Abstract

Miniature spectrometers have been drawn researchers much attention due to its wide variety of possible applications. In this paper, we show the achievability of a fine spectrometer on-a-chip based on a low-performance, low-cost filter-array. A low quality filter-array is augmented with digital signal processing techniques. A series of estimators for recovering target spectrum is introduced. By exploiting non-negative nature of spectral content, a non-negative least-square algorithm is found particularly useful for spectrum recovery. The concept is verified in a hardware implementation.

© 2008 Optical Society of America

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References

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  1. C. P. Bacon, Y. Mattley, and R. Defrece, "Miniature spectroscopic instrumentation: applications to biology and chemistry," Rev. Sci. Instrum. 75, 1-16 (2004).
    [CrossRef]
  2. D. C. Heinz, and C.-I Chang, "Fully constrained least-squares linear spectral mixture analysis method for material quantification in hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 39, 529-546 (2001).
    [CrossRef]
  3. O. Manzardo, H. P. Herzig, C. R. Marxer, and N. F. de Rooij, "Miniaturized time-scanning Fourier transform spectrometer based on silicon technology," Opt. Lett. 24, 1705-1707 (1999).
    [CrossRef]
  4. K. Chaganti, I. Salakhutdinov, I. Avrutsky, G. W. Auner, "A simple miniature optical spectrometer with a planar waveguide grating coupler in combination with a plano-convex leng," Opt. Express 14, 4064-4072 (2006).
    [CrossRef] [PubMed]
  5. R. F. Wolffenbuttel, "State-of-the-art in integrated optical microspectrometers," IEEE Trans. Instrum. Meas. 53, 197-202 (2004).
    [CrossRef]
  6. R. Shogenji, Y. Kitamura, K. Yamada, S. Miyatake, and J. Tanida, "Multispectral imaging using compact compound optics," Opt. Express 12, 1643-1655 (2004).
    [CrossRef] [PubMed]
  7. S.-W. Wang, C. Xia, X. Cheng, W. Lu, L. Wang, Y. Wu, and Z. Wang, "Integrated optical filter arrays fabricated by using the combinatorial etching technique," Opt. Lett. 31, 332-334 (2006).
    [CrossRef] [PubMed]
  8. S.-W. Wang, C. Xia, X. Cheng, W. Lu, M. Li, H. Wang, W. Zheng, and T. Zhang, "Concept of a high-resolution miniature spectrometer using an integrated filter array," Opt. Lett. 32, 632-634 (2007).
    [CrossRef] [PubMed]
  9. C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Prentice-Hall, 1974.
  10. J. G. Proakis, Digital Communications, McGraw Hill, 2000.

2007 (1)

2006 (2)

2004 (3)

R. F. Wolffenbuttel, "State-of-the-art in integrated optical microspectrometers," IEEE Trans. Instrum. Meas. 53, 197-202 (2004).
[CrossRef]

R. Shogenji, Y. Kitamura, K. Yamada, S. Miyatake, and J. Tanida, "Multispectral imaging using compact compound optics," Opt. Express 12, 1643-1655 (2004).
[CrossRef] [PubMed]

C. P. Bacon, Y. Mattley, and R. Defrece, "Miniature spectroscopic instrumentation: applications to biology and chemistry," Rev. Sci. Instrum. 75, 1-16 (2004).
[CrossRef]

2001 (1)

D. C. Heinz, and C.-I Chang, "Fully constrained least-squares linear spectral mixture analysis method for material quantification in hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 39, 529-546 (2001).
[CrossRef]

1999 (1)

Auner, G. W.

Avrutsky, I.

Bacon, C. P.

C. P. Bacon, Y. Mattley, and R. Defrece, "Miniature spectroscopic instrumentation: applications to biology and chemistry," Rev. Sci. Instrum. 75, 1-16 (2004).
[CrossRef]

Chaganti, K.

Chang, C.-I

D. C. Heinz, and C.-I Chang, "Fully constrained least-squares linear spectral mixture analysis method for material quantification in hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 39, 529-546 (2001).
[CrossRef]

Cheng, X.

de Rooij, N. F.

Defrece, R.

C. P. Bacon, Y. Mattley, and R. Defrece, "Miniature spectroscopic instrumentation: applications to biology and chemistry," Rev. Sci. Instrum. 75, 1-16 (2004).
[CrossRef]

Heinz, D. C.

D. C. Heinz, and C.-I Chang, "Fully constrained least-squares linear spectral mixture analysis method for material quantification in hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 39, 529-546 (2001).
[CrossRef]

Herzig, H. P.

Kitamura, Y.

Li, M.

Lu, W.

Manzardo, O.

Marxer, C. R.

Mattley, Y.

C. P. Bacon, Y. Mattley, and R. Defrece, "Miniature spectroscopic instrumentation: applications to biology and chemistry," Rev. Sci. Instrum. 75, 1-16 (2004).
[CrossRef]

Miyatake, S.

Salakhutdinov, I.

Shogenji, R.

Tanida, J.

Wang, H.

Wang, L.

Wang, S.-W.

Wang, Z.

Wolffenbuttel, R. F.

R. F. Wolffenbuttel, "State-of-the-art in integrated optical microspectrometers," IEEE Trans. Instrum. Meas. 53, 197-202 (2004).
[CrossRef]

Wu, Y.

Xia, C.

Yamada, K.

Zhang, T.

Zheng, W.

IEEE Trans. Geosci. Remote Sens. (1)

D. C. Heinz, and C.-I Chang, "Fully constrained least-squares linear spectral mixture analysis method for material quantification in hyperspectral imagery," IEEE Trans. Geosci. Remote Sens. 39, 529-546 (2001).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

R. F. Wolffenbuttel, "State-of-the-art in integrated optical microspectrometers," IEEE Trans. Instrum. Meas. 53, 197-202 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Rev. Sci. Instrum. (1)

C. P. Bacon, Y. Mattley, and R. Defrece, "Miniature spectroscopic instrumentation: applications to biology and chemistry," Rev. Sci. Instrum. 75, 1-16 (2004).
[CrossRef]

Other (2)

C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Prentice-Hall, 1974.

J. G. Proakis, Digital Communications, McGraw Hill, 2000.

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Figures (4)

Fig. 1.
Fig. 1.

System structure of the filter-array based spectrometers

Fig. 2.
Fig. 2.

System set-up for DSP implementation

Fig. 3.
Fig. 3.

Sensitivity response of the 1st, 10th, 20th, 30th,and 40th spectral detectors.

Fig. 4.
Fig. 4.

Experimental results for HLMP-4100 red LED, peak at 650nm: (a) spectrum of the LED provided by the manufacturer, (b) spectrum obtained directly from the spectral detector outputs, (c) spectrum obtained after digital-signal-processing (DSP) based on the NNLS algorithm, and (d) spectrum obtained after DSP based on the SVD algorithm.

Equations (7)

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r = Hs + n ,
s ̂ MAP = arg max S P ( s | r ) .
s ̂ ML = arg max S P ( r s ) .
P ( r | s ) = 1 ( 2 π ) N 2 R n 1 2 exp [ 1 2 ( r Hs ) T R n 1 ( r Hs ) ] .
s ̂ ML = ( H T R n 1 H ) 1 H T R n 1 r .
s ̂ LS = ( H T H ) 1 H T r .
s ̂ inv = ( H T H ) 1 H T r = H 1 r .

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