Abstract

In a previous work [J. Opt. Soc. Am. A 24, 942 (2007)] we made a complete theoretical and computational study of the influence of several parameters on the behavior of a planned multispectral system for imaging skylight, including the number of sensors and the spectral estimation algorithm. Here we follow up this study by using all the information obtained in the computational simulations to implement a real multispectral imaging system based on a monochrome CCD camera and a liquid-crystal tunable filter (LCTF). We were able to construct the optimum Gaussian sensors found in the simulations by adjusting the exposure times of some of the transmittance modes of the LCTF, hence obtaining really accurate spectral estimations of skylight with only a few optimum sensors.

© 2008 Optical Society of America

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References

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    [CrossRef]
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  9. M. A. López-Álvarez, E. M. Valero, and J. Hernández-Andrés, “Separating illuminant and surface reflectance spectra from filtered trichromatic camera measurements,” in Proceedings of the 3rd European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2006), pp. 370-373.
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    [CrossRef]
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    [CrossRef]
  12. J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696-5703 (2005).
    [CrossRef]
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    [CrossRef]
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  21. J. Hernández-Andrés, J. Romero, and R. L. Lee Jr., “Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain,” J. Opt. Soc. Am. A 18, 412-420 (2001).
    [CrossRef]
  22. M. de Lasarte, J. Pujol, M. Arjona, and M. Vilaseca, “Optimized algorithm for the spatial nonuniformity correction of an imaging system based on a charged-coupled device color camera,” Appl. Opt. 46, 167-174 (2007).
    [CrossRef]
  23. M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, “Colorimetric and spectral combined metric for the optimization of multispectral systems,” in Proceedings of the 10th Congress of the International Colour Association, J. Hernández-Andrés and J. L. Nieves, eds. (Association Internationale de la Couleur, 2005), pp. 1685-1688.
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    [CrossRef]

2007 (3)

2006 (1)

A. Ferrero, J. Campos, and A. Pons, “Low-uncertainty absolute radiometric calibration of a CCD,” Metrologia 43, S17-S21 (2006).

2005 (3)

2004 (1)

2003 (1)

R. A. Yotter and D. M. Wilson, “A review of photodetectors for sensing light-emitting reporters in biological systems,” IEEE Sens. J. 3, pp. 288-303 (2003).
[CrossRef]

2002 (1)

2001 (1)

2000 (1)

1999 (1)

D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788-791(1999).

1990 (1)

J. Ho, B. V. Funt, and M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).

1986 (1)

1985 (1)

J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439-445 (1985).

Arjona, M.

Berns, R. S.

F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, 1999), pp. 42-48.

P. D. Burns and R. S. Berns, “Quantization in multispectral color image acquisition,” in Proceedings of the IS&T 7th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 1999), pp. 32-35.

Burns, P. D.

P. D. Burns and R. S. Berns, “Quantization in multispectral color image acquisition,” in Proceedings of the IS&T 7th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 1999), pp. 32-35.

Campos, J.

A. Ferrero, J. Campos, and A. Pons, “Low-uncertainty absolute radiometric calibration of a CCD,” Metrologia 43, S17-S21 (2006).

Chandra, K.

Connah, D.

D. Connah, S. Westland, and M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 619-622.

Cui, G.

de Lasarte, M.

Drew, M. S.

J. Ho, B. V. Funt, and M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).

Ferrero, A.

A. Ferrero, J. Campos, and A. Pons, “Low-uncertainty absolute radiometric calibration of a CCD,” Metrologia 43, S17-S21 (2006).

Funt, B. V.

J. Ho, B. V. Funt, and M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).

García, P. A.

Goody, R. M.

R. M. Goody and Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford University Press, 1995), Chap. 5.

Haneishi, H.

Hardeberg, J. Y.

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1999), pp. 121-174.

Hasegawa, T.

Healey, G.

Hernández-Andrés, J.

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. Romero, “Selecting algorithms, sensors and linear bases for optimum spectral recovery of skylight,” J. Opt. Soc. Am. A 24, 942-956 (2007).
[CrossRef]

M. A. López-Álvarez, J. Hernández-Andrés, J. Romero, and R. L. Lee, Jr., “Designing a practical system for spectral imaging of skylight,” Appl. Opt. 44, 5688-5695 (2005).
[CrossRef]

J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696-5703 (2005).
[CrossRef]

J. Hernández-Andrés, J. Romero, and R. L. Lee Jr., “Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain,” J. Opt. Soc. Am. A 18, 412-420 (2001).
[CrossRef]

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, “Colorimetric and spectral combined metric for the optimization of multispectral systems,” in Proceedings of the 10th Congress of the International Colour Association, J. Hernández-Andrés and J. L. Nieves, eds. (Association Internationale de la Couleur, 2005), pp. 1685-1688.

M. A. López-Álvarez, E. M. Valero, and J. Hernández-Andrés, “Separating illuminant and surface reflectance spectra from filtered trichromatic camera measurements,” in Proceedings of the 3rd European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2006), pp. 370-373.

Ho, J.

J. Ho, B. V. Funt, and M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).

Hosoi, A.

Huertas, R.

Hyvärinen, A.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, 1st ed. (Wiley, 2001), pp. 147-292.

Imai, F. H.

F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, 1999), pp. 42-48.

Karhunen, J.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, 1st ed. (Wiley, 2001), pp. 147-292.

Lee, D. D.

D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788-791(1999).

Lee, R. L.

López-Álvarez, M. A.

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. Romero, “Selecting algorithms, sensors and linear bases for optimum spectral recovery of skylight,” J. Opt. Soc. Am. A 24, 942-956 (2007).
[CrossRef]

M. A. López-Álvarez, J. Hernández-Andrés, J. Romero, and R. L. Lee, Jr., “Designing a practical system for spectral imaging of skylight,” Appl. Opt. 44, 5688-5695 (2005).
[CrossRef]

M. A. López-Álvarez, E. M. Valero, and J. Hernández-Andrés, “Separating illuminant and surface reflectance spectra from filtered trichromatic camera measurements,” in Proceedings of the 3rd European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2006), pp. 370-373.

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, “Colorimetric and spectral combined metric for the optimization of multispectral systems,” in Proceedings of the 10th Congress of the International Colour Association, J. Hernández-Andrés and J. L. Nieves, eds. (Association Internationale de la Couleur, 2005), pp. 1685-1688.

Maloney, L. T.

Melgosa, M.

Michalsky, J. J.

J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439-445 (1985).

Miyake, Y.

Nascimento, S. M. C.

Nieves, J. L.

J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696-5703 (2005).
[CrossRef]

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, “Colorimetric and spectral combined metric for the optimization of multispectral systems,” in Proceedings of the 10th Congress of the International Colour Association, J. Hernández-Andrés and J. L. Nieves, eds. (Association Internationale de la Couleur, 2005), pp. 1685-1688.

Oja, E.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, 1st ed. (Wiley, 2001), pp. 147-292.

Pons, A.

A. Ferrero, J. Campos, and A. Pons, “Low-uncertainty absolute radiometric calibration of a CCD,” Metrologia 43, S17-S21 (2006).

Pujol, J.

Romero, J.

Seung, H. S.

D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788-791(1999).

Shi, M.

Shimano, N.

N. Shimano, “Evaluation of a multispectral image acquisition system aimed at reconstruction of spectral reflectances,” Opt. Eng. 44, 107005 (2005).

Thomson, M. G. A.

D. Connah, S. Westland, and M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 619-622.

Tsumura, N.

Valero, E. M.

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. Romero, “Selecting algorithms, sensors and linear bases for optimum spectral recovery of skylight,” J. Opt. Soc. Am. A 24, 942-956 (2007).
[CrossRef]

J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696-5703 (2005).
[CrossRef]

M. A. López-Álvarez, E. M. Valero, and J. Hernández-Andrés, “Separating illuminant and surface reflectance spectra from filtered trichromatic camera measurements,” in Proceedings of the 3rd European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2006), pp. 370-373.

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, “Colorimetric and spectral combined metric for the optimization of multispectral systems,” in Proceedings of the 10th Congress of the International Colour Association, J. Hernández-Andrés and J. L. Nieves, eds. (Association Internationale de la Couleur, 2005), pp. 1685-1688.

Vilaseca, M.

Wandell, B. A.

Westland, S.

D. Connah, S. Westland, and M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 619-622.

Wilson, D. M.

R. A. Yotter and D. M. Wilson, “A review of photodetectors for sensing light-emitting reporters in biological systems,” IEEE Sens. J. 3, pp. 288-303 (2003).
[CrossRef]

Yokoyama, Y.

Yotter, R. A.

R. A. Yotter and D. M. Wilson, “A review of photodetectors for sensing light-emitting reporters in biological systems,” IEEE Sens. J. 3, pp. 288-303 (2003).
[CrossRef]

Yung, Y. L.

R. M. Goody and Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford University Press, 1995), Chap. 5.

Appl. Opt. (4)

IEEE Sens. J. (1)

R. A. Yotter and D. M. Wilson, “A review of photodetectors for sensing light-emitting reporters in biological systems,” IEEE Sens. J. 3, pp. 288-303 (2003).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

J. Ho, B. V. Funt, and M. S. Drew, “Separating a color signal into illumination and surface reflectance components: theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966-977 (1990).

J. Opt. Soc. Am. A (6)

Metrologia (1)

A. Ferrero, J. Campos, and A. Pons, “Low-uncertainty absolute radiometric calibration of a CCD,” Metrologia 43, S17-S21 (2006).

Nature (1)

D. D. Lee and H. S. Seung, “Learning the parts of objects by non-negative matrix factorization,” Nature 401, 788-791(1999).

Opt. Eng. (1)

N. Shimano, “Evaluation of a multispectral image acquisition system aimed at reconstruction of spectral reflectances,” Opt. Eng. 44, 107005 (2005).

Sol. Energy (1)

J. J. Michalsky, “Estimation of continuous solar spectral distributions from discrete filter measurements: II. A demonstration of practicability,” Sol. Energy 34, 439-445 (1985).

Other (8)

R. M. Goody and Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford University Press, 1995), Chap. 5.

P. D. Burns and R. S. Berns, “Quantization in multispectral color image acquisition,” in Proceedings of the IS&T 7th Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, 1999), pp. 32-35.

J. Y. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. dissertation (Ecole Nationale Supérieure des Télécommunications, 1999), pp. 121-174.

D. Connah, S. Westland, and M. G. A. Thomson, “Optimization of a multispectral imaging system,” in Proceedings of the 1st European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 619-622.

F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society of Multispectral Imaging of Japan, 1999), pp. 42-48.

A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, 1st ed. (Wiley, 2001), pp. 147-292.

M. A. López-Álvarez, E. M. Valero, and J. Hernández-Andrés, “Separating illuminant and surface reflectance spectra from filtered trichromatic camera measurements,” in Proceedings of the 3rd European Conference on Colour Graphics, Image and Vision (Society for Imaging Science and Technology, 2006), pp. 370-373.

M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. L. Nieves, “Colorimetric and spectral combined metric for the optimization of multispectral systems,” in Proceedings of the 10th Congress of the International Colour Association, J. Hernández-Andrés and J. L. Nieves, eds. (Association Internationale de la Couleur, 2005), pp. 1685-1688.

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Figures (9)

Fig. 1
Fig. 1

Spectral transmittance of the 33 modes of the Varispec liquid-crystal tunable filter measured three times in our laboratory (error bars show the standard deviation obtained at each sampled wavelength).

Fig. 2
Fig. 2

Five optimum sensors found in the computational simulations (solid line) for the Imai–Berns method with a SNR equal to 26 dB . Seven transmittance modes of the LCTF (dashed line) used to implement the theoretical optimum sensors.

Fig. 3
Fig. 3

Spectral responsivity of the CCD camera (Model Retiga QImaging SRV1394) measured at our laboratory. Error bars show the uncertainty in these measurements.

Fig. 4
Fig. 4

(a) CIE-31 chromaticity diagram for the 1567 spectral measurements of skylight belonging to the training set. (b) Detail of (a).

Fig. 5
Fig. 5

(a) CIE-31 chromaticity diagram for the 125 spectral measurements of skylight belonging to the test set. (b) Detail of (a).

Fig. 6
Fig. 6

(a) 10th percentile ( CSCM = 6.00 ), (b) 50th percentile ( CSCM = 15.35 ), and (c) 90th percentile ( CSCM = 25.05 ) over the test set of 125 spectral measurements taken in Granada in 2007 when using the radiometric sampling method.

Fig. 7
Fig. 7

(a) 10th percentile ( CSCM = 3.28 ), (b) 50th percentile ( CSCM = 6.73 ), and (c) 90th percentile ( CSCM = 15.65 ) over the test set of 125 spectral measurements taken in Granada in 2007 when using the Linear Pseudoinverse method with k = 33 .

Fig. 8
Fig. 8

(a) 10th percentile ( CSCM = 3.00 ), (b) 50th percentile ( CSCM = 6.44 ), and (c) 90th percentile ( CSCM = 15.48 ) over the test set of 125 spectral measurements taken in Granada in 2007 when using the Imai–Berns method with k = 33 and n = 6 .

Fig. 9
Fig. 9

(a) 10th percentile ( CSCM = 3.12 ), (b) 50th percentile ( CSCM = 7.48 ), and (c) 90th percentile ( CSCM = 16.76 ) over the test set of 125 spectral measurements taken in Granada in 2007 when using the Imai–Berns method with five optimum sensors and five PCA vectors.

Tables (4)

Tables Icon

Table 1 Mean ± Standard Deviation Values of Various Metrics a

Tables Icon

Table 2 Mean ± Standard Deviation Values of Various Metrics a

Tables Icon

Table 3 Mean ± Standard Deviation Values of Various Metrics a

Tables Icon

Table 4 Mean ± Standard Deviation Values of Various Metrics a

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

ρ = R t E + σ ,
E = V ϵ ,
ε t s = G ρ t s ,
G = ε t s ρ t s + .
E R = V G ρ .
W = E t s ρ t s + .
R ( λ ) = C c E ( λ ) t exp ,
F k = C k c E k t exp , k , k = 1 , 33 ,
E k = C k c F k t exp , k , k = 1 , 33.
GFC = | j E ( λ j ) E R ( λ j ) | | j [ E ( λ j ) ] 2 | 1 / 2 | j [ E R ( λ j ) ] 2 | 1 / 2 ,
Δ E a b * = Δ L * 2 + Δ a * 2 + Δ b * 2 ,
IRE ( % ) = 100 | j = 1 N E ( λ j ) - E R ( λ j ) | j = 1 N E ( λ j ) ,
CSCM = Ln [ 1 + 1000 ( 1 GFC ) ] + Δ E a b * + IRE ( % ) .
C k , t s c = RE t s t exp , k
ρ k = C k c t exp , k k = 1 , 33.
E R = X ρ ,
E R = VG ρ = V ε t s ρ t s + ρ = E t s ρ t s + ρ = W ρ ,

Metrics