosc. (4)

Astrophys. J. (1)

F. D. Kahn, “The signal: noise ratio of a suggested spectral analyzer,” Astrophys. J. 129, 518–521 (1959).
[CrossRef]

Exp. Astron. (1)

W. H. Smith, W. V. Schempp, “Digital array scanned interferometers for astronomy,” Exp. Astron. 1, 389–405 (1991).
[CrossRef]

Infrared Phys. Technol. (1)

F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362 (2001).
[CrossRef]

J. Mol. Spectrosc. (1)

L. Genzel, “Aperiodic and periodic interference modulation for spectrographic purposes,” J. Mol. Spectrosc. 4, 241–261 (1960).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Technol. (1)

L. V. Egorova, I. E. Leshcheva, B. N. Popov, A. Y. Stroganova, “Static fast response Fourier spectrometer having a linear CCD image forming system,” J. Opt. Technol. 56, 220–221 (1989).

J. Phys. Radium (1)

P. Fellgett, “A propos de la theorie du spectrometre interferentiel multiplex,” J. Phys. Radium 19, 187–191 (1958).
[CrossRef]

Jpn. J. Appl. Phys. (3)

K. Yoshihara, A. Kitade, “Holographic spectra using a triangle path interferometer,” Jpn. J. Appl. Phys. 6, 116 (1967).
[CrossRef]

K. Kamiya, K. Yoshihara, K. Okada, “Holographic spectra obtained with a Lloyd’s mirror,” Jpn. J. Appl. Phys. 7, 1129 (1968).
[CrossRef]

K. Yoshihara, K. Nakashima, M. Higuchi, “Holographic spectroscopy using a Mach-Zehnder interferometer,” Jpn. J. Appl. Phys. 15, 1169–1170 (1976).
[CrossRef]

Math. Comput. (1)

J. W. Cooley, J. W. Tukey, “An algorithm for machine calculation of complex Fourier series,” Math. Comput. 19, 297–301 (1965).
[CrossRef]

Opt. Eng. (1)

R. G. Sellar, J. B. Rafert, “Effects of aberrations on spatially modulated Fourier transform spectrometers,” Opt. Eng. 33, 3087–3092 (1994).
[CrossRef]

Opt. Spectrosc. (1)

I. P. Petrov, B. N. Grechushnikov, “Photographic method of recording in Fourier spectrometry,” Opt. Spectrosc. 19, 82–83 (1965).

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]

Phys. Rev. Lett. (2)

I. G. Nolt, A. J. Sievers, “Stress induced frequency shift of a lattice resonant mode,” Phys. Rev. Lett. 16, 1103–1105 (1966).
[CrossRef]

H. D. Drew, A. J. Sievers, “Far-infrared absorption in superconducting and normal lead,” Phys. Rev. Lett. 19, 697–699 (1967).
[CrossRef]

Rep. Prog. Phys. (1)

P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 268–312 (1960).
[CrossRef]

Other (13)

S. P. Davis, M. C. Abrams, J. W. Brault, Fourier Transform Spectrometry (Academic, San Diego, Calif., 2001).

K. Ito, ed., Encyclopedic Dictionary of Mathematics, 2nd ed. (MIT, Cambridge, Mass., 1987), Vol. 2.

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

J. T. Daly, E. A. Johnson, A. Bodkin, W. A. Stevenson, D. A. White, “Recent advances in miniaturization of infrared spectrometers,” in Silicon-based Optoelectronics II, D. J. Robbins, D. C. Houghton, eds., Proc. SPIE3953, 70–87 (2000).
[CrossRef]

J. P. Ferguson, S. Schoenfelder, “Micromoulded spectrometers produced by the LIGA process,” in Proceedings of IEEE Colloquium on Microengineering in Optics and Optoelectronics (Institute of Electrical and Electronics Engineers, London, UK, 1999), pp. 11/11–11/10.

H. J. Caulfield, “Spectroscopy,” in Handbook of Optical Holography, H. J. Caulfield, ed. (Academic, New York, 1979), pp. 587–594.

A. Walther, The Ray and Wave Theory of Lenses, Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, UK, 1995).

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972).

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

K. Dohlen, “Interferometric spectrometer for liquid mirror survey telescopes,” in Optical Telescopes of Today and Tomorrow: Following in the Direction of Tycho Brahe, A. Ardeberg, ed., Proc. SPIE2871, 1359–1364 (1996).
[CrossRef]

W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, UK, 1986).

R. R. Shannon, The Art and Science of Optical Design (Cambridge U. Press, Cambridge, UK, 1997).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 2nd ed. (Pergamon, New York, 1964).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

Schematic illustration of the HFTS operation. Reference planes are perpendicular to the optical axis and pass through the front (object plane or field) and back (detector plane) foci of the Fourier lens F. Shearing in the interferometer is described as splitting of an arbitrary object point P by vectors ±δ/2 along the Y axis. Object and image reference planes have corresponding coordinate systems with vertical axes Y and Y′ (meridional direction) and horizontal axes X and X′ (saggital direction). The Z and Z′ axes (not shown) are both directed from the left to right and coincide with the optical axis.

Fig. 2
Fig. 2

Ray tracing for a HFTS made from standard microlenses and Littrow prisms. Asymmetry in the interferometer is introduced when one of the prims is shifted by the distance d along the hypotenuse.

Fig. 3
Fig. 3

Three-dimensional picture of the Littrow prism HFTS. The light from an infinite source is focused by the entrance lens 1 into the asymmetric Sagnac interferometer formed by beam splitter 2 and mirrors 3 and 4. The lens 5 collimates the exiting beams and overlaps them at detector 6.

Fig. 4
Fig. 4

Interference pattern produced in the Littrow prism HFTS by a He-Ne laser. Speckles are almost absent because of the high quality of the standard optical parts used in the interferometer.

Fig. 5
Fig. 5

Interferogram of the neon lamp measured with the Littrow prism HFTS. Intensity nonuniformities are removed.

Fig. 6
Fig. 6

Spectrum of the neon lamp calculated from the interferogram in Fig. 5 (solid curve). Spectrum of the UV LED emitting at 370 nm (dotted curve, multiplied by 15) demonstrates the wide spectral range of the spectrometer.

Fig. 7
Fig. 7

Shifts of the He-Ne laser fringes in the Littrow prism HFTS versus the normalized field coordinate ξ for two pupil positions: (a) at ξ P = 0.1, η P = 0; (b) at ξ P = η P = 0. The solid curve shows the fit of the experimental values with only primary aberrations taken into account. The dotted lines represent contributions from aberrations with linear field dependence.

Fig. 8
Fig. 8

Frequency shift due to the chromatic aberrations in the HFTS made from BK7 glass. The solid curve is calculated according to Eq. (43). The symbols are experimental values measured for several mercury emission lines.

Tables (1)

Tables Icon

Table 1 Values of Primary Aberration Coefficients

Equations (51)

Equations on this page are rendered with MathJax. Learn more.

Ur  1/2Ur-δ/2+1/2Ur+δ/2.
Ir=Ur2=KP*r1, rKPr2, rU*r1Ur2dr1dr2.
KPr, r=nnλnNnNτ1/2|Det11S1/2 exp ikS,
Det11S2Sxx2Sxy2Syx2Syy.
U*r1Ur2=14U*r1-δ/2Ur2-δ/2+U*r1+δ/2Ur2+δ/2+U*r1-δ/2Ur2+δ/2+U*r1+δ/2Ur2-δ/2=14Ir1-δ/2δr1-r2+Ir1+δ/2δr1-r2+Ir1-δ/2δr1-r2-δ+Ir1+δ/2δr1-r2+δ,
U*r1Ur2=Ir1δr1-r2.
Ir=1/4KPr-δ/2, r+KPr+δ/2, r2Ird2r.
KPr-δ/2, r+KPr+δ/2, r =nnλnNnNτ1/2Det11S1/2exp ikSr-δ/2, r+exp ikSr+δ/2, r.
S0x, y, x, y=-xx+yy/f,
KPr-δ/2, r+KPr+δ/2, r=2 nnλnNnNτ1/2Det11S1/2 exp ikS0r, rcoskδ2fy=2KPr, rcoskδ2fy.
Ir=1/21+coskδfyKPr, r2Ird2r=1/2I0r1+coskδfy=1/2I0r1+cos 2πσ δf y,
Ir=1/20I0r1+ cos2πσ δf yBσdσ.
σmax=f/2hδ.
L=0.5Nhδ/f=0.5Dδ/f=0.5nδ/F,
δσ=0.602/L=1.204f/Nhδ=1.204F/nδ,
R=N/2.408.
L=Nhδ/f=Dδ/f=nδ/F,
δσ=0.602/L=0.602f/Nhδ=0.602F/nδ,
R=N/1.204.
Iu=I00Bσcos 2πσudσ.
8πIu/I0=2/π0Bκ/2πcosκudκ.
Bσ=40Iu/I0cos2πσudu.
Bσ+ΔB=40Iν/I0+ΔI/I0cos2πσνdν.
ΔBσ=40ΔIu/I0cos2πσudu.
1/40ΔBσ2dσ=0ΔIu/I02du.
ΔB2¯σmax=4LΔI2¯/I02,
εσ=2εuL/σmax.
S/NuI0/I0/εu.
S/Nu=B¯σmax/0.5εσσmax/L=S/Nσ2σmaxL=S/Nσ2N,
εu=εu0hHT,
I0/I0=ΛAΩHFTT/N,
S/NHFT=ΛAΩHFTT/εu0N2NhH=ΛAΩHFTT/εu0N2Σ,
S/NMD=ΛAΩDT/Nεu0hH=ΛAΩDT/εu0NΣ,
S/N SD=Λ AΩ DT/N/Nεu0hH=Λ AΩ DT/εu0NΣ.
S/NuHFT=ΛAΩHFTT/N1/2.
S/NHFT=ΛAΩHFTT1/2/2N
S/NMD=ΛAΩDT1/2/N,
S/NSD=ΛAΩDT1/2/N.
S/NHFT/S/NMD=2N-1/2AΩHFT/AΩD×ΣMD/ΣHFT1/2,
S/NHFT/S/NM=2N-1/2AΩH/AΩD1/2>1, AΩH/AΩD>2N.
exp ikSr-δ/2, r+exp ikSr+δ/2, r=exp ikSr, rexp-ik δ2Sy+expik δ2Sy =expikSr, r2 cos2πσ δ2Sy.
Ir=Kpr, r20.51+cos 2πσδSyIrd2r.
S4=a100K+a010P+a001T+a200K2+a020P2+a002T2+a110KP+a011PT+a101KT.
K=1/2ξ2+η2, P=ξξP+ηηP, T=1/2ξP2+ηP2
ξ=y/f, η=x/f, ξP=y/f, ηP=x/f.
fSy=Sξ=SKKξ+SPPξ=SKξ+SPξP,
fS4y=a100ξ+a010ξP+a2002Kξ+a0202PξP+a110Pξ+KξP+a011TξP+a101Tξ.
f S4y=a100ξ+a200ξ3, fS4y=-fξP+1/2a011ξP3+α100+2a020+1/2a101ξP2ξ + 3/2a101ξPξ2 + a200ξ3.
2a020+1/2a101=3/2 SIII+1/2SIV.
σm=σf0/f=σn0n-n/nn0-n0,
δf-f0/f0<ρ, n-n0/n-1<ρ/δ,

Metrics