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

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2013

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]

2012

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. 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]

2011

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]

2010

2009

2008

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]

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]

2006

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]

2005

R. G. Sellar, G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. 44(1), 013602 (2005).
[CrossRef]

2004

D. A. Naylor, B. G. Gom, “SCUBA-2 imaging Fourier transform spectrometer,” Proc. SPIE 5159, 91–101 (2004).
[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]

2002

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]

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]

2000

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

1995

1967

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

1966

Aalderink, B. J.

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]

Alcock, R.

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]

Allen, P.

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]

Barducci, A.

Barnsley, M. J.

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]

Bianco, P.

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]

Boreman, G. D.

R. G. Sellar, G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. 44(1), 013602 (2005).
[CrossRef]

Brady, D. J.

Braun, R.

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]

Brettel, H.

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]

Brunetti, B. G.

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]

Chau, F. S.

Cheo, K. K. L.

Choi, K.

Cook, W. B.

Coupland, J.

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]

Cull, C. F.

Cutter, M. A.

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]

De Bruin, G.

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]

Du, Y.

ElMasry, G.

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]

Feng, H.

Forman, M. L.

Garciano, L. O.

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]

Gat, N.

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

Gerhards, M.

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]

Gom, B. G.

D. A. Naylor, B. G. Gom, “SCUBA-2 imaging Fourier transform spectrometer,” Proc. SPIE 5159, 91–101 (2004).
[CrossRef]

Guzzi, D.

Hardeberg, J. Y.

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]

Harig, R.

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]

Hays, P. B.

Hoffmann, L.

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]

Kamruzzaman, M.

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]

Klein, M. E.

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]

Lagueux, P.

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]

Lastri, C.

Lobb, D. R.

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]

Lomheim, T. S.

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]

Marcoionni, P.

Mertz, L.

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

Miliani, C.

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]

Nardino, V.

Naylor, D. A.

D. A. Naylor, B. G. Gom, “SCUBA-2 imaging Fourier transform spectrometer,” Proc. SPIE 5159, 91–101 (2004).
[CrossRef]

Nie, Y.

Y. Nie, B. Xiangli, J. Zhou, X. Wei, “Design of airborne imaging spectrometer based on curved prism,” Proc. SPIE 8197, 81970U (2011).
[CrossRef]

Okamoto, H.

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]

Oliver, T.

Padoan, R.

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]

Pippi, I.

Pisani, M.

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]

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]

Rock, G.

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]

Ronellenfitsch, F.

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]

Rosi, F.

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]

Sakai, K.

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]

Sali, D.

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]

Schlerf, M.

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]

Schmitt, F.

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]

Schumann, L. W.

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]

Sellar, R. G.

R. G. Sellar, G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. 44(1), 013602 (2005).
[CrossRef]

Settle, J. J.

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]

Sgamellotti, A.

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]

Snell, H. E.

Steel, W. H.

Steemers, T. A.

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]

Sun, D. W.

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]

Teston, F.

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]

Udelhoven, T.

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]

Vanasse, G. A.

Wei, X.

Y. Nie, B. Xiangli, J. Zhou, X. Wei, “Design of airborne imaging spectrometer based on curved prism,” Proc. SPIE 8197, 81970U (2011).
[CrossRef]

Xiangli, B.

Y. Nie, B. Xiangli, J. Zhou, X. Wei, “Design of airborne imaging spectrometer based on curved prism,” Proc. SPIE 8197, 81970U (2011).
[CrossRef]

Ye, X.

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]

Zhang, Q.

Zhou, G.

Zhou, J.

Y. Nie, B. Xiangli, J. Zhou, X. Wei, “Design of airborne imaging spectrometer based on curved prism,” Proc. SPIE 8197, 81970U (2011).
[CrossRef]

Zucco, M.

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]

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]

Angew. Chem. Int. Ed. Engl.

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]

Appl. Opt.

Appl. Phys. B

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]

Comput. Electron. Agric.

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]

IEEE Trans. Geosci. Remote Sens.

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]

Infrared Phys.

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

J. Food Eng.

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]

J. Opt. Soc. Am.

Meas. Sci. Technol.

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]

Opt. Eng.

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]

R. G. Sellar, G. D. Boreman, “Classification of imaging spectrometers for remote sensing applications,” Opt. Eng. 44(1), 013602 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

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

D. A. Naylor, B. G. Gom, “SCUBA-2 imaging Fourier transform spectrometer,” Proc. SPIE 5159, 91–101 (2004).
[CrossRef]

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]

Y. Nie, B. Xiangli, J. Zhou, X. Wei, “Design of airborne imaging spectrometer based on curved prism,” Proc. SPIE 8197, 81970U (2011).
[CrossRef]

Remote Sens.

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]

Sensors

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]

Other

http://projects.pmodwrc.ch/env03/ .

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).

M. Pisani and M. Zucco, “Fourier transform based hyperspectral imaging,” in Fourier Transforms - Approach to Scientific Principles, G. Nikolic, ed. (Intech, 2011), Chap. 21.

J. Vaughan, The Fabry-Perot Interferometer: History, Theory, Practice, and Applications (CRC, 1989).

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Figures (8)

Fig. 1
Fig. 1

HSI acquisition set-up. The target is a Cameratrax standard that is illuminated by a xenon discharge lamp. The reference used to calibrate the retardation is a laser at 532 nm. A photographic objective is used to create the image on the monochromatic camera. The F-P interferometer is inserted in a metallic structure. The retardation is varied by evacuating air with a peristaltic pump (not visible in the image). The flux is controlled with a variable leak valve.

Fig. 2
Fig. 2

Scheme of the set-up to measure the phase correction of the dielectric HSI. The incandescent lamp shines through the F-P interferometer and the transmitted light is collected by an optical fiber and sent to a grating spectrophotometer. The F-P is mounted in a metallic structure and the mirrors come to contact evacuating air with a peristaltic pump. The tightness is assured by an O-ring fixed on the outer part of the mirrors.

Fig. 3
Fig. 3

Four spectra measured with the grating spectrophotometer for different retardations. The first spectra is measured with the mirrors in contact (δ = 0 μm). The other three are calculated for retardation of 6.1 μm, 13.5 μm and 31.1 μm. The colored points represent the value of the spectra in different wavelength bins.

Fig. 4
Fig. 4

(a). A detail of the interferograms obtained ordering the value in the five wavelength bins in Fig. 3. Figure 4(b). The five interferograms are calibrated and resampled with reference to the interferogram at 532 nm.

Fig. 5
Fig. 5

The black line is the measured phase correction Θ as a function of wavelength for dielectric mirrors obtained by fitting with Airy functions the measured interferograms measured with the set-up in Fig. 2. The 13 red squares are the phase Θ measured with HSI with the set-up in Fig. 1 with 13 different sources.

Fig. 6
Fig. 6

The spectra of the radiation of a laser at 633 nm measured with the dielectric HSI for two different phase correction Θ values. The black line is the distorted spectrum calculated with Θ=0rad in Eq. (6), the red line is the symmetric spectrum calculated with Θ=0.15rad in Eq. (6).

Fig. 7
Fig. 7

In black the spectra of radiation from different LEDs extracted from the HSI hypercube measured by applying Eq. (6). In red the same LED radiation measured with a reference spectrophotometer. In this measurement the ILS of F-P HSI is about 10 THz.

Fig. 8
Fig. 8

Spectra of a scene containing Macbeth reference. The solid lines are the spectra of radiation extracted from the hypercube normalized with respect to the white at the top left of the standard in the range 520 nm – 720 nm. The dashed lines are the reference spectra measured with a grating spectrophotometer.

Equations (9)

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S( ν ˜ )=2 0 I( δ )cos( 2π ν ˜ δ ) dδ
S[ mΔ ν ˜ ]= n=0 N1 I[ nΔs ]cos( 2πmΔ ν ˜ nΔs )
Δ ν ˜ 1 δ max = 1 NΔs
S'( ν ˜ )= I( δ ) e i2π ν ˜ δ( ν ˜ ) dδ.
S( ν ˜ )=Re( ν ˜ )cos( Θ( ν ˜ ) )+Im( ν ˜ )sin( Θ( ν ˜ ) )
S[ mΔ ν ˜ ]=[ n=N+1 N1 I[ nΔs ]cos( 2πmΔ ν ˜ nΔs ) ]cos( Θ( mΔ ν ˜ ) ) +[ n=N+1 N1 I[ nΔs ]sin( 2πmΔ ν ˜ nΔs ) ]sin( Θ( mΔ ν ˜ ) )
Θ( ν ˜ )=arctan( Im( ν ˜ ) Re( ν ˜ ) )
I( δ )= 1 1+( 4R ( 1R ) 2 ) sin 2 ( 2π ν ˜ d ) 1 2R +2Rcos( 4π ν ˜ d )
I( δ )= A 1+( 4R ( 1R ) 2 ) sin 2 ( 2π ν ˜ d+Θ( ν ˜ ) )

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