# The magnitude of nonconstant luminance errors

#### Abstract

The magnitude of nonconstant luminance errors This note outlines the magnitude of the errors introduced by the failure of contemporary video systems to adhere to the Principle of constant luminance. I assume that you are familiar with chapters 5 through 9 of my book, and that you are aware of the ambiguity and confusion in television engineering concerning the term luminance. I express signal processing operations in Mathematica-like pseudocode. The midline dot symbol (·) represents the dot product operation. To compute true, CIE luminance from tristimulus (linear light) RGB components according to Rec. 709 requires weighting the RGB components with these luminance coefficients: Eq 1 Luma 709 = {0.2125, 0.7154, 0.0721} Consider a fully-saturated magenta pixel, represented in Rec. 709 RGB primaries. Its RGB (tristimulus, linear light) components are {1, 0, 1}. Its true, CIE luminance value is this: Eq 2 Luma 709 · {1, 0, 1} 0.2846 In video, we do not compute a true, CIE luminance signal according to the principles of color science. Instead, we gamma-correct the RGB components, then sum them to form a nonlinear component that I denote luma. If you approximate gamma correction as a square root, the encoded luma value is this: Eq 3 Luma 709 · {Sqrt[1], Sqrt[0], Sqrt[1]} 0.533479 At the color difference decoder, we reconstruct gamma-corrected R'G'B' components {1, 0, 1}; these are presented to the display. The display imposes approximately a 2.5-power function. For the purposes of this note, we can approximate the power function as a square. The

### Cite this paper

@inproceedings{Poynton1997TheMO, title={The magnitude of nonconstant luminance errors}, author={Charles A. Poynton}, year={1997} }