Luminance and lightness

In Colour science for video, on page 287, I will describe how spectral power distributions (SPDs) in the range 400 nm to 700 nm are related to colours.

The term luminance is often carelessly and incorrectly used to refer to what is now properly called luma. See Relative luminance, on page 258, and Appendix A, YUV and luminance considered harmful, on page 567.

Perceptual coding is essential to maximize the performance of an image coding system. In commercial imaging, we rarely use pixel values proportional to luminance; instead, we use pixel values that approximate lightness. This chapter introduces luminance and lightness.

Relative luminance, denoted Y, is what I call a linearlight quantity; it is directly proportional to physical radiance weighted by the spectral sensitivity of human vision. Luminance involves light having wavelengths in the range of about 400 nm to 700 nm. (Luminance can also be computed as a properly weighted sum of linearlight red, green, and blue tristimulus components according to the principles and standards of the CIE.)

Video signal processing equipment does not compute the linear-light luminance of colour science; nor does it compute lightness. Instead, it computes an approximation of lightness, called luma (denoted Y’), as a weighted sum of nonlinear (gamma-corrected) R’, G’, and B’ components. Luma is only loosely related to true (CIE) luminance. In Constant luminance, on page 107, I explained why video systems approximate lightness instead of computing it directly. I will detail the nonlinear coding used in video in Gamma, on page 315. In Luma and colour differences, on page 335, I will

outline how luma is augmented with colour information.

Radiance, intensity

Image science concerns optical power incident upon the image plane of a sensor device, and optical power emergent from the image plane of a display device.

See Introduction to radiometry and photometry, on page 573. Some people believe that light is defined by what we can see; for them, electromagnetic radiation outside the band 360 nm to 830 nm isn’t light!

The unit of luminous intensity is the candela [cd]. It is one of the seven base units in the SI system; the others are meter, kilogram, second, ampere, kelvin, and mole.

I presented a brief introduction to lightness terminology on page 27.

Radiometry concerns the measurement of radiant optical power in the electromagnetic spectrum from 3× 1011 Hz to 3× 1016 Hz, corresponding to wavelengths from 1 mm down to 10 nm. There are four fundamental quantities in radiometry:

•Radiant optical power, flux, is expressed in units of watts [W].

•Radiant flux per unit area is irradiance; its units are watts per meter squared [W·m-2].

•Radiant flux in a certain direction – that is, radiant flux per unit of solid angle – is radiant intensity; its units are watts per steradian [W·sr-1].

•Flux in a certain direction, per unit area, is radiance; its units are watts per steradian per meter squared [W·sr-1·m-2].

Wideband radiance is measured with an instrument called a radiometer. A spectroradiometer measures spectral radiance – that is, radiance per unit wavelength incident upon the instrument. A spectrophotometer incorporates a light source, and measures spectral reflectance (or for an instrument specialized for film, spectral transmittance).

Photometry is essentially radiometry as sensed by human vision: In photometry, radiometric measurements are weighted by the spectral response of human vision (to be described). This involves wavelengths (symbolized λ) between 360 nm to 830 nm, or in practical terms, 400 nm to 700 nm. Each of the four fundamental quantities of radiometry – flux, irradiance, radiant intensity, and radiance – has an analog in photometry. The photometric quantities are luminous flux, illuminance, luminous intensity, and (absolute) luminance. In video engineering, luminance is the most important of these.

Luminance

The Commission Internationale de L’Éclairage (CIE, or International Commission on Illumination) is the international body responsible for standards in the area of colour. The CIE defines brightness as the attribute of a visual sensation according to which an area appears to

exhibit more or less light. Brightness is, by the CIE’s definition, a subjective quantity: It cannot be measured.

CIE Publication 15:2004,

Colorimetry, 3rd Edition (Vienna, Austria: Commission Internationale de L’Éclairage).

The y is pronounced WYE-bar. The luminous efficiency function is sometimes denoted V(λ), pronounced VEE-lambda.

The CIE has defined an objective quantity that is related to brightness. Luminance is defined as radiance weighted by the spectral sensitivity function – the sensitivity to power at different wavelengths – that is characteristic of vision. Put succinctly, brightness is apparent luminance.

The luminous efficiency of the CIE Standard Observer,

_

denoted y(λ), is graphed as the solid line of Figure 24.1 above._The luminous efficiency function is also known as the y(λ) colour-matching function (CMF). It is defined numerically, is everywhere positive, and peaks at about 555 nm. When a spectral power distribution (SPD) is integrated using this weighting function, the result is luminance, symbolized Lv (or, where radiometry isn’t in the context, just L). Luminance has units of candelas per meter squared, cd·m-2 (colloquially, “nits” or nt).

In continuous terms, luminance is an integral of spectral radiance across the spectrum. It can be represented in discrete terms as a dot product. The magnitude of luminance is proportional to physical power; in that sense it resembles intensity. However, its spectral composition is intimately related to the lightness sensitivity of human vision.

Luminance factor is not a synonym for relative luminance: Luminance factor refers to the reflectance – relative to a perfect diffuse reflector – of a reflective surface.

I will introduce XYZ and LMS in The CIE system of colorimetry, on

page 265. I will introduce RGB in

Colour science for video, on page 287.

You might intuitively associate pure luminance with grey, but a spectral power distribution having the shape of Figure 24.1 would not appear neutral grey! In fact, an SPD of that shape would appear distinctly green. As

I will detail in The CIE system of colorimetry, on page 265, it is very important to distinguish analysis

functions – called colour-matching functions (CMFs) of human vision, or the spectral responsivity functions

(SRFs) of an image sensor – from synthesis functions, spectral power distributions (SPDs). The luminous efficiency function takes the role of an analysis function, not a synthesis function.

Relative luminance

In image reproduction – including photography, cinema, video, and print – we rarely, if ever, reproduce the absolute luminance of the original scene. Instead, we reproduce luminance roughly proportional to scene luminance, up to the maximum luminance available in the presentation medium. We process or record an approximation to relative luminance. To use the unqualified term luminance would suggest that we are processing or recording absolute luminance.

Once normalized to a specified or implied reference white, relative luminance is given the symbol Y; it has a purely numeric value (without units) which runs from 0 to 1 (which I prefer), or traditionally, 0 to 100. (Relative luminance is often called just “luminance.”)

Relative luminance, Y, is one of three distinguished tristimulus values. The other two, X and Z, are also unitless. Various other sets of tristimulus values, such as LMS and RGB, have an implied absolute reference, come in sets of three, and also carry no units.

Luminance from red, green, and blue

The luminous efficiency of vision peaks in the mediumwave region of the spectrum: If three monochromatic sources appear red, green, and blue, and have the same radiant power in the visible spectrum, then the green will appear the brightest of the three, the red will appear less bright, and the blue will be the darkest of the three. As a consequence of the luminous efficiency function, all saturated blue colours are quite dark, and all saturated yellows are quite light.