Abstract

The resolution of a miniature spectrometer with a multichannel detector is limited by its throughput. A subpixel deconvolution method is proposed to enhance resolution without physically reducing the throughput. The method introduces subpixel reconstruction to overcome undersampling during deconvolution processing. The experimental result has shown a 36.6% reduction in FWHM of spectral lines, indicating the effectiveness of the method.

© 2007 Optical Society of America

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References

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  1. P. Jacquinot, "The luminosity of spectrometers with prisms, gratings, or Fabry-Perot etalons," J. Opt. Soc. Am. A 44, 761-765 (1954).
    [CrossRef]
  2. J. F. James and R. S. Sternberg, The Design of Optical Spectrometers (Chapman and Hall, 1969).
  3. A. P. Thorne, Spectrophysics, 2nd ed. (Chapman and Hall, 1988).
    [CrossRef]
  4. R. W. Esplin, "Use of curved slits to increase throughput of a Hadamard spectrometer," Opt. Eng. 19, 623-627 (1980).
  5. M. Futamata, T. Takenouchi, and K.-I. Katakura, "Highly efficient and aberration-corrected spectrometer for advanced Raman spectroscopy," Appl. Opt. 41, 4655-4665 (2002).
    [CrossRef] [PubMed]
  6. P. A. Jansson, Deconvolution with Applications in Spectroscopy (Academic, 1984).
  7. H. Yang, L. Xu, K. Chen, Q. He, S. He, Q. Tan, and G. Jin, "The effect of the photoelectric detector on the accuracy of the spectrometer," Spectrosc. Spectral Anal. (Beijing) 25, 1520-1523 (2005) (in Chinese).
  8. C. Pernechele, L. Poletto, P. Nicolosi, and G. Naletto, "Spectral resolution improvement technique for a spectrograph mounting a discrete array detector," Opt. Eng. 35, 1503-1510 (1996).
    [CrossRef]
  9. S. S. Young and R. G. Driggers, "Superresolution image reconstruction from a sequence of aliased imagery," Appl. Opt. 45, 5073-5085 (2006).
    [CrossRef] [PubMed]
  10. Z. Mou-yan, Deconvolution and Signal Recovery (National Defence Industry Press, 2001) (in Chinese).
  11. R. A. L. Tolboom, N. J. Dam, H. ter Meulen, J. Mooij, and H. Maassen, "Quantitative imaging through a spectrograph. 1. Principles and theory," Appl. Opt. 43, 5669-5681 (2004).
    [CrossRef] [PubMed]
  12. R. A. L. Tolboom, N. J. Dam, and H. ter Meulen, "Quantitative imaging through a spectrograph. 2. Stoichiometry mapping by Raman scattering," Appl. Opt. 43, 5682-5690 (2004).
    [CrossRef] [PubMed]
  13. R. A. L. Tolboom, N. J. Dam, N. M. Sijtsema, and J. J. ter Meulen, "Quantitative spectrally resolved imaging through a spectrograph," Opt. Lett. 28, 2046-2048 (2003).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

H. Yang, L. Xu, K. Chen, Q. He, S. He, Q. Tan, and G. Jin, "The effect of the photoelectric detector on the accuracy of the spectrometer," Spectrosc. Spectral Anal. (Beijing) 25, 1520-1523 (2005) (in Chinese).

2004 (2)

2003 (1)

2002 (1)

1996 (1)

C. Pernechele, L. Poletto, P. Nicolosi, and G. Naletto, "Spectral resolution improvement technique for a spectrograph mounting a discrete array detector," Opt. Eng. 35, 1503-1510 (1996).
[CrossRef]

1980 (1)

R. W. Esplin, "Use of curved slits to increase throughput of a Hadamard spectrometer," Opt. Eng. 19, 623-627 (1980).

1954 (1)

P. Jacquinot, "The luminosity of spectrometers with prisms, gratings, or Fabry-Perot etalons," J. Opt. Soc. Am. A 44, 761-765 (1954).
[CrossRef]

Chen, K.

H. Yang, L. Xu, K. Chen, Q. He, S. He, Q. Tan, and G. Jin, "The effect of the photoelectric detector on the accuracy of the spectrometer," Spectrosc. Spectral Anal. (Beijing) 25, 1520-1523 (2005) (in Chinese).

Dam, N. J.

Driggers, R. G.

Esplin, R. W.

R. W. Esplin, "Use of curved slits to increase throughput of a Hadamard spectrometer," Opt. Eng. 19, 623-627 (1980).

Futamata, M.

He, Q.

H. Yang, L. Xu, K. Chen, Q. He, S. He, Q. Tan, and G. Jin, "The effect of the photoelectric detector on the accuracy of the spectrometer," Spectrosc. Spectral Anal. (Beijing) 25, 1520-1523 (2005) (in Chinese).

He, S.

H. Yang, L. Xu, K. Chen, Q. He, S. He, Q. Tan, and G. Jin, "The effect of the photoelectric detector on the accuracy of the spectrometer," Spectrosc. Spectral Anal. (Beijing) 25, 1520-1523 (2005) (in Chinese).

Jacquinot, P.

P. Jacquinot, "The luminosity of spectrometers with prisms, gratings, or Fabry-Perot etalons," J. Opt. Soc. Am. A 44, 761-765 (1954).
[CrossRef]

James, J. F.

J. F. James and R. S. Sternberg, The Design of Optical Spectrometers (Chapman and Hall, 1969).

Jansson, P. A.

P. A. Jansson, Deconvolution with Applications in Spectroscopy (Academic, 1984).

Jin, G.

H. Yang, L. Xu, K. Chen, Q. He, S. He, Q. Tan, and G. Jin, "The effect of the photoelectric detector on the accuracy of the spectrometer," Spectrosc. Spectral Anal. (Beijing) 25, 1520-1523 (2005) (in Chinese).

Katakura, K.-I.

Maassen, H.

Mooij, J.

Mou-yan, Z.

Z. Mou-yan, Deconvolution and Signal Recovery (National Defence Industry Press, 2001) (in Chinese).

Naletto, G.

C. Pernechele, L. Poletto, P. Nicolosi, and G. Naletto, "Spectral resolution improvement technique for a spectrograph mounting a discrete array detector," Opt. Eng. 35, 1503-1510 (1996).
[CrossRef]

Nicolosi, P.

C. Pernechele, L. Poletto, P. Nicolosi, and G. Naletto, "Spectral resolution improvement technique for a spectrograph mounting a discrete array detector," Opt. Eng. 35, 1503-1510 (1996).
[CrossRef]

Pernechele, C.

C. Pernechele, L. Poletto, P. Nicolosi, and G. Naletto, "Spectral resolution improvement technique for a spectrograph mounting a discrete array detector," Opt. Eng. 35, 1503-1510 (1996).
[CrossRef]

Poletto, L.

C. Pernechele, L. Poletto, P. Nicolosi, and G. Naletto, "Spectral resolution improvement technique for a spectrograph mounting a discrete array detector," Opt. Eng. 35, 1503-1510 (1996).
[CrossRef]

Sijtsema, N. M.

Sternberg, R. S.

J. F. James and R. S. Sternberg, The Design of Optical Spectrometers (Chapman and Hall, 1969).

Takenouchi, T.

Tan, Q.

H. Yang, L. Xu, K. Chen, Q. He, S. He, Q. Tan, and G. Jin, "The effect of the photoelectric detector on the accuracy of the spectrometer," Spectrosc. Spectral Anal. (Beijing) 25, 1520-1523 (2005) (in Chinese).

ter Meulen, H.

ter Meulen, J. J.

Thorne, A. P.

A. P. Thorne, Spectrophysics, 2nd ed. (Chapman and Hall, 1988).
[CrossRef]

Tolboom, R. A. L.

Xu, L.

H. Yang, L. Xu, K. Chen, Q. He, S. He, Q. Tan, and G. Jin, "The effect of the photoelectric detector on the accuracy of the spectrometer," Spectrosc. Spectral Anal. (Beijing) 25, 1520-1523 (2005) (in Chinese).

Yang, H.

H. Yang, L. Xu, K. Chen, Q. He, S. He, Q. Tan, and G. Jin, "The effect of the photoelectric detector on the accuracy of the spectrometer," Spectrosc. Spectral Anal. (Beijing) 25, 1520-1523 (2005) (in Chinese).

Young, S. S.

Appl. Opt. (4)

J. Opt. Soc. Am. A (1)

P. Jacquinot, "The luminosity of spectrometers with prisms, gratings, or Fabry-Perot etalons," J. Opt. Soc. Am. A 44, 761-765 (1954).
[CrossRef]

Opt. Eng. (2)

R. W. Esplin, "Use of curved slits to increase throughput of a Hadamard spectrometer," Opt. Eng. 19, 623-627 (1980).

C. Pernechele, L. Poletto, P. Nicolosi, and G. Naletto, "Spectral resolution improvement technique for a spectrograph mounting a discrete array detector," Opt. Eng. 35, 1503-1510 (1996).
[CrossRef]

Opt. Lett. (1)

Spectrosc. Spectral Anal. (1)

H. Yang, L. Xu, K. Chen, Q. He, S. He, Q. Tan, and G. Jin, "The effect of the photoelectric detector on the accuracy of the spectrometer," Spectrosc. Spectral Anal. (Beijing) 25, 1520-1523 (2005) (in Chinese).

Other (4)

Z. Mou-yan, Deconvolution and Signal Recovery (National Defence Industry Press, 2001) (in Chinese).

P. A. Jansson, Deconvolution with Applications in Spectroscopy (Academic, 1984).

J. F. James and R. S. Sternberg, The Design of Optical Spectrometers (Chapman and Hall, 1969).

A. P. Thorne, Spectrophysics, 2nd ed. (Chapman and Hall, 1988).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Structure of a typical reflective grating spectrometer: S, entrance slit; M1, collimating mirror; G, plane grating; M2, camera mirror; P, detector plane.

Fig. 2
Fig. 2

Subpixel reconstruction process.

Fig. 3
Fig. 3

(Color online) Subpixel reconstruction at 546 .074   nm : (a) data points of one original frame and the subpixel result and (b) a five-point moving average process to filter the noise.

Fig. 4
Fig. 4

(Color online) Subpixel deconvoluted result at 546 .074   nm .

Fig. 5
Fig. 5

(Color online) Comparison at 576.960 and 579 .066   nm : (a) 40   μm slit, deconvoluted only (one frame); (b) 40   μm slit, subpixel deconvoluted, five frames; (c) 40   μm slit, subpixel deconvoluted, 25 frames; (d) 5   μm slit, subpixel reconstructed only, five frames.

Equations (13)

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t ( x ) = s ( x ) r ( x ) ,
T 0 ( n ) = t ( n × d ) , n = 1 , 2 , 3 , …  , N
T 0 ( n ) = t ( n × d ) ,
T 1 ( n ) = t ( n × d + x 1 ) ,
T m 1 ( n ) = t ( n × d + x 1 + x 2 + + x m 1 ) , n = 1 , 2 , 3 , …  , N ,
T 0 ( n ) = t ( n × d ) ,
T 1 ( n ) = t ( n × d + d / m ) ,
T m 1 ( n ) = t [ n × d + ( m 1 ) × d / m ] , n = 1 , 2 , 3 , …  , N .
T 0 ( 1 ) , T 1 ( 1 ) , …  , T m 1 ( 1 ) , T 0 ( 2 ) , T 1 ( 2 ) , …  , T m 1 ( 2 ) , …  , T 0 ( n ) , T 1 ( n ) , …  , T m 1 ( n ) ,
T ( n ) = t ( n × d / m ) , n = 1 , 2 , 3 , …  , m × N ,
R ( k + 1 ) ( n ) = R ( k ) ( n ) T ( n ) s ( n ) R ( k ) ( n ) ,

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