Recent games have been heading towards Physically Based Rendering and this requires a solid understanding on lighting theory more than ever before. This time, I'm posting my note on Radiometry and Photometry.

Radiometry

Radiometry is basically ideas + mathematical tools to describe light propagation + reflection. Radiative Transfer is a study of transfer of radiant energy (which operates on geometric optics level - macroscopic properties of light suffice to describe how light interacts with objects much larger than light's wavelength).

Four Radiometric Quantities:

1. Flux (Radiant Flux/Power) - total amount of energy passing through a surface or region of space per unit time (J/s or Watt). Total emission from light sources is generally described in terms of flux.
2. Irradiance (E) - area density of flux arriving at a surface (Watt/m2)
Radiant Exitance (M) - area density of flux leaving a surface (Watt/m2)
3. Radiant Intensity (I) - flux density per solid angle (Watt/sr)
4. Radiance (L) - flux density per unit area, per unit solid angle (Watt/m2-sr)

Photometry

Photometry is a study of visible electromagnetic radiation in terms of its (human) perception. Each spectral radiometric quantity can be converted to its corresponding photometric quantity.
Luminance (Y) measures how bright a spectral power distribution appears to a human observer. The unit is cd/m2 or nit. Cd is the photometric equivalent of radiant intensity (Watt/sr).

Connecting Radiometry with Photometry
Photometric quantity can be obtained by integrating spectral radiometric quantity against the spectral response curve V(lambda) (the relative sensitivity of the human to various wavelengths).

QuantityRadiometric NameRadiometric UnitPhometric NamePhotometric Unit
powerRadiant FluxWLuminous Fluxlumen (lm)
power per unit areaIrradianceW/m2Illuminancelm/m2 = lux (lx)
power per unit solid angleRadiant IntensityW/srLuminous Intensitylm/sr = candela (cd)
power per unit area per unit solid angleRadianceW/m2-srLuminancelm/m2-sr = cd/m2 = nit

References

1. Radiometry and Photometry FAQ - http://fp.optics.arizona.edu/Palmer/rpfaq/rpfaq.pdf
2. Philips Lighting Theory - http://www.lighting.philips.com/main/connect/lighting_university/internet-courses/lighting-theory/lighting-theory/
3. Moving Frostbite to PBR - http://www.frostbite.com/wp-content/uploads/2014/11/course_notes_moving_frostbite_to_pbr.pdf
4. IES File Format - http://www.cn-hopu.com/upload/file/IES.pdf
5. Radiometry Summary - http://cs.brown.edu/~ls/teaching/RadiometrySummary.pdf