Mathematical limitations when choosing psychophysical methods

The grey scale method is commonly used for investigating differences in material appearance. Specifically, for testing color difference equations, perceived color differences between sample pairs are obtained by visually comparing to differences in a series of achromatic sample pairs. Two types of grey scales are known: linear and geometric. Their instrumental color differences vary linearly or geometrically (i.e., exponentially), respectively. Geometric grey scales are used in ISO standards and standard procedures of the textile industries.