Abstract

In this paper we propose a modification to the ordinary moving-optical–wedge interferometer used for Fourier transform spectrometry. The ordinary wedge interferometer suffers from asymmetry in the visibility pattern, asymmetry in the interferogram, large volume, large weight, and greater motion of the wedge. Our proposed interferometer is based on using two pair of wedges. This results in symmetry in visibility pattern, symmetry in interferogram, halved size, halved motion, and more throughput.

© 2013 Optical Society of America

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References

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  1. Q. Yang, R. Zhou, and B. Zhaao, “Principle and analysis of the moving-optical-wedge interferometer,” Appl. Opt. 47, 2186–2191 (2008).
    [CrossRef]
  2. T. Mu, C. Zhang, and B. Zhao, “Analysis of a moderate resolution Fourier transform imaging spectrometer,” Opt. Commun. 282, 1699–1705 (2009).
    [CrossRef]
  3. T. A. Al-Saeed and D. A. Khalil, “Dispersion compensation in moving-optical-wedge Fourier transform spectrometer,” Appl. Opt. 48, 3979–3987 (2009).
    [CrossRef]
  4. T. A. Al-Saeed and D. A. Khalil, “Spot size effects in miniaturized moving-optical-wedge interferometer,” Appl. Opt. 50, 2671–2678 (2011).
    [CrossRef]
  5. T. A. Al-Saeed and D. A. Khalil, “Signal-to-noise ratio calculation in a moving-optical-wedge spectrometer,” Appl. Opt. 51, 7206–7213 (2012).
    [CrossRef]
  6. B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” presented at the IEEE LEOS Optical MEMS and Nanophotonics Conference, Clearwater Beach, Fl, 17–20 August2009.
  7. 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]
  8. K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics, 2nd ed. (Springer, 2008), pp. 577–593.

2012

2011

2010

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]

2009

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

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

2008

Al-Saeed, T. A.

Bourouina, T.

B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” presented at the IEEE LEOS Optical MEMS and Nanophotonics Conference, Clearwater Beach, Fl, 17–20 August2009.

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,” presented at the IEEE LEOS Optical MEMS and Nanophotonics Conference, Clearwater Beach, Fl, 17–20 August2009.

Khalil, D. A.

Li, D.

K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics, 2nd ed. (Springer, 2008), pp. 577–593.

Marty, F.

B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” presented at the IEEE LEOS Optical MEMS and Nanophotonics Conference, Clearwater Beach, Fl, 17–20 August2009.

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,” presented at the IEEE LEOS Optical MEMS and Nanophotonics Conference, Clearwater Beach, Fl, 17–20 August2009.

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,” presented at the IEEE LEOS Optical MEMS and Nanophotonics Conference, Clearwater Beach, Fl, 17–20 August2009.

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,” presented at the IEEE LEOS Optical MEMS and Nanophotonics Conference, Clearwater Beach, Fl, 17–20 August2009.

Yang, Q.

Zhaao, B.

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]

Zhang, K.

K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics, 2nd ed. (Springer, 2008), pp. 577–593.

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]

Zhou, R.

Appl. Opt.

Opt. Commun.

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

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

K. Zhang and D. Li, Electromagnetic Theory for Microwaves and Optoelectronics, 2nd ed. (Springer, 2008), pp. 577–593.

B. Saadany, H. Omran, M. Medhat, F. Marty, D. Khalil, and T. Bourouina, “MEMS tunable Michelson interferometer with robust beam splitting architecture,” presented at the IEEE LEOS Optical MEMS and Nanophotonics Conference, Clearwater Beach, Fl, 17–20 August2009.

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Figures (10)

Fig. 1.
Fig. 1.

Asymmetric wedge interferometer.

Fig. 2.
Fig. 2.

Proposed symmetric wedge interferometer.

Fig. 3.
Fig. 3.

q-parameter transformation at oblique incidence at the interface between two media.

Fig. 4.
Fig. 4.

Visibility versus OPD for the asymmetric wedge interferometer and the symmetric one, structure 1. Wavelength=1.5μm; beam waist=15 and 25 μm; detector size is 600μm×600μm.

Fig. 5.
Fig. 5.

Visibility versus detector size for different OPD. Wavelength=1.5μm; beam waist=15μm. We use symmetric structure 2. (a) OPD=750 and 1500μm. (b) OPD=+750 and +1500μm.

Fig. 6.
Fig. 6.

Visibility versus detector size for different spot sizes. Wavelength=1.5μm; beam waists=15 and 25 μm. We use symmetric structure 2. (a) OPD=1000μm. (b) OPD=+1000μm.

Fig. 7.
Fig. 7.

2D plot of intensity at the detector. Wavelength=1.5μm; beam waist=15μm. (a) Asymmetric wedge at OPD=+2000μm. (b) Symmetric wedge at OPD=2000. (c) Symmetric wedge structure 2 at OPD=+2000μm.

Fig. 8.
Fig. 8.

Interferogram for asymmetric wedge and symmetric wedge structure 2. Detector size=20μm×20μm; beamwaist=15μm. (a) Asymmetric wedge. (b) Symmetric wedge. The insets show the interferograms for smaller OPD.

Fig. 9.
Fig. 9.

Source and recovered spectra by asymmetric and symmetric wedge interferometers. We use symmetric structure 2. Detector size=20μm×20μm; beam waist=15μm.

Fig. 10.
Fig. 10.

Error as a function of detector size. We used the two symmetric structures. (a) Beam waist=15μm. (b) Beam waist=25μm.

Equations (20)

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OPD=fL=2sin(α)n2sin2(α)cos(α)L,
OPD+=fLm,
OPD=fLr,
ψ(x,z,y)=jkπ(sxsy4qx(z)qy(z))(exp{jn[kz+kx22qx(z)+ky22qy(z)]}),
qx(z)=(zz0x)+jsx,
qy(z)=(zz0y)+jsy,
sx=12nkw0x2,
sy=12nkw0y2,
qx=qx+d,qy=qy+d,
qy=qyn2n1,
qx=qxn2n1cos2(θt)cos2(θi).
q=js=12jkW02.
A|Em|2dxdy=erf(Dxks2|qxm|)erf(Dyks2|qym|),
A|Er|2dxdy=erf(Dxks2|qxr|)erf(Dyks2|qyr|),
2Re[AEm*Erdxdy]=2Re{2serf(aDx2)erf(bDy2)jqxm*qxrqym*qyrexp(jkfL)},
a=jk2(1qxm*1qxr),
b=jk2(1qym*1qyr).
V=ImaxIminImax+Imin,
B(σ)=exp[(σσ0)2s02]+0.5exp[(σσ1)2s12],
E=|S(σ)B(σ)|2|B(σ)|2,

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