Abstract

We replace the traditional grating used in a dispersive spectrometer with a multiplex holographic grating to increase the spectral range sensed by the instrument. The multiplexed grating allows us to measure three different, overlapping spectral bands on a color digital focal plane. The detector's broadband color filters, along with a computational inversion algorithm, let us disambiguate measurements made from the three bands. The overlapping spectral bands allow us to measure a greater spectral bandwidth than a traditional spectrometer with the same sized detector. Additionally, our spectrometer uses a static coded aperture mask in the place of a slit. The aperture mask allows increased light throughput, offsetting the photon loss at the broadband filters. We present our proof-of-concept dispersion multiplexing spectrometer design with experimental measurements to verify its operation.

© 2007 Optical Society of America

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  1. H. Owen, D. E. Battey, M. J. Pelletier, and J. B. Slater, "New spectroscopic instrument based on volume holographic optical elements," in Proc. SPIE 2406, 260-267 (1995).
  2. D. J. Brady, "Multiplex sensors and the constant radiance theorem," Opt. Lett. 27, 16-18 (2002).
    [CrossRef]
  3. S. D. Schwab and R. L. McCreery, "Versatile, efficient Raman sampling with fiber optics," Anal. Chem. 56, 2199-2204 (1984).
    [CrossRef]
  4. J. Zhao, "Image curvature correction and cosmic removal for high-throughput dispersive Raman spectroscopy," Appl. Spectrosc. 57, 1368-1375 (2003).
    [CrossRef] [PubMed]
  5. M. J. E. Golay, "Multi-slit spectrometry," J. Opt. Soc. Am. 39, 437-444 (1949).
    [CrossRef] [PubMed]
  6. A. Girard, "Spectrometre a grilles," Appl. Opt. 2, 79-87 (1963).
    [CrossRef]
  7. R. N. Ibbett, D. Aspinall, and J. F. Grainger, "Real-time multiplexing of dispersed spectra in any wavelength region," Appl. Opt. 7, 1089-1094 (1968).
    [CrossRef] [PubMed]
  8. M. O. Harwitt and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).
  9. A. Wuttig and R. Riesenberg, "Sensitive Hadamard transform imaging spectrometer with a simple MEMS," in Proc. SPIE 4881, 167-178 (2002).
    [CrossRef]
  10. Q. S. Hanley, P. J. Verveer, and T. M. Jovin, "Spectral imaging in a programmable array microscope by Hadamard transform fluorescence spectroscopy," Appl. Spectrosc. 53, 1-10 (1999).
    [CrossRef]
  11. M. E. Gehm, S. T. McCain, N. P. Pitsiantis, D. J. Brady, P. Potuluri, and M. E. Sullivan, "Static 2D aperture coding for multimodal multiplex spectroscopy," Appl. Opt. 54, 2965-2974 (2006).
    [CrossRef]
  12. A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications (Springer-Verlag, 1999).
  13. D. J. Schroeder, Astronomical Optics (Academic, 1987).
  14. S. T. McCain, M. E. Gehm, Y. Wang, N. P. Pitsianis, and D. J. Brady, "Coded aperture Raman spectroscopy for quantitative measurements of ethanol in a tissue phantom," Appl. Spectrosc. 60, 663-671 (2006).
    [CrossRef] [PubMed]
  15. HoloPlex Holographic Transmission Grating, Technical Rep. 1201 (Kaiser Optical Systems, Inc., 2001).
  16. B. E. Bayer, "Color imaging array," U.S. patent 3,971,065 (20 July 1976).
  17. G. Barbastathis and D. Psaltis, Volume Holographic Multiplexing Methods (Springer, 2000), pp. 21-59.
  18. H. Kogelnik, "Coupled wave theory for thick hologram grating," Bell Syst. Tech. J. 48, 2909-2948 (1969).

2006

M. E. Gehm, S. T. McCain, N. P. Pitsiantis, D. J. Brady, P. Potuluri, and M. E. Sullivan, "Static 2D aperture coding for multimodal multiplex spectroscopy," Appl. Opt. 54, 2965-2974 (2006).
[CrossRef]

S. T. McCain, M. E. Gehm, Y. Wang, N. P. Pitsianis, and D. J. Brady, "Coded aperture Raman spectroscopy for quantitative measurements of ethanol in a tissue phantom," Appl. Spectrosc. 60, 663-671 (2006).
[CrossRef] [PubMed]

2003

2002

D. J. Brady, "Multiplex sensors and the constant radiance theorem," Opt. Lett. 27, 16-18 (2002).
[CrossRef]

A. Wuttig and R. Riesenberg, "Sensitive Hadamard transform imaging spectrometer with a simple MEMS," in Proc. SPIE 4881, 167-178 (2002).
[CrossRef]

1999

1995

H. Owen, D. E. Battey, M. J. Pelletier, and J. B. Slater, "New spectroscopic instrument based on volume holographic optical elements," in Proc. SPIE 2406, 260-267 (1995).

1984

S. D. Schwab and R. L. McCreery, "Versatile, efficient Raman sampling with fiber optics," Anal. Chem. 56, 2199-2204 (1984).
[CrossRef]

1969

H. Kogelnik, "Coupled wave theory for thick hologram grating," Bell Syst. Tech. J. 48, 2909-2948 (1969).

1968

1963

1949

Aspinall, D.

Barbastathis, G.

G. Barbastathis and D. Psaltis, Volume Holographic Multiplexing Methods (Springer, 2000), pp. 21-59.

Battey, D. E.

H. Owen, D. E. Battey, M. J. Pelletier, and J. B. Slater, "New spectroscopic instrument based on volume holographic optical elements," in Proc. SPIE 2406, 260-267 (1995).

Bayer, B. E.

B. E. Bayer, "Color imaging array," U.S. patent 3,971,065 (20 July 1976).

Brady, D. J.

Gehm, M. E.

M. E. Gehm, S. T. McCain, N. P. Pitsiantis, D. J. Brady, P. Potuluri, and M. E. Sullivan, "Static 2D aperture coding for multimodal multiplex spectroscopy," Appl. Opt. 54, 2965-2974 (2006).
[CrossRef]

S. T. McCain, M. E. Gehm, Y. Wang, N. P. Pitsianis, and D. J. Brady, "Coded aperture Raman spectroscopy for quantitative measurements of ethanol in a tissue phantom," Appl. Spectrosc. 60, 663-671 (2006).
[CrossRef] [PubMed]

Girard, A.

Golay, M. J. E.

Grainger, J. F.

Hanley, Q. S.

Harwitt, M. O.

M. O. Harwitt and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

Hedayat, A. S.

A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications (Springer-Verlag, 1999).

Ibbett, R. N.

Jovin, T. M.

Kogelnik, H.

H. Kogelnik, "Coupled wave theory for thick hologram grating," Bell Syst. Tech. J. 48, 2909-2948 (1969).

McCain, S. T.

M. E. Gehm, S. T. McCain, N. P. Pitsiantis, D. J. Brady, P. Potuluri, and M. E. Sullivan, "Static 2D aperture coding for multimodal multiplex spectroscopy," Appl. Opt. 54, 2965-2974 (2006).
[CrossRef]

S. T. McCain, M. E. Gehm, Y. Wang, N. P. Pitsianis, and D. J. Brady, "Coded aperture Raman spectroscopy for quantitative measurements of ethanol in a tissue phantom," Appl. Spectrosc. 60, 663-671 (2006).
[CrossRef] [PubMed]

McCreery, R. L.

S. D. Schwab and R. L. McCreery, "Versatile, efficient Raman sampling with fiber optics," Anal. Chem. 56, 2199-2204 (1984).
[CrossRef]

Owen, H.

H. Owen, D. E. Battey, M. J. Pelletier, and J. B. Slater, "New spectroscopic instrument based on volume holographic optical elements," in Proc. SPIE 2406, 260-267 (1995).

Pelletier, M. J.

H. Owen, D. E. Battey, M. J. Pelletier, and J. B. Slater, "New spectroscopic instrument based on volume holographic optical elements," in Proc. SPIE 2406, 260-267 (1995).

Pitsianis, N. P.

Pitsiantis, N. P.

M. E. Gehm, S. T. McCain, N. P. Pitsiantis, D. J. Brady, P. Potuluri, and M. E. Sullivan, "Static 2D aperture coding for multimodal multiplex spectroscopy," Appl. Opt. 54, 2965-2974 (2006).
[CrossRef]

Potuluri, P.

M. E. Gehm, S. T. McCain, N. P. Pitsiantis, D. J. Brady, P. Potuluri, and M. E. Sullivan, "Static 2D aperture coding for multimodal multiplex spectroscopy," Appl. Opt. 54, 2965-2974 (2006).
[CrossRef]

Psaltis, D.

G. Barbastathis and D. Psaltis, Volume Holographic Multiplexing Methods (Springer, 2000), pp. 21-59.

Riesenberg, R.

A. Wuttig and R. Riesenberg, "Sensitive Hadamard transform imaging spectrometer with a simple MEMS," in Proc. SPIE 4881, 167-178 (2002).
[CrossRef]

Schroeder, D. J.

D. J. Schroeder, Astronomical Optics (Academic, 1987).

Schwab, S. D.

S. D. Schwab and R. L. McCreery, "Versatile, efficient Raman sampling with fiber optics," Anal. Chem. 56, 2199-2204 (1984).
[CrossRef]

Slater, J. B.

H. Owen, D. E. Battey, M. J. Pelletier, and J. B. Slater, "New spectroscopic instrument based on volume holographic optical elements," in Proc. SPIE 2406, 260-267 (1995).

Sloane, N. J. A.

M. O. Harwitt and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications (Springer-Verlag, 1999).

Stufken, J.

A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications (Springer-Verlag, 1999).

Sullivan, M. E.

M. E. Gehm, S. T. McCain, N. P. Pitsiantis, D. J. Brady, P. Potuluri, and M. E. Sullivan, "Static 2D aperture coding for multimodal multiplex spectroscopy," Appl. Opt. 54, 2965-2974 (2006).
[CrossRef]

Verveer, P. J.

Wang, Y.

Wuttig, A.

A. Wuttig and R. Riesenberg, "Sensitive Hadamard transform imaging spectrometer with a simple MEMS," in Proc. SPIE 4881, 167-178 (2002).
[CrossRef]

Zhao, J.

Anal. Chem.

S. D. Schwab and R. L. McCreery, "Versatile, efficient Raman sampling with fiber optics," Anal. Chem. 56, 2199-2204 (1984).
[CrossRef]

Appl. Opt.

A. Girard, "Spectrometre a grilles," Appl. Opt. 2, 79-87 (1963).
[CrossRef]

R. N. Ibbett, D. Aspinall, and J. F. Grainger, "Real-time multiplexing of dispersed spectra in any wavelength region," Appl. Opt. 7, 1089-1094 (1968).
[CrossRef] [PubMed]

M. E. Gehm, S. T. McCain, N. P. Pitsiantis, D. J. Brady, P. Potuluri, and M. E. Sullivan, "Static 2D aperture coding for multimodal multiplex spectroscopy," Appl. Opt. 54, 2965-2974 (2006).
[CrossRef]

Appl. Spectrosc.

Bell Syst. Tech. J.

H. Kogelnik, "Coupled wave theory for thick hologram grating," Bell Syst. Tech. J. 48, 2909-2948 (1969).

J. Opt. Soc. Am.

Opt. Lett.

Proc. SPIE

H. Owen, D. E. Battey, M. J. Pelletier, and J. B. Slater, "New spectroscopic instrument based on volume holographic optical elements," in Proc. SPIE 2406, 260-267 (1995).

A. Wuttig and R. Riesenberg, "Sensitive Hadamard transform imaging spectrometer with a simple MEMS," in Proc. SPIE 4881, 167-178 (2002).
[CrossRef]

Other

M. O. Harwitt and N. J. A. Sloane, Hadamard Transform Optics (Academic, 1979).

A. S. Hedayat, N. J. A. Sloane, and J. Stufken, Orthogonal Arrays: Theory and Applications (Springer-Verlag, 1999).

D. J. Schroeder, Astronomical Optics (Academic, 1987).

HoloPlex Holographic Transmission Grating, Technical Rep. 1201 (Kaiser Optical Systems, Inc., 2001).

B. E. Bayer, "Color imaging array," U.S. patent 3,971,065 (20 July 1976).

G. Barbastathis and D. Psaltis, Volume Holographic Multiplexing Methods (Springer, 2000), pp. 21-59.

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Figures (13)

Fig. 1
Fig. 1

System diagram showing coordinate systems.

Fig. 2
Fig. 2

Diagram of a row-doubled Hadamard aperture mask based on an order-12 Hadamard matrix. White areas indicate light transmission, and black areas indicate where light is blocked.

Fig. 3
Fig. 3

(Color online) Spectral responses of each grating recorded in the hologram due to Bragg selectivity.

Fig. 4
Fig. 4

(Color online) Bayer filter pattern. Each square represents a pixel, and each letter represents either a red, green, or blue filter.

Fig. 5
Fig. 5

(Color online) Spectral response of Bayer filters.

Fig. 6
Fig. 6

(Color online) Optical component layout of the dispersion multiplexing spectrometer.

Fig. 7
Fig. 7

(Color online) A: Photograph of the dispersion multiplexing spectrometer's internal structure. B: Photograph of the spectrometer with keys to show approximate size.

Fig. 8
Fig. 8

Original 550   nm data captured by CCD (top) and unprocessed data separated into the RGB color channels (lower images).

Fig. 9
Fig. 9

(Color online) Spectra for 550   nm input, RGB color channels separated by rows. Results from coded aperture inversion appear in the left column, and the results after applying the dispersion multiplexing correction appear in the right column. Note the differing scale of the y axis for the different color channels.

Fig. 10
Fig. 10

Fullyprocessed spectrum measured from a 550   nm source.

Fig. 11
Fig. 11

Original fluorescent light data captured by a CCD (top) and unprocessed data separated into the RGB color channels (lower images).

Fig. 12
Fig. 12

(Color online) DMS spectra for a fluorescent lamp. Results from coded aperture inversion (left column) and dispersion multiplexing correction (right column). The rows show the separate RGB color channels.

Fig. 13
Fig. 13

Fullyprocessed spectrum of a fluorescent lamp from the DMS (top) compared with a measurement made with a commercial spectrometer (bottom).

Tables (1)

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Table 1 Spectral Band Data

Equations (18)

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I ( x , y ) = δ ( x ( x + α ( λ λ c ) ) ) δ ( y y ) × T ( x , y ) S ( x , y ; λ ) d x d y d λ .
I ( x , y ) = T ( x , y ) S ( λ = x x α + λ c ) d x .
I ( x , y ) = S ( λ = x 0 x α + λ c ) .
H W = M .
R = r F red ( λ r ) + g F red ( λ g ) + b F red ( λ b ) ,
G = r F green ( λ r ) + g F green ( λ g ) + b F green ( λ b ) ,
B = r F blue ( λ r ) + g F blue ( λ g ) + b F blue ( λ b ) .
K g 1 = 4 π sin ( θ r 1 ) λ rec .
η = γ 2 sin 2 ( ξ 2 + γ 2 ) ξ 2 + γ 2 ,
γ = π n 1 L Z λ cos ( θ )  PF ,
ξ = ( λ B λ ) K g 1 2 L Z 8 π n cos ( θ ) .
PF = { 1 for   TE   polarization cos [ 2 arcsin ( λ sin ( θ r 1 ) λ rec ) ] for   TM   polarization .
λ B = λ rec sin ( θ ) sin ( θ r 1 ) .
n 1 = arcsin ( η r 1 ) λ rec cos ( θ r 1 ) π L Z ,
η Tot = η TE T TE + η TM T TM π L Z ,
T TE = 1 sin 2 ( θ θ ) sin 2 ( θ + θ ) ,
T TM = 1 tan 2 ( θ θ ) tan 2 ( θ + θ ) ,
Δ λ = d λ d x δ .

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