The mathematical expression of damage law of museum lighting on dyed artworks

Abstract Dyed artworks are highly sensitive to light and are easily affected by museum lighting, resulting in irreversible permanent color damage such as fading and discoloration. Exposure, light source spectrum and material properties are the three indicators causing damage to artworks. Therefore, it is the basis for effective lighting protection to reveal the quantitative influence of exposure and light source spectrum composition on the damage degree of different pigments and establish a mathematical model that can accurately express the above rules. At present, the color damage calculation model of dyed artworks under three parameters’ coupling action is missing. This research established a visual three-dimensional change surface of the color difference values of 23 pigments varying with the spectral wavelength and exposure through experimental methods. The relative responsivity function ΔEn = fn(λ, Q), where n = 1 ~ 23, was obtained for 23 pigments under the coupling effects of exposure and light source spectra. Furthermore, a mathematical model $$D_{n} = \mathop \smallint \limits_{380}^{780} S\left( \lambda \right) \cdot f_{n} \left( {\lambda ,Q} \right)d\lambda$$ D n = ∫ 380 780 S λ · f n λ , Q d λ calculating the color damage of pigments in the range of visible light was proposed. The proposed model was verified by the experimental method, which realizes the mathematical expression of the damage law of museum lighting on dyed artworks.