Abstract

In this study, a spectral acquisition method is proposed in which axial chromatic and spherical aberrations are introduced as an error function. These aberrations lead to changes in the focal lengths as the wavelengths of the incident light changes. A coefficient matrix representing the variation in the intensity distribution of each image, formed at the focal point (the detection position) corresponding to a wavelength, is obtained by calibration. The least square method is used to reconstruct the spectrum. The numerical simulation results show that the spectral correlation coefficient and the spectral mean square error between the reconstructed spectrum and the original spectrum are 0.9997 and 0.0025, and 0.9683 and 0.0204, respectively, for the polychromatic light spectrum obtained from the mercury lamp using our experimental set-up. These results confirm the feasibility and efficiency of the proposed spectral imaging method.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

A. Ojaghi and F. E. Robles, “Ultraviolet multi-spectral microscopy using iterative phase-recovery from chromatic aberrations,” Proc. SPIE 10087, 100870M (2019).
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2018 (1)

2016 (2)

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

L. Zhang, D. Liang, D. Zhang, X. Gao, and X. Ma, “Study of Spectral Reflectance Reconstruction Based on an Algorithm for Improved Orthogonal Matching Pursuit,” J. Opt. Soc. Korea 20(4), 515–523 (2016).
[Crossref]

2015 (2)

2014 (1)

L. Su, Y. Yuan, B. Xiangli, F. Huang, J. Cao, L. Li, and S. Zhou, “Spectrum reconstruction method for airborne temporally–spatially modulated Fourier transform imaging spectrometers,” IEEE Trans. Geosci. Remote Sens. 52(6), 3720–3728 (2014).
[Crossref]

2013 (1)

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

2012 (1)

J. Antila, R. Mannila, U. Kantojärvi, C. Holmlund, A. Rissanen, I. Näkki, J. Ollila, and H. Saari, “Spectral imaging device based on a tuneable MEMS Fabry-Perot interferometer,” Proc. SPIE 8374, 83740F (2012).
[Crossref]

2010 (1)

G. Thomas and G. Laurenz, “Synthetic Approaches Towards CGA 293′343: A Novel Broad-Spectrum Insecticide,” Pestic. Sci. 55(3), 355–357 (2010).

2009 (1)

L. Perez-Freire, “Spread-spectrum watermarking security,” IEEE TIFS 4(1), 2–24 (2009).

2008 (2)

2004 (1)

1997 (2)

M. Hinnrichs and M. A. Massie, “New approach to imaging spectroscopy using diffractive optics,” Proc. SPIE 3118, 194–205 (1997).
[Crossref]

A. R. Fitzgerrell, E. R. Dowski, and W. T. Cathey, “Defocus transfer function for circularly symmetric pupils,” Appl. Opt. 36(23), 5796–5804 (1997).
[Crossref] [PubMed]

1995 (1)

D. M. Lyons, “Image spectrometry with a diffractive optic,” Proc. SPIE 2480, 123–131 (1995).
[Crossref]

1992 (1)

1991 (1)

1990 (1)

1986 (2)

A. Faggiano, C. Gadda, P. Moro, G. Molesini, and F. Quercioli, “Longitudinal Chromatic Aberration Spectroscope,” Proc. SPIE 656, 213–219 (1986).

G. Molesini and F. Quercioli, “Pseudocolor effects of longitudinal chromatic aberration,” J. Opt. 17(6), 279–282 (1986).
[Crossref]

1983 (1)

Abel Tibérini, L.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

Achard, V.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Antila, J.

J. Antila, R. Mannila, U. Kantojärvi, C. Holmlund, A. Rissanen, I. Näkki, J. Ollila, and H. Saari, “Spectral imaging device based on a tuneable MEMS Fabry-Perot interferometer,” Proc. SPIE 8374, 83740F (2012).
[Crossref]

Aroldi, G.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

Axelsson, M.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Belli, F.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

Benoist, K.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Bergström, D.

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

Borghys, D.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Briottet, X.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Bulir, J.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

Cao, J.

L. Su, Y. Yuan, B. Xiangli, F. Huang, J. Cao, L. Li, and S. Zhou, “Spectrum reconstruction method for airborne temporally–spatially modulated Fourier transform imaging spectrometers,” IEEE Trans. Geosci. Remote Sens. 52(6), 3720–3728 (2014).
[Crossref]

Cathey, W. T.

Chen, S.

Chicarella, L.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

Dami, M.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

De Vidi, R.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

Dekker, R.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Dimmeler, A.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Dowski, E. R.

Faggiano, A.

A. Faggiano, C. Gadda, P. Moro, G. Molesini, and F. Quercioli, “Longitudinal Chromatic Aberration Spectroscope,” Proc. SPIE 656, 213–219 (1986).

Fitzgerrell, A. R.

Frieden, B. R.

Friman, O.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Gadda, C.

A. Faggiano, C. Gadda, P. Moro, G. Molesini, and F. Quercioli, “Longitudinal Chromatic Aberration Spectroscope,” Proc. SPIE 656, 213–219 (1986).

Gao, X.

Gu, M.

Gupta, N.

N. Gupta, “Hyperspectral imager development at Army Research Laboratory,” Proc. SPIE 6940, 69401P (2008).
[Crossref]

Haavardsholm, T. V.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Harnisch, B.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

Hedborg, J.

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

Hinnrichs, M.

M. Hinnrichs and M. A. Massie, “New approach to imaging spectroscopy using diffractive optics,” Proc. SPIE 3118, 194–205 (1997).
[Crossref]

Holmlund, C.

J. Antila, R. Mannila, U. Kantojärvi, C. Holmlund, A. Rissanen, I. Näkki, J. Ollila, and H. Saari, “Spectral imaging device based on a tuneable MEMS Fabry-Perot interferometer,” Proc. SPIE 8374, 83740F (2012).
[Crossref]

Huang, F.

L. Su, Y. Yuan, B. Xiangli, F. Huang, J. Cao, L. Li, and S. Zhou, “Spectrum reconstruction method for airborne temporally–spatially modulated Fourier transform imaging spectrometers,” IEEE Trans. Geosci. Remote Sens. 52(6), 3720–3728 (2014).
[Crossref]

Ikonen, E.

Ivanova, A. A.

Iwai, K.

Junttila, M.-L.

Kantojärvi, U.

J. Antila, R. Mannila, U. Kantojärvi, C. Holmlund, A. Rissanen, I. Näkki, J. Ollila, and H. Saari, “Spectral imaging device based on a tuneable MEMS Fabry-Perot interferometer,” Proc. SPIE 8374, 83740F (2012).
[Crossref]

Kåsen, I.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Kauppinen, J.

Kim, J. G.

Kim, V. E.

Laurenz, G.

G. Thomas and G. Laurenz, “Synthetic Approaches Towards CGA 293′343: A Novel Broad-Spectrum Insecticide,” Pestic. Sci. 55(3), 355–357 (2010).

Lemarquis, F.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

Lequime, M.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

Letalick, D.

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

Li, C.

Li, L.

L. Su, Y. Yuan, B. Xiangli, F. Huang, J. Cao, L. Li, and S. Zhou, “Spectrum reconstruction method for airborne temporally–spatially modulated Fourier transform imaging spectrometers,” IEEE Trans. Geosci. Remote Sens. 52(6), 3720–3728 (2014).
[Crossref]

Liang, D.

Lutsiv, V. R.

Lyons, D. M.

D. M. Lyons, “Image spectrometry with a diffractive optic,” Proc. SPIE 2480, 123–131 (1995).
[Crossref]

Ma, X.

Mahajan, V. N.

Mannila, R.

J. Antila, R. Mannila, U. Kantojärvi, C. Holmlund, A. Rissanen, I. Näkki, J. Ollila, and H. Saari, “Spectral imaging device based on a tuneable MEMS Fabry-Perot interferometer,” Proc. SPIE 8374, 83740F (2012).
[Crossref]

Massie, M. A.

M. Hinnrichs and M. A. Massie, “New approach to imaging spectroscopy using diffractive optics,” Proc. SPIE 3118, 194–205 (1997).
[Crossref]

Matteoli, S.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Miyagi, M.

Molesini, G.

G. Molesini and F. Quercioli, “Pseudocolor effects of longitudinal chromatic aberration,” J. Opt. 17(6), 279–282 (1986).
[Crossref]

A. Faggiano, C. Gadda, P. Moro, G. Molesini, and F. Quercioli, “Longitudinal Chromatic Aberration Spectroscope,” Proc. SPIE 656, 213–219 (1986).

Möller, S.

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

Moro, M. L.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Moro, P.

A. Faggiano, C. Gadda, P. Moro, G. Molesini, and F. Quercioli, “Longitudinal Chromatic Aberration Spectroscope,” Proc. SPIE 656, 213–219 (1986).

Näkki, I.

J. Antila, R. Mannila, U. Kantojärvi, C. Holmlund, A. Rissanen, I. Näkki, J. Ollila, and H. Saari, “Spectral imaging device based on a tuneable MEMS Fabry-Perot interferometer,” Proc. SPIE 8374, 83740F (2012).
[Crossref]

Nedoshivina, L. S.

Ojaghi, A.

A. Ojaghi and F. E. Robles, “Ultraviolet multi-spectral microscopy using iterative phase-recovery from chromatic aberrations,” Proc. SPIE 10087, 100870M (2019).
[Crossref]

Ollila, J.

J. Antila, R. Mannila, U. Kantojärvi, C. Holmlund, A. Rissanen, I. Näkki, J. Ollila, and H. Saari, “Spectral imaging device based on a tuneable MEMS Fabry-Perot interferometer,” Proc. SPIE 8374, 83740F (2012).
[Crossref]

Opsahl, T. O.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Özcan, M.

Perez-Freire, L.

L. Perez-Freire, “Spread-spectrum watermarking security,” IEEE TIFS 4(1), 2–24 (2009).

Phillips, Z.

Piegari, A.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
[Crossref]

Quercioli, F.

A. Faggiano, C. Gadda, P. Moro, G. Molesini, and F. Quercioli, “Longitudinal Chromatic Aberration Spectroscope,” Proc. SPIE 656, 213–219 (1986).

G. Molesini and F. Quercioli, “Pseudocolor effects of longitudinal chromatic aberration,” J. Opt. 17(6), 279–282 (1986).
[Crossref]

Renhorn, I.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

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I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
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I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Rissanen, A.

J. Antila, R. Mannila, U. Kantojärvi, C. Holmlund, A. Rissanen, I. Näkki, J. Ollila, and H. Saari, “Spectral imaging device based on a tuneable MEMS Fabry-Perot interferometer,” Proc. SPIE 8374, 83740F (2012).
[Crossref]

Robles, F. E.

A. Ojaghi and F. E. Robles, “Ultraviolet multi-spectral microscopy using iterative phase-recovery from chromatic aberrations,” Proc. SPIE 10087, 100870M (2019).
[Crossref]

Saari, H.

J. Antila, R. Mannila, U. Kantojärvi, C. Holmlund, A. Rissanen, I. Näkki, J. Ollila, and H. Saari, “Spectral imaging device based on a tuneable MEMS Fabry-Perot interferometer,” Proc. SPIE 8374, 83740F (2012).
[Crossref]

Sardari, B.

Schilling, H.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

Schwering, P.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
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L. Su, Y. Yuan, B. Xiangli, F. Huang, J. Cao, L. Li, and S. Zhou, “Spectrum reconstruction method for airborne temporally–spatially modulated Fourier transform imaging spectrometers,” IEEE Trans. Geosci. Remote Sens. 52(6), 3720–3728 (2014).
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Sytchkova, A.

M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
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Thomas, G.

G. Thomas and G. Laurenz, “Synthetic Approaches Towards CGA 293′343: A Novel Broad-Spectrum Insecticide,” Pestic. Sci. 55(3), 355–357 (2010).

van Persie, M.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
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Viallefont, F.

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
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Wang, S. I.

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L. Su, Y. Yuan, B. Xiangli, F. Huang, J. Cao, L. Li, and S. Zhou, “Spectrum reconstruction method for airborne temporally–spatially modulated Fourier transform imaging spectrometers,” IEEE Trans. Geosci. Remote Sens. 52(6), 3720–3728 (2014).
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C. Zhang, B. Zhao, and B. Xiangli, “Wide-field-of-view polarization interference imaging spectrometer,” Appl. Opt. 43(33), 6090–6094 (2004).
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Yuan, Y.

L. Su, Y. Yuan, B. Xiangli, F. Huang, J. Cao, L. Li, and S. Zhou, “Spectrum reconstruction method for airborne temporally–spatially modulated Fourier transform imaging spectrometers,” IEEE Trans. Geosci. Remote Sens. 52(6), 3720–3728 (2014).
[Crossref]

Zhang, C.

Zhang, D.

Zhang, L.

Zhao, B.

Zhou, S.

L. Su, Y. Yuan, B. Xiangli, F. Huang, J. Cao, L. Li, and S. Zhou, “Spectrum reconstruction method for airborne temporally–spatially modulated Fourier transform imaging spectrometers,” IEEE Trans. Geosci. Remote Sens. 52(6), 3720–3728 (2014).
[Crossref]

Zhu, X. S.

Zhu, Y.

Appl. Opt. (6)

Appl. Spectrosc. (1)

Biomed. Opt. Express (1)

IEEE TIFS (1)

L. Perez-Freire, “Spread-spectrum watermarking security,” IEEE TIFS 4(1), 2–24 (2009).

IEEE Trans. Geosci. Remote Sens. (1)

L. Su, Y. Yuan, B. Xiangli, F. Huang, J. Cao, L. Li, and S. Zhou, “Spectrum reconstruction method for airborne temporally–spatially modulated Fourier transform imaging spectrometers,” IEEE Trans. Geosci. Remote Sens. 52(6), 3720–3728 (2014).
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J. Opt. (1)

G. Molesini and F. Quercioli, “Pseudocolor effects of longitudinal chromatic aberration,” J. Opt. 17(6), 279–282 (1986).
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J. Opt. Soc. Am. A (1)

J. Opt. Soc. Korea (2)

J. Opt. Technol. (1)

Opt. Eng. (1)

I. G. E. Renhorn, D. Bergström, J. Hedborg, D. Letalick, and S. Möller, “High spatial resolution hyperspectral camera based on a linear variable filter,” Opt. Eng. 55(11), 114105 (2016).
[Crossref]

Pestic. Sci. (1)

G. Thomas and G. Laurenz, “Synthetic Approaches Towards CGA 293′343: A Novel Broad-Spectrum Insecticide,” Pestic. Sci. 55(3), 355–357 (2010).

Proc. SPIE (7)

I. Renhorn, V. Achard, M. Axelsson, K. Benoist, D. Borghys, X. Briottet, R. Dekker, A. Dimmeler, O. Friman, I. Kåsen, S. Matteoli, M. L. Moro, T. O. Opsahl, M. van Persie, S. Resta, H. Schilling, P. Schwering, M. Shimoni, T. V. Haavardsholm, and F. Viallefont, “Hyperspectral reconnaissance in urban environment,” Proc. SPIE 8704, 87040L (2013).
[Crossref]

J. Antila, R. Mannila, U. Kantojärvi, C. Holmlund, A. Rissanen, I. Näkki, J. Ollila, and H. Saari, “Spectral imaging device based on a tuneable MEMS Fabry-Perot interferometer,” Proc. SPIE 8374, 83740F (2012).
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A. Ojaghi and F. E. Robles, “Ultraviolet multi-spectral microscopy using iterative phase-recovery from chromatic aberrations,” Proc. SPIE 10087, 100870M (2019).
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M. Dami, R. De Vidi, G. Aroldi, F. Belli, L. Chicarella, A. Piegari, A. Sytchkova, J. Bulir, F. Lemarquis, M. Lequime, L. Abel Tibérini, and B. Harnisch, “Ultra compact spectrometer using linear variable filters,” International Conference on Space Optics ISOP-10565 (2018).
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Figures (13)

Fig. 1
Fig. 1 Illustration of chromatic aberration.
Fig. 2
Fig. 2 Illustration of spherical aberration.
Fig. 3
Fig. 3 Monochromatic diffraction, (a) is the 2D view of diffuse spot, (b) is the 3D view of diffuse spot.
Fig. 4
Fig. 4 Simulated normalized intensity curves for selected discrepancy coefficients.
Fig. 5
Fig. 5 Simulated results for λ1λ20 light imaged at the focal point, z1. The top portion shows the 2D view of the diffuse spots, from left to right corresponding to wavelengths, and the bottom portion shows the normalized intensity at the central point of the respective diffuse spots.
Fig. 6
Fig. 6 Simulated results for λ1 light imaged at different detection positions, z1z20. The top portion shows the 2D view of diffuse spots, from left to right corresponding to different detection positions, and the bottom portion shows the normalized intensity at the spot center.
Fig. 7
Fig. 7 Simulated results of the polychromatic light imaged at z1z20. The top portion is the 2D view of diffuse spots, from left to right correspond to different positions; the bottom portion shows the normalized intensity at the central position of each diffuse spot.
Fig. 8
Fig. 8 Simulated original and the reconstructed spectrum with the normalized intensities corresponding to the selected wavelengths.
Fig. 9
Fig. 9 Illustration of the experimental set-up.
Fig. 10
Fig. 10 Actual experimental set-up, the collimating systems are replaced by a collimator.
Fig. 11
Fig. 11 Diffraction images of monochromatic light at different detection positions.
Fig. 12
Fig. 12 Diffraction images of the polychromatic light from the mercury lamp at different detection positions.
Fig. 13
Fig. 13 Reconstructed spectrum and original spectrum for the polychromatic light from the mercury lamp used in experiment.

Equations (18)

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δ defocus =[ 1 z j 1 f( λ ) ],
δ sph,λ = f λ ( r 1 ) f λ ( r 2 )
δ sph,λ = C 1 r 1 2 + C 2 r 1 4 = C 1 ( x 2 + y 2 )+ C 2 ( x 2 + y 2 ) 2 ,
δ vsph,λ = δ sph,λ tan U 2 =[ C 1 ( x 2 + y 2 )+ C 2 ( x 2 + y 2 ) 2 ]tan x 2 + y 2 f λ ( r 2 ) ,
P'( x j , y j , z j )=P(x,y,z)( δ defocus + δ sph,λ + δ vsph,λ ) =P(x,y,z){ [ 1 z j 1 f( λ ) ] +[ C 1 ( x 2 + y 2 )+ C 2 ( x 2 + y 2 ) 2 ]( 1+tan x 2 + y 2 f λ ( r ) ) },
E( x j , y j , z j , λ i )=P'( x j , y j , z j ) A i λ i z j 2 exp[ i k i 2 z j ( x 2 + y 2 ) ] exp[ i k i ( x j z j x+ y j z j y) ] dxdy,
I i,j ( x j , y j )= | E( x j , y j , z j , λ i ) | 2 ,
a i,j = max( I i,j ( x j , y j )) max( I i,i ( x j , y j )) ,
N I i,j = I i,j ( x j , y j ) max( I i,i ( x j , y j )) ,
P j = I 1,j + I 2,j + I i,j ,
[ P 1 P 2 P j1 P j ]=[ a 1,1 a 1,2 a 1,j1 a 1,j a 2,1 a 2,2 a 2,j1 a 2,j a i1,1 a i1,2 a i1,j1 a i1,j a i,1 a i,2 a i,j1 a i,j ][ I λ1 I λ2 I λi1 I λi ]=AI,
min I AI-P 2 2 = ( AIP ) T ( AI-P ),
φ( I )= I T A T AI I T A T P P T AI+ P T P,
dφ dI =2 A T AI2 A T P,
I= ( A T A ) 1 A T P,
SCC(u,v)= i=1 n ( u i u ¯ )( v i v ¯ ) i=1 n ( u i u ¯ ) 2 i=1 n ( v i v ¯ ) 2 ,
SMSE( u,v )= i=1 n ( u i v i ) 2 n 2 .
A=[ 1 0.6087 0.3393 0.2583 0.1702 0.1481 0.1398 0.1305 0.7341 1 0.3920 0.2328 0.1907 0.1694 0.1602 0.1448 0.1302 0.4661 1 0.7073 0.3607 0.2244 0.1912 0.1629 0.0726 0.0370 0.0195 0.0128 0.0113 0.2387 0.0952 0.0360 0.0220 0.0173 0.6521 0.2858 0.0872 0.0360 0.0286 1 0.7398 0.2367 0.0812 0.0606 0.4419 1 0.5334 0.2068 0.1518 0.2674 0.4365 1 0.5493 0.4267 0.2087 0.3127 0.7034 1 0.7827 0.1705 0.2781 0.4072 0.9334 1 ]

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