Abstract

In this paper the concept of a microspectrometer based on a Linear Variable Optical Filter (LVOF) for operation in the visible spectrum is presented and used in two different designs: the first is for the narrow spectral band between 610 nm and 680 nm, whereas the other is for the wider spectral band between 570 nm and 740 nm. Design considerations, fabrication and measurement results of the LVOF are presented. An iterative signal processing algorithm based on an initial calibration has been implemented to enhance the spectral resolution. Experimental validation is based on the spectrum of a Neon lamp. The results of measurements have been used to analyze the operating limits of the concept and to explain the sources of error in the algorithm. It is shown that the main benefits of a LVOF-based microspectrometer are in case of implementation in a narrowband application. The realized LVOF microspectrometers show a spectral resolution of 2.2 nm in the wideband design and 0.7 nm in the narrowband design.

© 2011 OSA

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References

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  1. R. F. Wolffenbuttel, “MEMS-based optical mini- and microspectrometers for the visible and infrared spectral range,” J. Micromech. Microeng. 15(7), S145–S152 (2005).
    [CrossRef]
  2. G. Minas, R. F. Wolffenbuttel, and J. H. Correia, “A lab-on-a-chip for spectrophotometric analysis of biological fluids,” Lab Chip 5(11), 1303–1309 (2005).
    [CrossRef] [PubMed]
  3. J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A Phys. 82(1-3), 191–197 (2000).
    [CrossRef]
  4. S. W. Wang, M. Li, C. S. Xia, H. Q. Wang, X. S. Chen, and W. Lu, “128 channels of integrated filter array rapidly fabricated by using the combinatorial deposition technique,” Appl. Phys. B 88(2), 281–284 (2007).
    [CrossRef]
  5. R. R. McLeod and T. Honda, “Improving the spectral resolution of wedged etalons and linear variable filters with incidence angle,” Opt. Lett. 30(19), 2647–2649 (2005).
    [CrossRef] [PubMed]
  6. A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “CMOS-compatible LVOF-based visible microspectrometer,” Proc. SPIE 7680, 76800W (2010).
    [CrossRef]
  7. A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
    [CrossRef]
  8. A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
    [CrossRef]
  9. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed., 360–376 (Cambridge University Press, 1999).
  10. A. Emadi, H. Wu, S. Grabarnik, G. de Graaf, and R. F. Wolffenbuttel, “Vertically tapered layers for optical applications fabricated using resist reflow,” J. Micromech. Microeng. 19(7), 074014 (2009).
    [CrossRef]
  11. A. Emadi, “Linear-variable optical filters for microspectrometer application,” PhD Thesis, Technical University of Delft (2010).
  12. V. Krajicek and M. Vrbova, “Laser-induced fluorescence spectra of plants,” Remote Sens. Environ. 47(1), 51–54 (1994).
    [CrossRef]
  13. K. Burns, K. B. Adams, and J. Longwell, “Interference measurements in the spectra of neon and natural mercury,” J. Opt. Soc. Am. 40(6), 339–344 (1950).
    [CrossRef]
  14. NIST atomic spectra database, Online: http://www.nist.gov/pml/data/asd.cfm
  15. M. P. Wisniewski, R. Z. Morawski, and A. Barwicz, “Algorithms for interpretation of spectrometric data- A comparative study,” Instrumentation and Measurement Technology Conference, 2000. IMTC 2000. Proceedings of the 17th IEEE, 2, 703–706 (2000).
  16. D. Massicotte, R. Z. Morawski, and A. Barwicz, “Kalman-filter-based algorithms of spectrometric data correction-Part I: an iterative algorithm of deconvolution,” IEEE Trans. Instrum. Meas. 46(3), 678–684 (1997).
    [CrossRef]
  17. M. H. Hayes and H. Monson, “Recursive least squares,” in Statistical Digital Signal Processing and Modeling (Wiley, 1996), ch. 9.4.
  18. S. Grabarnik, A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “High-resolution microspectrometer with an aberration-correcting planar grating,” Appl. Opt. 47(34), 6442–6447 (2008).
    [CrossRef] [PubMed]

2010

A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “CMOS-compatible LVOF-based visible microspectrometer,” Proc. SPIE 7680, 76800W (2010).
[CrossRef]

A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
[CrossRef]

2009

A. Emadi, H. Wu, S. Grabarnik, G. de Graaf, and R. F. Wolffenbuttel, “Vertically tapered layers for optical applications fabricated using resist reflow,” J. Micromech. Microeng. 19(7), 074014 (2009).
[CrossRef]

2008

2007

S. W. Wang, M. Li, C. S. Xia, H. Q. Wang, X. S. Chen, and W. Lu, “128 channels of integrated filter array rapidly fabricated by using the combinatorial deposition technique,” Appl. Phys. B 88(2), 281–284 (2007).
[CrossRef]

2005

R. R. McLeod and T. Honda, “Improving the spectral resolution of wedged etalons and linear variable filters with incidence angle,” Opt. Lett. 30(19), 2647–2649 (2005).
[CrossRef] [PubMed]

R. F. Wolffenbuttel, “MEMS-based optical mini- and microspectrometers for the visible and infrared spectral range,” J. Micromech. Microeng. 15(7), S145–S152 (2005).
[CrossRef]

G. Minas, R. F. Wolffenbuttel, and J. H. Correia, “A lab-on-a-chip for spectrophotometric analysis of biological fluids,” Lab Chip 5(11), 1303–1309 (2005).
[CrossRef] [PubMed]

2000

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A Phys. 82(1-3), 191–197 (2000).
[CrossRef]

1997

D. Massicotte, R. Z. Morawski, and A. Barwicz, “Kalman-filter-based algorithms of spectrometric data correction-Part I: an iterative algorithm of deconvolution,” IEEE Trans. Instrum. Meas. 46(3), 678–684 (1997).
[CrossRef]

1994

V. Krajicek and M. Vrbova, “Laser-induced fluorescence spectra of plants,” Remote Sens. Environ. 47(1), 51–54 (1994).
[CrossRef]

1950

Adams, K. B.

Bartek, M.

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A Phys. 82(1-3), 191–197 (2000).
[CrossRef]

Barwicz, A.

D. Massicotte, R. Z. Morawski, and A. Barwicz, “Kalman-filter-based algorithms of spectrometric data correction-Part I: an iterative algorithm of deconvolution,” IEEE Trans. Instrum. Meas. 46(3), 678–684 (1997).
[CrossRef]

Burns, K.

Chen, X. S.

S. W. Wang, M. Li, C. S. Xia, H. Q. Wang, X. S. Chen, and W. Lu, “128 channels of integrated filter array rapidly fabricated by using the combinatorial deposition technique,” Appl. Phys. B 88(2), 281–284 (2007).
[CrossRef]

Correia, J. H.

A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
[CrossRef]

G. Minas, R. F. Wolffenbuttel, and J. H. Correia, “A lab-on-a-chip for spectrophotometric analysis of biological fluids,” Lab Chip 5(11), 1303–1309 (2005).
[CrossRef] [PubMed]

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A Phys. 82(1-3), 191–197 (2000).
[CrossRef]

De Graaf, G.

A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
[CrossRef]

A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “CMOS-compatible LVOF-based visible microspectrometer,” Proc. SPIE 7680, 76800W (2010).
[CrossRef]

A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. de Graaf, and R. F. Wolffenbuttel, “Vertically tapered layers for optical applications fabricated using resist reflow,” J. Micromech. Microeng. 19(7), 074014 (2009).
[CrossRef]

S. Grabarnik, A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “High-resolution microspectrometer with an aberration-correcting planar grating,” Appl. Opt. 47(34), 6442–6447 (2008).
[CrossRef] [PubMed]

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A Phys. 82(1-3), 191–197 (2000).
[CrossRef]

Emadi, A.

A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
[CrossRef]

A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “CMOS-compatible LVOF-based visible microspectrometer,” Proc. SPIE 7680, 76800W (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. de Graaf, and R. F. Wolffenbuttel, “Vertically tapered layers for optical applications fabricated using resist reflow,” J. Micromech. Microeng. 19(7), 074014 (2009).
[CrossRef]

S. Grabarnik, A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “High-resolution microspectrometer with an aberration-correcting planar grating,” Appl. Opt. 47(34), 6442–6447 (2008).
[CrossRef] [PubMed]

Enoksson, P.

A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
[CrossRef]

A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
[CrossRef]

Grabarnik, S.

A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
[CrossRef]

A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. de Graaf, and R. F. Wolffenbuttel, “Vertically tapered layers for optical applications fabricated using resist reflow,” J. Micromech. Microeng. 19(7), 074014 (2009).
[CrossRef]

S. Grabarnik, A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “High-resolution microspectrometer with an aberration-correcting planar grating,” Appl. Opt. 47(34), 6442–6447 (2008).
[CrossRef] [PubMed]

Hedsten, K.

A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
[CrossRef]

Honda, T.

Kong, S. H.

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A Phys. 82(1-3), 191–197 (2000).
[CrossRef]

Krajicek, V.

V. Krajicek and M. Vrbova, “Laser-induced fluorescence spectra of plants,” Remote Sens. Environ. 47(1), 51–54 (1994).
[CrossRef]

Li, M.

S. W. Wang, M. Li, C. S. Xia, H. Q. Wang, X. S. Chen, and W. Lu, “128 channels of integrated filter array rapidly fabricated by using the combinatorial deposition technique,” Appl. Phys. B 88(2), 281–284 (2007).
[CrossRef]

Longwell, J.

Lu, W.

S. W. Wang, M. Li, C. S. Xia, H. Q. Wang, X. S. Chen, and W. Lu, “128 channels of integrated filter array rapidly fabricated by using the combinatorial deposition technique,” Appl. Phys. B 88(2), 281–284 (2007).
[CrossRef]

Massicotte, D.

D. Massicotte, R. Z. Morawski, and A. Barwicz, “Kalman-filter-based algorithms of spectrometric data correction-Part I: an iterative algorithm of deconvolution,” IEEE Trans. Instrum. Meas. 46(3), 678–684 (1997).
[CrossRef]

McLeod, R. R.

Minas, G.

G. Minas, R. F. Wolffenbuttel, and J. H. Correia, “A lab-on-a-chip for spectrophotometric analysis of biological fluids,” Lab Chip 5(11), 1303–1309 (2005).
[CrossRef] [PubMed]

Morawski, R. Z.

D. Massicotte, R. Z. Morawski, and A. Barwicz, “Kalman-filter-based algorithms of spectrometric data correction-Part I: an iterative algorithm of deconvolution,” IEEE Trans. Instrum. Meas. 46(3), 678–684 (1997).
[CrossRef]

Vrbova, M.

V. Krajicek and M. Vrbova, “Laser-induced fluorescence spectra of plants,” Remote Sens. Environ. 47(1), 51–54 (1994).
[CrossRef]

Wang, H. Q.

S. W. Wang, M. Li, C. S. Xia, H. Q. Wang, X. S. Chen, and W. Lu, “128 channels of integrated filter array rapidly fabricated by using the combinatorial deposition technique,” Appl. Phys. B 88(2), 281–284 (2007).
[CrossRef]

Wang, S. W.

S. W. Wang, M. Li, C. S. Xia, H. Q. Wang, X. S. Chen, and W. Lu, “128 channels of integrated filter array rapidly fabricated by using the combinatorial deposition technique,” Appl. Phys. B 88(2), 281–284 (2007).
[CrossRef]

Wolffenbuttel, R. F.

A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
[CrossRef]

A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “CMOS-compatible LVOF-based visible microspectrometer,” Proc. SPIE 7680, 76800W (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. de Graaf, and R. F. Wolffenbuttel, “Vertically tapered layers for optical applications fabricated using resist reflow,” J. Micromech. Microeng. 19(7), 074014 (2009).
[CrossRef]

S. Grabarnik, A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “High-resolution microspectrometer with an aberration-correcting planar grating,” Appl. Opt. 47(34), 6442–6447 (2008).
[CrossRef] [PubMed]

R. F. Wolffenbuttel, “MEMS-based optical mini- and microspectrometers for the visible and infrared spectral range,” J. Micromech. Microeng. 15(7), S145–S152 (2005).
[CrossRef]

G. Minas, R. F. Wolffenbuttel, and J. H. Correia, “A lab-on-a-chip for spectrophotometric analysis of biological fluids,” Lab Chip 5(11), 1303–1309 (2005).
[CrossRef] [PubMed]

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A Phys. 82(1-3), 191–197 (2000).
[CrossRef]

Wu, H.

A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “CMOS-compatible LVOF-based visible microspectrometer,” Proc. SPIE 7680, 76800W (2010).
[CrossRef]

A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. de Graaf, and R. F. Wolffenbuttel, “Vertically tapered layers for optical applications fabricated using resist reflow,” J. Micromech. Microeng. 19(7), 074014 (2009).
[CrossRef]

S. Grabarnik, A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “High-resolution microspectrometer with an aberration-correcting planar grating,” Appl. Opt. 47(34), 6442–6447 (2008).
[CrossRef] [PubMed]

Xia, C. S.

S. W. Wang, M. Li, C. S. Xia, H. Q. Wang, X. S. Chen, and W. Lu, “128 channels of integrated filter array rapidly fabricated by using the combinatorial deposition technique,” Appl. Phys. B 88(2), 281–284 (2007).
[CrossRef]

Appl. Opt.

Appl. Phys. B

S. W. Wang, M. Li, C. S. Xia, H. Q. Wang, X. S. Chen, and W. Lu, “128 channels of integrated filter array rapidly fabricated by using the combinatorial deposition technique,” Appl. Phys. B 88(2), 281–284 (2007).
[CrossRef]

IEEE Trans. Instrum. Meas.

D. Massicotte, R. Z. Morawski, and A. Barwicz, “Kalman-filter-based algorithms of spectrometric data correction-Part I: an iterative algorithm of deconvolution,” IEEE Trans. Instrum. Meas. 46(3), 678–684 (1997).
[CrossRef]

J. Micromech. Microeng.

R. F. Wolffenbuttel, “MEMS-based optical mini- and microspectrometers for the visible and infrared spectral range,” J. Micromech. Microeng. 15(7), S145–S152 (2005).
[CrossRef]

A. Emadi, H. Wu, S. Grabarnik, G. de Graaf, and R. F. Wolffenbuttel, “Vertically tapered layers for optical applications fabricated using resist reflow,” J. Micromech. Microeng. 19(7), 074014 (2009).
[CrossRef]

J. Opt. Soc. Am.

Lab Chip

G. Minas, R. F. Wolffenbuttel, and J. H. Correia, “A lab-on-a-chip for spectrophotometric analysis of biological fluids,” Lab Chip 5(11), 1303–1309 (2005).
[CrossRef] [PubMed]

Opt. Lett.

Proc. SPIE

A. Emadi, H. Wu, G. de Graaf, and R. F. Wolffenbuttel, “CMOS-compatible LVOF-based visible microspectrometer,” Proc. SPIE 7680, 76800W (2010).
[CrossRef]

A. Emadi, S. Grabarnik, H. Wu, G. de Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Spectral measurement using IC-compatible linear variable optical filter,” Proc. SPIE 7716, 77162G (2010).
[CrossRef]

Remote Sens. Environ.

V. Krajicek and M. Vrbova, “Laser-induced fluorescence spectra of plants,” Remote Sens. Environ. 47(1), 51–54 (1994).
[CrossRef]

Sens. Actuators A Phys.

A. Emadi, H. Wu, S. Grabarnik, G. De Graaf, K. Hedsten, P. Enoksson, J. H. Correia, and R. F. Wolffenbuttel, “Fabrication and characterization of IC-compatible linear variable optical filters with application in a micro-spectrometer,” Sens. Actuators A Phys. 162(2), 400–405 (2010).
[CrossRef]

J. H. Correia, G. de Graaf, S. H. Kong, M. Bartek, and R. F. Wolffenbuttel, “Single-chip CMOS optical microspectrometer,” Sens. Actuators A Phys. 82(1-3), 191–197 (2000).
[CrossRef]

Other

A. Emadi, “Linear-variable optical filters for microspectrometer application,” PhD Thesis, Technical University of Delft (2010).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed., 360–376 (Cambridge University Press, 1999).

NIST atomic spectra database, Online: http://www.nist.gov/pml/data/asd.cfm

M. P. Wisniewski, R. Z. Morawski, and A. Barwicz, “Algorithms for interpretation of spectrometric data- A comparative study,” Instrumentation and Measurement Technology Conference, 2000. IMTC 2000. Proceedings of the 17th IEEE, 2, 703–706 (2000).

M. H. Hayes and H. Monson, “Recursive least squares,” in Statistical Digital Signal Processing and Modeling (Wiley, 1996), ch. 9.4.

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Figures (21)

Fig. 1
Fig. 1

A schematic view of a tapered Fabry-Perot type of Linear-variable Optical Filter.

Fig. 2
Fig. 2

Simulated transmission of a FP filter with R = 0.9, n = 1.5 and d = 900 nm. Both FSR and FWHM reduce with increasing resonance order, N.

Fig. 3
Fig. 3

Simulated spectra of LVOF for three values of the cavity thickness.

Fig. 4
Fig. 4

Process flow for fabrication of Linear Variable Optical Filters.

Fig. 5
Fig. 5

Schematic for characterization of Linear Variable Optical Filters.

Fig. 6
Fig. 6

Plotting rows and columns of the calibration matrix, the plot of the m-th column demonstrates the recorded intensity on the detector array for the mth monochromatic wavelength and the plot of nth row demonstrates the spectral response of the nth detector in the array. The surface plot of an ideal calibration matrix is strictly linear.

Fig. 7
Fig. 7

Simulated intensity profiles on the detector for a wideband application, when two resonance peaks of different orders pass light at a particular location of the LVOF.

Fig. 8
Fig. 8

Measured intensity profiles for monochromatic signals with 5nm separation, between 615 and 670nm (black = 615nm, red = 620nm, etc). Note that the entire length consists of two LVOF wedges with the thick parts meeting in the center, resulting in two peaks per wavelength. Also note that the numbers on the vertical axis are digitized pixels output.

Fig. 9
Fig. 9

a) Structure of a LVOF microspectrometer b) Simulated transmission through Fabry-Perot at different angles.

Fig. 10
Fig. 10

LVOF mounted on the CMOS camera together with the C-mount holder for the collimating optics.

Fig. 11
Fig. 11

Surface plot for calibration matrix.

Fig. 12
Fig. 12

Image recorded by the camera with narrowband LVOF illuminated by the Neon lamp.

Fig. 13
Fig. 13

Recorded intensity in the pixels along the AÁ line shown in the middle of the Fig. 12. The number of the pixels increases from the right side of the line to the middle of the image.

Fig. 14
Fig. 14

LMS algorithm finds weighing coefficients in a way that the superposition of the curves converges to the recorded image. Note that channels are N equally spaced pixels in the detector array.

Fig. 15
Fig. 15

a) Comparison between fitted and measured intensity in the channels b) Plot of the final error (difference between the fitted and measured pixels output).

Fig. 16
Fig. 16

Comparison of the spectrum of the Neon lamp that results from the LVOF (solid black line) with a commercially available spectrometer (blue dashed line), arbitrary units are used on the y-axis.

Fig. 17
Fig. 17

Comparison between the spectrum of the Neon lamp calculated from LVOF (solid black line) and measured by a high-resolution grating-based microspectrometer (blue dashed line), arbitrary units are used on y-axis.

Fig. 18
Fig. 18

Image recorded on the camera for LVOF to cover 570 nm – 740 nm for several monochromatic input signals.

Fig. 19
Fig. 19

(a) Recorded image on the LVOF camera and (b) recorded intensity in the pixels along the AÁ shown in the middle of the image. The number of the pixels increases from the right side of the line to the middle of the image.

Fig. 20
Fig. 20

Surface plot for calibration matrix.

Fig. 21
Fig. 21

Comparison between spectrum of the Neon lamp calculated from LVOF (blue solid line) and measured by a commercial spectrometer (black dashed line).

Tables (1)

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Table 1 Layers thicknesses of multilayered UV Linear Variable Filter

Equations (10)

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FSR N = 2nd N(N+1)
f= FSR FWHM = π 2asin(1/ F ) FWH M N = 4ndasin(1/ F ) πN(N+1)
Δλ λ 0 = 4 π asin( n 2 n 1 n 2 + n 1 )
[ d 1 d 2 ... d N ]= [ c 11 c 21 ... c N1 c 12 c 22 ... c N2 ... ... ... ... c 1N c 21 ... c NN ][ I 1 I 2 ... I N ] or D 1N = C NN . I 1N
[ d 1 d 2 ... ... ... d N ]= [ c 11 c 21 ... ... ... c N1 c 12 c 22 ... ... ... c N2 ... ... ... ... ... ... c 1N c 21 ... ... ... c NN ][ 0 0 ... I m =1 ... 0 ][ d 1 d 2 ... d N ]=[ c 1m c 2m ... c Nm ]
E=[ d 1 d 2 ... d N ] [ c 11 c 21 ... c N1 c 12 c 22 ... c N2 ... ... ... ... c 1N c 21 ... c NN ][ I 1 ^ I 2 ^ ... I N ^ ]
E n =dC I ^ n I ^ n+1 = I ^ n +μC E n
f= D 2NA .
d= Dφ NA
[ c 11 c 21 ... c N1 c 12 c 22 ... c N2 ... ... ... ... c 1N c 21 ... c NN ][ I 1 ^ I 2 ^ ... I N ^ ]

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