Berns, Roy S., Ricardo J. Motta, and Mark E. Gorzynski (1993), “CRT colorimetry,” in Color Research and Application 18: 299–325.

Cowan, William B. (1983), “An inexpensive scheme for calibration of a colour monitor in terms of CIE standard coordinates,” in Computer Graphics 17 (3): 315–321 (July).

point-gamma values will be low, and the average gamma estimate will be reduced. In some formulations (such as that of the EBU), Li in the numerator is replaced by Li -L0, subtracting the zero-code luminance; that subtraction leads to errors.

In my view, a better way to characterize gamma is to perform a numerical fit to an appropriate model, such as the GOGO model of Berns, Mottta, and Gorzynski.

Video displays have historically been aligned in the studio using the pluge test signal, adjusting black level (brightness, or offset) so that 0% video and -2% video signals were just barely under the threshold of visibility. That procedure leaves video signal zero producing

a small amount of light, typically between 0.01 and 0.1 nt for 100 nt reference white. For a pure 2.4-power function, the video signal corresponding to absolute, theoretical black is about -2% of the reference white signal, that is, around 10-bit interface code 32.

If you want to determine the nonlinearity of your display, consult the classic article by Cowan. In addition to describing how to measure the nonlinearity, he describes how to determine other characteristics of your display – such as the chromaticity of its white point and its primaries – that are important for accurate colour reproduction.

Gamma in video, CGI, and Macintosh

Transfer functions in video (and PC), computer-gener- ated imagery, and Macintosh are sketched in the rows of Figure 27.5 opposite. Each row shows four function blocks; from left to right, these are a camera or scanner LUT, an image storage device, an output LUT, and

a display.

In video, sketched in the top row, the camera applies a transfer function to accomplish gamma correction. Signals are then maintained in a perceptual domain throughout the system until conversion to tristimulus values at the display. I show the output LUT with

a ramp that leaves data unaltered: Video systems conventionally use no LUT, but the comparison is clarified if I portray the four rows with the same blocks.

PC graphics hardware ordinarily implements lookup tables at the output of the framestore, as I detailed in Raster images, on page 67. However, most PC software

GAMMA

CORRECTION FRAMESTORE

Video, PC

TRISTIM.

0.5

TRISTIM.

RAMP

Code 100 problem/8-bit Bottleneck

SCANNER

LUT FRAMEBUFFER

SGI

TRISTIM.

1⁄1.41

≈0.71

SCANNER

LUT FRAMEBUFFER

Historical

Macintosh

TRISTIM.

1⁄1.66

≈0.6

Macintosh RGB codes

(implicit) DISPLAY

2.4

1.0

1⁄1.45

≈0.69

The Macintosh computer historically implemented a 1⁄1.45-power function at the output LUT. John Knoll’s Gamma Control Panel was commonly used to load the output LUT. When set to a gamma value g, the Control Panel loaded the LUT

with a power function whose exponent is 2.61⁄g. Strangely, gamma on

Macintosh computers came to be quoted as the exponent applied prior to the framebuffer (whereas in other computers it is the exponent of the table loaded into the output LUT). So, the Mac’s default gamma was said to be 1.8, not 1.45. A more reasonable value of display gamma of 2.2 results in tristimulus value proportional to code value raised to the 1.66-power (see Figure 27.6).

A Macintosh could be set to handle video (or PC) R’G’B’ data by loading a ramp into its output LUT. Using Knoll’s control panel, this is accomplished by setting gamma to 2.61.

JPEG/JFIF files originated on Macintosh historically represented R, G, and B display tristimulus values raised to the 0.6 power (that is, about 1⁄1.65).

As of Mac OS X 10.6 (“Snow Leopard”), Macintosh software has been brought into conformance with the colour properties of sRGB.

accommodates display hardware without lookup tables. When the LUT is absent, code values map directly to voltage, and the situation is equivalent to video. So, the top row in the diagram pertains to PCs.

Computer graphics systems generally store tristimulus values in the framebuffer, and use hardware LUTs, in the path to the display, to gamma-correct on the fly. This is illustrated in the second row. Typically,

a 1⁄2.2-power function is loaded into the output LUT; in this case, picture rendering of 1.1 is achieved.

Macintosh computers, prior to Mac OS X 10.6, used the approach shown in the bottom row. The output LUT is, by default, loaded with a 1⁄1.45-power function. The combination of the default LUT and the usual 2.4-power display function results in a 1.66-power function that relates Macintosh R’G’B’ values (such as the values stored in a PICT file or data structure) to displayed tristimulus values.

If a desktop scanner is to produce Macintosh R’G’B’ values that display relative luminance correctly, then a 1.66-power function must be loaded to the scanner LUT. In the typical Macintosh situation, the 1⁄1.66, 1⁄1.45, and 2.4 exponents combine to achieve an end- to-end exponent of unity. This is suitable for scanning photographs or offset printed matter, where picture rendering is already incorporated into the image.

For Macintosh R’G’B’ values originated by application software, part of Macintosh gamma correction must be effected by application software prior to presentation of R’G’B’ values to the Macintosh graphics subsystem; the remainder is accomplished in the output LUTs. When scanning, part of Macintosh gamma correction is effected by the LUT in the scanner driver, and the remainder is accomplished in the output LUTs.

Halftoned printing has a builtin nonlinearity, owing to the phenomenon of dot gain. Reflectance from the printed page is approximately proportional to the 1.8-power of [1-CMYK] code values. Macintosh R’G’B’ values are not perceptually optimum; however, apparently by serendipity, Macintosh R’G’B’ coding is nearly perfectly matched to the dot gain of halftone printing. This led to the dominance of Macintosh computers in graphic arts and prepress, and made “gamma 1.8” image encoding a de facto standard for graphic arts.