Colour science/07/Light ↔ signal ↔ display

Light ↔ signal ↔ display

Gamma and transfer functions: OETF, EOTF and OOTF

Why video encodes light non-linearly, how strict gamma differs from a transfer function, how OETF/EOTF/OOTF relate, and where Gamma 2.2/2.4, BT.1886, sRGB, PQ, HLG and camera Log fit.

Linear lightOETFEOTFOOTFBT.1886

In plain language

A transfer function explains what a numeric code value means in relation to light. Until you know that function, 0.5 is just a number: it does not have to represent half the scene exposure or half the display luminance.

10 sections4 primary references

Quick reference

Definitions and numbers worth keeping in view

OETF

Scene light → encoded signal

Encoding side; BT.709 is a classic example.

EOTF

Encoded signal → display light

Display side; BT.1886 defines a reference HDTV EOTF.

OOTF

Scene → display relationship

Describes the system/rendering relationship and is tied to OETF/EOTF.

Not all gamma

Log · PQ · HLG ≠ pure power

In interfaces, Gamma is often the label for a broader transfer-encoding category.

Transfer functions

Linear light and encoded signal are different domains

Conceptual curves: real standards use specific equations and breakpoints. The drawing explains direction and domain, not exact code values.

OETF · EOTF · OOTF

OETF

scene light → electrical / encoded signal

EOTF

signal → display light

OOTF

scene light → display light (system relationship)

Important

sRGB is piecewise; Rec.709 OETF is not simply 'Gamma 2.4'; PQ and HLG are different transfer-function families.

Start with linear light

In a linear-light representation, doubling the numeric value corresponds to doubling the physical light quantity within the chosen normalisation. This is useful for physically meaningful operations such as compositing, blur, some transforms and light-transport maths. But storing an entire practical dynamic range directly in a limited number of code values is often inefficient: too many levels are spent where vision distinguishes them poorly and too few where it is more sensitive.

Why signals are made non-linear

Historically, television transfer curves were connected both to CRT electro-physics and to efficient allocation of signal levels. In digital systems the latter idea remains important: non-linear encoding distributes precision more usefully across the range. Encoded 0.5 therefore usually represents much less than 50% linear light, and an inverse transform is needed to recover a physically meaningful light domain.

Why the word Gamma is constantly misleading

Strictly, gamma is the exponent in a power function such as y=x^γ. Camera, NLE and CST interfaces, however, often use Gamma as a broad category for transfer encodings: power-law gamma, Rec.709-like curves, camera Log, HLG and others. A menu labelled Gamma therefore does not imply that every option is mathematically a pure power function.

OETF: scene light → encoded video signal

The Opto-Electronic Transfer Function describes the conversion of scene light or a normalised camera signal into a non-linear video signal. A classic example is the OETF in BT.709. It is not the monitor EOTF and should not automatically be read as 'Gamma 2.4'. OETF belongs to the encoding side of the system.

EOTF: encoded signal → display light

The Electro-Optical Transfer Function performs the inverse conceptual job on the display side: it defines how much luminance the screen should emit for a given signal value. ITU-R BT.1886 defines a reference EOTF for flat-panel displays used in HDTV studio production. In practical conversation it is often associated with gamma ≈2.4, but BT.1886 incorporates display black/white levels and is not merely one universal pure power equation in every condition.

OOTF: the overall scene → display relationship and rendering intent

OOTF describes the system relationship between scene-referred light and display-referred output light. It can include not only technical decoding but rendering intent — how the scene should be visually adapted to the viewing system. BT.2100 treats OETF, EOTF and OOTF as related functions: given two, the third can be derived.

Gamma 2.2 and 2.4: not better/worse, but different viewing assumptions

Gamma 2.2 is historically close to computer/desktop-display context, while 2.4 is widely used for reference SDR video monitoring in a darker controlled surround. The choice should not be made as '2.4 is more contrasty, therefore more professional': the standard, display calibration, output tagging and real viewing environment all matter.

sRGB is not a pure Gamma 2.2 either

sRGB uses a piecewise transfer: a linear segment near black followed by a power segment with exponent 2.4 in the decoding formula. It is often loosely described as gamma 2.2 because of its overall effective behaviour, but precise colour transforms require the actual piecewise function. This matters especially for linear compositing and conversions between sRGB and video spaces.

Log, PQ and HLG may live in the same menu but solve different problems

Camera Log is a scene-referred encoding for a large exposure range; PQ is display-referred perceptual quantisation for HDR; HLG is an HDR television transfer system with a different architecture. All connect numbers to light, so they are conveniently grouped as transfer functions, but calling them all the same 'gamma' is technically inaccurate.

How to read Gamma in CST and Color Management

If CST says Input Color Space = ARRI Wide Gamut 4 and Input Gamma = LogC4, the first parameter describes chromaticities/primaries and the second the transfer encoding. They form a pair. Output Rec.709 + Gamma 2.4 describes another signal state. Gamma cannot be chosen by visual contrast alone; you first need to know what the source actually encodes and what state you need to convert it into.

What this changes in post

The key skill is to stop reading Gamma as a contrast knob. In a technical pipeline it is part of the definition of how code values relate to scene light or display light.

Common mistakes

Calling every transfer function an ordinary power gamma.

Treating the Rec.709 OETF and Gamma 2.4 as the same thing.

Treating BT.1886 as merely a fixed 2.4 power function without display black/white context.

Choosing Input Gamma by how flat the picture looks.

Performing compositing in a non-linear domain when the operation requires linear light.

Standards and primary references

Technical definitions are anchored to standards bodies and primary specifications wherever that distinction matters.

ITU-R BT.709

HDTV standard containing signal parameters and the classic Rec.709 OETF.

ITU-R BT.1886

Reference EOTF for flat-panel HDTV studio displays.