Logarithms can be used in gamma calculations and also to display the function graphically. A graph having logarithmic scales on both axes, a so-called log-log graph, displays a power function as a straight line, where the slope is gamma.

Hurter and Driffield, who did the definitive research on how photographic emulsion works, pointed out the inherent non-linearity of film chemistry over a hundred years ago. What they did was so well founded that it remains correct and useful today. The transfer function of a photographic emulsion relates density to exposure.

Fig.1 shows a typical transfer function. Note that the density rises with the amount of light resulting in a negative image. Density is defined as the log of the ratio of incident to transmitted power, and exposure is also a logarithmic parameter, where one stop is a step on a base-2 logarithmic scale.

The Hurter-Driffield curve for an emulsion is thus a log-log graph. The graph is basically S-shaped where over- and under-exposure is approached at the ends of the transfer function, but the mid-section of the function is straight, confirming that on a linear scale the density of an emulsion follows a power function of exposure. The slope of the function is the gamma of the emulsion. When the cathode ray tube was found to have a power function response, the term gamma was borrowed from photography to describe it.

The S-curve of film chemistry works well because there is no abrupt change in the transfer function. Contrast in parts of the scene at the limits of the exposure latitude becomes steadily more compressed as Fig.1 shows. Electronic camera sensors are quite different. They are linear and at a certain light level they will clip. At low light levels the signal disappears into the noise floor.

Traditional television cameras incorporate signal processing that simulates to some extent the soft-clip of film so that the wide dynamic range of real life can be mapped onto the limited dynamic range of television. The so-called knee in the transfer function may be adjustable.

In considering the overall television system, it is important to realize that before any non-linearity based on gamma correction is applied, the signal may already have suffered the non-linearity of a camera knee.

The era of mechanical television, with its Rube Goldberg* spinning disks and rotating prisms turned out to be a dead end and was given a decent burial by the development of the cathode ray tube (CRT) that was capable of much faster scanning than any mechanical system. Even the name gives away the age of this device because it was applied before it was understood that the rays emanating from the cathode are actually electrons.

A CRT is basically a triode vacuum tube having a hole in the anode through which an electron beam emerges to be further accelerated by an extra-high tension (EHT) supply that would spoil your whole day if you touched it. Tension was the early term used to describe potential difference, which today is called Voltage.

That beam can be raster-scanned across a screen internally coated with some sort of phosphor, which emits visible light when struck by the electrons. The whole system has to be in a vacuum, and one of the biggest problems with CRTs is providing enough mechanical strength to resist the atmospheric pressure on the outside.

Atmospheric pressure is about 15 pounds per square inch at sea level, which means that every square foot of CRT screen experiences a force of nearly a ton. In order to resist that, the face of the tube was actually a shallow dome, and atmospheric pressure would try to flatten the dome, thereby increasing its diameter. Fig.2 shows that a stout steel band was placed around the perimeter of the dome to resist that, just as is done in architecture.

Architects have the advantage that the mass of a building is relatively unimportant, whereas in CRTs a size was reached where there was real danger of the TV set falling through the floor. The large screens needed by high definition television would have to wait until flat screen technologies became viable. Not only did flat screens allow pictures to be considerably larger, they also evolved to allow considerably greater brightness and dynamic range.

Early CRTs had circular faces that were set behind a mask in a TV set. The circular shape resisted pressure efficiently, in the same way that aerosol cans, airliners and submarines use circular cross sections. During WWII the development of broadcast television was abandoned and work was instead focused on radar, where a circular display was needed to work with rotating radar beams.

Those are the reasons why the first TV systems had an aspect ratio of 4:3, as that shape would fit into a circle reasonably well. A secondary reason was that a square-ish image puts the least stress on the performance of the camera lens where resolution tends to be worse as distance from the optical axis increases.

As television was for a long time stuck with the aspect ratio of 4:3, the cinema adopted extremely wide aspect ratios for movies, because the CRT technology of the day couldn't do it.

The intensity of the CRT beam is controlled by voltage applied to the grid. Electrons, which have negative charge, are produced by the cathode and are naturally attracted towards the positive anode. The grid has to be biased with a negative voltage to interrupt the beam in the black parts of the picture.

The CRT has two mechanisms in series. One is the generation of the electron beam and the other is the conversion of electron energy to visible light in the phosphors. The transfer function of phosphors between electrons and light is very nearly linear, whereas the transfer function of the electron gun is anything but. The electron gun produces a beam intensity that is proportional to the input voltage raised to a power of 2.5, which is the gamma of the tube. The maximum brightness a CRT can produce is around 100 candela per square meter.

That figure of gamma comes from the physics of the gun and is fixed for a tube with the black level correctly set. The spread of gammas reported for CRTs is likely to be due to the use of maladjusted black levels.

The voltage of the video signal driving the grid could be shifted up and down and its amplitude could be altered by a couple of controls. If the grid bias should be too high, the darker parts of the picture would almost cut off the electron beam and appear nearly black. If the grid bias was too low the beam would not cut off and all black areas would appear grey, destroying contrast.

Clearly there is only one correct setting for the grid bias, which is where the black level is correct. In TV stations, a special test signal called PLUGE (picture line-up generating equipment) could be used. This signal included three bars, one at black, one slightly above black and one slightly below, and so technically out of gamut. The grid bias could accurately be set by ensuring the below black bar was invisible and the black bar was barely visible.

Analog television distribution systems would use black level clamps to keep the DC level correct. Part of the analog video waveform was always at black and that part was sampled and used to shift the DC conditions until the correct voltage was obtained.

With the black level of the video signal and of the CRT correctly set, the brightest part of the picture could be adjusted with the gain control. In consumer TVs, these controls were misleadingly labeled brightness and contrast. There was only one correct setting for the "brightness" control, and trying to use it to make the picture brighter simply destroyed contrast. To make the picture brighter required use of the "contrast" control as Fig.3 shows. 

As all CRTs apply the same power function to the video signal, it has to be subject to an opposing function somewhere between the camera and the display. If the opposing function, known as gamma correction, should be made slightly weaker than the mathematical ideal, there would be an overall gamma function.

Fig.4 shows two possibilities for the use of gamma correction. At a) the correction is done at the camera and the transmission is non-linear. At b) the correction is done at the receiver and the transmission is linear. Superficially, there seems to be no difference, but a more detailed study shows advantages and disadvantages to both approaches. In a broadcast system there are many more displays than cameras, so it was more economic to gamma correct at the camera as the receiver was simplified.

When gamma was first adopted, there was no alternative to the CRT and pictures on all CRTs would have limited brightness and would all be viewed in similar surroundings. There was then no obvious difficulty in introducing an overall gamma at the camera. This overall gamma introduced early into the video signal can be thought of as a rendering intent built in to the television standard.

Display technology has improved by leaps and bounds and there is now a wide range of brightness available permitting greater variation in viewing environment. A single overall gamma introduced at or near the camera can no longer be optimal.

*Rube Goldberg in USA corresponds to Heath Robinson in UK.