## 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.