OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 34 — Dec. 1, 2011
  • pp: 6377–6383

Spectrum constructing with nonuniform samples using least-squares approximation by cosine polynomials

Cong Feng, Jingqiu Liang, and Zhongzhu Liang  »View Author Affiliations


Applied Optics, Vol. 50, Issue 34, pp. 6377-6383 (2011)
http://dx.doi.org/10.1364/AO.50.006377


View Full Text Article

Enhanced HTML    Acrobat PDF (668 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The least-squares approximation of cosine polynomials is used to construct the spectrum from the simulated nonuniform samples of the interferogram given by a step-mirror-based static Fourier transform spectrometer. Numerical and experimental results show the stability of the algorithm and a spectrum-constructing error of 0.03%.

© 2011 Optical Society of America

OCIS Codes
(300.6190) Spectroscopy : Spectrometers
(300.6300) Spectroscopy : Spectroscopy, Fourier transforms
(070.2025) Fourier optics and signal processing : Discrete optical signal processing

ToC Category:
Spectroscopy

History
Original Manuscript: August 8, 2011
Revised Manuscript: October 6, 2011
Manuscript Accepted: October 6, 2011
Published: November 25, 2011

Citation
Cong Feng, Jingqiu Liang, and Zhongzhu Liang, "Spectrum constructing with nonuniform samples using least-squares approximation by cosine polynomials," Appl. Opt. 50, 6377-6383 (2011)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-34-6377


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. P. R. Griffiths and J. A. de Haseth, “Signal-to-noise ratio,” in Fourier Transform Infrared Spectrometry (Wiley & Sons, 2007), pp. 167–168
  2. O. Manzardo, “Micro-sized Fourier spectrometers,” Ph.D. dissertation (University of Neuchatel, 2002).
  3. J. Sin, W. H. Lee, D. Popa, and H. E. Stephanou, “Assembled Fourier transform micro-spectrometer,” Proc. SPIE 6109, 1–8(2006). [CrossRef]
  4. U. Wallrabe, C. Solf, J. Mohr, and J. G. Korvink, “Miniaturized Fourier transform spectrometer for the near infrared wavelength regime incorporating an electromagnetic linear actuator,” Sens. Actuators A 123, 459–467 (2005). [CrossRef]
  5. G. Boer, P. Ruffieux, T. Scharf, P. Seitz, and R. Dandliker, “Compact liquid-crystal-polymer Fourier-transform spectrometer,” Appl. Opt. 43, 2201–2208 (2004). [CrossRef] [PubMed]
  6. B. Martin, A. Morand, P. Benech, G. Leblond, S. Blaize, G. Lerondel, P. Royer, P. Kern, and E. L. Coarer, “Design of a compact static Fourier transform spectrometer in integrated optics based on a leaky loop structure,” Opt. Lett. 34, 184–186(2009). [CrossRef] [PubMed]
  7. K. D. Moller, “Wave-front-dividing array interferometers without moving parts for real-time spectroscopy from the IR to the UV,” Appl. Opt. 34, 1493–1501 (1995). [CrossRef] [PubMed]
  8. A. Lacan, F.-M. Bréon, A. Rosak, F. Brachet, L. Roucayrol, P. Etcheto, C. Casteras, and Y. Salaün, “A static Fourier transform spectrometer for atmospheric sounding: concept and experimental implementation,” Opt. Express 18, 8311–8331(2010). [CrossRef] [PubMed]
  9. E. V. Ivanov, “Static Fourier transform spectroscopy with enhanced resolving power,” J. Opt. A 2, 519–528 (2000). [CrossRef]
  10. Y. M. Kong, J. Q. Liang, Z. Z. Liang, B. Wang, and J. Zhang, “Microassembled Fourier transform spectrometer,” Proc. SPIE 7283, 728304 (2009). [CrossRef]
  11. C. Feng, B. Wang, Z. Liang, and J. Liang, “Miniaturization of step mirrors in a static Fourier transform spectrometer theory and simulation,” J. Opt. Soc. Am. B 28, 128–133 (2010). [CrossRef]
  12. H. G. Feichtinger, K. Grochenig, and T. Strohmer, “Efficient numerical methods in non-uniform sampling theory,” Numer. Math. 69, 423–440 (1995). [CrossRef]
  13. F. Marvasti and M. Analoui, “Recovery of signals from nonuniform samples using iterative methods,” in Proceedings of IEEE International Symposium on Circuits and Systems (IEEE, 1989), pp. 1021–1024. [CrossRef]
  14. K. Grochenig, “A discrete theory of irregular sampling,” Linear Algebra Appl. 193, 129–150 (1993). [CrossRef]
  15. Y. Shen, C. Zhu, L. Liu, Q. Wang, J. Jin, and Y. Lin, “Explicit solution for nonuniform discrete fourier transform,” in Proceedings of IEEE Instrumentation and Measurement Technology Conference (I2MTC) (IEEE, 2010), pp. 1505–1509. [CrossRef]
  16. E. Margolis and Y. C. Eldar, “Nonuniform sampling of periodic bandlimited signals,” IEEE Trans. Signal Process. 56, 2728–2745 (2008). [CrossRef]
  17. Y. D. Siem, E. de Klerk, and D. den Hertog, “Discrete least-norm approximation by nonnegative (trigonometric) polynomials and rational functions,” Struct. Multidisc. Optim. 35, 327–339 (2008). [CrossRef]
  18. T. Strohmer, “Numerical analysis of the non-uniform sampling problem,” J. Comput. Appl. Math. 122, 297–316(2000). [CrossRef]
  19. K. Yao and J. B. Thomas, “On some stability and interpolatory properties of nonuniform sampling expansions,” IEEE Trans. Circuit Theory CT-14, 404–408 (1967). [CrossRef]
  20. R. F. Bass and K. Grochenig, “Random sampling of multivariate trigonometric polynomials,” SIAM J. Math. Anal. 36, 773–795 (2005). [CrossRef]
  21. Q. H. Liu and N. Nguyen, “An accurate algorithm for nonuniform fast Fourier transforms (NUFFTs),” IEEE Microwave Guided Wave Lett. 8, 18–20 (1998). [CrossRef]
  22. L. Palchetti and D. Lastrucci, “Spectral noise due to sampling errors in Fourier-transform spectroscopy,” Appl. Opt. 40, 3235–3243 (2001). [CrossRef]
  23. E. E. Bell and R. B. Sanderson, “Spectral errors resulting from random sampling-position errors in Fourier transform spectroscopy,” Appl. Opt. 11, 688–689 (1972). [CrossRef] [PubMed]
  24. D. L. Cohen, “Noise-equivalent change in radiance for sampling noise in a double-sided interferogram,” Appl. Opt. 42, 2289–2300 (2003). [CrossRef] [PubMed]
  25. A. Papoulis, “Error analysis in sampling theory,” Proc. IEEE 54, 947–955 (1966). [CrossRef]
  26. E. Sarkissian and K. W. Bowman, “Application of a nonuniform spectral resampling transform in Fourier-transform spectrometry,” Appl. Opt. 42, 1122–1131 (2003). [CrossRef] [PubMed]

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited