Abstract

We propose a procedure to determine the spectral response of digital dispersive spectrometers without previous knowledge of any parameter of the system. The method consists of applying the Fourier transform spectroscopy technique to each pixel of the detection plane, a CCD camera, to obtain its individual spectral response. From this simple procedure, the system-point spread function and the effect of the finite pixel width are taken into account giving rise to a response matrix that fully characterizes the spectrometer. Using the response matrix information we find the resolving power of a given spectrometer, predict in advance its response to any virtual input spectrum and improve numerically the spectrometer’s resolution. We consider that the presented approach could be useful in most spectroscopic branches such as in computational spectroscopy, optical coherence tomography, hyperspectral imaging, spectral interferometry and analytical chemistry, among others.

© 2017 Optical Society of America

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References

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    [Crossref]
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2015 (3)

2014 (4)

2013 (1)

K. Liu and F. Yu, “Accurate wavelength calibration method using system parameters for grating spectrometers,” Opt. Eng. 52, 013603 (2013).
[Crossref]

2012 (3)

A. Emadi, H. Wu, G. Graff, and R. Wolffenbuttel, “Design and implementation of a sub-nm resolution microespectrometer based on a linear-variable optical filter,” Opt. Express 20, 489–507 (2012).
[Crossref] [PubMed]

B. Redding and H. Cao, “Using a multimode fiber as a high-resolution, low-loss spectrometer,” Opt. Lett. 37, 3384–3386 (2012).
[Crossref]

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

2010 (3)

2007 (3)

Z. Hu, Y. Pan, and A. M. Rollins, “Analytical model of spectrometer-based two-beam spectral interferometry,” Appl. Opt. 46, 8499–8505 (2007).
[Crossref] [PubMed]

P. Hlubina, D. Ciprian, J. Luňáček, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88, 397–403 (2007).
[Crossref]

R. Chelebus, P. Hlubina, and D. Ciprian, “Dispersion measurements of anisotropic materials and a new fiber-optic sensor configuration,” Proc. SPIE 6609, 66090H1 (2007).

2006 (2)

P. Hlubina, D. Ciprian, and L. Knyblová, “Interference of white light in tandem configuration of birefringent crystal and sensing birefringent fiber,” Opt. Commun. 260, 535–541 (2006).
[Crossref]

P. Hlubina, D. Ciprian, J. Luňáňek, and M. Lesňák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678–7685 (2006).
[Crossref] [PubMed]

2005 (1)

P. Hlubina and W. Urbanczyk, “Dispersion of the group birefringence of a calcite crystal measured by white-light spectral interferometry,” Meas. Sci. Technol. 16, 1267 (2005).
[Crossref]

2004 (1)

P. Hlubina, “Dispersive spectral-domain two-beam interference analysed by a fibre-optic spectrometer,” J. Mod. Opt. 51, 537–547 (2004).
[Crossref]

2003 (2)

P. Hlubina, V. Chugunov, and I. Gurov, “Dispersion compensation in temporal fourier holography and spectral fringe phase retrieval using a phase-locked loop method,” Proc. SPIE 5481, 120–128 (2003).

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photon. 7, 746–751 (2003).
[Crossref]

2001 (1)

V. N. Kumar and D. N. Rao, “Two-beam interference experiments in the frequency-domain to measure the complex degree of spectral coherence,” J. Mod. Opt. 48, 1455–1465 (2001).

1999 (1)

1996 (1)

1981 (1)

1978 (2)

K. Kozima, H. Kanamori, and O. Matsuda, “Direct measurement of optical transfer functions of spectroscopic systems,” JPN. J. Appl. Phys. 17, 1271 (1978).
[Crossref]

W. Frank, K. Goerke, and M. Pietralla, “Demonstrating fourier transform spectroscopy for students,” Appl. Opt. 17, 1413–1417 (1978).
[Crossref] [PubMed]

1970 (1)

T. Katayama and A. Takahashi, “Optical transfer function of concave grating spectrometer based on wave optical method,” Jpn. J. Appl. Phys. 9, 1509 (1970).
[Crossref]

1967 (1)

1955 (1)

Adams, D. E.

Akca, B. M.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Belanger, A. M.

Brown, S.

C. E. Cramer, S. Brown, N. Caldwell, A. K. Dupree, S. G. Korzennik, K. R. Lykke, and A. Szentgyorgyi, “A tunable laser system for the wavelength calibration of astronomical spectrographs,” in Proceedings of IEEE Conference on Lasers and Electro-Optics and Conference on Quantum electronics and Laser Science Conference (IEEE, 2009) pp. 1–2.

Caldwell, N.

C. E. Cramer, S. Brown, N. Caldwell, A. K. Dupree, S. G. Korzennik, K. R. Lykke, and A. Szentgyorgyi, “A tunable laser system for the wavelength calibration of astronomical spectrographs,” in Proceedings of IEEE Conference on Lasers and Electro-Optics and Conference on Quantum electronics and Laser Science Conference (IEEE, 2009) pp. 1–2.

Cao, H.

B. Redding and H. Cao, “Using a multimode fiber as a high-resolution, low-loss spectrometer,” Opt. Lett. 37, 3384–3386 (2012).
[Crossref]

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photon. 7, 746–751 (2003).
[Crossref]

Chelebus, R.

R. Chelebus, P. Hlubina, and D. Ciprian, “Dispersion measurements of anisotropic materials and a new fiber-optic sensor configuration,” Proc. SPIE 6609, 66090H1 (2007).

Chlebus, R.

P. Hlubina, D. Ciprian, J. Luňáček, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88, 397–403 (2007).
[Crossref]

Chugunov, V.

P. Hlubina, V. Chugunov, and I. Gurov, “Dispersion compensation in temporal fourier holography and spectral fringe phase retrieval using a phase-locked loop method,” Proc. SPIE 5481, 120–128 (2003).

Ciprian, D.

P. Hlubina, D. Ciprian, and M. Kadulová, “Measurement of chromatic dispersion of polarization modes in optical fibres using white-light spectral interferometry,” Meas. Sci. Technol. 21, 045302 (2010).
[Crossref]

R. Chelebus, P. Hlubina, and D. Ciprian, “Dispersion measurements of anisotropic materials and a new fiber-optic sensor configuration,” Proc. SPIE 6609, 66090H1 (2007).

P. Hlubina, D. Ciprian, J. Luňáček, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88, 397–403 (2007).
[Crossref]

P. Hlubina, D. Ciprian, and L. Knyblová, “Interference of white light in tandem configuration of birefringent crystal and sensing birefringent fiber,” Opt. Commun. 260, 535–541 (2006).
[Crossref]

P. Hlubina, D. Ciprian, J. Luňáňek, and M. Lesňák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678–7685 (2006).
[Crossref] [PubMed]

Coates, V. J.

Cramer, C. E.

C. E. Cramer, S. Brown, N. Caldwell, A. K. Dupree, S. G. Korzennik, K. R. Lykke, and A. Szentgyorgyi, “A tunable laser system for the wavelength calibration of astronomical spectrographs,” in Proceedings of IEEE Conference on Lasers and Electro-Optics and Conference on Quantum electronics and Laser Science Conference (IEEE, 2009) pp. 1–2.

de la Fuente, R.

Dorrer, C.

Driessen, A.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Dupree, A. K.

C. E. Cramer, S. Brown, N. Caldwell, A. K. Dupree, S. G. Korzennik, K. R. Lykke, and A. Szentgyorgyi, “A tunable laser system for the wavelength calibration of astronomical spectrographs,” in Proceedings of IEEE Conference on Lasers and Electro-Optics and Conference on Quantum electronics and Laser Science Conference (IEEE, 2009) pp. 1–2.

Durfee, C. G.

Dybwad, P.

Emadi, A.

Frank, W.

Fujiwara, H.

Galloway, B.

Goerke, K.

Graff, G.

Gurov, I.

P. Hlubina, V. Chugunov, and I. Gurov, “Dispersion compensation in temporal fourier holography and spectral fringe phase retrieval using a phase-locked loop method,” Proc. SPIE 5481, 120–128 (2003).

Han, J.-H.

Hausdorff, H.

Hlubina, P.

P. Hlubina, D. Ciprian, and M. Kadulová, “Measurement of chromatic dispersion of polarization modes in optical fibres using white-light spectral interferometry,” Meas. Sci. Technol. 21, 045302 (2010).
[Crossref]

P. Hlubina, D. Ciprian, J. Luňáček, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88, 397–403 (2007).
[Crossref]

R. Chelebus, P. Hlubina, and D. Ciprian, “Dispersion measurements of anisotropic materials and a new fiber-optic sensor configuration,” Proc. SPIE 6609, 66090H1 (2007).

P. Hlubina, D. Ciprian, and L. Knyblová, “Interference of white light in tandem configuration of birefringent crystal and sensing birefringent fiber,” Opt. Commun. 260, 535–541 (2006).
[Crossref]

P. Hlubina, D. Ciprian, J. Luňáňek, and M. Lesňák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14, 7678–7685 (2006).
[Crossref] [PubMed]

P. Hlubina and W. Urbanczyk, “Dispersion of the group birefringence of a calcite crystal measured by white-light spectral interferometry,” Meas. Sci. Technol. 16, 1267 (2005).
[Crossref]

P. Hlubina, “Dispersive spectral-domain two-beam interference analysed by a fibre-optic spectrometer,” J. Mod. Opt. 51, 537–547 (2004).
[Crossref]

P. Hlubina, V. Chugunov, and I. Gurov, “Dispersion compensation in temporal fourier holography and spectral fringe phase retrieval using a phase-locked loop method,” Proc. SPIE 5481, 120–128 (2003).

Hu, Z.

Iliev, M.

Ismail, N.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Jeong, J.

Kadulová, M.

P. Hlubina, D. Ciprian, and M. Kadulová, “Measurement of chromatic dispersion of polarization modes in optical fibres using white-light spectral interferometry,” Meas. Sci. Technol. 21, 045302 (2010).
[Crossref]

Kalkman, J.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Kanamori, H.

K. Kozima, H. Kanamori, and O. Matsuda, “Direct measurement of optical transfer functions of spectroscopic systems,” JPN. J. Appl. Phys. 17, 1271 (1978).
[Crossref]

Katayama, T.

T. Katayama and A. Takahashi, “Optical transfer function of concave grating spectrometer based on wave optical method,” Jpn. J. Appl. Phys. 9, 1509 (1970).
[Crossref]

Kim, J.-H.

Knyblová, L.

P. Hlubina, D. Ciprian, and L. Knyblová, “Interference of white light in tandem configuration of birefringent crystal and sensing birefringent fiber,” Opt. Commun. 260, 535–541 (2006).
[Crossref]

Korb, A. R.

Korzennik, S. G.

C. E. Cramer, S. Brown, N. Caldwell, A. K. Dupree, S. G. Korzennik, K. R. Lykke, and A. Szentgyorgyi, “A tunable laser system for the wavelength calibration of astronomical spectrographs,” in Proceedings of IEEE Conference on Lasers and Electro-Optics and Conference on Quantum electronics and Laser Science Conference (IEEE, 2009) pp. 1–2.

Kozima, K.

K. Kozima, H. Kanamori, and O. Matsuda, “Direct measurement of optical transfer functions of spectroscopic systems,” JPN. J. Appl. Phys. 17, 1271 (1978).
[Crossref]

Kumar, V. N.

V. N. Kumar and D. N. Rao, “Two-beam interference experiments in the frequency-domain to measure the complex degree of spectral coherence,” J. Mod. Opt. 48, 1455–1465 (2001).

Laserna, J.

J. Serrano, J. Moros, and J. Laserna, “Exploring the formation routes of diatomic hydrogenated radicals using femtosecond laser-induced breakdown spectroscopy of deuterated molecular solids,” J. Anal. At. Spectrom. 30, 2343–2352 (2015).
[Crossref]

Lesnák, M.

Liew, S. F.

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photon. 7, 746–751 (2003).
[Crossref]

Liu, K.

K. Liu and F. Yu, “Accurate wavelength calibration method using system parameters for grating spectrometers,” Opt. Eng. 52, 013603 (2013).
[Crossref]

Lunácek, J.

P. Hlubina, D. Ciprian, J. Luňáček, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88, 397–403 (2007).
[Crossref]

Lunánek, J.

Lykke, K. R.

C. E. Cramer, S. Brown, N. Caldwell, A. K. Dupree, S. G. Korzennik, K. R. Lykke, and A. Szentgyorgyi, “A tunable laser system for the wavelength calibration of astronomical spectrographs,” in Proceedings of IEEE Conference on Lasers and Electro-Optics and Conference on Quantum electronics and Laser Science Conference (IEEE, 2009) pp. 1–2.

Matsuda, O.

K. Kozima, H. Kanamori, and O. Matsuda, “Direct measurement of optical transfer functions of spectroscopic systems,” JPN. J. Appl. Phys. 17, 1271 (1978).
[Crossref]

Meier, A. K.

Menon, R.

Moros, J.

J. Serrano, J. Moros, and J. Laserna, “Exploring the formation routes of diatomic hydrogenated radicals using femtosecond laser-induced breakdown spectroscopy of deuterated molecular solids,” J. Anal. At. Spectrom. 30, 2343–2352 (2015).
[Crossref]

Nguyen, V. D.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Pan, Y.

Pietralla, M.

Pollnau, M.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Rao, D. N.

V. N. Kumar and D. N. Rao, “Two-beam interference experiments in the frequency-domain to measure the complex degree of spectral coherence,” J. Mod. Opt. 48, 1455–1465 (2001).

Redding, B.

B. Redding and H. Cao, “Using a multimode fiber as a high-resolution, low-loss spectrometer,” Opt. Lett. 37, 3384–3386 (2012).
[Crossref]

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photon. 7, 746–751 (2003).
[Crossref]

Ridder, R. M.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Rollins, A. M.

Salisbury, J. W.

Sarma, R.

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photon. 7, 746–751 (2003).
[Crossref]

Sengo, G.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Serrano, J.

J. Serrano, J. Moros, and J. Laserna, “Exploring the formation routes of diatomic hydrogenated radicals using femtosecond laser-induced breakdown spectroscopy of deuterated molecular solids,” J. Anal. At. Spectrom. 30, 2343–2352 (2015).
[Crossref]

Simmons, S. M.

Squier, J. A.

Stewart, J. E.

Sun, F.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Szentgyorgyi, A.

C. E. Cramer, S. Brown, N. Caldwell, A. K. Dupree, S. G. Korzennik, K. R. Lykke, and A. Szentgyorgyi, “A tunable laser system for the wavelength calibration of astronomical spectrographs,” in Proceedings of IEEE Conference on Lasers and Electro-Optics and Conference on Quantum electronics and Laser Science Conference (IEEE, 2009) pp. 1–2.

Takahashi, A.

T. Katayama and A. Takahashi, “Optical transfer function of concave grating spectrometer based on wave optical method,” Jpn. J. Appl. Phys. 9, 1509 (1970).
[Crossref]

Urbanczyk, W.

P. Hlubina and W. Urbanczyk, “Dispersion of the group birefringence of a calcite crystal measured by white-light spectral interferometry,” Meas. Sci. Technol. 16, 1267 (2005).
[Crossref]

VanLeeuwen, T. G.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Wadsworth, W.

Wang, P.

Wojtkowski, M.

Wolffenbuttel, R.

Wörhoff, K.

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

Wu, H.

Youngquist, R. C.

Yu, F.

K. Liu and F. Yu, “Accurate wavelength calibration method using system parameters for grating spectrometers,” Opt. Eng. 52, 013603 (2013).
[Crossref]

Appl. Opt. (5)

Appl. Phys. B (1)

P. Hlubina, D. Ciprian, J. Luňáček, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88, 397–403 (2007).
[Crossref]

Appl. Spectrosc. (1)

IEEE J. Sel. Top. Quantum Electron. (1)

B. M. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, T. G. VanLeeuwen, M. Pollnau, K. Wörhoff, and R. M. Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE J. Sel. Top. Quantum Electron. 18, 1223–1233 (2012).
[Crossref]

J. Anal. At. Spectrom. (1)

J. Serrano, J. Moros, and J. Laserna, “Exploring the formation routes of diatomic hydrogenated radicals using femtosecond laser-induced breakdown spectroscopy of deuterated molecular solids,” J. Anal. At. Spectrom. 30, 2343–2352 (2015).
[Crossref]

J. Lightwave Technol. (1)

J. Mod. Opt. (2)

P. Hlubina, “Dispersive spectral-domain two-beam interference analysed by a fibre-optic spectrometer,” J. Mod. Opt. 51, 537–547 (2004).
[Crossref]

V. N. Kumar and D. N. Rao, “Two-beam interference experiments in the frequency-domain to measure the complex degree of spectral coherence,” J. Mod. Opt. 48, 1455–1465 (2001).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

T. Katayama and A. Takahashi, “Optical transfer function of concave grating spectrometer based on wave optical method,” Jpn. J. Appl. Phys. 9, 1509 (1970).
[Crossref]

K. Kozima, H. Kanamori, and O. Matsuda, “Direct measurement of optical transfer functions of spectroscopic systems,” JPN. J. Appl. Phys. 17, 1271 (1978).
[Crossref]

Meas. Sci. Technol. (2)

P. Hlubina, D. Ciprian, and M. Kadulová, “Measurement of chromatic dispersion of polarization modes in optical fibres using white-light spectral interferometry,” Meas. Sci. Technol. 21, 045302 (2010).
[Crossref]

P. Hlubina and W. Urbanczyk, “Dispersion of the group birefringence of a calcite crystal measured by white-light spectral interferometry,” Meas. Sci. Technol. 16, 1267 (2005).
[Crossref]

Nat. Photon. (1)

B. Redding, S. F. Liew, R. Sarma, and H. Cao, “Compact spectrometer based on a disordered photonic chip,” Nat. Photon. 7, 746–751 (2003).
[Crossref]

Opt. Commun. (1)

P. Hlubina, D. Ciprian, and L. Knyblová, “Interference of white light in tandem configuration of birefringent crystal and sensing birefringent fiber,” Opt. Commun. 260, 535–541 (2006).
[Crossref]

Opt. Eng. (1)

K. Liu and F. Yu, “Accurate wavelength calibration method using system parameters for grating spectrometers,” Opt. Eng. 52, 013603 (2013).
[Crossref]

Opt. Express (5)

Opt. Lett. (2)

Optica (1)

Proc. SPIE (2)

R. Chelebus, P. Hlubina, and D. Ciprian, “Dispersion measurements of anisotropic materials and a new fiber-optic sensor configuration,” Proc. SPIE 6609, 66090H1 (2007).

P. Hlubina, V. Chugunov, and I. Gurov, “Dispersion compensation in temporal fourier holography and spectral fringe phase retrieval using a phase-locked loop method,” Proc. SPIE 5481, 120–128 (2003).

Other (1)

C. E. Cramer, S. Brown, N. Caldwell, A. K. Dupree, S. G. Korzennik, K. R. Lykke, and A. Szentgyorgyi, “A tunable laser system for the wavelength calibration of astronomical spectrographs,” in Proceedings of IEEE Conference on Lasers and Electro-Optics and Conference on Quantum electronics and Laser Science Conference (IEEE, 2009) pp. 1–2.

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Figures (6)

Fig. 1
Fig. 1 Experimental setup to characterize a digital dispersive spectrometer. The Michelson Interferometer is used to illuminate the spectrometer with a time dependent interference pattern. Inset 1: photograph recorded by the camera and its normalized intensity profile. Inset 2: temporal signal recorded by an individual pixel as a function of the time delay. The Fourier transformation of this signal is the spectral response at each pixel, that represents a column vector in Fig. 2(b).
Fig. 2
Fig. 2 OTF registered by each pixel of the camera, (a)–(c), for spectrometers S1–S3, respectively. Response Matrix and a zoom around pixel number 600, (d)–(f), for spectrometers S1–S3, respectively. The Response Matrix is calculated by Fourier transforming the OTF at each pixel and centering the spectrum to its carrier frequency. The vertical and horizontal arrows indicate the cross-section directions in Fig. 3 (OTFs and the spectral response) and in Fig. 5 (spatial response), respectively.
Fig. 3
Fig. 3 Figures (a), (c) and (e) are the OTFs corresponding to the vertical cross-sections of Figs. 2(a)–2(c), respectively. Figures (b), (d) and (f) are the spectral response corresponding to the vertical cross-sections of Figs. 2(d)–2(f), respectively. The cross-sections are evaluated at the positions pointed by the vertical arrows in Fig. 2. The color lines in the figure are correlated with the color arrows in Fig. 2. The spectrum is analyzed around wavelengths λ =486.1 nm, 532.0 nm and 632.8 nm.
Fig. 4
Fig. 4 Resolving power for the three spectrometers evaluated at each pixel of the camera. The curve for S1 has been magnified for easy viewing.
Fig. 5
Fig. 5 Comparison of the horizontal cross-sections of Fig. 2, blue lines, with the image recorded directly by the camera, red lines, under quasy-monochromatic illumination. The cross-sections are indicated by the horizontal arrows in Fig. 2, corresponding to λ =486.1 nm, 532.0 nm and 632.0 nm. The quasy-monochromatic sources are the spectral line of a hydrogen discharge lamp centered at 486.1 nm, a solid state laser emitting at 532.0 nm and He-Ne laser emitting at 632.8 nm. Figures (a)–(c) are the results for S1, Figs. (d)–(f) for S2 and Figs. (g)–(i) for S3.
Fig. 6
Fig. 6 Resolution enhancement results for spectrometer S2. Image recorded by the camera, blue lines, and the composed signal using the RM and the best input spectrum, red lines, for the laser (a) and the Sodium D-lines (b). Best input spectrum, black lines, and the experimental results expressed in wavelengths by means of the calibration curve, blue lines, for the laser (c) and the sodium D-lines (d).

Tables (2)

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Table 1 Slit and grating width for the three spectrometers, S1–S3.

Tables Icon

Table 2 Test spectrum parameters.

Equations (5)

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S ( x , τ ) = I [ ν ( x ) ] { 1 + f [ ν ( x ) , τ ] cos ( 4 π ν ( x ) τ ) }
PSF ( x , λ ) ~ | rect ( f 1 f 2 x a ) sinc [ b ( x λ f 2 1 Λ ) ] | 2 ,
| rect ( f 1 f 2 a ( x λ f 2 Λ ) ) | 2 ,
| sinc [ b ( x λ f 2 1 Λ ) ] | 2 ,
Δ ( a 1 , a 2 , , a n ) = 1 N i = 1 N ( S ( x i ) j = 1 M I ( λ j , a 1 , a 2 , , a n ) R M ( λ j , x i ) ) 2

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