Current Optics and Photonics

Optical Society of Korea (한국광학회)
권호 표지
DOI QR코드

DOI QR Code

Spectral Reconstruction for High Spectral Resolution in a Static Modulated Fourier-transform Spectrometer

  • Cho, Ju Yong (Department of Aeronautic Electricity, Hanseo University) ;
  • Lee, Seunghoon (Satellite Research Directorate, Korea Aerospace Research Institute) ;
  • Kim, Hyoungjin (Department of Aeronautic Electricity, Hanseo University) ;
  • Jang, Won Kweon (Department of Aeronautic Electricity, Hanseo University)
  • Received : 2021.12.06
  • Accepted : 2022.03.22
  • Published : 2022.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

We introduce a spectral reconstruction method to enhance the spectral resolution in a static modulated Fourier-transform spectrometer. The optical-path difference and the interferogram in the focal plane, as well as the relationship of the interferogram and the spectrum, are discussed. Additionally, for better spectral reconstruction, applications of phase-error correction and apodization are considered. As a result, the transfer function of the spectrometer is calculated, and then the spectrum is reconstructed based on the relationship between the transfer function and the interferogram. The spectrometer comprises a modified Sagnac interferometer. The spectral reconstruction is conducted with a source with central wave number of 6,451 cm-1 and spectral width of 337 cm-1. In a conventional Fourier-transform method the best spectral resolution is 27 cm-1, but by means of the spectral reconstruction method the spectral resolution improved to 8.7 cm-1, without changing the interferometric structure. Compared to a conventional Fourier-transform method, the spectral width in the reconstructed spectrum is narrower by 20 cm-1, and closer to the reference spectrum. The proposed method allows high performance for static modulated Fourier-transform spectrometers.

Keywords

Acknowledgement

We thank the anonymous referees for their useful suggestions.

References

  1. T. Okamoto, S. Kawata, and S. Minami, "Fourier transform spectrometer with a self-scanning photodiode array," Appl. Opt. 23, 269-273 (1984). https://doi.org/10.1364/AO.23.000269
  2. Y. Ferrec, J. Taboury, H. Sauer, and P. Chavel, "Compactness of lateral shearing interferometers," Appl. Opt. 50, 4656-4663 (2011). https://doi.org/10.1364/AO.50.004656
  3. J. He and Q. Zhang, "Design and analysis of a modified Sagnac interferometer for upper atmospheric wind measurement," Optik 124, 2658-2660 (2013). https://doi.org/10.1016/j.ijleo.2012.07.048
  4. S. Chatterjee and Y. P. Kumar, "White light differential interference contrast microscope with a Sagnac interferometer," Appl. Opt. 53, 296-300 (2014). https://doi.org/10.1364/AO.53.000296
  5. M. J. Padgett and A. R. Harvey, "A static Fourier-transform spectrometer based on Wollaston prisms," Rev. Sci. Instrum. 66, 2807-2811 (1995). https://doi.org/10.1063/1.1145559
  6. X. Lin, F. Zhou, H. Li, and H. B. Zhao, "Static Fourier-transform spectrometer based on Wollaston prism," Optik 125, 3482-3484 (2014). https://doi.org/10.1016/j.ijleo.2014.01.062
  7. Q. Liu, C. Bai, J. Liu, J. He, and J. Li, "Fourier transform imaging spectropolarimeter using ferroelectric liquid crystals and Wollaston interferometer," Opt. Express 25, 19904-19922 (2017). https://doi.org/10.1364/OE.25.019904
  8. J. Rehault, R. Borrego-Varillas, A. Oriana, C. Manzoni, C. P. Hauri, J. Helbing, and G. Cerullo, "Fourier transform spectroscopy in the vibrational fingerprint region with a birefringent interferometer," Opt. Express 25, 4403-4412 (2017). https://doi.org/10.1364/OE.25.004403
  9. M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, "Static Fourier transform infrared spectrometer," Opt. Express 24, 7767-7776 (2016). https://doi.org/10.1364/OE.24.007767
  10. J. Li, C. Qu, H. Wu, and C. Qi, "Spectral resolution enhanced static Fourier transform spectrometer based on a birefringent retarder array," Opt. Express 27, 15505-15517 (2019). https://doi.org/10.1364/oe.27.015505
  11. M. H. Kohler, M. Schardt, M. Muller, P. Kienle, K. Wang, X. Dong, C. Giebeler, B. R. Wiesent, M. Jakobi, and A. W. Koch, "Static Fourier transform mid-infrared spectrometer with increased spectral resolution using a stepped mirror," OSA Continuum 3, 2134-2142 (2020). https://doi.org/10.1364/osac.397095
  12. A. Watanabe and H. Furukawa, "High-resolution and high-throughput multichannel Fourier transform spectrometer with two-dimensional interferogram warping compensation," Opt. Commun. 413, 8-13 (2018). https://doi.org/10.1016/j.optcom.2017.12.024
  13. J. Y. Cho, S. H. Lee, and W. K. Jang, "Improvement of spectral resolution by signal padding method in the spatially modulated Fourier transform spectrometer based on a Sagnac interferometer," Appl. Opt. 58, 6755-6761 (2019). https://doi.org/10.1364/ao.58.006755
  14. D. M. Kita, B. Miranda, D. Favela, D. Bono, J. Michon, H. Lin, T. Hu, and J. Hu, "High-performance and scalable on-chip digital Fourier transform spectroscopy," Nat. Commun. 9, 4405 (2018). https://doi.org/10.1038/s41467-018-06773-2
  15. M.-L. Junttila, J. Kauppinen, and E. Ikonen, "Performance limits of stationary Fourier spectrometers," J. Opt. Soc. Am. A 8, 1457-1462 (1991). https://doi.org/10.1364/josaa.8.001457
  16. F. J. Harris, "On the Use of Windows for Harmonic Analysis with the Discrete Fourier transform," Proc. IEEE 66, 51-83 (1978). https://doi.org/10.1109/PROC.1978.10837
  17. K. Rahmelow and W. Hubner, "Phase correction in Fourier transform spectroscopy: subsequent displacement correction and error limit," Appl. Opt. 36, 6678-6686 (1997). https://doi.org/10.1364/AO.36.006678
  18. H. Zou and T. Hastie, "Regularization and variable selection via the elastic net," J. R. Stat. Soc. B 67, 301-320 (2005). https://doi.org/10.1111/j.1467-9868.2005.00503.x
  19. A. Hoerl, and R. Kennard, "Ridge regression," in Encyclopedia of Statistical Sciences, S. Kotz, C. B. Read, N. Balakrishnan, B. Vidakovic, and N. L. Johnson, Eds., (John Wiley & Sons, USA, 2004).
  20. R. Tibshirani, "Regression shrinkage and selection via the lasso," J. R. Stat. Soc. B 58, 267-288 (1996).
  21. S. S. Shai and B. D. Shai, Understanding Machine Learning: From Theory to Algorithms (Cambridge University Press, Cambridge, UK, 2014), Chapter 11.
  22. J. Friedman, T. Hastie, and R. Tibshirani, "Regularization paths for generalized linear models via coordinate descent," J. Stat. Softw. 33, 1-22 (2010).