Abstract

A miniaturized FTIR spectrometer based on lamellar grating interferometry is being developed for passive remote-sensing. Consisting of a pair of micro-mirror arrays, the lamellar grating can be fabricated using MEMS technology. This paper describes a method to compute the optical field in the interferometer to optimize the design parameters of the lamellar grating FTIR spectrometer. The lower limit of the micro-mirror width in the grating is related to the formation of a Talbot image in the near field and is estimated to be about 100 μm for the spectrometer to be used for the wavelength range of 7-14 μm. In calculating the far field at the detection window, the conventional Fraunhofer equation is inadequate for detection distance of our application, misleading the upper limit of the micro-mirror width to avoid interference from higher order diffractions. Instead, the far field is described by the unperturbed plane-wave combined with the boundary diffraction wave. As a result, the interference from the higher order diffractions turns out to be negligible as the micro-mirror width increases. Therefore, the upper limit of the micro-mirror width does not need to be set. Under this scheme, the interferometer patterns and their FT spectra are successfully generated.

© 2016 Optical Society of Korea

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  1. R. Harig, “Passive remote sensing of pollutant clouds by Fourier-transform infrared spectrometry: signal-to-noise ratio as a function of spectral resolution,” Appl. Opt. 43, 4603-4610 (2004).
    [Crossref]
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    [Crossref]
  4. P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 267-312 (1960).
    [Crossref]
  5. Refer the following web pages: https://www.technikon.com/projects/former/memfis, http://home.ku.edu.tr/~mems/memfisproject.html, http://cordis.europa.eu/project/rcn/86631_en.html.
  6. J. Strong and G. A. Vanasse, “Lamellar grating far-infrared interferometer,” J. Opt. Soc. Am. 50, 113-118 (1960).
    [Crossref]
  7. O. Manzardo, R. Michaely, F. Schädelin, W. Noell, T. Overstolz, N. D. Rooij, and H. P. Herzig, “Miniature lamellar grating interferometer based on silicon technology,” Opt. Lett. 29, 1437-1439 (2004).
    [Crossref]
  8. Y. Hongbin, Z. Guangya, C. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” Micromech. Microeng. 18, 055016 (2008).
    [Crossref]
  9. W. Shouhua, Y. Hongbin, and C. F. Siong, “A miniaturized lamellar grating based Fourier transform spectrometer with electrostatic actuation,” IEEE Sensors J. 10, 1869-1874 (2010).
    [Crossref]
  10. C. Ataman, H. Urey, and A. Wolter, “A Fourier transform spectrometer using resonant vertical comb actuators,” J. Micromech. Microeng. 16, 2517-2523 (2006).
    [Crossref]
  11. O. Ferhanoglu, H. R. Seren, S. Lüttjohann, and H. Urey, “Lamellar grating optimization for miniaturized fourier transform spectrometers,” Opt. Express 17, 21289-21301 (2009).
    [Crossref]
  12. H. R. Seren, S. Holmstrom, N. P. Ayerden, J. Sharma, and H. Urey, “Lamellar-grating-based MEMS fourier transform spectrometer,” J. Microelectrochem. Sys. 21, 331-339 (2012).
    [Crossref]
  13. N. P. Ayerden, U. Aygun, S. T. S. Holmstrom, S. Olcer, B. Can, J.-L. Stehle, and H. Urey, “High-speed broadband FTIR system using MEMS,” Appl. Opt. 53, 7267-7272 (2014).
    [Crossref]
  14. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, Englewood, CO, USA, 2005).
  15. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).
  16. H. F. Talbot, “Facts relating to optical science No. IV,” Philos. Mag. Ser. III, 9, No. 56 (1836).
  17. G. A. Maggi, “Sulla propagazione libera e perturbata delle onde luminose in mezzo isotropo,” Ann. di Math. IIa 16, 21-48 (1888).
  18. A. Rubinowicz, “Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen,” Ann. Physik, 53, 257-278 (1917).
  19. J. B. Keller, “Geometrical theory of diffraction,” J. Opt. Soc. Am. 52, 116-130 (1962).
    [Crossref]
  20. S. Ganci, “Boundary diffraction wave theory of Rubinowicz for rectilinear apertures,” Eur. J. Phys 18. 229-236 (1997).
    [Crossref]
  21. U. Yalҫin, “Uniform scattered fields of the extended theory of boundary diffraction wave for PEC surfaces,” Prog. Electromag. Res. 7, 29-39 (2009).
    [Crossref]
  22. S. Wang, “On principles of diffraction,” Optik, 100, 107-108 (1995).
  23. J. H. Hannay, “Fresnel diffraction as an aperture edge integral,” J. Mod. Opt. 47, 121-124 (2000).
    [Crossref]
  24. Y. Z. Umul, “Uniform boundary diffraction wave theory of Rubinowicz,” J. Opt. Soc. Am. A. 27, 1613-1619 (2010).
    [Crossref]
  25. R. Borghi, “Uniform asymptotics of paraxial boundary diffraction wave,” J. Opt. Soc. Am. A. 32, 685-696 (2015).
  26. S. Anokhov, “On problem of the rigorous diffraction quantitative description,” Semicon. Phys. Quant. Elect. Optoelec. 2, 66-69 (1999).
  27. R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction as an interference phenomenon: an experimental reality”, Opt. Laser Tech. 39, 256-261(2007).
    [Crossref]

2015 (1)

R. Borghi, “Uniform asymptotics of paraxial boundary diffraction wave,” J. Opt. Soc. Am. A. 32, 685-696 (2015).

2014 (1)

2012 (1)

H. R. Seren, S. Holmstrom, N. P. Ayerden, J. Sharma, and H. Urey, “Lamellar-grating-based MEMS fourier transform spectrometer,” J. Microelectrochem. Sys. 21, 331-339 (2012).
[Crossref]

2010 (2)

W. Shouhua, Y. Hongbin, and C. F. Siong, “A miniaturized lamellar grating based Fourier transform spectrometer with electrostatic actuation,” IEEE Sensors J. 10, 1869-1874 (2010).
[Crossref]

Y. Z. Umul, “Uniform boundary diffraction wave theory of Rubinowicz,” J. Opt. Soc. Am. A. 27, 1613-1619 (2010).
[Crossref]

2009 (2)

U. Yalҫin, “Uniform scattered fields of the extended theory of boundary diffraction wave for PEC surfaces,” Prog. Electromag. Res. 7, 29-39 (2009).
[Crossref]

O. Ferhanoglu, H. R. Seren, S. Lüttjohann, and H. Urey, “Lamellar grating optimization for miniaturized fourier transform spectrometers,” Opt. Express 17, 21289-21301 (2009).
[Crossref]

2008 (1)

Y. Hongbin, Z. Guangya, C. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” Micromech. Microeng. 18, 055016 (2008).
[Crossref]

2007 (1)

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction as an interference phenomenon: an experimental reality”, Opt. Laser Tech. 39, 256-261(2007).
[Crossref]

2006 (1)

C. Ataman, H. Urey, and A. Wolter, “A Fourier transform spectrometer using resonant vertical comb actuators,” J. Micromech. Microeng. 16, 2517-2523 (2006).
[Crossref]

2004 (2)

2000 (1)

J. H. Hannay, “Fresnel diffraction as an aperture edge integral,” J. Mod. Opt. 47, 121-124 (2000).
[Crossref]

1999 (1)

S. Anokhov, “On problem of the rigorous diffraction quantitative description,” Semicon. Phys. Quant. Elect. Optoelec. 2, 66-69 (1999).

1997 (1)

S. Ganci, “Boundary diffraction wave theory of Rubinowicz for rectilinear apertures,” Eur. J. Phys 18. 229-236 (1997).
[Crossref]

1995 (1)

S. Wang, “On principles of diffraction,” Optik, 100, 107-108 (1995).

1962 (1)

1960 (2)

J. Strong and G. A. Vanasse, “Lamellar grating far-infrared interferometer,” J. Opt. Soc. Am. 50, 113-118 (1960).
[Crossref]

P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 267-312 (1960).
[Crossref]

1949 (1)

1917 (1)

A. Rubinowicz, “Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen,” Ann. Physik, 53, 257-278 (1917).

1888 (1)

G. A. Maggi, “Sulla propagazione libera e perturbata delle onde luminose in mezzo isotropo,” Ann. di Math. IIa 16, 21-48 (1888).

1836 (1)

H. F. Talbot, “Facts relating to optical science No. IV,” Philos. Mag. Ser. III, 9, No. 56 (1836).

Aggarwal, A. K.

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction as an interference phenomenon: an experimental reality”, Opt. Laser Tech. 39, 256-261(2007).
[Crossref]

Anokhov, S.

S. Anokhov, “On problem of the rigorous diffraction quantitative description,” Semicon. Phys. Quant. Elect. Optoelec. 2, 66-69 (1999).

Ataman, C.

C. Ataman, H. Urey, and A. Wolter, “A Fourier transform spectrometer using resonant vertical comb actuators,” J. Micromech. Microeng. 16, 2517-2523 (2006).
[Crossref]

Ayerden, N. P.

N. P. Ayerden, U. Aygun, S. T. S. Holmstrom, S. Olcer, B. Can, J.-L. Stehle, and H. Urey, “High-speed broadband FTIR system using MEMS,” Appl. Opt. 53, 7267-7272 (2014).
[Crossref]

H. R. Seren, S. Holmstrom, N. P. Ayerden, J. Sharma, and H. Urey, “Lamellar-grating-based MEMS fourier transform spectrometer,” J. Microelectrochem. Sys. 21, 331-339 (2012).
[Crossref]

Aygun, U.

Borghi, R.

R. Borghi, “Uniform asymptotics of paraxial boundary diffraction wave,” J. Opt. Soc. Am. A. 32, 685-696 (2015).

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).

Can, B.

Chhachhia, D. P.

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction as an interference phenomenon: an experimental reality”, Opt. Laser Tech. 39, 256-261(2007).
[Crossref]

de Haseth, J. A.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectroscopy, 2nd ed., (John Wiley & Sons, Inc., New York, NY, USA, 2007).

Feiwen, L.

Y. Hongbin, Z. Guangya, C. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” Micromech. Microeng. 18, 055016 (2008).
[Crossref]

Fellgett, P. B.

Ferhanoglu, O.

Ganci, S.

S. Ganci, “Boundary diffraction wave theory of Rubinowicz for rectilinear apertures,” Eur. J. Phys 18. 229-236 (1997).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, Englewood, CO, USA, 2005).

Griffiths, P. R.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectroscopy, 2nd ed., (John Wiley & Sons, Inc., New York, NY, USA, 2007).

Guangya, Z.

Y. Hongbin, Z. Guangya, C. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” Micromech. Microeng. 18, 055016 (2008).
[Crossref]

Hannay, J. H.

J. H. Hannay, “Fresnel diffraction as an aperture edge integral,” J. Mod. Opt. 47, 121-124 (2000).
[Crossref]

Harig, R.

Herzig, H. P.

Holmstrom, S.

H. R. Seren, S. Holmstrom, N. P. Ayerden, J. Sharma, and H. Urey, “Lamellar-grating-based MEMS fourier transform spectrometer,” J. Microelectrochem. Sys. 21, 331-339 (2012).
[Crossref]

Holmstrom, S. T. S.

Hongbin, Y.

W. Shouhua, Y. Hongbin, and C. F. Siong, “A miniaturized lamellar grating based Fourier transform spectrometer with electrostatic actuation,” IEEE Sensors J. 10, 1869-1874 (2010).
[Crossref]

Y. Hongbin, Z. Guangya, C. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” Micromech. Microeng. 18, 055016 (2008).
[Crossref]

Jacquinot, P.

P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 267-312 (1960).
[Crossref]

Kaura, S. K.

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction as an interference phenomenon: an experimental reality”, Opt. Laser Tech. 39, 256-261(2007).
[Crossref]

Keller, J. B.

Kumar, R.

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction as an interference phenomenon: an experimental reality”, Opt. Laser Tech. 39, 256-261(2007).
[Crossref]

Lüttjohann, S.

Maggi, G. A.

G. A. Maggi, “Sulla propagazione libera e perturbata delle onde luminose in mezzo isotropo,” Ann. di Math. IIa 16, 21-48 (1888).

Manzardo, O.

Michaely, R.

Mingsheng, Z.

Y. Hongbin, Z. Guangya, C. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” Micromech. Microeng. 18, 055016 (2008).
[Crossref]

Noell, W.

Olcer, S.

Overstolz, T.

Rooij, N. D.

Rubinowicz, A.

A. Rubinowicz, “Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen,” Ann. Physik, 53, 257-278 (1917).

Schädelin, F.

Seren, H. R.

H. R. Seren, S. Holmstrom, N. P. Ayerden, J. Sharma, and H. Urey, “Lamellar-grating-based MEMS fourier transform spectrometer,” J. Microelectrochem. Sys. 21, 331-339 (2012).
[Crossref]

O. Ferhanoglu, H. R. Seren, S. Lüttjohann, and H. Urey, “Lamellar grating optimization for miniaturized fourier transform spectrometers,” Opt. Express 17, 21289-21301 (2009).
[Crossref]

Sharma, A. K.

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction as an interference phenomenon: an experimental reality”, Opt. Laser Tech. 39, 256-261(2007).
[Crossref]

Sharma, J.

H. R. Seren, S. Holmstrom, N. P. Ayerden, J. Sharma, and H. Urey, “Lamellar-grating-based MEMS fourier transform spectrometer,” J. Microelectrochem. Sys. 21, 331-339 (2012).
[Crossref]

Shouhua, W.

W. Shouhua, Y. Hongbin, and C. F. Siong, “A miniaturized lamellar grating based Fourier transform spectrometer with electrostatic actuation,” IEEE Sensors J. 10, 1869-1874 (2010).
[Crossref]

Y. Hongbin, Z. Guangya, C. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” Micromech. Microeng. 18, 055016 (2008).
[Crossref]

Siong, C. F.

W. Shouhua, Y. Hongbin, and C. F. Siong, “A miniaturized lamellar grating based Fourier transform spectrometer with electrostatic actuation,” IEEE Sensors J. 10, 1869-1874 (2010).
[Crossref]

Y. Hongbin, Z. Guangya, C. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” Micromech. Microeng. 18, 055016 (2008).
[Crossref]

Stehle, J.-L.

Strong, J.

Talbot, H. F.

H. F. Talbot, “Facts relating to optical science No. IV,” Philos. Mag. Ser. III, 9, No. 56 (1836).

Umul, Y. Z.

Y. Z. Umul, “Uniform boundary diffraction wave theory of Rubinowicz,” J. Opt. Soc. Am. A. 27, 1613-1619 (2010).
[Crossref]

Urey, H.

N. P. Ayerden, U. Aygun, S. T. S. Holmstrom, S. Olcer, B. Can, J.-L. Stehle, and H. Urey, “High-speed broadband FTIR system using MEMS,” Appl. Opt. 53, 7267-7272 (2014).
[Crossref]

H. R. Seren, S. Holmstrom, N. P. Ayerden, J. Sharma, and H. Urey, “Lamellar-grating-based MEMS fourier transform spectrometer,” J. Microelectrochem. Sys. 21, 331-339 (2012).
[Crossref]

O. Ferhanoglu, H. R. Seren, S. Lüttjohann, and H. Urey, “Lamellar grating optimization for miniaturized fourier transform spectrometers,” Opt. Express 17, 21289-21301 (2009).
[Crossref]

C. Ataman, H. Urey, and A. Wolter, “A Fourier transform spectrometer using resonant vertical comb actuators,” J. Micromech. Microeng. 16, 2517-2523 (2006).
[Crossref]

Vanasse, G. A.

Wang, S.

S. Wang, “On principles of diffraction,” Optik, 100, 107-108 (1995).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).

Wolter, A.

C. Ataman, H. Urey, and A. Wolter, “A Fourier transform spectrometer using resonant vertical comb actuators,” J. Micromech. Microeng. 16, 2517-2523 (2006).
[Crossref]

Yal?in, U.

U. Yalҫin, “Uniform scattered fields of the extended theory of boundary diffraction wave for PEC surfaces,” Prog. Electromag. Res. 7, 29-39 (2009).
[Crossref]

Ann. di Math. IIa (1)

G. A. Maggi, “Sulla propagazione libera e perturbata delle onde luminose in mezzo isotropo,” Ann. di Math. IIa 16, 21-48 (1888).

Ann. Physik (1)

A. Rubinowicz, “Die Beugungswelle in der Kirchhoffschen Theorie der Beugungserscheinungen,” Ann. Physik, 53, 257-278 (1917).

Appl. Opt. (2)

Eur. J. Phys. (1)

S. Ganci, “Boundary diffraction wave theory of Rubinowicz for rectilinear apertures,” Eur. J. Phys 18. 229-236 (1997).
[Crossref]

IEEE Sensors J. (1)

W. Shouhua, Y. Hongbin, and C. F. Siong, “A miniaturized lamellar grating based Fourier transform spectrometer with electrostatic actuation,” IEEE Sensors J. 10, 1869-1874 (2010).
[Crossref]

J. Microelectrochem. Sys. (1)

H. R. Seren, S. Holmstrom, N. P. Ayerden, J. Sharma, and H. Urey, “Lamellar-grating-based MEMS fourier transform spectrometer,” J. Microelectrochem. Sys. 21, 331-339 (2012).
[Crossref]

J. Micromech. Microeng. (1)

C. Ataman, H. Urey, and A. Wolter, “A Fourier transform spectrometer using resonant vertical comb actuators,” J. Micromech. Microeng. 16, 2517-2523 (2006).
[Crossref]

J. Mod. Opt. (1)

J. H. Hannay, “Fresnel diffraction as an aperture edge integral,” J. Mod. Opt. 47, 121-124 (2000).
[Crossref]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A. (2)

Y. Z. Umul, “Uniform boundary diffraction wave theory of Rubinowicz,” J. Opt. Soc. Am. A. 27, 1613-1619 (2010).
[Crossref]

R. Borghi, “Uniform asymptotics of paraxial boundary diffraction wave,” J. Opt. Soc. Am. A. 32, 685-696 (2015).

Micromech. Microeng. (1)

Y. Hongbin, Z. Guangya, C. F. Siong, L. Feiwen, W. Shouhua, and Z. Mingsheng, “An electromagnetically driven lamellar grating based Fourier transform microspectrometer,” Micromech. Microeng. 18, 055016 (2008).
[Crossref]

Opt. Express (1)

Opt. Laser Tech. (1)

R. Kumar, S. K. Kaura, A. K. Sharma, D. P. Chhachhia, and A. K. Aggarwal, “Knife-edge diffraction as an interference phenomenon: an experimental reality”, Opt. Laser Tech. 39, 256-261(2007).
[Crossref]

Opt. Lett. (1)

Optik (1)

S. Wang, “On principles of diffraction,” Optik, 100, 107-108 (1995).

Philos. Mag. Ser. III (1)

H. F. Talbot, “Facts relating to optical science No. IV,” Philos. Mag. Ser. III, 9, No. 56 (1836).

Prog. Electromag. Res. (1)

U. Yalҫin, “Uniform scattered fields of the extended theory of boundary diffraction wave for PEC surfaces,” Prog. Electromag. Res. 7, 29-39 (2009).
[Crossref]

Rep. Prog. Phys. (1)

P. Jacquinot, “New developments in interference spectroscopy,” Rep. Prog. Phys. 23, 267-312 (1960).
[Crossref]

Semicon. Phys. Quant. Elect. Optoelec. (1)

S. Anokhov, “On problem of the rigorous diffraction quantitative description,” Semicon. Phys. Quant. Elect. Optoelec. 2, 66-69 (1999).

Other (4)

Refer the following web pages: https://www.technikon.com/projects/former/memfis, http://home.ku.edu.tr/~mems/memfisproject.html, http://cordis.europa.eu/project/rcn/86631_en.html.

P. R. Griffiths and J. A. de Haseth, Fourier Transform Infrared Spectroscopy, 2nd ed., (John Wiley & Sons, Inc., New York, NY, USA, 2007).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company Publishers, Englewood, CO, USA, 2005).

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, Cambridge, UK, 1999).

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