Page 125 - Computational Colour Science Using MATLAB

112 CHARACTERIZATION OF COMPUTER DISPLAYS
iteration may be required to perform the inverse mapping (Hardeberg, 2001).
Bala (2003) provides an excellent source of further information on computa-
tional methods for device characterization.
For many devices the process of characterization can be considered to consist
of two stages. The first stage performs a linearization, sometimes termed gamma
correction, for certain devices. The second stage transforms the linearized values
into the CIE XYZ tristimulus values. Practical device characterization will
almost certainly require, in addition, that the spatial and temporal properties of
the device be accounted for. Johnson (2002) notes that, even if a non-linear
transform is used, usually it is better to perform the linearization process and
then use approximately linear values as input to the non-linear transform.
In this chapter we describe some methods for the characterization of
computer-display devices or monitors.

7.2 Gamma

The luminance generated by a computer monitor generally is not a linear
function of the applied signal. Most CRT devices exhibit a power-law response
to voltage so that the luminance produced at the face of the display is
approximately proportional to the applied voltage raised to a power in the range
2.35–2.55 (Poynton, 2002). The value of the exponent of this power function is
sometimes called the gamma of the CRT or monitor. Figure 7.1 shows the
relationship between applied voltage and displayed luminance for a typical CRT
at three different settings of picture control (sometimes referred to as contrast).
In a typical 8-bit digital-to-analogue converter (DAC), the lowest voltage
shown in Figure 7.1 will be coded by the value 0, whereas the highest voltage will
8
be coded by the value 255 (2 1).
The relationship between the voltage applied to the CRT’s phosphors and the
displayed luminance can be approximated by the gamma relationship
L ¼ V , ð7:1Þ
g
where L is the luminance of the display, V is the applied voltage (this is linearly
related to the RGB values) and g is the gamma.

7.3 The GOG model

Although all vacuum tubes, including CRTs, exhibit an inherent non-linearity,
the term gamma is commonly used to represent the non-linearity of the entire
opto-electonic transfer function of the display system. Berns et al. (1993a, 1993b)
have studied the relationship between the digital monitor values (sometimes
referred to as DAC values) and the displayed luminance for a range of typical