Abstract

Microfabricated Lamellar grating interferometers (LGI) require fewer components compared to Michelson interferotemeters and offer compact and broadband Fourier transform spectrometers (FTS) with good spectral resolution, high speed and high efficiency. This study presents the fundamental equations that govern the performance and limitations of LGI based FTS systems. Simulations and experiments were conducted to demonstrate and explain the periodic nature of the interferogram envelope due to Talbot image formation. Simulations reveal that the grating period should be chosen large enough to avoid Talbot phase reversal at the expense of mixing of the diffraction orders at the detector. Optimal LGI grating period selection depends on a number of system parameters and requires compromises in spectral resolution and signal-to-bias ratio (SBR) of the interferogram within the spectral range of interest. New analytical equations are derived for spectral resolution and SBR of LGI based FTS systems.

© 2009 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Saptari, “Fourier-Transform Spectroscopy Instrumentation Engineering”, SPIE International Society for Optical Engineering, 2003.
  2. T. Sandner, C. Drabe, H. Schenk, A. Kenda, and W. Scherf, “Translatory MEMS actuators for optical path length modulation in miniaturized Fourier-transform infrared spectrometers,” MEMS MOEMS 7(2), 021006 (2008).
    [CrossRef]
  3. J. Strong and G. A. Vanasse, “Lamellar grating far-infrared interferometer,” J. Opt. Soc. Am. 50(2Issue 2), 113 (1960).
    [CrossRef]
  4. O. Manzardo, R. Michaely, F. Schädelin, W. Noell, T. Overstolz, N. De Rooij, and H. P. Herzig, “Miniature lamellar grating interferometer based on silicon technology,” Opt. Lett. 29(13), 1437–1439 (2004).
    [CrossRef] [PubMed]
  5. C. Ataman, H. Urey, and A. Wolter, “MEMS-based Fourier Transform Spectrometer,” J. Micromechanics and Microengineering 16, 2516–2523 (2006).
  6. J. W. Goodman, Introduction to Fourier Optics, Roberts & Company Publishers, 2005.
  7. C. Ataman, H. Urey, “Compact Fourier Transform Spectrometers using FR4 Platform” SNA: A. Physical, A 151 (2009) 9–16.
  8. R. T. Hall, D. Vrabec, and J. M. Dowling, “A High-Resolution, Far Infrared Double-Beam Lamellar Grating Interferometer,” Appl. Opt. 5(7), (1966).
    [CrossRef] [PubMed]
  9. R. L. Henry and D. B. Tanner, “A Lamellar Grating Interferometer for the Far-Infrared,” Infrared Phys. 19(2), 163–174 (1979).
    [CrossRef]
  10. F. Lee, G. Zhou, H. Yu, and F. S. Chau, “A MEMS-based resonant-scanning lamellar grating Fourier transform micro-spectrometer with laser reference system,” Sens. Actuators A Phys. 149(2), 221–228 (2009).
    [CrossRef]

2009

F. Lee, G. Zhou, H. Yu, and F. S. Chau, “A MEMS-based resonant-scanning lamellar grating Fourier transform micro-spectrometer with laser reference system,” Sens. Actuators A Phys. 149(2), 221–228 (2009).
[CrossRef]

2008

T. Sandner, C. Drabe, H. Schenk, A. Kenda, and W. Scherf, “Translatory MEMS actuators for optical path length modulation in miniaturized Fourier-transform infrared spectrometers,” MEMS MOEMS 7(2), 021006 (2008).
[CrossRef]

2006

C. Ataman, H. Urey, and A. Wolter, “MEMS-based Fourier Transform Spectrometer,” J. Micromechanics and Microengineering 16, 2516–2523 (2006).

2004

1979

R. L. Henry and D. B. Tanner, “A Lamellar Grating Interferometer for the Far-Infrared,” Infrared Phys. 19(2), 163–174 (1979).
[CrossRef]

1966

R. T. Hall, D. Vrabec, and J. M. Dowling, “A High-Resolution, Far Infrared Double-Beam Lamellar Grating Interferometer,” Appl. Opt. 5(7), (1966).
[CrossRef] [PubMed]

1960

Ataman, C.

C. Ataman, H. Urey, and A. Wolter, “MEMS-based Fourier Transform Spectrometer,” J. Micromechanics and Microengineering 16, 2516–2523 (2006).

Chau, F. S.

F. Lee, G. Zhou, H. Yu, and F. S. Chau, “A MEMS-based resonant-scanning lamellar grating Fourier transform micro-spectrometer with laser reference system,” Sens. Actuators A Phys. 149(2), 221–228 (2009).
[CrossRef]

De Rooij, N.

Dowling, J. M.

R. T. Hall, D. Vrabec, and J. M. Dowling, “A High-Resolution, Far Infrared Double-Beam Lamellar Grating Interferometer,” Appl. Opt. 5(7), (1966).
[CrossRef] [PubMed]

Drabe, C.

T. Sandner, C. Drabe, H. Schenk, A. Kenda, and W. Scherf, “Translatory MEMS actuators for optical path length modulation in miniaturized Fourier-transform infrared spectrometers,” MEMS MOEMS 7(2), 021006 (2008).
[CrossRef]

Hall, R. T.

R. T. Hall, D. Vrabec, and J. M. Dowling, “A High-Resolution, Far Infrared Double-Beam Lamellar Grating Interferometer,” Appl. Opt. 5(7), (1966).
[CrossRef] [PubMed]

Henry, R. L.

R. L. Henry and D. B. Tanner, “A Lamellar Grating Interferometer for the Far-Infrared,” Infrared Phys. 19(2), 163–174 (1979).
[CrossRef]

Herzig, H. P.

Kenda, A.

T. Sandner, C. Drabe, H. Schenk, A. Kenda, and W. Scherf, “Translatory MEMS actuators for optical path length modulation in miniaturized Fourier-transform infrared spectrometers,” MEMS MOEMS 7(2), 021006 (2008).
[CrossRef]

Lee, F.

F. Lee, G. Zhou, H. Yu, and F. S. Chau, “A MEMS-based resonant-scanning lamellar grating Fourier transform micro-spectrometer with laser reference system,” Sens. Actuators A Phys. 149(2), 221–228 (2009).
[CrossRef]

Manzardo, O.

Michaely, R.

Noell, W.

Overstolz, T.

Sandner, T.

T. Sandner, C. Drabe, H. Schenk, A. Kenda, and W. Scherf, “Translatory MEMS actuators for optical path length modulation in miniaturized Fourier-transform infrared spectrometers,” MEMS MOEMS 7(2), 021006 (2008).
[CrossRef]

Schädelin, F.

Schenk, H.

T. Sandner, C. Drabe, H. Schenk, A. Kenda, and W. Scherf, “Translatory MEMS actuators for optical path length modulation in miniaturized Fourier-transform infrared spectrometers,” MEMS MOEMS 7(2), 021006 (2008).
[CrossRef]

Scherf, W.

T. Sandner, C. Drabe, H. Schenk, A. Kenda, and W. Scherf, “Translatory MEMS actuators for optical path length modulation in miniaturized Fourier-transform infrared spectrometers,” MEMS MOEMS 7(2), 021006 (2008).
[CrossRef]

Strong, J.

Tanner, D. B.

R. L. Henry and D. B. Tanner, “A Lamellar Grating Interferometer for the Far-Infrared,” Infrared Phys. 19(2), 163–174 (1979).
[CrossRef]

Urey, H.

C. Ataman, H. Urey, and A. Wolter, “MEMS-based Fourier Transform Spectrometer,” J. Micromechanics and Microengineering 16, 2516–2523 (2006).

Vanasse, G. A.

Vrabec, D.

R. T. Hall, D. Vrabec, and J. M. Dowling, “A High-Resolution, Far Infrared Double-Beam Lamellar Grating Interferometer,” Appl. Opt. 5(7), (1966).
[CrossRef] [PubMed]

Wolter, A.

C. Ataman, H. Urey, and A. Wolter, “MEMS-based Fourier Transform Spectrometer,” J. Micromechanics and Microengineering 16, 2516–2523 (2006).

Yu, H.

F. Lee, G. Zhou, H. Yu, and F. S. Chau, “A MEMS-based resonant-scanning lamellar grating Fourier transform micro-spectrometer with laser reference system,” Sens. Actuators A Phys. 149(2), 221–228 (2009).
[CrossRef]

Zhou, G.

F. Lee, G. Zhou, H. Yu, and F. S. Chau, “A MEMS-based resonant-scanning lamellar grating Fourier transform micro-spectrometer with laser reference system,” Sens. Actuators A Phys. 149(2), 221–228 (2009).
[CrossRef]

Appl. Opt.

R. T. Hall, D. Vrabec, and J. M. Dowling, “A High-Resolution, Far Infrared Double-Beam Lamellar Grating Interferometer,” Appl. Opt. 5(7), (1966).
[CrossRef] [PubMed]

Infrared Phys.

R. L. Henry and D. B. Tanner, “A Lamellar Grating Interferometer for the Far-Infrared,” Infrared Phys. 19(2), 163–174 (1979).
[CrossRef]

J. Micromechanics and Microengineering

C. Ataman, H. Urey, and A. Wolter, “MEMS-based Fourier Transform Spectrometer,” J. Micromechanics and Microengineering 16, 2516–2523 (2006).

J. Opt. Soc. Am.

MEMS MOEMS

T. Sandner, C. Drabe, H. Schenk, A. Kenda, and W. Scherf, “Translatory MEMS actuators for optical path length modulation in miniaturized Fourier-transform infrared spectrometers,” MEMS MOEMS 7(2), 021006 (2008).
[CrossRef]

Opt. Lett.

Sens. Actuators A Phys.

F. Lee, G. Zhou, H. Yu, and F. S. Chau, “A MEMS-based resonant-scanning lamellar grating Fourier transform micro-spectrometer with laser reference system,” Sens. Actuators A Phys. 149(2), 221–228 (2009).
[CrossRef]

Other

V. Saptari, “Fourier-Transform Spectroscopy Instrumentation Engineering”, SPIE International Society for Optical Engineering, 2003.

J. W. Goodman, Introduction to Fourier Optics, Roberts & Company Publishers, 2005.

C. Ataman, H. Urey, “Compact Fourier Transform Spectrometers using FR4 Platform” SNA: A. Physical, A 151 (2009) 9–16.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

(a) Cartoon drawing of an LGI based FTS system illustrating IR source, parabolic and elliptic mirrors, LGI, sample plane and IR photodetector. Side view illustrates the moving and fixed fingers (b) Microscope picture of a MEMS LGI fabricated on Silicon wafer. Each grating finger is 1.2 mm long, 70um wide with 5um gap in between [5].

Fig. 2
Fig. 2

Intensity pattern of Talbot (plane II) and phase reversed Talbot (plane I) images created when an amplitude grating is illuminated from top with a plane wave (only fixed grating is shown): (a) COMSOL FEM simulation tool results (b) results of our wave propagation code using scalar diffraction theory.

Fig. 3
Fig. 3

(a) Lamellar grating interferometer with grating period grating deflection d, and top and bottom reflector reflectivities of R 1 and R 2; (b) diffraction calculation algorithm used for the numerical simulations.

Fig. 4
Fig. 4

Far field (observed 15 cm away from LGI for λ = 2.5 um, Λ = 100 um) pattern of a) d = k.λ/2 b) d = λ/4 + k.λ/2 c) = k.λ/2 + λ/8 for all angles between −2.5 and + 2.5 degrees with 0.5 degree intervals. Integration window is illustrated in red.

Fig. 5
Fig. 5

Interferograms and their spectrum for 16 um illumination wavelength, Λ = 50, 100 um and θ d = 0° and θ d = 2.5°. All plots in the same column have the same scale.

Fig. 6
Fig. 6

Interferograms and their spectrum for 16 um illumination wavelength, Λ = 50, 100 um and θ d = 0° and θ d = 2.5°. All plots in the same column have the same scale..

Fig. 7
Fig. 7

Spectral resolution and signal to bias ratio contours for all wavelength and grating period range for a) θ d = 0 and b) θ d = 2.5°.

Fig. 8
Fig. 8

a) An approximate interferogram corresponding to d, λ, and Λ combination. The interferogram envelope is obtained using Talbot phase reversal distance of T where fringe contrast vanishes. b) Corresponding spectrum

Fig. 9
Fig. 9

spectral resolution and signal to bias ratio contours for all wavelength and grating period range, plotted using approximate analytical formulas given in Eq. (12) and Eq. (13).

Fig. 10
Fig. 10

(a) Interferogram obtained from simulation (b) Interferogram obtained from experiment

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

θ d λ min 2 d = Δ k k max
sin ( 2 θ d ) λ min / Λ
Λ > λ max d = λ max 2 Δ k
I ( x ' ) = { [ 0. 5cos ( π x ' / T )   + 0.5 ] . [ 0 .5cos ( 2 π x ' / λ 0 ) ]+0 .5 } r e c t ( x ' / 4 d )
S ( k ) k ~ k 0 = [ 0. 5 δ (k- 1 λ 0 )+0 .25 δ (k+ 1 2 T - 1 λ 0 )+0 .25 δ (k- 1 2 T + 1 λ 0 ) ] * sinc ( 4 d ( k ) )
Δ k = 1 T + 1 2 d

Metrics