As you’ve probably already noticed, this and the previous constant luminance post are based on the book: “DITITAL VIDEO AND HDTV Algorithm and Interfaces” Charles Ponyton. I’m studying this book and summarizing what I learn for my educational purpose.
In the previous post, we’ve learned how and why video system applies transfer function to accomplish the constant luminance. However, in the real world scenario, the strict constant luminance is not really what we want.
When watching video on TV, the surround luminance is much darker than the one of the real scene luminance. When the surround luminance is dark, it’s known by experiment that we feel less sensitive to the contrast. To make the video reasonably high contrast, we have to modify the color value to increase contrast artificially.
In television, it’s known that applying 1.25 power function results in the good tone scale.
In cinema, where the surrounding luminance is much darker, 1.5 power function would be required.
Let’s bring back the block diagram from the previous post.
To accomplish good video in TV, we need 1.25-power before the display.
Now, we can combine the 0.4-power in camera and 1.25-power in the post processing because both of them are under our control. (The display 2.5-power comes from physics limitation, so we cannot change). Here is the math:
Therefore, we should apply 0.5-power instead of 0.4-power in the camera.
Now, let’s verify it against Rec 709. The Rec 709 specifies the encoding gamma (The transfer function applied in the camera) to be the following formula.
The red line below is the plot of Rec 709 transfer function. The red line is 0.5-power function. They are almost matched.
Note that it’s wrong to use 0.45-power just because the exponent component of Rec 709 is 0.45. Due to the offset, 0.5-power is much closer to the Rec 709. See the graph below. Green is Rec 709 and red is 0.45-power.
Conclusively, it explains the rational of Rec 709 and the reason video system uses 0.5-power function as the encoding gamma.