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Applied Optics

Applied 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)

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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:

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

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)

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  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]

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