Abstract

Current multispectral imaging systems use narrowband filters to capture the spectral content of a scene, which necessitates different filters to be designed for each application. In this paper, we demonstrate the concept of Fourier multispectral imaging which uses filters with sinusoidally varying transmittance. We designed and built these filters employing a single-cavity resonance, and made spectral measurements with a multispectral LED array. The measurements show that spectral features such as transmission and absorption peaks are preserved with this technique, which makes it a versatile technique than narrowband filters for a wide range of multispectral imaging applications.

© 2015 Optical Society of America

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References

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  1. M. T. Eismann, Hyperspectral Remote Sensing(SPIE Press, 2012).
    [Crossref]
  2. B. Geelen, N. Gack, and A. Lambrechts, “A compact snapshot multispectral imager with a monolithically integrated per-pixel filter mosaic,” in SPIE MOEMS-MEMS, International Society for Optics and Photonics (SPIE, 2014), paper 89740L.
  3. D. Yi and L. Kong, “Fabrication of densely patterned micro-arrayed multichannel optical filter mosaic,” Journal of Micro/Nanolithography, MEMS, and MOEMS 10(3), 033020 (2011).
    [Crossref]
  4. G. Themelis, J. S. Yoo, and V. Ntziachristos, “Multispectral imaging using multiple-bandpass filters,” Opt. Lett. 33, 1023–1025 (2008).
    [Crossref] [PubMed]
  5. K. C. Balram and D. A. B. Miller, “Self-aligned silicon fins in metallic slits as a platform for planar wavelength-selective nanoscale resonant photodetectors,” Opt. Express 20, 22735–22742 (2012).
    [Crossref] [PubMed]
  6. K. Hirakawa and K. J. Barnard, “Fourier spectral filter array design for multispectral image recovery,” in OSA Imaging Systems and Applications, Optical Society of America (OSA, 2014), pp. IM1C-5.
  7. J. Jia and K. Hirakawa, “Single-shot fourier yransform multispectroscopy,” in IEEE International Conference on Image Processing, Institute of Electrical and Electronics Engineering (2015).
  8. C. Ni, J. Jia, K. Hirakawa, and A. M. Sarangan, “Design and fabrication of sinusoidal spectral filters for multispectral imaging,” in SPIE Optics + Photonics, International Society for Optics and Photonics (SPIE, 2015), paper 9556-19.
  9. J. W. Goodman and R. L. Haupt, Statistical Optics (John Wiley & Sons, 2015).
  10. A. Chakrabarti and T. Zickler, “Statistics of real-world hyperspectral images,” in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 193–200.
  11. H. A. Macleod, Thin-film Optical Filters(Institute of Physics Publishing Bristol and Philadelphia, 2001).
    [Crossref]

2012 (1)

2011 (1)

D. Yi and L. Kong, “Fabrication of densely patterned micro-arrayed multichannel optical filter mosaic,” Journal of Micro/Nanolithography, MEMS, and MOEMS 10(3), 033020 (2011).
[Crossref]

2008 (1)

Balram, K. C.

Barnard, K. J.

K. Hirakawa and K. J. Barnard, “Fourier spectral filter array design for multispectral image recovery,” in OSA Imaging Systems and Applications, Optical Society of America (OSA, 2014), pp. IM1C-5.

Chakrabarti, A.

A. Chakrabarti and T. Zickler, “Statistics of real-world hyperspectral images,” in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 193–200.

Eismann, M. T.

M. T. Eismann, Hyperspectral Remote Sensing(SPIE Press, 2012).
[Crossref]

Gack, N.

B. Geelen, N. Gack, and A. Lambrechts, “A compact snapshot multispectral imager with a monolithically integrated per-pixel filter mosaic,” in SPIE MOEMS-MEMS, International Society for Optics and Photonics (SPIE, 2014), paper 89740L.

Geelen, B.

B. Geelen, N. Gack, and A. Lambrechts, “A compact snapshot multispectral imager with a monolithically integrated per-pixel filter mosaic,” in SPIE MOEMS-MEMS, International Society for Optics and Photonics (SPIE, 2014), paper 89740L.

Goodman, J. W.

J. W. Goodman and R. L. Haupt, Statistical Optics (John Wiley & Sons, 2015).

Haupt, R. L.

J. W. Goodman and R. L. Haupt, Statistical Optics (John Wiley & Sons, 2015).

Hirakawa, K.

J. Jia and K. Hirakawa, “Single-shot fourier yransform multispectroscopy,” in IEEE International Conference on Image Processing, Institute of Electrical and Electronics Engineering (2015).

C. Ni, J. Jia, K. Hirakawa, and A. M. Sarangan, “Design and fabrication of sinusoidal spectral filters for multispectral imaging,” in SPIE Optics + Photonics, International Society for Optics and Photonics (SPIE, 2015), paper 9556-19.

K. Hirakawa and K. J. Barnard, “Fourier spectral filter array design for multispectral image recovery,” in OSA Imaging Systems and Applications, Optical Society of America (OSA, 2014), pp. IM1C-5.

Jia, J.

J. Jia and K. Hirakawa, “Single-shot fourier yransform multispectroscopy,” in IEEE International Conference on Image Processing, Institute of Electrical and Electronics Engineering (2015).

C. Ni, J. Jia, K. Hirakawa, and A. M. Sarangan, “Design and fabrication of sinusoidal spectral filters for multispectral imaging,” in SPIE Optics + Photonics, International Society for Optics and Photonics (SPIE, 2015), paper 9556-19.

Kong, L.

D. Yi and L. Kong, “Fabrication of densely patterned micro-arrayed multichannel optical filter mosaic,” Journal of Micro/Nanolithography, MEMS, and MOEMS 10(3), 033020 (2011).
[Crossref]

Lambrechts, A.

B. Geelen, N. Gack, and A. Lambrechts, “A compact snapshot multispectral imager with a monolithically integrated per-pixel filter mosaic,” in SPIE MOEMS-MEMS, International Society for Optics and Photonics (SPIE, 2014), paper 89740L.

Macleod, H. A.

H. A. Macleod, Thin-film Optical Filters(Institute of Physics Publishing Bristol and Philadelphia, 2001).
[Crossref]

Miller, D. A. B.

Ni, C.

C. Ni, J. Jia, K. Hirakawa, and A. M. Sarangan, “Design and fabrication of sinusoidal spectral filters for multispectral imaging,” in SPIE Optics + Photonics, International Society for Optics and Photonics (SPIE, 2015), paper 9556-19.

Ntziachristos, V.

Sarangan, A. M.

C. Ni, J. Jia, K. Hirakawa, and A. M. Sarangan, “Design and fabrication of sinusoidal spectral filters for multispectral imaging,” in SPIE Optics + Photonics, International Society for Optics and Photonics (SPIE, 2015), paper 9556-19.

Themelis, G.

Yi, D.

D. Yi and L. Kong, “Fabrication of densely patterned micro-arrayed multichannel optical filter mosaic,” Journal of Micro/Nanolithography, MEMS, and MOEMS 10(3), 033020 (2011).
[Crossref]

Yoo, J. S.

Zickler, T.

A. Chakrabarti and T. Zickler, “Statistics of real-world hyperspectral images,” in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 193–200.

Journal of Micro/Nanolithography, MEMS, and MOEMS (1)

D. Yi and L. Kong, “Fabrication of densely patterned micro-arrayed multichannel optical filter mosaic,” Journal of Micro/Nanolithography, MEMS, and MOEMS 10(3), 033020 (2011).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

Other (8)

M. T. Eismann, Hyperspectral Remote Sensing(SPIE Press, 2012).
[Crossref]

B. Geelen, N. Gack, and A. Lambrechts, “A compact snapshot multispectral imager with a monolithically integrated per-pixel filter mosaic,” in SPIE MOEMS-MEMS, International Society for Optics and Photonics (SPIE, 2014), paper 89740L.

K. Hirakawa and K. J. Barnard, “Fourier spectral filter array design for multispectral image recovery,” in OSA Imaging Systems and Applications, Optical Society of America (OSA, 2014), pp. IM1C-5.

J. Jia and K. Hirakawa, “Single-shot fourier yransform multispectroscopy,” in IEEE International Conference on Image Processing, Institute of Electrical and Electronics Engineering (2015).

C. Ni, J. Jia, K. Hirakawa, and A. M. Sarangan, “Design and fabrication of sinusoidal spectral filters for multispectral imaging,” in SPIE Optics + Photonics, International Society for Optics and Photonics (SPIE, 2015), paper 9556-19.

J. W. Goodman and R. L. Haupt, Statistical Optics (John Wiley & Sons, 2015).

A. Chakrabarti and T. Zickler, “Statistics of real-world hyperspectral images,” in Proc. IEEE Conf. on Computer Vision and Pattern Recognition (IEEE, 2011), pp. 193–200.

H. A. Macleod, Thin-film Optical Filters(Institute of Physics Publishing Bristol and Philadelphia, 2001).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Hyperspectral image cube in Space-OPD representation. Shown using dataset in [10].
Fig. 2
Fig. 2 Percent error between the Fabry-Perot filter function and the ideal sinusoidal function as a function of the filter contrast χ.
Fig. 3
Fig. 3 Multispectral imaging testbed. The peaks of LEDs in (c) occur at 460nm, 515nm, 565nm, 590nm, 627nm, 655nm, 850nm, and 880nm.
Fig. 4
Fig. 4 The blue lines show the desired pure sinusoidal transmittance function. The green lines are the designed filter spectra that best approximates the blue line. The red lines are measured transmission spectra from the fabricated filters.
Fig. 5
Fig. 5 Reconstructed spectra for the target shown in Fig. 3(c). LEDs were lit one at a time. The eight different colors in this plot represent eight reconstructions we made on eight different LEDs, respectively. Spectra were normalized to their peak heights.
Fig. 6
Fig. 6 Raw sensor measurements under different filters and reconstructed image when multiple LEDs are lit. LED peaks (top row) at 515nm and 850nm, (middle row) at 565nm and 655nm, and (bottom row) at 565nm, 655nm, and 850nm. (a–g) The seven multispectral measurements {Z0,…,Z6} taken. (h) Color image rendered from reconstructed spectra. Note that 850nm emission is outside of visible range, so it does not appear in color rendering.
Fig. 7
Fig. 7 Reconstructed spectra in Fig. 6 with the specified LEDs turned on. The blue and red lines represent reconstructions from 6 and 7 measurements, respectively. In (b–c) 565nm and 655nm LED can be distinguished using K = 7 measurements, but peaks are indistinguishable with only K = 6 measurements. The ability to resolve multiple spectral features that are close in wavenumber or wavelength determines the number of filters needed.

Tables (2)

Tables Icon

Table 1 Designed ZnS thickness of Fourier spectral filters

Tables Icon

Table 2 Comparisons of reconstructed and actual spectral peaks of LEDs in Fig. 5.

Equations (11)

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X ( n , ζ ) = X ^ ( n , σ ) e j 2 π ζ σ d σ .
Y k ( n ) : = X ( n , k Δ ζ ) = cos ( 2 π k Δ ξ σ ) X ^ ( n , σ ) d σ , k { 0 , 1 , , K 1 }
X ^ ( n , σ ) = Δ ξ k = X ( n , k Δ ξ ) e j 2 π σ k Δ ξ ,
X ( n , 0 ) | X ( n , ζ ) | ζ .
Y ^ ( n , σ ) = 1 σ M A X k = ( K 1 ) K 1 Y | k | ( n ) e j 2 π σ k σ M A X = 1 σ M A X k = I K ( k ) X ( n , k σ M A X ) e j 2 π σ k σ M A X = 1 σ M A X 0 σ M A X I ^ K ( σ τ ) k = X ( n , k σ M A X ) e j 2 π τ k σ M A X X ^ ( n , σ ) d τ ,
Z k ( n ) = { X ^ ( n , σ ) d σ k = 0 ( α k + χ k 2 cos ( 2 π k σ M A X ) ) X ^ ( n , σ ) d σ k > 0 ,
Y k ( n ) = { Z 0 ( n ) k = 0 2 χ k ( Z k ( n ) α k Z 0 ( n ) ) k > 0.
T f p = T a T b ( 1 ( R a R b ) 1 2 ) 2 [ 1 + 4 ( R a R b ) 1 2 ( 1 ( R a R b ) 1 2 ) 2 sin 2 ( 2 π n s d s cos θ s σ ) ] 1
χ = T a T b ( 1 ( R a R b ) 1 2 ) 2 [ 1 ( 1 + 4 ( R a R b ) 1 2 ( 1 ( R a R b ) 1 2 ) 2 ) 1 ] .
T sin = χ 2 cos ( 4 π n s d s cos θ s σ ) + max ( T f p ) χ 2 .
ε = 1 900 nm 1 450 nm | T f p T sin | T sin d σ .

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