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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 10207–10207
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Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer: erratum

Wenyi Ren, Chunmin Zhang, Tingkui Mu, Lili Fu, and Chenling Jia  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 10207-10207 (2013)
http://dx.doi.org/10.1364/OE.21.010207


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Abstract

An erratum is presented to correct an error in an equation used to determine the interferogram without background and the estimated background of the recorded interferogram based on empirical mode decomposition.

© 2013 OSA

In the recent paper on the empirical mode decomposition based background removal of the interferogram [1

1. C. M. Zhang, W. Y. Ren, T. K. Mu, L. L. Fu, and C. L. Jia, “Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer,” Opt. Express 21(3), 2592–2605 (2013). [CrossRef] [PubMed]

], the mathematical form of Eq. (4) in section 2.1 is incorrect as published. It was a careless error of us. The other contents proposed in Ref [1

1. C. M. Zhang, W. Y. Ren, T. K. Mu, L. L. Fu, and C. L. Jia, “Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer,” Opt. Express 21(3), 2592–2605 (2013). [CrossRef] [PubMed]

]. are correct. The correct expression of Eq. (4) in Ref [1

1. C. M. Zhang, W. Y. Ren, T. K. Mu, L. L. Fu, and C. L. Jia, “Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer,” Opt. Express 21(3), 2592–2605 (2013). [CrossRef] [PubMed]

]. is

Ip(x)=i=1i=Dci(x),be(x)=i=D+1i=Kci(x)+r(x).
(6)

The interferogram without background is reconstructed by the low order IMFs without background contamination. According to the expression in Ref [1

1. C. M. Zhang, W. Y. Ren, T. K. Mu, L. L. Fu, and C. L. Jia, “Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer,” Opt. Express 21(3), 2592–2605 (2013). [CrossRef] [PubMed]

], Ip(x) and be(x), respectively, are reconstructed by the IMFs from c1(x) to cD(x) and from cD+1(x) to cK(x). The authors regret any confusion and misunderstanding that may have been caused by the careless mistake.

Acknowledgments

This work was supported by the 863 Program (2012AA121101), the major state special project (E0310/1112/JC02), the National Natural Science Foundation (61275184, 2006AA12Z152), the Scientific Research Support Program for New Teacher of Xi’an Jiaotong University (08142024) and the Fundamental Research Funds for the Central Universities (08143082).

References and links

1.

C. M. Zhang, W. Y. Ren, T. K. Mu, L. L. Fu, and C. L. Jia, “Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer,” Opt. Express 21(3), 2592–2605 (2013). [CrossRef] [PubMed]

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(300.0300) Spectroscopy : Spectroscopy

ToC Category:
Spectroscopy

History
Original Manuscript: April 15, 2013
Published: April 16, 2013

Citation
Wenyi Ren, Chunmin Zhang, Tingkui Mu, Lili Fu, and Chenling Jia, "Empirical mode decomposition based background removal and de-noising in polarization interference imaging spectrometer: erratum," Opt. Express 21, 10207-10207 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-10207


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