Standard Colorimetry: Definitions, Algorithms and Software

Book Preface

This chapter has solely educational purposes and only recalls classical optical phenomena, therefore its bibliography consist of textbooks, manuals and tutorials.
This chapter considers the physical nature of colour stimuli.

“Colour stimulus – visible radiation entering the eye and producing a sensation of colour, either chromatic or achromatic.”1–3

“Colour stimulus function ϕλ – description of a colour stimulus by the spectral concentration of a radiometric quantity, such as radiance or radiant power, as a function of wavelength.”1–3

“Relative colour stimulus function ϕ(λ) – relative spectral power distribution of the colour stimulus function.”1–3

“The psychophysical specification of a colour stimulus is termed again colour stimulus and is denoted by a symbol in square brackets, for example, [ϕ]”1–3 (the context avoids ambiguity). Since the psycophysical colour stimulus is mathematically a vector, in this book the colour stimulus is always indicated in bold roman letters as scientific convention requires.

The colour stimulus function is a physical quantity measured in W/nm if it is the spectral distribution of the radiant power – also spectral flux –, or in W/(m2 sterad nm) if it is the spectral distribution of the radiance. The relative colour stimulus function is dimensionless and the spectral plots of this function and that of the colour stimulus function are proportional, that is, ϕλ = k ϕ(λ), where k is a constant with a suitable physical dimension. The colour stimulus functions must be used for the computations of absolute quantities as, for example, the illuminance and the luminance, but generally the use of the relative colour stimulus function is more convenient and almost all the colour specification is made on a relative scale. [In colorimetry and photometry the absolute spectral distribution functions have dependence on the wavelength λ written as a subscript while the relative spectral distribution functions have dependence written in brackets (λ).]
These definitions of colour stimulus are merely radiometric (Section 2.4) and only physical operations on these quantities are considered, for example, addition of many colour stimuli.
Colour stimuli produce colour sensations, that usually continue to be called colour stimuli, which should not be confused with the previous colour stimuli (the context avoids ambiguity). Psychophysical operations can be made on these last colour stimuli, for example, addition, comparison and colour matching, and in this case colour stimuli, which represent colour sensations, are written in square brackets [ψ] or as vectors.
The colour stimulus function characterized by a spectral power distribution constant is termed equal-energy (or equi-energy) stimulus function and denoted by the relative spectral radiance EE(λ) = 1. The equal energy stimulus function often plays a role in the normalization of the tristimulus space, used for the psychophysical specification of colour stimuli (Section 6.13).