Gamma Correction Technical Memo 9

Gamma is one of the most misunderstood concepts in computer imaging applications. Part of the reason is that the term is used to mean several different things, completely confusing the user. The purpose of this memo is to draw distinctions between the several uses and to propose a fixed meaning for the term: Gamma is the term used to describe the nonlinearity of a display monitor. This is the historical first meaning of the term. A corollary of this definition is that all other uses of the term gamma should be dropped, or the imaging industry will continue to stumble. In particular, this means that gamma should not be used to describe nonlinearity introduced into the image data itself. Image data, especially images intended for reuse, should always contain linear data, as commonly assumed by all computer graphics algorithms. Historical Gamma Definition All computer display monitors (and all TV sets) are nonlinear. This means that if the voltage on their electronics is doubled, their brightness does not double as you might expect it to. In fact, it varies approximately as the square of the voltage. If it varied by the square exactly, we would say it had a gamma of 2. In other (mathematical) words, gamma is an exponent. But all monitors are slightly different, so the actual gamma of a monitor might be anywhere from 1.4 to 2.6, instead of 2. Very typical gamma numbers are 1.8 for the PC and Mac worlds and 2.2 for the broadcast TV world (and for PCs using TV graphics boards, such as Truevision Targa+), but these should not be taken as gospel. They vary from display to display, even on displays from the same manufacturer. Any gamma other than 1 is nonlinear. The term gamma comes from the electronics industry. The equation derived by electronics engineers to describe the intensity I, or brightness, out of a cathode-ray tube (CRT) for a given voltage V applied to it its inputs is I = kV where the exponent of V is the Greek letter gamma (and k is some proportionality constant)1. Most computer displays are still based on CRTs. So the historical 1 Equivalently, the intensity is related by the same exponent γ to the number of electrons in the CRT that strike the phosphors on the face of the tube and cause them to emit light. This is because the number N of electrons is directly proportional to the voltage V.