Transfer Functions

You may have heard of gamma, a power function that corrects for non-linear response in CRT displays and was introduced back when television was in its infancy. Transfer Function is a more accurate term to describe gamma, as a strict power function is only one method of creating the function's curve. Other methods use a linear section at the bottom of the curve. The main difference between the major transfer functions supported by HiRes are the slope of the linear portion, the transition point ("knee") to a power function, and the exponent of the power function.

HiRes supports three widely used transfer functions in addition to the simple power function.
To the left are the curves of the functions that are used for converting from linear intensity values. These functions are well documented on the web, particularly at wikipedia.

sRGB is the default transfer function for all still images.

SMPTE 170M is the same function used in ITU 709, and the default for mpeg video.

As can be seen, sRGB closely follows the power function of 2.2, while the two SMPTE functions are very similar.
The general formula for transfer functions is:

Encoding Decoding

V = S * Lc for LC < Ke Lc = V / S for V < Kd

V = (1 + A) * Lc^p - A Lc = ((V + A) / (1 + A))^1/p

symbol meaning sRGB SMPTE 170M
ITU 709 SMPTE 240M

S slope of linear portion 12.92 4.5 4.5

Ke encoding knee 0.00304 0.0180 0.0228

Kd decoding knee 0.03928 0.0812 0.0912

A offset 0.055 0.099 0.1115

p power 1/2.4 0.45 0.45

Also note that S = Kd / Ke

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