Abstract

In this paper we study the signal-to-noise ratio degradation in a moving-optical-wedge interferometer when used as an optical spectrometer. Both the mechanical vibration and temperature fluctuation effects are studied, and the effects are compared to their counterparts in a conventional Michelson interferometer. While the wedge interferometer is found to be more immune to linear translational vibration, it shows much higher sensitivity to rotational vibration.

© 2012 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 Spectroscopy, 2nd ed. (Wiley, 2007).
  2. B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” in Proceedings of 2009 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics, Clearwater Beach, Florida, USA, 17–20 August 2009 (IEEE, 2009), pp. 49–50.
  3. T. A. Al-Saeed and D. A. Khalil, “Diffraction effects in optical microelectromechanical system Michelson interferometers,” Appl. Opt. 49, 3960–3966 (2010).
    [CrossRef]
  4. D. Khalil, H. Omran, M. Medhat, and B. Saadany, “Miniaturized tunable integrated Mach–Zehnder MEMS interferometer for spectrometer applications,” Proc. SPIE 7594, 75940T (2010).
    [CrossRef]
  5. Q. Yang, R. Zhou, and B. Zhao, “Principle and analysis of the moving-optical-wedge interferometer,” Appl. Opt. 47, 2186–2191 (2008).
    [CrossRef]
  6. T. Mu, C. Zhang, and B. Zhao, “Analysis of a moderate resolution Fourier transform imaging spectrometer,” Opt. Commun. 282, 1699–1705 (2009).
    [CrossRef]
  7. T. A. Al-Saeed and D. A. Khalil, “Dispersion compensation in moving-optical-wedge Fourier transform spectrometer,” Appl. Opt. 48, 3979–3987 (2009).
    [CrossRef]
  8. A. S. Zachor, “Drive nonlinearities: their effects in Fourier spectroscopy,” Appl. Opt. 16, 1412–1424 (1977).
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    [CrossRef]
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    [CrossRef]
  13. V. Saptari, Fourier-Transform Spectroscopy Instrumentation Engineering, Vol. TT61 of SPIE Tutorial Texts in Optical Engineering (SPIE, 2003).
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    [CrossRef]
  15. T. Hirschfeld, “Quantative FT-IR: a detailed look at the problems involved,” in Fourier Transform Infrared Spectroscopy: Application to Chemical Systems, J. R. Ferraro and L. J. Basile, eds., (Academic, 1979), Vol. 2, pp. 193–242.

2010 (2)

D. Khalil, H. Omran, M. Medhat, and B. Saadany, “Miniaturized tunable integrated Mach–Zehnder MEMS interferometer for spectrometer applications,” Proc. SPIE 7594, 75940T (2010).
[CrossRef]

T. A. Al-Saeed and D. A. Khalil, “Diffraction effects in optical microelectromechanical system Michelson interferometers,” Appl. Opt. 49, 3960–3966 (2010).
[CrossRef]

2009 (2)

T. A. Al-Saeed and D. A. Khalil, “Dispersion compensation in moving-optical-wedge Fourier transform spectrometer,” Appl. Opt. 48, 3979–3987 (2009).
[CrossRef]

T. Mu, C. Zhang, and B. Zhao, “Analysis of a moderate resolution Fourier transform imaging spectrometer,” Opt. Commun. 282, 1699–1705 (2009).
[CrossRef]

2008 (1)

2001 (1)

1999 (1)

1997 (1)

1979 (1)

1977 (1)

1972 (1)

Aaronson, S. M.

Al-Saeed, T. A.

Bell, E. E.

Bourouina, T.

B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” in Proceedings of 2009 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics, Clearwater Beach, Florida, USA, 17–20 August 2009 (IEEE, 2009), pp. 49–50.

Cohen, D. L.

de Haseth, J. A.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectroscopy, 2nd ed. (Wiley, 2007).

Griffiths, P. R.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectroscopy, 2nd ed. (Wiley, 2007).

Hirschfeld, T.

T. Hirschfeld, “Quantative FT-IR: a detailed look at the problems involved,” in Fourier Transform Infrared Spectroscopy: Application to Chemical Systems, J. R. Ferraro and L. J. Basile, eds., (Academic, 1979), Vol. 2, pp. 193–242.

Khalil, D.

D. Khalil, H. Omran, M. Medhat, and B. Saadany, “Miniaturized tunable integrated Mach–Zehnder MEMS interferometer for spectrometer applications,” Proc. SPIE 7594, 75940T (2010).
[CrossRef]

B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” in Proceedings of 2009 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics, Clearwater Beach, Florida, USA, 17–20 August 2009 (IEEE, 2009), pp. 49–50.

Khalil, D. A.

Lastrucci, D.

Marty, F.

B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” in Proceedings of 2009 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics, Clearwater Beach, Florida, USA, 17–20 August 2009 (IEEE, 2009), pp. 49–50.

Medhat, M.

D. Khalil, H. Omran, M. Medhat, and B. Saadany, “Miniaturized tunable integrated Mach–Zehnder MEMS interferometer for spectrometer applications,” Proc. SPIE 7594, 75940T (2010).
[CrossRef]

B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” in Proceedings of 2009 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics, Clearwater Beach, Florida, USA, 17–20 August 2009 (IEEE, 2009), pp. 49–50.

Mu, T.

T. Mu, C. Zhang, and B. Zhao, “Analysis of a moderate resolution Fourier transform imaging spectrometer,” Opt. Commun. 282, 1699–1705 (2009).
[CrossRef]

Omran, H.

D. Khalil, H. Omran, M. Medhat, and B. Saadany, “Miniaturized tunable integrated Mach–Zehnder MEMS interferometer for spectrometer applications,” Proc. SPIE 7594, 75940T (2010).
[CrossRef]

B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” in Proceedings of 2009 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics, Clearwater Beach, Florida, USA, 17–20 August 2009 (IEEE, 2009), pp. 49–50.

Palchetti, L.

Saadany, B.

D. Khalil, H. Omran, M. Medhat, and B. Saadany, “Miniaturized tunable integrated Mach–Zehnder MEMS interferometer for spectrometer applications,” Proc. SPIE 7594, 75940T (2010).
[CrossRef]

B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” in Proceedings of 2009 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics, Clearwater Beach, Florida, USA, 17–20 August 2009 (IEEE, 2009), pp. 49–50.

Sanderson, R. B.

Saptari, V.

V. Saptari, Fourier-Transform Spectroscopy Instrumentation Engineering, Vol. TT61 of SPIE Tutorial Texts in Optical Engineering (SPIE, 2003).

Yang, Q.

Zachor, A. S.

Zhang, C.

T. Mu, C. Zhang, and B. Zhao, “Analysis of a moderate resolution Fourier transform imaging spectrometer,” Opt. Commun. 282, 1699–1705 (2009).
[CrossRef]

Zhao, B.

T. Mu, C. Zhang, and B. Zhao, “Analysis of a moderate resolution Fourier transform imaging spectrometer,” Opt. Commun. 282, 1699–1705 (2009).
[CrossRef]

Q. Yang, R. Zhou, and B. Zhao, “Principle and analysis of the moving-optical-wedge interferometer,” Appl. Opt. 47, 2186–2191 (2008).
[CrossRef]

Zhou, R.

Appl. Opt. (9)

Opt. Commun. (1)

T. Mu, C. Zhang, and B. Zhao, “Analysis of a moderate resolution Fourier transform imaging spectrometer,” Opt. Commun. 282, 1699–1705 (2009).
[CrossRef]

Proc. SPIE (1)

D. Khalil, H. Omran, M. Medhat, and B. Saadany, “Miniaturized tunable integrated Mach–Zehnder MEMS interferometer for spectrometer applications,” Proc. SPIE 7594, 75940T (2010).
[CrossRef]

Other (4)

V. Saptari, Fourier-Transform Spectroscopy Instrumentation Engineering, Vol. TT61 of SPIE Tutorial Texts in Optical Engineering (SPIE, 2003).

T. Hirschfeld, “Quantative FT-IR: a detailed look at the problems involved,” in Fourier Transform Infrared Spectroscopy: Application to Chemical Systems, J. R. Ferraro and L. J. Basile, eds., (Academic, 1979), Vol. 2, pp. 193–242.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectroscopy, 2nd ed. (Wiley, 2007).

B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” in Proceedings of 2009 IEEE/LEOS International Conference on Optical MEMS and Nanophotonics, Clearwater Beach, Florida, USA, 17–20 August 2009 (IEEE, 2009), pp. 49–50.

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Figures (12)

Fig. 1.
Fig. 1.

Conventional Michelson interferometer.

Fig. 2.
Fig. 2.

Moving-optical-wedge interferometer.

Fig. 3.
Fig. 3.

Factor f 1 versus wedge angle for silicon and glass.

Fig. 4.
Fig. 4.

Rotated wedge.

Fig. 5.
Fig. 5.

Comparison of SNR dependence on sampling error, δ = 4000 cm 1 .(a) Our numerical analysis versus the work done in [14] and (b) factor F S for different δ [14].

Fig. 6.
Fig. 6.

SNR for both Michelson and wedge interferometers. The Michelson interferometer and the moving wedge have the same resolution and maximum OPD. (a) Figure showing only horizontal axis from 1 to 50 nm and (b) same figure with logarithmic scale.

Fig. 7.
Fig. 7.

SNR versus temperature fluctuation in wedge interferometer.

Fig. 8.
Fig. 8.

SNR variation in Michelson and wedge interferometers with random position error and random temperature variation ( 20 ° ± 1 ° in one case and 20 ° ± 0.5 ° in the other), keeping the same resolution in both interferometers.

Fig. 9.
Fig. 9.

SNR of Michelson interferometer versus wedge interferometer for different α with random temperature variations around 20 ° ± 1 ° .

Fig. 10.
Fig. 10.

SNR versus position error for three different resolutions in the wedge interferometer. Nearly the same response is obtained.

Fig. 11.
Fig. 11.

Spectra for the ideal case and the case with a random misalignment angle with maximum 1 mrad.

Fig. 12.
Fig. 12.

SNR for the wedge interferometer with a random misalignment angle.

Equations (21)

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I ( x ) = 2 0 B ( σ ) cos 2 π x σ d σ ,
B ( σ ) = 2 0 I ( x ) cos 2 π σ x d x .
Δ 0 = f 0 L = 2 L with f 0 = 2 .
Δ 1 = f 1 L ,
f 1 = 2 sin α · [ n 2 sin 2 α cos α ] ,
N ( σ ) = 1 T b ( σ ) T a ( σ ) ,
N rms = 1 n i = 1 n [ N ( σ i ) ] 2 ,
SNR = 10 log ( 1 N rms ) ,
b = 2 π E [ σ B ( σ ) ] rms ,
( σ B ( σ ) ] rms ) 2 = 1 σ 2 σ 1 σ 1 σ 2 σ 2 B ( σ ) 2 d σ .
B ¯ = 1 σ 2 σ 1 σ 1 σ 2 B ( σ ) d σ .
b / B ¯ = 2 π E F S σ M ,
B ( σ ) = exp [ ( σ σ 0 δ ) 2 ] ,
SNR max = 4 / ( d rms σ max ) .
n 2 ( λ , T ) 1 = i = 1 3 S i ( T ) λ 2 λ 2 λ i 2 ( T ) ,
S i ( T ) = j = 0 4 S i j T j ,
λ i ( T ) = j = 0 4 λ i j T j .
δ ( OPD ) = L f 1 T δ T + f 1 L T δ T ,
L T = X T ,
X T = α th X .
δ ( OPD ) = L f 1 T δ T + f 1 α th X δ T = δ 1 + δ 2 .

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