Gamma Calculation

A computer monitor is able to display any number of pixel intensities. Therefore depending on the resolution of the monitor you might for example display 256 gray levels. Intuitively it might seem proper to divide the total range of the itensities by 256 to come up with the different intesities levels to use. This however when viewed by the human eye will seem very unnatural.

This is because the eye is sensitive to ratios of intensity levels rather than absolute intensity. This means that the perceived change in intensity from 0.1 to 0.11 is the same as the perceived change in intensity from 0.5 to 0.55. Therefore to select the n+1 intensities between 0 and 1 so that they have equal steps in brightness (perceived intensity) we have the relationship

I0=I0,  I1=rI0,  I2=rI1=r2I0, .... , In=rnI0=1

Therefore,

r=(1/I0)1/n

and

Ij = r j-1 I0 = I0(n-j)/n

The intensity of a display is given by the formula

I=a(v) gamma

where v=voltalge applied to electron gun and gamma and a are constants and depend on a particulat device. ( A typical value for gamma is 2.2)

Therefore to find the voltage that will be applied to the electron for a given I (intensity) we have the formula

V = (I/a)1/gamma

For more information on gamma correction or to read the Frequently Asked Questions see the links below.

An Explanation of Monitor Gamma

Gamma FAQ from SUN

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