Gamma correction

In this month's Transition to Digital, Michael Robin discusses the nonlinear relationship between a pixel's value and its displayed intensity on a color TV monitor
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The cathode ray tube (CRT), the display device used in most computer displays, video monitors, television receivers and oscilloscopes, was invented by German scientist Karl Ferdinand Braun in 1897. It features a phosphor-coated screen that emits a visible light when struck by a beam of electrons emitted by a heated cathode. The electrons are concentrated into a beam, and this beam is deflected by a magnetic field to scan the viewing end (anode), which is lined with phosphorescent material. When the electrons hit this material, light is emitted.

In a television CRT, the entire area of the tube is scanned in a fixed pattern called a raster. A picture is created by the video signal modulating the intensity of the electron beam. In modern television sets, the beam is scanned with a magnetic field applied to the neck of the tube by a magnetic yoke, a set of coils driven by electronic circuits. Color CRTs use three different materials that specifically emit green, blue and red light closely packed together in strips (in aperture grille designs) or clusters (in shadow mask CRTs). There are three electron guns, one for each color, and each gun can reach the dots of only one color.

The transfer characteristic

In the early days of television, it was discovered that CRTs do not produce a light intensity that is proportional to the input voltage. The relationship between the video signal and the CRT-generated light (the transfer function) is nonlinear and is usually described as a power law:

Light intensity = Voltγ

Gamma (γ) has a value of 2.8 (PAL and SECAM) or 2.2 (NTSC). The transfer function is commonly referred to as gamma curve. It is caused by electrostatic effects inside the electron gun.

Figure 1. Correction of a CRT nonlinear transfer curve. Click here to see an enlarged diagram.

Because most sensors used in television cameras produce output voltages proportional to the scene light intensity, a correction for CRT gamma must be applied somewhere in the system. Figure 1 shows how a nonlinear CRT display is compensated by a pre-correction of the original signal. In this drawing, the input and the output are both scaled to the range of 0 to 1, with 0 representing black and 1 representing maximum white (or red, etc.).

Historically, the gamma correction is effected in the camera. This has a positive effect on visibility of the transmission-generated noise in the reproduced picture. This is due to the fact that the human eye is more sensitive to noise in the dark areas, where the gamma behavior of the CRT reduces its visibility. Essentially, the gamma pre-correction acts as a “pre-emphasis” compensating the “de-emphasis” effect of the CRT. In a color television camera, the green, blue and red signals are pre-distorted to match the reference characteristic of the CRT as follows:

Gtransmit = Gpickup1/γ = E'G

Btransmit = Bpickup1/γ = E'B

Rtransmit = Rpickup1/γ = E'R

E' is the conventional symbol of a gamma-corrected video signal.

Early cameras using tubes were notoriously unstable. In a multicamera studio, each camera had to be optimized using a gray-scale backlit test-picture source. After each camera was optimized, the cameras had to be matched to produce identical signals. These camera adjustments used to take a long time, and it was usual to let them heat up and achieve constant temperature. It was not unusual for the cameras to be switched on in the morning and adjusted at 12.00 for the evening news show. The gamma compensation was marginal at best, but that's all that the technology had to offer at the time.

Contemporary methods

The appearance on the market of solid-state cameras resulted in more stable and predictable performance and the possibility of an improved CRT gamma pre-correction. The ANSI/SMPTE 170M-1994 Standard (SDTV) and ITU-R BT.709 Standard (HDTV) reflect this situation by redefining the CRT electro-optical characteristic and the compensating opto-electronic characteristic of the reference camera.

The CRT electro-optical transfer characteristic is divided into two regions identified as follows:

  • The region where Vr varies between 0.0812 and 1. In this region, the CRT transfer characteristic is expressed as:LT = [(Vr + 0.99/1.099)/1.099]γ
  • The region where Vr varies between 0 and 0.0812. In this region, the CRT transfer characteristic is expressed as:

LT = Vr/4.5


Vr is the video signal level driving the reference CRT reproducer normalized to the system reference white.

LT is the light output from the reference reproducer, normalized to the system reference white.

γ = 2.2

The opto-electronic transfer characteristic of the reference camera is similarly divided into two regions identified as follows:

  • The region where LC varies between 0.018 and 1. In this region, the camera transfer characteristic is expressed as:VC = 1.099 × LC(1/γ) - 0.099
  • The region where LC varies between 0 and 0.018. In this region, the camera transfer function is expressed as:

VC = 4.500 × LC


VC is the video signal output of the reference camera, normalized to the system reference white.

LC is the light input to the reference camera, normalized to the system reference white.

γ = 2.2

While superior to earlier standards, there still remains a nonlinearity problem in the region of near-black because the CRT curve cannot be perfectly compensated. This has a main effect of the crushing of detail near black (e.g. shadows) and the reduction of saturation of dark colors. These effects are commonly referred-to as “the video look.”

Depending on the camera design, the gamma correction may be fixed, variable or missing altogether, e.g. in inexpensive consumer products. Various cameras available on the market offer the operator an additional transfer characteristic control called the “knee.” The knee function is used to overcome clipping problems by attenuating or compressing highlights that might otherwise overload the system. Essentially, the transfer characteristic follows the prescribed curve up to a “knee break-point.” Above that level, the gain is considerably reduced.

Depending on the camera design, the knee curve function operates before or after the gamma-correction. Thus, it may be curved or flat. Used by an astute operator, the gamma and the knee controls may be used to create the elusive “film look.” Try to standardize this!

Plasma and LCD displays

Unlike CRT displays, plasma and LCD displays feature a linear transfer characteristic. Early uses of plasma and LCD displays were with laptop computers. With rare exceptions, such as computers used in editing suites, their linear transfer characteristic was ignored.

However, the side-by-side display of the same television picture on a plasma and CRT display revealed that the CRT displayed correct blacks, while plasma displays were unable to display true blacks, turning them into grays. The availability of large plasma displays for home use forced the manufacturers to consider the problem, and they came out with a handy remote-selected black level rendition left to the choice of the user. This function, when selected, forces a nonlinear transfer curve on the plasma display, making its response similar to that of a CRT. Leaving the choice in the hands of the viewer brings back memories of the “hue control,” which, when left in the hands of an inexperienced viewer, all but ensured the display of people with green faces.

In a few years, plasma displays will replace aging CRT-display television sets. Given the large quantity of television archives encoded with gamma pre-correction, we are faced with an incompatibility problem that cannot be ignored. Neither the removal of the gamma pre-correction in cameras nor modifying the response of plasma display offers an ideal solution. Suggestions anyone?

Michael Robin, a fellow of the SMPTE and former engineer with the Canadian Broadcasting Corp.'s engineering headquarters, is an independent broadcast consultant located in Montreal, Canada. He is co-author of Digital Television Fundamentals, published by McGraw-Hill and translated into Chinese and Japanese.

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