Abstract

For applications where only moderate spectral resolution is required, static Fourier transform infrared spectrometers (sFTS) offer a comparatively cost-effective alternative to classical scanning instruments. In this paper, we present an sFTS based on a single-mirror interferometer using only standard optical components and an uncooled microbolometer array. Because the instrument features concave mirrors rather than lenses, dispersion effects can be minimized. This enables broadband operation in the mid-infrared range from 2800  cm−1 to 600  cm−1 at a spectral resolution of 12  cm−1. In addition, the design guarantees comparatively high light throughput and can potentially be designed for increased temperature stability. Alongside a simulation of the temperature- and wavenumber-dependent behavior of the system, we provide a proof of principle of the proposed design by means of experimental results.

© 2019 Optical Society of America

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References

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  1. P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).
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    [Crossref]
  3. M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995).
    [Crossref]
  4. F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362(2001).
    [Crossref]
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  7. G. Zhan, “Static Fourier-transform spectrometer with spherical reflectors,” Appl. Opt. 41, 560–563 (2002).
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  8. H. Mortimer, “Compact interferometer spectrometer,” U.S. patent9,046,412 (2June2015).
  9. P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
    [Crossref]
  10. M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
    [Crossref]
  11. M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
    [Crossref]
  12. M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).
  13. M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
    [Crossref]
  14. M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).
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    [Crossref]
  19. J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
    [Crossref]

2017 (4)

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

2016 (2)

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

2006 (1)

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

2004 (1)

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46, 443–454 (2004).
[Crossref]

2002 (1)

2001 (1)

F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362(2001).
[Crossref]

1995 (1)

M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995).
[Crossref]

1993 (1)

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

1991 (1)

M.-L. Junttila, “Performance limits of stationary Fourier spectrometers,” J. Opt. Soc. Am. A. 8, 1457–1462 (1991).
[Crossref]

1989 (1)

1984 (1)

1979 (1)

1965 (1)

Barnes, N. P.

Budney, C.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Chen, J.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Crastes, A.

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

de Haseth, J. A.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).

Denton, M. B.

Dubey, M. K.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Fieque, B.

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

Franklin, J. E.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Gillespie, D. T.

Gottlieb, E. W.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Greengard, L.

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46, 443–454 (2004).
[Crossref]

Griffiths, P. R.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).

Harvey, A. R.

M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995).
[Crossref]

Hedelius, J. K.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Hinck, K.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Horton, K.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Jones, T.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Junttila, M.-L.

M.-L. Junttila, “Performance limits of stationary Fourier spectrometers,” J. Opt. Soc. Am. A. 8, 1457–1462 (1991).
[Crossref]

Kawata, S.

Koch, A. W.

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

Köhler, M. H.

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

Lee, J.-Y.

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46, 443–454 (2004).
[Crossref]

Legras, O.

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

Lucey, P. G.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Minami, S.

Mortimer, H.

H. Mortimer, “Compact interferometer spectrometer,” U.S. patent9,046,412 (2June2015).

Murr, P. J.

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

Nichols, L. W.

Okamoto, T.

Olsen, A. L.

Padgett, M. J.

M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995).
[Crossref]

Parker, H.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Piltch, M. S.

Rauscher, M. S.

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

Reininger, F. M.

F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362(2001).
[Crossref]

Schardt, M.

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

Schwaller, C.

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

Sweedler, J. V.

Tissot, J. L.

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

Tremmel, A. J.

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, P. J. Murr, M. S. Rauscher, A. J. Tremmel, B. R. Wiesent, and A. W. Koch, “Static Fourier transform infrared spectrometer,” Opt. Express 24, 7767–7776 (2016).
[Crossref]

Trouilleau, C.

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

Viatte, C.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Wennberg, P. O.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Wiesent, B. R.

Williams, T.

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Wofsy, S. C.

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Zhan, G.

Appl. Opt. (3)

Appl. Spectrosc. (1)

Atmos. Chem. Phys. (1)

J. Chen, C. Viatte, J. K. Hedelius, T. Jones, J. E. Franklin, H. Parker, E. W. Gottlieb, P. O. Wennberg, M. K. Dubey, and S. C. Wofsy, “Differential column measurements using compact solar-tracking spectrometers,” Atmos. Chem. Phys. 16, 8479–8498 (2016).
[Crossref]

Infrared Phys. Technol. (1)

F. M. Reininger, “The application of large format, broadband quantum well infrared photodetector arrays to spatially modulated prism interferometers,” Infrared Phys. Technol. 42, 345–362(2001).
[Crossref]

J. Opt. Soc. Am. (1)

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

M.-L. Junttila, “Performance limits of stationary Fourier spectrometers,” J. Opt. Soc. Am. A. 8, 1457–1462 (1991).
[Crossref]

Opt. Express (1)

Opto-Electronics Rev. (1)

J. L. Tissot, C. Trouilleau, B. Fieque, A. Crastes, and O. Legras, “Uncooled microbolometer detector: recent development at ULIS,” Opto-Electronics Rev. 14, 25–32 (2006).
[Crossref]

Proc. SPIE (3)

M. Schardt, A. J. Tremmel, M. S. Rauscher, P. J. Murr, and A. W. Koch, “Spectral bandwidth limitations of static common-path and single-mirror Fourier transform infrared spectrometers,” Proc. SPIE 10210, 102100X (2017).

M. Schardt, C. Schwaller, A. J. Tremmel, and A. W. Koch, “Thermal stabilization of static single-mirror Fourier transform spectrometers,” Proc. SPIE 10210, 102100X (2017).
[Crossref]

P. G. Lucey, K. Horton, T. Williams, K. Hinck, and C. Budney, “SMIFTS: a cryogenically-cooled spatially-modulated imaging infrared interferometer spectrometer,” Proc. SPIE 1937, 130–142 (1993).
[Crossref]

Rev. Sci. Instrum. (1)

M. J. Padgett and A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 519–528 (1995).
[Crossref]

Sensors (1)

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Gas measurement using static Fourier transform infrared spectrometers,” Sensors 17, 2612 (2017).
[Crossref]

SIAM Rev. (1)

L. Greengard and J.-Y. Lee, “Accelerating the nonuniform fast Fourier transform,” SIAM Rev. 46, 443–454 (2004).
[Crossref]

Tech. Mess. (1)

M. H. Köhler, M. Schardt, M. S. Rauscher, and A. W. Koch, “Measurement rates of static single-mirror Fourier transform infrared spectrometers using microbolometer detectors,” Tech. Mess. 84, 144–156 (2017).

Other (2)

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectrometry (Wiley, 2007).

H. Mortimer, “Compact interferometer spectrometer,” U.S. patent9,046,412 (2June2015).

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Figures (12)
Fig. 1.
Fig. 1. Design principle of a static single-mirror Fourier transform spectrometer [10].

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Fig. 2.
Fig. 2. Typical pattern of optical path differences generated by a single-mirror interferometer. The main path difference modulation occurs along the x axis. As indicated, the signal can be averaged along the curved lines of equal optical path difference along the y axis.

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Fig. 3.
Fig. 3. Temperature- and wavelength-dependent virtual source model of a static single-mirror Fourier transform spectrometer.

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Fig. 4.
Fig. 4. (a) Simulation of the Michelson contrast for typical lens-based spectrometer configurations. Solid lines indicate a focal length of 75 mm, dashed lines a focal length of 40 mm. The radius of the light source is set to 1 mm. (b) Simulation of the wavenumber shift due to a changing distance between the virtual sources and a varying focal length of the Fourier lens.

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Fig. 5.
Fig. 5. (a) Top view of the proposed bsFTS. (b) Side view of the proposed bsFTS.

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Fig. 6.
Fig. 6. (a) Simulation of the wavenumber shift due to a changing distance between the virtual sources and a fixed focal length of the spherical mirror. (b) Simulation of the standard deviation of optical path differences imaged onto the 2D detector by a tilted spherical mirror. The off-axis angle is 16° to the y axis.

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Fig. 7.
Fig. 7. Ray-tracing model of the experimental transmission measurement setup.

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Fig. 8.
Fig. 8. Photo of the current laboratory prototype used to carry out the experiments in this paper.

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Fig. 9.
Fig. 9. (a) High-pass-filtered detector image of the background interference pattern recorded with the presented setup. Zoomed to the interferogram midpeak. (b) High-pass-filtered apodized 1D background interferogram averaged over the highlighted 350 pixels in the y direction. The signal is normalized to the maximum peak.

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Fig. 10.
Fig. 10. (a) High-pass-filtered detector image of the polystyrene interference pattern recorded with the presented setup. Zoomed to the interferogram midpeak. (b) High-pass-filtered apodized 1D polystyrene interferogram averaged over the highlighted 350 pixels in the y direction. The signal is normalized to the maximum peak of the background interferogram.

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Fig. 11.
Fig. 11. (a) Measured background spectrum using the presented prototype as well as transmittance curves of the long-pass filter, beam splitter, and microbolometer array influencing the background envelope. (b) Background signal-to-noise ratio of the proposed prototype averaging over 350 pixels in the y direction without time averaging.

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Fig. 12.
Fig. 12. Comparison of the proposed broadband static Fourier transform spectrometer (bsFTS) with a scanning FTIR by measuring a 3 mil polystyrene calibration standard.

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Equations (8)

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I ( x , y ) = ∫ 0 ∞ S ( ν ˜ ) B ( ν ˜ ) ⁢ { 1 + cos ( 2 π ν ˜ ( x s Q f F + Δ x nonlin ( x , y ) ) ) } d ν ˜ .
Δ ν ˜ = 1 OPD max ≥ 2 · ν ˜ max g m · N x .
ν ˜ max ≤ f F 2 · s Q · p pix .
s Q ( λ , T ) = d bs − pm + T bs · ( n s · sin ( π 4 − arcsin ( n s n b s ( λ , T ) · 2 ) ) 1 − ( n s n b s ( λ , T ) · 2 ) 2 ) .
Δ f F ( λ , T ) = f F , des · n des − n ( λ , T ) n ( λ , T ) − 1 .
n ( λ , T ) = ( A + B λ 2 ( λ 2 − C ) + D λ 2 ( λ 2 − E ) ) − 1 / 2 .
ν s ( λ , T ) = f F ( λ , T ) s Q ( λ , T ) · p pix ,
ν ˜ shift = ν ˜ ( 1 − ν s ( λ , T ) ν s , design ) .

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