Gamma and its Bases

Michael H. Brill
(from Information Display, January 1998)

When voltage in a cathode tube sends slow electrons speeding,
That cause the phosphor dots to glow, the light for TV's needing
Is made according to a law that varies day-by-day.
That law says voltage makes the light with power gamma. Pray
What gamma is the proper one that heaven handed down?
That number is a vagary that makes grave sages frown.

One group of such, NTSC, declared it 2.2.
The makers of the cameras, and of home receivers too
Agreed, and signed a pact, and went their merry ways, but when
The TV sets themselves belied the hallowed value, then
The sages separately declared two better values. Who
Could argue with the averages or with a purpose true?

Sir Charles1 announced a purpose, and the value 2.5.
He said the TV watchers and the viewers who're alive
Undo the bloody gamma and retrieve the voltage V:
A marvelous coincidence--a clever fellow, he!
But 2.5 is not quite the inverse of 1 on 3,
The exponent that sages say is part of you and me,
That hammers frightful wattages into benign perception.
To say we're made for 2.5 perhaps is self-deception.

I much prefer the gamma that Sir Denis2 claims is true.
That gamma value's 2.3 and holds a secret too.
When input by a voltage in a base Napierian,
This gamma makes a luminance whose value in base ten
Is proportional to voltage in the base "au naturel,"
And serves us folks who work in tens and count on fingers well.

And so I end this essay of the gamma, put to song,
And hope that betas strike me if my tale of gamma's wrong.

1 Charles Poynton, "Gamma" and its disguises: The nonlinear mappings of intensity in perception, CRTs, film and video, SMPTE J., December 1993, 1099-1108.

2 Denis Pelli, Pixel independence: Measuring spatial interactions on a CRT display, Spatial Vision 10 (1997), 443-446. The value 2.3 is from this paper, but the log-base interpretation is not his fault!

Reprinted by permission of the author.