Luminance

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A tea light-type candle, imaged with a luminance camera; false colors indicate luminance levels per the bar on the right (cd/m²)

Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction.<ref>Template:Cite encyclopedia</ref> It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls within a given solid angle.

The procedure for conversion from spectral radiance to luminance is standardized by the CIE and ISO.<ref>Template:Cite book</ref>

Brightness is the term for the subjective impression of the objective luminance measurement standard (see Template:Section link for the importance of this contrast).

The SI unit for luminance is candela per square metre (cd/m²). A non-SI term for the same unit is the nit. The unit in the Centimetre–gram–second system of units (CGS) (which predated the SI system) is the stilb, which is equal to one candela per square centimetre or 10 kcd/m².

Description

Luminance is often used to characterize emission or reflection from flat, diffuse surfaces. Luminance levels indicate how much luminous power could be detected by the human eye looking at a particular surface from a particular angle of view. Luminance is thus an indicator of how bright the surface will appear. In this case, the solid angle of interest is the solid angle subtended by the eye's pupil.

Luminance is used in the video industry to characterize the brightness of displays. A typical computer display emits between Template:Val. The sun has a luminance of about Template:Val at noon.<ref>Template:Cite web</ref>

Luminance is invariant in geometric optics.<ref>Template:Cite book</ref> This means that for an ideal optical system, the luminance at the output is the same as the input luminance.

For real, passive optical systems, the output luminance is Template:Em equal to the input. As an example, if one uses a lens to form an image that is smaller than the source object, the luminous power is concentrated into a smaller area, meaning that the illuminance is higher at the image. The light at the image plane, however, fills a larger solid angle so the luminance comes out to be the same assuming there is no loss at the lens. The image can never be "brighter" than the source.

Health effects

Template:Further Retinal damage can occur when the eye is exposed to high luminance. Damage can occur because of local heating of the retina. Photochemical effects can also cause damage, especially at short wavelengths.<ref name="iec-2060825-1">IEC 60825-1:2014 Template:Cite book - TC 76 - Optical radiation safety and laser equipment</ref>

The IEC 60825 series gives guidance on safety relating to exposure of the eye to lasers, which are high luminance sources. The IEC 62471 series gives guidance for evaluating the photobiological safety of lamps and lamp systems including luminaires. Specifically it specifies the exposure limits, reference measurement technique and classification scheme for the evaluation and control of photobiological hazards from all electrically powered incoherent broadband sources of optical radiation, including LEDs but excluding lasers, in the wavelength range from Template:Val through Template:Val. This standard was prepared as Standard CIE S 009:2002 by the International Commission on Illumination.

Luminance meter

A luminance meter is a device used in photometry that can measure the luminance in a particular direction and with a particular solid angle. The simplest devices measure the luminance in a single direction while imaging luminance meters measure luminance in a way similar to the way a digital camera records color images.<ref>Template:Cite web</ref>

Formulation

File:Etendue.svg

Parameters for defining the luminance

The luminance of a specified point of a light source, in a specified direction, is defined by the mixed partial derivative <math display="block">L_\mathrm{v} = \frac{\mathrm{d}^2\Phi_\mathrm{v}}{\mathrm{d}\Sigma\,\mathrm{d}\Omega_\Sigma \cos \theta_\Sigma}</math> where

Template:Math is the luminance (cd/m²);
Template:Math is the luminous flux (lm) leaving the area Template:Math in any direction contained inside the solid angle Template:Math;
Template:Math is an infinitesimal area (m²) of the source containing the specified point;
Template:Math is an infinitesimal solid angle (sr) containing the specified direction; and
Template:Math is the angle between the normal Template:Math to the surface Template:Math and the specified direction.<ref>Template:Cite book</ref>

If light travels through a lossless medium, the luminance does not change along a given light ray. As the ray crosses an arbitrary surface Template:Mvar, the luminance is given by <math display="block">L_\mathrm{v} = \frac{\mathrm{d}^2\Phi_\mathrm{v}}{\mathrm{d}S\,\mathrm{d}\Omega_S \cos \theta_S}</math> where

Template:Math is the infinitesimal area of Template:Mvar seen from the source inside the solid angle Template:Math;
Template:Math is the infinitesimal solid angle subtended by Template:Math as seen from Template:Math; and
Template:Mvar is the angle between the normal Template:Math to Template:Math and the direction of the light.

More generally, the luminance along a light ray can be defined as <math display="block">L_\mathrm{v} = n^2\frac{\mathrm{d}\Phi_\mathrm{v}}{\mathrm{d}G}</math> where

Template:Math is the etendue of an infinitesimally narrow beam containing the specified ray;
Template:Math is the luminous flux carried by this beam; and
Template:Mvar is the index of refraction of the medium.

Relation to illuminance

File:Photometry radiometry units.svg

Comparison of photometric and radiometric quantities

The luminance of a reflecting surface is related to the illuminance it receives: <math display="block">\int_{\Omega_\Sigma} L_\text{v} \mathrm{d}\Omega_\Sigma \cos \theta_\Sigma = M_\text{v} = E_\text{v} R,</math> where the integral covers all the directions of emission Template:Math,

Template:Math is the surface's luminous exitance;
Template:Math is the received illuminance; and
Template:Mvar is the reflectance.

In the case of a perfectly diffuse reflector (also called a Lambertian reflector), the luminance is isotropic, per Lambert's cosine law. Then the relationship is simply <math display="block">L_\text{v} = \frac{E_\text{v} R}{\pi}.</math>

Units

A variety of units have been used for luminance, besides the candela per square metre. Luminance is essentially the same as surface brightness, the term used in astronomy. This is measured with a logarithmic scale, magnitudes per square arcsecond (MPSAS). Template:Luminance conversions

References

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External links

A Kodak guide to Estimating Luminance and Illuminance using a camera's exposure meter. Also available in PDF form.
Autodesk Design Academy Measuring Light Levels

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