Abstract

We have analyzed the results of the reconstruction quality of 252 daylight spectral curves measured at Granada, Spain, using four bases obtained from measurements in different areas of the world. For these reconstructions we used two different methods (orthogonality of characteristic vectors and chromaticity coordinates) to study the influence of the wavelength range and spectral resolution. The reconstruction method from chromaticity coordinates presents difficulties for the spectral recovery of daylight spectral power distributions regardless of the basis used. The orthogonality method makes clear that the best bases were those proposed by the CIE, but more than two characteristic CIE vectors were needed for good reconstruction.

© 1998 Optical Society of America

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References

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1997 (1)

1992 (1)

1989 (1)

1987 (1)

B. A. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

1986 (1)

1978 (1)

1971 (1)

V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
[CrossRef]

1968 (1)

1967 (1)

Y. Nayatani, M. Hitani, H. Minato, “Chromaticity and spectral energy distribution of daylight from north sky at Amagasaki, Japan,” Bull. Electrotech. Lab. 31, 1127–1135 (1967).

1965 (1)

1964 (2)

1963 (2)

S. T. Henderson, D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–131 (1963).
[CrossRef]

J. L. Simonds, “Application of characteristic vector analysis to photographic and optical response data,” J. Opt. Soc. Am. 53, 968–974 (1963).
[CrossRef]

1940 (1)

P. Moon, “Proposed standard solar-radiation curves for engineering use,” J. Franklin Inst. 230, 583–617 (1940).
[CrossRef]

Condit, H. R.

Das, S. R.

Dixon, E. R.

García-Beltrán, A.

Grum, F.

Hallikainen, J.

Henderson, S. T.

S. T. Henderson, D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–131 (1963).
[CrossRef]

Hernández-Andrés, J.

Hitani, M.

Y. Nayatani, M. Hitani, H. Minato, “Chromaticity and spectral energy distribution of daylight from north sky at Amagasaki, Japan,” Bull. Electrotech. Lab. 31, 1127–1135 (1967).

Hodgkiss, D.

S. T. Henderson, D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–131 (1963).
[CrossRef]

Jaaskelainen, T.

Judd, D. B.

MacAdam, D. L.

Maloney, L. T.

Manamohanan, S. B.

V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
[CrossRef]

Marimont, D. H.

Minato, H.

Y. Nayatani, M. Hitani, H. Minato, “Chromaticity and spectral energy distribution of daylight from north sky at Amagasaki, Japan,” Bull. Electrotech. Lab. 31, 1127–1135 (1967).

Moon, P.

P. Moon, “Proposed standard solar-radiation curves for engineering use,” J. Franklin Inst. 230, 583–617 (1940).
[CrossRef]

Nayatani, Y.

Y. Nayatani, M. Hitani, H. Minato, “Chromaticity and spectral energy distribution of daylight from north sky at Amagasaki, Japan,” Bull. Electrotech. Lab. 31, 1127–1135 (1967).

Nimeroff, I.

Parkkinen, J. P. S.

Romero, J.

Sastri, V. D. P.

V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
[CrossRef]

V. D. P. Sastri, S. R. Das, “Typical spectral distributions and color for tropical daylight,” J. Opt. Soc. Am. 58, 391–398 (1968).
[CrossRef]

Simonds, J. L.

Wandell, B. A.

Wyszecki, G.

Yurow, J. A.

Br. J. Appl. Phys. (1)

S. T. Henderson, D. Hodgkiss, “The spectral energy distribution of daylight,” Br. J. Appl. Phys. 14, 125–131 (1963).
[CrossRef]

Bull. Electrotech. Lab. (1)

Y. Nayatani, M. Hitani, H. Minato, “Chromaticity and spectral energy distribution of daylight from north sky at Amagasaki, Japan,” Bull. Electrotech. Lab. 31, 1127–1135 (1967).

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

B. A. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

J. Franklin Inst. (1)

P. Moon, “Proposed standard solar-radiation curves for engineering use,” J. Franklin Inst. 230, 583–617 (1940).
[CrossRef]

J. Opt. Soc. Am. (6)

J. Opt. Soc. Am. A (4)

J. Phys. D (1)

V. D. P. Sastri, S. B. Manamohanan, “Spectral distribution and colour of north sky at Bombay,” J. Phys. D 4, 381–386 (1971).
[CrossRef]

Other (3)

Colorimetry, 2nd ed., CIE Publication No. 15.2 (Central Bureau of the CIE, Vienna, 1986), pp. 70–72.

International Standard ISO/CIE 10526, CIE standard colorimetric illuminants (International Organization for Standardization/CIE, Geneva, 1991).

Licor Incorporated, 4421 Superior St., P.O. Box 4425, Lincoln, Neb.

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Figures (4)

Fig. 1
Fig. 1

Chromaticity of Granada daylight on the 1931 CIE chromaticity diagram.

Fig. 2
Fig. 2

Spectral profiles of the CIE (open circles), Sastri and Das (solid circles) mean vectors, and the Granada (crossed circles) first eigenvector in the 300–700-nm spectral range with a spectral resolution of 10 nm.

Fig. 3
Fig. 3

Example of reconstruction from the chromaticity coordinates by use of the CIE basis with a GFC of 0.9987 in the 330–700-nm spectral range with a spectral resolution of 5 nm. Solid curve, original curves; squares connected by dotted curve, reconstruction.

Fig. 4
Fig. 4

(a) Example of reconstruction from the orthogonality properties by use of the CIE mean and first two characteristic vectors with a GFC of 0.99925 in the 330–700-nm spectral range with a spectral resolution of 5 nm. Solid curve, original curves; squares connected by dotted curve, reconstruction. (b) Example of reconstruction from the orthogonality properties by use of the Granada first three eigenvectors with a GFC of 0.99996 in the 330–700-nm spectral range with a spectral resolution of 5 nm. Solid curve, original curves; squares connected by dotted curve, reconstruction.

Tables (5)

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Table 1 Coefficient Values for Eqs. (2) and (3)

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Table 2 Average GFC for the 252 Curves from x, y Data with Different Bases, Spectral Ranges, and Spectral Resolutionsa

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Table 3 Percentage of Reconstructions (from x, y Data) that Surpass a Given GFC Valuea

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Table 4 Average GFC for the 252 Curves by use of Orthogonalitya

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Table 5 Percentage of Reconstructions from Orthogonality Properties that Surpass a Given GFC Valuea

Equations (7)

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

ERλ=E1λ+M1V1λ+M2V2λ,
M1=a1+a2x+a3yc1+c2x+c3y,
M2=b1+b2x+b3yc1+c2x+c3y.
Va|Vb=0=i VaλiVbλi ab.
ERλ=E1λ+j=1p EEλ|VjλVjλ,
ERλ=i=1p EEλ|WiλWiλ,
GFC=j EE(λj)ER(λj)j[EE(λj)]21/2j[ER(λj)]21/2.

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