## A hyperspectral imager based on a Fabry-Perot interferometer with dielectric mirrors |

Optics Express, Vol. 22, Issue 2, pp. 1824-1834 (2014)

http://dx.doi.org/10.1364/OE.22.001824

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### Abstract

In this paper we present a new hyperspectral imager based on a Fabry-Perot interferometer with low reflectivity dielectric mirrors. This set-up has been validated by measuring hypercubes of scenes containing emitting bodies and reflective surfaces in the visible region and compared with success with reference spectra. The system is based on dielectric mirrors which, with respect to similar systems based on metallic mirrors, have lower losses at lower cost and are available off-the-shelf. The spectra calculation is carried out with a Fourier transform based algorithm which takes into account the not negligible dispersion of the mirrors.

© 2014 Optical Society of America

## 1. Introduction

1. J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. **41**(10), 2532–2548 (2002). [CrossRef]

2. M. E. Klein, B. J. Aalderink, R. Padoan, G. De Bruin, and T. A. Steemers, “Quantitative hyperspectral reflectance imaging,” Sensors **8**(9), 5576–5618 (2008). [CrossRef]

3. F. Rosi, C. Miliani, R. Braun, R. Harig, D. Sali, B. G. Brunetti, and A. Sgamellotti, “Noninvasive analysis of paintings by mid-infrared hyperspectral imaging,” Angew. Chem. Int. Ed. Engl. **52**(20), 5258–5261 (2013). [CrossRef] [PubMed]

4. M. Schlerf, G. Rock, P. Lagueux, F. Ronellenfitsch, M. Gerhards, L. Hoffmann, and T. Udelhoven, “A hyperspectral thermal infrared imaging instrument for natural resources applications,” Remote Sens. **4**(12), 3995–4009 (2012). [CrossRef]

5. M. J. Barnsley, J. J. Settle, M. A. Cutter, D. R. Lobb, and F. Teston, “The PROBA/CHRIS mission: A low-cost smallsat for hyperspectral multiangle observations of the earth surface and atmosphere,” IEEE Trans. Geosci. Remote Sens. **42**(7), 1512–1520 (2004). [CrossRef]

7. X. Ye, K. Sakai, H. Okamoto, and L. O. Garciano, “A ground-based hyperspectral imaging system for characterizing vegetation spectral features,” Comput. Electron. Agric. **63**(1), 13–21 (2008). [CrossRef]

8. C. F. Cull, K. Choi, D. J. Brady, and T. Oliver, “Identification of fluorescent beads using a coded aperture snapshot spectral imager,” Appl. Opt. **49**(10), B59–B70 (2010). [CrossRef] [PubMed]

9. M. Kamruzzaman, G. ElMasry, D. W. Sun, and P. Allen, “Application of NIR hyperspectral imaging for discrimination of lamb muscles,” J. Food Eng. **104**(3), 332–340 (2011). [CrossRef]

12. N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE **4056**, 50–64 (2000). [CrossRef]

22. M. Pisani and M. Zucco, “Compact imaging spectrometer combining Fourier transform spectroscopy with a Fabry-Perot interferometer,” Opt. Express **17**(10), 8319–8331 (2009). [CrossRef] [PubMed]

23. M. Pisani, P. Bianco, and M. Zucco, “Hyperspectral imaging for thermal analysis and remote gas sensing in the short wave infrared,” Appl. Phys. B **108**(1), 231–236 (2012). [CrossRef]

## 2. Discussion about Fourier transform spectroscopy

*δ*is the retardation or optical path delay [18],

*s*and consists of

*N*discrete, equidistant points and Eq. (1) transforms in Eq. (2), where all the constants have been discarded. The discrete version of the cosine Fourier transform is

*δ*is a function of wavenumber due to dispersive components in the optical path like beam splitters or mirrors, to non-symmetric sampling with respect to zero retardation and to electronic filtering of the acquired signal. In presence of dispersive effects, the interferogram is no longer symmetric around the zero retardation. The dispersive effect is contained in a phase correction

24. L. Mertz, “Auxiliary computation for Fourier spectrometry,” Infrared Phys. **7**(1), 17–23 (1967). [CrossRef]

25. M. L. Forman, W. H. Steel, and G. A. Vanasse, “Correction of asymmetric interferograms obtained in Fourier spectroscopy,” J. Opt. Soc. Am. **56**(1), 59–61 (1966). [CrossRef]

## 3. Description of the HSI based on metallic mirror F-P interferometers

22. M. Pisani and M. Zucco, “Compact imaging spectrometer combining Fourier transform spectroscopy with a Fabry-Perot interferometer,” Opt. Express **17**(10), 8319–8331 (2009). [CrossRef] [PubMed]

23. M. Pisani, P. Bianco, and M. Zucco, “Hyperspectral imaging for thermal analysis and remote gas sensing in the short wave infrared,” Appl. Phys. B **108**(1), 231–236 (2012). [CrossRef]

*R*/

^{n}*n*where

*R*is the reflectivity and

*n*the order of the harmonic [20

20. H. E. Snell, W. B. Cook, and P. B. Hays, “Multiplex Fabry-Perot interferometer: II. Laboratory prototype,” Appl. Opt. **34**(24), 5268–5277 (1995). [CrossRef] [PubMed]

*R*≈ 20%) in such a way that the Airy function could be approximated by a cosine function plus a constant term, as in Eq. (8), and oversample the interferogram with a sampling rate with a sufficient number of points per fringe: in our application eight samples for each fringe of the reference laser are used.

22. M. Pisani and M. Zucco, “Compact imaging spectrometer combining Fourier transform spectroscopy with a Fabry-Perot interferometer,” Opt. Express **17**(10), 8319–8331 (2009). [CrossRef] [PubMed]

**17**(10), 8319–8331 (2009). [CrossRef] [PubMed]

23. M. Pisani, P. Bianco, and M. Zucco, “Hyperspectral imaging for thermal analysis and remote gas sensing in the short wave infrared,” Appl. Phys. B **108**(1), 231–236 (2012). [CrossRef]

## 4. Description of the new dielectric mirror prototype

*δ*= 6.1 μm,

*δ*= 13.5 μm and

*δ*= 31.1 μm). The colored points on the graphs represent the value of the spectra in different wavelength bins (

*λ*= 400 nm, 500 nm, 600 nm, 700 nm and 800 nm). From the full set of spectra acquired for retardations ranging from 0 μm (mirrors in contact) to 31.1 μm, we have extracted the interferograms for each wavelength bin, ranging from 400 nm to 900 nm. To go into details of the technique, in Fig. 3 we have reported on the graph the values of the spectra at five different wavelengths (

*λ*= 400 nm, 500 nm, 600 nm, 700 nm and 800 nm). By grouping and ordering all the values belonging to a wavelength bin, we have finally obtained the interferograms associated to each wavelength bin, obtaining the interferogram as the F-P was illuminated with a quasi-monochromatic source, as reported in Fig. 4(a). The dispersion is measured with respect to the reference wavelength bin at 532 nm which is the same used for the HSI set-up. All the interferograms are then calibrated and resampled using the reference interferogram at 532 nm in Fig. 4(b).

*λ*is relative to the phase at the reference wavelength of 532 nm and is presented with a black line for the dielectric mirror F-P in Fig. 5. Only the beams with incidence angle equal to zero are taken into account with this set-up.

**17**(10), 8319–8331 (2009). [CrossRef] [PubMed]

## 5. Results and discussion

## 6. Conclusions

## Acknowledgments

## References and links

1. | J. Y. Hardeberg, F. Schmitt, and H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. |

2. | M. E. Klein, B. J. Aalderink, R. Padoan, G. De Bruin, and T. A. Steemers, “Quantitative hyperspectral reflectance imaging,” Sensors |

3. | F. Rosi, C. Miliani, R. Braun, R. Harig, D. Sali, B. G. Brunetti, and A. Sgamellotti, “Noninvasive analysis of paintings by mid-infrared hyperspectral imaging,” Angew. Chem. Int. Ed. Engl. |

4. | M. Schlerf, G. Rock, P. Lagueux, F. Ronellenfitsch, M. Gerhards, L. Hoffmann, and T. Udelhoven, “A hyperspectral thermal infrared imaging instrument for natural resources applications,” Remote Sens. |

5. | M. J. Barnsley, J. J. Settle, M. A. Cutter, D. R. Lobb, and F. Teston, “The PROBA/CHRIS mission: A low-cost smallsat for hyperspectral multiangle observations of the earth surface and atmosphere,” IEEE Trans. Geosci. Remote Sens. |

6. | |

7. | X. Ye, K. Sakai, H. Okamoto, and L. O. Garciano, “A ground-based hyperspectral imaging system for characterizing vegetation spectral features,” Comput. Electron. Agric. |

8. | C. F. Cull, K. Choi, D. J. Brady, and T. Oliver, “Identification of fluorescent beads using a coded aperture snapshot spectral imager,” Appl. Opt. |

9. | M. Kamruzzaman, G. ElMasry, D. W. Sun, and P. Allen, “Application of NIR hyperspectral imaging for discrimination of lamb muscles,” J. Food Eng. |

10. | Y. Nie, B. Xiangli, J. Zhou, and X. Wei, “Design of airborne imaging spectrometer based on curved prism,” Proc. SPIE |

11. | G. Zhou, K. K. L. Cheo, Y. Du, F. S. Chau, H. Feng, and Q. Zhang, “Hyperspectral imaging using a microelectrical-mechanical-systems-based in-plane vibratory grating scanner with a single photodetector,” Opt. Lett. |

12. | N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE |

13. | A. Barducci, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, and I. Pippi, “Theoretical aspects of Fourier transform spectrometry and common path triangular interferometers,” Opt. Express |

14. | D. A. Naylor and B. G. Gom, “SCUBA-2 imaging Fourier transform spectrometer,” Proc. SPIE |

15. | R. Alcock and J. Coupland, “A compact, high numerical aperture imaging Fourier transform spectrometer and its application,” Meas. Sci. Technol. |

16. | M. Pisani and M. Zucco, “Fourier transform based hyperspectral imaging,” in |

17. | L. W. Schumann and T. S. Lomheim, “Infrared hyperspectral imaging Fourier transform and dispersive spectrometers: comparison of signal-to-noise based performance,” Proc. SPIE |

18. | P. Griffiths and J. A. De Haseth, |

19. | S. W. Smith, |

20. | H. E. Snell, W. B. Cook, and P. B. Hays, “Multiplex Fabry-Perot interferometer: II. Laboratory prototype,” Appl. Opt. |

21. | R. G. Sellar and G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. |

22. | M. Pisani and M. Zucco, “Compact imaging spectrometer combining Fourier transform spectroscopy with a Fabry-Perot interferometer,” Opt. Express |

23. | M. Pisani, P. Bianco, and M. Zucco, “Hyperspectral imaging for thermal analysis and remote gas sensing in the short wave infrared,” Appl. Phys. B |

24. | L. Mertz, “Auxiliary computation for Fourier spectrometry,” Infrared Phys. |

25. | M. L. Forman, W. H. Steel, and G. A. Vanasse, “Correction of asymmetric interferograms obtained in Fourier spectroscopy,” J. Opt. Soc. Am. |

26. | J. Vaughan, |

**OCIS Codes**

(070.4790) Fourier optics and signal processing : Spectrum analysis

(100.5070) Image processing : Phase retrieval

(300.6300) Spectroscopy : Spectroscopy, Fourier transforms

(110.3175) Imaging systems : Interferometric imaging

(110.4234) Imaging systems : Multispectral and hyperspectral imaging

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: September 24, 2013

Revised Manuscript: November 21, 2013

Manuscript Accepted: November 22, 2013

Published: January 21, 2014

**Citation**

Massimo Zucco, Marco Pisani, Valentina Caricato, and Andrea Egidi, "A hyperspectral imager based on a Fabry-Perot interferometer with dielectric mirrors," Opt. Express **22**, 1824-1834 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-2-1824

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### References

- J. Y. Hardeberg, F. Schmitt, H. Brettel, “Multispectral color image capture using a liquid crystal tunable filter,” Opt. Eng. 41(10), 2532–2548 (2002). [CrossRef]
- M. E. Klein, B. J. Aalderink, R. Padoan, G. De Bruin, T. A. Steemers, “Quantitative hyperspectral reflectance imaging,” Sensors 8(9), 5576–5618 (2008). [CrossRef]
- F. Rosi, C. Miliani, R. Braun, R. Harig, D. Sali, B. G. Brunetti, A. Sgamellotti, “Noninvasive analysis of paintings by mid-infrared hyperspectral imaging,” Angew. Chem. Int. Ed. Engl. 52(20), 5258–5261 (2013). [CrossRef] [PubMed]
- M. Schlerf, G. Rock, P. Lagueux, F. Ronellenfitsch, M. Gerhards, L. Hoffmann, T. Udelhoven, “A hyperspectral thermal infrared imaging instrument for natural resources applications,” Remote Sens. 4(12), 3995–4009 (2012). [CrossRef]
- M. J. Barnsley, J. J. Settle, M. A. Cutter, D. R. Lobb, F. Teston, “The PROBA/CHRIS mission: A low-cost smallsat for hyperspectral multiangle observations of the earth surface and atmosphere,” IEEE Trans. Geosci. Remote Sens. 42(7), 1512–1520 (2004). [CrossRef]
- http://projects.pmodwrc.ch/env03/ .
- X. Ye, K. Sakai, H. Okamoto, L. O. Garciano, “A ground-based hyperspectral imaging system for characterizing vegetation spectral features,” Comput. Electron. Agric. 63(1), 13–21 (2008). [CrossRef]
- C. F. Cull, K. Choi, D. J. Brady, T. Oliver, “Identification of fluorescent beads using a coded aperture snapshot spectral imager,” Appl. Opt. 49(10), B59–B70 (2010). [CrossRef] [PubMed]
- M. Kamruzzaman, G. ElMasry, D. W. Sun, P. Allen, “Application of NIR hyperspectral imaging for discrimination of lamb muscles,” J. Food Eng. 104(3), 332–340 (2011). [CrossRef]
- Y. Nie, B. Xiangli, J. Zhou, X. Wei, “Design of airborne imaging spectrometer based on curved prism,” Proc. SPIE 8197, 81970U (2011). [CrossRef]
- G. Zhou, K. K. L. Cheo, Y. Du, F. S. Chau, H. Feng, Q. Zhang, “Hyperspectral imaging using a microelectrical-mechanical-systems-based in-plane vibratory grating scanner with a single photodetector,” Opt. Lett. 34(6), 764–766 (2009). [CrossRef] [PubMed]
- N. Gat, “Imaging spectroscopy using tunable filters: a review,” Proc. SPIE 4056, 50–64 (2000). [CrossRef]
- A. Barducci, D. Guzzi, C. Lastri, P. Marcoionni, V. Nardino, I. Pippi, “Theoretical aspects of Fourier transform spectrometry and common path triangular interferometers,” Opt. Express 18(11), 11622–11649 (2010). [CrossRef] [PubMed]
- D. A. Naylor, B. G. Gom, “SCUBA-2 imaging Fourier transform spectrometer,” Proc. SPIE 5159, 91–101 (2004). [CrossRef]
- R. Alcock, J. Coupland, “A compact, high numerical aperture imaging Fourier transform spectrometer and its application,” Meas. Sci. Technol. 17(11), 2861–2868 (2006). [CrossRef]
- M. Pisani and M. Zucco, “Fourier transform based hyperspectral imaging,” in Fourier Transforms - Approach to Scientific Principles, G. Nikolic, ed. (Intech, 2011), Chap. 21.
- L. W. Schumann, T. S. Lomheim, “Infrared hyperspectral imaging Fourier transform and dispersive spectrometers: comparison of signal-to-noise based performance,” Proc. SPIE 4480, 1–14 (2002). [CrossRef]
- P. Griffiths and J. A. De Haseth, Fourier Transform Infrared Spectrometry, Vol. 171 (John Wiley, 2007).
- S. W. Smith, The Scientist and Engineer’s Guide to Digital Signal Processing (California Technical, 1997).
- H. E. Snell, W. B. Cook, P. B. Hays, “Multiplex Fabry-Perot interferometer: II. Laboratory prototype,” Appl. Opt. 34(24), 5268–5277 (1995). [CrossRef] [PubMed]
- R. G. Sellar, G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. 44(1), 013602 (2005). [CrossRef]
- M. Pisani, M. Zucco, “Compact imaging spectrometer combining Fourier transform spectroscopy with a Fabry-Perot interferometer,” Opt. Express 17(10), 8319–8331 (2009). [CrossRef] [PubMed]
- M. Pisani, P. Bianco, M. Zucco, “Hyperspectral imaging for thermal analysis and remote gas sensing in the short wave infrared,” Appl. Phys. B 108(1), 231–236 (2012). [CrossRef]
- L. Mertz, “Auxiliary computation for Fourier spectrometry,” Infrared Phys. 7(1), 17–23 (1967). [CrossRef]
- M. L. Forman, W. H. Steel, G. A. Vanasse, “Correction of asymmetric interferograms obtained in Fourier spectroscopy,” J. Opt. Soc. Am. 56(1), 59–61 (1966). [CrossRef]
- J. Vaughan, The Fabry-Perot Interferometer: History, Theory, Practice, and Applications (CRC, 1989).

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