Patent ID: 7110142

Claim:
A method of obtaining marking substrate area coverage information, comprising: obtaining a base reflectance of an unmarked portion of a marking substrate; obtaining a reference reflectance of a reference marked patch of the marking substrate at substantially complete coverage; obtaining a target reflectance of a target marked patch of the marking substrate; and obtaining an estimated marking substrate area coverage ĉ of the target marked patch by a least squares algorithm, based on the base reflectance, the reference reflectance and the target reflectance, using a Neugebauer model of the form y=Ac where y _ = [ r 1 / n ⁡ ( λ 1 ) - r 1 1 / n ⁡ ( λ 1 ) r 1 / n ⁡ ( λ 2 ) - r 1 1 / n ⁡ ( λ 2 ) ⋮ r 1 / n ⁡ ( λ N ) - r 1 1 / n ⁡ ( λ N ) ] ⁢ ⁢ and ⁢ ⁢ A _ = [ r 2 1 / n ⁡ ( λ 1 ) - r 1 1 / n ⁡ ( λ 1 ) r 2 1 / n ⁡ ( λ 2 ) - r 1 1 / n ⁡ ( λ 2 ) ⋮ r 2 1 / n ⁡ ( λ N ) - r 1 1 / n ⁡ ( λ N ) ] , and c is the actual marking substrate area coverage, where λ 1 , λ 2 , . . . λ N represent the wavelengths at which reflectance values are measured, r 1 (λ) is the spectral reflectance of the base color of the marking substrate, r 2 (λ) is the spectral reflectance of a marked patch of substantially 100% area coverage, r(λ) is a predicted spectral reflectance corresponding to a marked patch under analysis, n is a Yule-Nielsen correction factor, and N is a number of measured wavelengths of visible light, and wherein the least squares equation is defined by ĉ=[A T A] −1 A T y where T indicates a matrix transpose.