OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 11 — May. 24, 2010
  • pp: 11622–11649

Theoretical aspects of Fourier Transform Spectrometry and common path triangular interferometers

Alessandro Barducci, Donatella Guzzi, Cinzia Lastri, Paolo Marcoionni, Vanni Nardino, and Ivan Pippi  »View Author Affiliations

Optics Express, Vol. 18, Issue 11, pp. 11622-11649 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (1700 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Recent investigations have induced relevant advancements of imaging interferometry, which is becoming a viable option for Earth remote sensing. Various research programs have chosen the Sagnac configuration for new imaging interferometers. Due to the growing diffusion of this technique, we have developed a self-contained theory for describing the signal produced by triangular FTSs and its optimal processing. We investigate the relevant disadvantages of multiplexing, and compare dispersive with FTS instruments. The paper addresses some methods for correcting the phase error, and the non-unitary transformation performed by a Sagnac interferometer. The effect of noise on spectral estimations is discussed.

© 2010 OSA

OCIS Codes
(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(300.6190) Spectroscopy : Spectrometers
(300.6300) Spectroscopy : Spectroscopy, Fourier transforms
(280.4991) Remote sensing and sensors : Passive remote sensing

ToC Category:

Original Manuscript: February 24, 2010
Revised Manuscript: March 17, 2010
Manuscript Accepted: March 19, 2010
Published: May 18, 2010

Alessandro Barducci, Donatella Guzzi, Cinzia Lastri, Paolo Marcoionni, Vanni Nardino, and Ivan Pippi, "Theoretical aspects of Fourier Transform Spectrometry and common path triangular interferometers," Opt. Express 18, 11622-11649 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. J. Persky, “A review of spaceborne infrared Fourier transform spectrometers for remote sensing,” Rev. Sci. Instrum. 66(10), 4763–4797 (1995). [CrossRef]
  2. B. Harnisch, W. Posselt, K. Holota, H. O. Tittel, and M. Rost, “Compact Fourier-transform imaging spectrometer for small satellite missions,” Acta Astronaut. 52(9-12), 803–811 (2003). [CrossRef]
  3. M.-L. Junttila, “Stationary Fourier transform spectrometer,” Appl. Opt. 31(21), 4106–4112 (1992). [CrossRef] [PubMed]
  4. L. J. Otten, A. D. Meigs, B. A. Jones, P. Prinzing, and D. S. Fronterhouse, “Payload Qualification and Optical Performance Test Results for the MightySat II.1 Hyperspectral Imager,” Proc. SPIE 3498, 231–238 (1998). [CrossRef]
  5. P. G. Lucey, T. Williams, K. Horton, C. Budney, J. B. Ratfer, and E. T. Risk, “SMIFTS: A cryogenically cooled spatially modulate, imaging, Fourier transform spectrometer for remote sensing applications,” Proceeding of the International Conference on Spectral Sensing Research, Vol. 1, 251 – 262, (1992).
  6. Y. Ferrec, J. Taboury, H. Sauer, and P. Chavel, “Optimal geometry for Sagnac and Michelson interferometers used as spectral imagers,” Opt. Eng. 45(11), 115601-115606 (2006). [CrossRef]
  7. L. J. Otten, R. G. Sellar, and J. B. Rafert, “MightySatII.1 Fourier transform hyperspectral imager payload performance,” Proc. SPIE 2583, 566–575 (1995). [CrossRef]
  8. P. G. Lucey, K. A. Horton, and T. Williams, “Performance of a long-wave infrared hyperspectral imager using a Sagnac interferometer and an uncooled microbolometer array,” Appl. Opt. 47(28), F107–F113 (2008). [CrossRef] [PubMed]
  9. A. Barducci, P. Marcoionni, I. Pippi, and M. Poggesi, “Simulation of the Performance of a Stationary Imaging Interferometer for High Resolution Monitoring of the Earth,” Proc. SPIE 4540, 112–121 (2001). [CrossRef]
  10. A. Barducci, A. Casini, F. Castagnoli, P. Marcoionni, M. Morandi, and I. Pippi, “Performance assessment of a Stationary Interferometer for High-Resolution Remote Sensing,” Proc. SPIE 4725, 547–555 (2002). [CrossRef]
  11. M. Bliss, “Demonstration of a static Fourier transform spectrometer,” Proc. SPIE 3541, 103–109 (1999). [CrossRef]
  12. S. J. Katzberg, and R. B. Statham, “Performance Assessment of the Digital Array Scanned Interferometers (DASI) Concept,” NASA Technical Paper 3570, August 1996.
  13. P. D. Hammer, F. P. J. Valero, and D. L. Peterson, “An imaging interferometer for terrestrial remote sensing,” Proc. SPIE 1937, 244–255 (1993). [CrossRef]
  14. S. Subramaniam, B. Y. Ravindra, B. Rabindranath, B. G. Basheerullah, P. V. Viswanath, and O. P. Bajpai, “Stationary spatially modulated fourier transform spectro-radiometer,” J. Indian Soc. Remote Sens. 31(3), 187–196 (2003). [CrossRef]
  15. R. F. Horton, “Optical Design for High Ètendue Imaging Fourier Transform Spectrometer,” Proc. SPIE 2819, 300–315 (1996). [CrossRef]
  16. D. Cabib, R. A. Buckwald, Y. Garin, and D. G. Soenksen, “Spatially resolved Fourier transform spectroscopy (spectral imaging): a powerful tool for quantitative analytical microscopy”, in Optical diagnostics of living cells on biofluids,” Proc. SPIE 2678, 278–291 (1996). [CrossRef]
  17. J. Genest, P. Tremblay, and A. Villemaire, “Throughput of tilted interferometers,” Appl. Opt. 37(21), 4819–4822 (1998). [CrossRef]
  18. P. Jacquinot, “The luminosity of spectrometers with Prisms, Grating, or Fabry-Perot Etalons,” J. Opt. Soc. Am. 44(10), 761–765 (1954). [CrossRef]
  19. M. R. Descour, “The Throughput Advantage In Imaging Fourier-Transform Spectrometers,” Proc. SPIE 2819, 285–290 (1997). [CrossRef]
  20. R. G. Sellar and G. D. Boreman, “Comparison of relative signal-to-noise ratios of different classes of imaging spectrometer,” Appl. Opt. 44(9), 1614–1624 (2005). [CrossRef] [PubMed]
  21. F. A. Jankins and H. E. White, Fundamentals of Optics, (Mcgraw-Hill College; 4th edition, 1976).
  22. W. Goodman, Introduction to Fourier Optics, (McGraw-Hill, New York, 1968).
  23. R. Bracewell, The Fourier transform and its applications, (McGraw-Hill, New York, 1965).
  24. D. A. Walmsley, T. A. Clark, and R. E. Jennings, “Correction of off-center sampled interferograms by a change of origin in the fourier transform; the important effect of overlapping aliases,” Appl. Opt. 11(5), 1148–1151 (1972). [CrossRef] [PubMed]
  25. M.-L. Junttila, J. Kauppinen, and E. Ikonen, “Performance limits of stationary Fourier spectrometers,” J. Opt. Soc. Am. A 8(9), 1457–1462 (1991). [CrossRef]
  26. R. L. Hilliard and G. G. Shepherd, “Wide-Angle Michelson Interferometer for Measuring Doppler Line Widths,” J. Opt. Soc. Am. 56(3), 362–369 (1966). [CrossRef]
  27. P. Hlubina, D. Ciprian, J. Lunacek, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88(3), 397–403 (2007), doi:. [CrossRef]
  28. L. Mertz, “Auxiliary computation for Fourier spectrometry,” Infrared Phys. 7(1), 17–23 (1967). [CrossRef]
  29. H. Sakai, G. A. Vanasse, and M. L. Forman, “Spectral Recovery in Fourier Spectroscopy,” J. Opt. Soc. Am. 58(1), 84–90 (1968). [CrossRef]
  30. M. L. Forman, W. H. Steel, and G. A. Vanasse, “Correction of Asymmetric Interferograms Obtained in Fourier Spectroscopy,” J. Opt. Soc. Am. 56(1), 59–63 (1966). [CrossRef]
  31. J. Connes, “Recherches sur la spectroscopie par transformation de Fourier,” Revue d’Optique 40, 45–265 (1961).
  32. T. Okamoto, S. Kawata, and S. Minami, “Fourier transform spectrometer with a self-scanning photodiode array,” Appl. Opt. 23(2), 269–273 (1984). [CrossRef] [PubMed]
  33. A. Papoulis, Probability Random Variables, and Stochastic Processes, (McGraw-Hill International Editions, Third Edition, 1991).
  34. P. R. Griffiths, H. J. Sloane, and R. W. Hannah, “Interferometers vs monochromators: separating the optical and digital advantages,” Appl. Spectrosc. 31(6), 485–495 (1977). [CrossRef]
  35. R. J. Bell, Introductory Fourier Transform Spectroscopy, (Academic Press, New York and London, 1972).
  36. P. B. Fellgett, “Conclusions on multiplex methods,” Journal de Physique, Colloque C2, Supplément au n. 3–4 Tome 28, mars-avril 1967, pp.: 165–171, (1967).
  37. P. B. Fellgett, “I. — les principes généraux des méthodes nouvelles en spectroscopie interférentielle A propos de la théorie du spectromètre interférentiel multiplex,” J. Phys. Radium 19(3), 187–191 (1958). [CrossRef]
  38. P. B. Fellgett, “The nature and origin of multiplex Fourier spectrometry,” Notes Rec. R. Soc. 60(1), 91–93 (2006). [CrossRef]
  39. F. D. Kahn, “The signal: noise ratio of a suggested spectral analyzer,” Astrophys. J. 129, 518–520 (1959). [CrossRef]
  40. W. Schumann and T. S. Lomheim, “Infrared hyperspectral imaging Fourier transform and dispersive spectrometers: comparison of signal-to-noise-based performance,” Imaging Spectrometry VII, San Diego, CA, USA, SPIE 4480,1-14 (2001).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited