Barco - RHDM-2301 - User manual ____________________________________________________ 95
Video signal processing
5.4 Effective gamma
The Rec.709 encoding equation assumes a linear tail and a power function with an
exponent 0.45. However, because of the linear offset and scaling, it is not correct to state
that the Rec.709 encoding equation is described by a gamma of 0.45. The Rec.709
encoding equation is best fitted with a pure power function with an exponent 0.52 (see
figure below). We call this “best fit” the “
effective gamma
”
.
The Rec.709 encoding equation fitted with a power function
5.5 Rendering intent
It is important to realize that the following statement is wrong:
“The video signal must be decoded at the display side in such a way to guarantee a linear
system transfer (a linear relation between the scene luminance and display luminance,
called ‘scene-to-screen’ or ‘end-to-end’ transfer)”
The mathematical inversion of the Rec.709 encoding equation that guarantees a linear
end-to-end luminance transfer is:
However, because of the linear offset, this inverse does not correspond to an effective
gamma of 2.2, but rather to an “effective gamma” of around 2.0 (as discussed in the
section “effective gamma” and illustrated in the figure below).
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