OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Steven A. Burns
  • Vol. 24, Iss. 9 — Sep. 1, 2007
  • pp: 2817–2821

Signal-to-noise ratio trade-offs associated with coarsely sampled Fourier transform spectroscopy

Samuel T. Thurman and James R. Fienup  »View Author Affiliations


JOSA A, Vol. 24, Issue 9, pp. 2817-2821 (2007)
http://dx.doi.org/10.1364/JOSAA.24.002817


View Full Text Article

Enhanced HTML    Acrobat PDF (275 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We derive the spectral signal-to-noise ratio (SNR) trade-offs associated with coarsely sampled Fourier transform spectroscopy using a step-and-integrate measurement scheme. We show that there is no SNR penalty in the shot noise limit and a slight SNR benefit in the detector noise limit for the case of coarse sampling to achieve the same spectral resolution as a baseline Nyquist sampling scenario, where the total detector integration time is the same for both sampling cases.

© 2007 Optical Society of America

OCIS Codes
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(300.6300) Spectroscopy : Spectroscopy, Fourier transforms

ToC Category:
Spectroscopy

History
Original Manuscript: March 5, 2007
Manuscript Accepted: April 26, 2007
Published: August 9, 2007

Citation
Samuel T. Thurman and James R. Fienup, "Signal-to-noise ratio trade-offs associated with coarsely sampled Fourier transform spectroscopy," J. Opt. Soc. Am. A 24, 2817-2821 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-9-2817


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. H. Nyquist, "Certain topics in telegraph transmission theory," Trans. Am. Inst. Electr. Eng. 47, 617-644 (1928). [CrossRef]
  2. E. T. Whittaker, "On the functions which are represented by the expansions of the interpolation theory," Proc. R. Soc. Edinburgh, Sect. A: Math. Phys. Sci. 35, 181-194 (1915).
  3. C. E. Shannon, "Communication in the presence of noise," Proc. Inst. Radio Eng. 37, 10-21 (1949).
  4. J. Connes, "Spectroscopic studies using Fourier transformations," Rev. Opt. Theor. Instrum. 40, 116 (1961).
  5. G. A. Vanasse and H. Sakai, "Fourier spectroscopy," in Progress in Optics, Vol. 6, E.Wolf, ed. (North-Holland, 1967), pp. 261-330.
  6. J. Kauppinen, "Correction of the linear phase errors of one-sided interferograms," Infrared Phys. 16, 359-366 (1976). [CrossRef]
  7. D. A. Naylor, B. G. Gom, M. K. Tahic, and G. R. Davis, "Astronomical spectroscopy using an aliased, step-and-integrate, Fourier transform spectrometer," Proc. SPIE 5498, 685-694 (2004). [CrossRef]
  8. D. A. Naylor, B. G. Gom, T. R. Fulton, M. K. Tahic, and G. R. Davis, "Increased efficiency through undersampling in Fourier transform spectroscopy," presented at the OSA Topical Meeting, "Fourier Transform Spectroscopy/Hyperspectral Imaging and Sounding of the Environment," Alexandria, Va., January 31-February 3, 2005.
  9. J. Kauppinen and J. Partanen, Fourier Transforms in Spectroscopy (Wiley-VCH, 2001). [CrossRef]
  10. ASTM International, "Standard tables for reference solar spectral irradiances: direct normal and hemispherical on 37° tilted surface," standard G173-03, http://www.astm.org (2003).

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.

Figures

Fig. 1
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited