Abstract

A spectrometer based on a Sagnac interferometer, where one of the mirrors is replaced by a transmission grating, is introduced. Since the action of a transmission grating is reversible, both directions experience the same diffraction at a given wavelength. At the output, the crossed wavefronts are imaged onto a camera, where their Fizeau fringe pattern is recorded. Each spectral element produces a unique spatial frequency, hence the Fourier transform of the recorded interferogram contains the spectrum. Since the grating is tuned to place zero spatial frequency at a selected wavelength, the adjoining spectrum is heterodyned with respect to this wavelength. This spectrum can then be discriminated at a high spectral resolution from relatively low spatial frequencies. The spectrometer can be designed without moving parts for a relatively narrow spectral range or with a rotatable grating. The latter version bears the potential to be calibrated without a calibrated light source.

© 2017 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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  5. L. Xia, Z. Yang, S. Yin, Q. Deng, and C. Du, “Method of realizing compact fourier transform spectrometer without moving parts based on birefringent liquid crystal,” Opt. Eng. 53, 074109 (2014).
    [Crossref]
  6. E. Szarmes and H. Ma, “Sagnac Fourier transform spectrometer having improved resolution” US Patent 8,736,844 B2, May2014,.
  7. B. D. Maione, D. Luo, M. Miskiewicz, M. Escuti, and M. W. Kudenov, “Spatially heterodyned snapshot imaging spectrometer,” Appl. Opt. 55, 8667–8675 (2016).
    [Crossref] [PubMed]
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    [Crossref]
  9. M. Lenzner and J. C. Diels, “Concerning the spatial heterodyne spectrometer,” Opt. Express 24, 1829–1839 (2016).
    [Crossref] [PubMed]
  10. Z. Bor and B. Rácz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165–170 (1985).
    [Crossref]
  11. C. P. Perkins, J. P. Kerekes, and M. G. Gartley, “Spatial heterodyne spectrometer: modeling and interferogram processing for calibrated spectral radiance measurements,” in Imaging Spectrometry XVIII, T. S. P. P. Mouroulis, ed., 8870, 88700R (2013).
    [Crossref]
  12. M. Lenzner, “Sagnac Fourier spectrometer (SAFOS)” US Patent Application 15/341,104, November2016.

2016 (2)

2014 (1)

L. Xia, Z. Yang, S. Yin, Q. Deng, and C. Du, “Method of realizing compact fourier transform spectrometer without moving parts based on birefringent liquid crystal,” Opt. Eng. 53, 074109 (2014).
[Crossref]

1997 (1)

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[Crossref]

1994 (1)

1992 (1)

J. Harlander, R. J. Reynolds, and F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[Crossref]

1985 (1)

Z. Bor and B. Rácz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165–170 (1985).
[Crossref]

1962 (1)

Amat, G.

Arsac, A.

Bor, Z.

Z. Bor and B. Rácz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165–170 (1985).
[Crossref]

Brochard, J.

Brossel, J.

Connes, P.

Couture, L.

Deng, Q.

L. Xia, Z. Yang, S. Yin, Q. Deng, and C. Du, “Method of realizing compact fourier transform spectrometer without moving parts based on birefringent liquid crystal,” Opt. Eng. 53, 074109 (2014).
[Crossref]

Diels, J. C.

Du, C.

L. Xia, Z. Yang, S. Yin, Q. Deng, and C. Du, “Method of realizing compact fourier transform spectrometer without moving parts based on birefringent liquid crystal,” Opt. Eng. 53, 074109 (2014).
[Crossref]

Duncan, A. J.

Escuti, M.

Gartley, M. G.

C. P. Perkins, J. P. Kerekes, and M. G. Gartley, “Spatial heterodyne spectrometer: modeling and interferogram processing for calibrated spectral radiance measurements,” in Imaging Spectrometry XVIII, T. S. P. P. Mouroulis, ed., 8870, 88700R (2013).
[Crossref]

Harlander, J.

J. Harlander, R. J. Reynolds, and F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[Crossref]

Harvey, A. R.

Jacquinot, P.

Kerekes, J. P.

C. P. Perkins, J. P. Kerekes, and M. G. Gartley, “Spatial heterodyne spectrometer: modeling and interferogram processing for calibrated spectral radiance measurements,” in Imaging Spectrometry XVIII, T. S. P. P. Mouroulis, ed., 8870, 88700R (2013).
[Crossref]

Kudenov, M. W.

Lenzner, M.

M. Lenzner and J. C. Diels, “Concerning the spatial heterodyne spectrometer,” Opt. Express 24, 1829–1839 (2016).
[Crossref] [PubMed]

M. Lenzner, “Sagnac Fourier spectrometer (SAFOS)” US Patent Application 15/341,104, November2016.

Luo, D.

Ma, H.

E. Szarmes and H. Ma, “Sagnac Fourier transform spectrometer having improved resolution” US Patent 8,736,844 B2, May2014,.

Maione, B. D.

Maréchal, A.

Miskiewicz, M.

Padgett, M. J.

Perkins, C. P.

C. P. Perkins, J. P. Kerekes, and M. G. Gartley, “Spatial heterodyne spectrometer: modeling and interferogram processing for calibrated spectral radiance measurements,” in Imaging Spectrometry XVIII, T. S. P. P. Mouroulis, ed., 8870, 88700R (2013).
[Crossref]

Rácz, B.

Z. Bor and B. Rácz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165–170 (1985).
[Crossref]

Reynolds, R. J.

J. Harlander, R. J. Reynolds, and F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[Crossref]

Roesler, F. L.

J. Harlander, R. J. Reynolds, and F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[Crossref]

Seitz, P.

P. Seitz and M. Stalder, “Wollaston prism and use of it in a Fourier-transform spectrometer” US Patent 6,222,627 B1, April2001.

Sibbett, W.

Stalder, M.

P. Seitz and M. Stalder, “Wollaston prism and use of it in a Fourier-transform spectrometer” US Patent 6,222,627 B1, April2001.

Stedman, G. E.

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[Crossref]

Szarmes, E.

E. Szarmes and H. Ma, “Sagnac Fourier transform spectrometer having improved resolution” US Patent 8,736,844 B2, May2014,.

Xia, L.

L. Xia, Z. Yang, S. Yin, Q. Deng, and C. Du, “Method of realizing compact fourier transform spectrometer without moving parts based on birefringent liquid crystal,” Opt. Eng. 53, 074109 (2014).
[Crossref]

Yang, Z.

L. Xia, Z. Yang, S. Yin, Q. Deng, and C. Du, “Method of realizing compact fourier transform spectrometer without moving parts based on birefringent liquid crystal,” Opt. Eng. 53, 074109 (2014).
[Crossref]

Yin, S.

L. Xia, Z. Yang, S. Yin, Q. Deng, and C. Du, “Method of realizing compact fourier transform spectrometer without moving parts based on birefringent liquid crystal,” Opt. Eng. 53, 074109 (2014).
[Crossref]

Appl. Opt. (3)

Astrophys. J. (1)

J. Harlander, R. J. Reynolds, and F. L. Roesler, “Spatial heterodyne spectroscopy for the exploration of diffuse interstellar emission lines at far-ultraviolet wavelengths,” Astrophys. J. 396, 730–740 (1992).
[Crossref]

Opt. Commun. (1)

Z. Bor and B. Rácz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165–170 (1985).
[Crossref]

Opt. Eng. (1)

L. Xia, Z. Yang, S. Yin, Q. Deng, and C. Du, “Method of realizing compact fourier transform spectrometer without moving parts based on birefringent liquid crystal,” Opt. Eng. 53, 074109 (2014).
[Crossref]

Opt. Express (1)

Rep. Prog. Phys. (1)

G. E. Stedman, “Ring-laser tests of fundamental physics and geophysics,” Rep. Prog. Phys. 60, 615–688 (1997).
[Crossref]

Other (4)

E. Szarmes and H. Ma, “Sagnac Fourier transform spectrometer having improved resolution” US Patent 8,736,844 B2, May2014,.

P. Seitz and M. Stalder, “Wollaston prism and use of it in a Fourier-transform spectrometer” US Patent 6,222,627 B1, April2001.

C. P. Perkins, J. P. Kerekes, and M. G. Gartley, “Spatial heterodyne spectrometer: modeling and interferogram processing for calibrated spectral radiance measurements,” in Imaging Spectrometry XVIII, T. S. P. P. Mouroulis, ed., 8870, 88700R (2013).
[Crossref]

M. Lenzner, “Sagnac Fourier spectrometer (SAFOS)” US Patent Application 15/341,104, November2016.

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Figures (5)

Fig. 1
Fig. 1

Principal scheme of the Sagnac Fourier Spectrometer (SAFOS). The green and red lines show the wavefront tilt of the respective directions for a wavelength that is smaller than the design wavelength.

Fig. 2
Fig. 2

Tuning curve of the SAFOS, showing the wavelength that propagates on the optical axis (i.e. the heterodyne wavelength) in dependence on the angle of incidence α on the grating. Curves are shown for different design angles γ, which is constant for a given configuration. The dotted line connects the maxima of the curves, where α = β.

Fig. 3
Fig. 3

Two modes of operating the SAFOS.

Fig. 4
Fig. 4

Experimental results for a SAFOS configuration in which the wavelength to be measured (horizontal line) is outside the scan range (corresponding to range A in Fig. 3(a)). The red line is a fit using a design angle of 151.978°. The green lines show fits with a deviation of γ of only ±0.01°.

Fig. 5
Fig. 5

Experimental data for a SAFOS configuration in which the wavelength to be measured is within the scan range (corresponding to range B in Fig. 3(b)).

Equations (7)

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Δ x = λ 0 2 Δ β = λ 0 cos β 2 g Δ λ ,
tan γ = λ 0 g cos β = sin α + sin β cos β
λ = 1 g [ sin ( α ) + sin ( α + γ ) ]
2 x p = λ 0 2 Δ β = λ 0 cos β 2 g | Δ λ | ,
Δ λ B = sin 2 β 4 g 2 x p .
1 Δ x Δ λ = 2 g λ 0 cos β
λ = Δ λ + 2 g cos ( Δ α ) cos ( γ 2 )

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