Studies on Color Rendering and Illuminant Metamerisn (Part 2)

Based on the spectral power distributions of actual fluorescent lamps (about 6, 500 K in color temperature), the amounts of line spectra were pre-assigned as 80.0 to 405 nm, 200.0 to 436 nm, 100.0 to 546 nm and 30.0 to 578 nm, respectively.The existence of the spectral power distributions of the test illuminants with these amounts of line spectra, which fulfil the following requiremnts further was examined.(1) With respect to any of the reference illuminatnts, the test illuminants have the same chromaticity coordinates and the general color-rendering index of Ra=100, provided that the spectral power distributions of the reference illuminants are normalized as 100 or near 100 at the wavelength of 560 nm.(2) In addition to the requirement 1), the minimum value of the sum of squares is expected with respected to the difference in spectral power distributions between the reference and the test illuminantsThese conditions are reduced to solving the linear homogeneous equations derived by applying the Lagrange multiplier method. The spectral power distributions Jt (λ) of the test illuminant was obtained with respect to the CIE standard illuminant C as the reference, which also satisfied the above two requirements.However, the computed results give an imaginary spectral power distribution which corresponds to negative radiations in some of the visible spectra. This might suggest the impossibility to realize the general color rendering index of Ra=100 with a fluorescent lamp having the pre-assigned amounts of line spectra shown above.