Radiance and Luminance – the many funny units

In electronics, we typically have very well standardized measurement units, at least when it comes to units as Volts, Amperes, Watts and so on… However, I cannot say the same about the optics field. I have always been confused when having to deal with photometric units, but after a recent discussion with one of the camera gurus in our field, I got even more confused, which also gave the inspiration for this writing. So what is the difference between radiance and luminance and how obscure can the life of a camera designer get with such a cocktail of measurement units?

Radiance is a measure of radiometric power ꟷ it measures the rate of light energy flow. So far so good! It is (normally!) expressed in watts or joules/sec per unit area, usually steradian per squere meter.

Luminance is a measure of the power of visible light. But what is visible light? This is where things get confusing. Within Luminance, we can get (generally) two different flavours, possibly inspired by the fact that a human eye has two different photoreceptor cells:

rods ꟷ which are extremely sensitive, and can be triggered by a single photon. So at very low light levels, what we see is primarily due to the rod signal. Which also explains why colors cannot be seen at low light levels, a single photon does not carry color information.
cones ꟷ they require significantly brighter light (more photons) in order to produce a signal. And thus provide us with color information.
photosensitive gangleon cells ꟷ these were discovered recently and are responsible for our biological clock’s synchronization and I assimilate them with electronic comparators.

Okay the last paragraph drifted a bit, back to luminance, the two different flavours of it are:

  • Photopic flux is expressed in lumens and is weighted to match the responsivity of the human eye, which is mostly sensitive to yellow-green. But still? What is mostly sensitive to yellow-green? We are all different and there is no single sharp standard.
  • Scotopic flux is weighted to the sensitivity of the human eye in the dark adapted state, here as well, what is dark anyway?

Two derivatives of luminance and radiance are irradiance and illuminance accordingly. These are measures of the corresponding light flux per unit area at the receiver side. In other words, radiance is the energy radiated from the light source towards a unit area, and irradiance is the energy received without the light loss during its pathway. Typically expressed as W/m2/sr and lm/m2/sr. But there is more to it, there exist a dozen of other measurement units, and here is where you should get some popcorn and start reading or browsing around wikipeida:

Let’s start with the candela as I will have to refer everything to this unit which is part of the SI standard.

1 candela (new candela) is the intensity of a source that emits monochromatic light of frequency 540×1012 hertz and that has an intensity of 1683 watts per steradian. But why 1683 watts? The number 683 very much smells like a weak british horse’s power to me… Prior to 1948 the candela unit was not standartized and a number of countries used different values for luminous intensity, typically based on the brightness of the flame from a “standard candle”. Ha-ha-ha!

Then we start:

Nit ꟷ 1 cd/m2

Stlib ꟷ it is a unit of luminance for objects that are not self-luminous. Comes from the Greek word stilbein which means “flicker”. 1 stlib = 104 candelas per square meter

Apostlib ꟷ 3.14 apostlib = 1 cd/m2 – somebody thought that can neglect the rest of pi with an such an easy hand!?

Blondel ꟷ 1 blondel = 1/π .10−4 stlib – this unit is obviously reserved to blonde people

Lambert ꟷ 1 lambert = 1/π per candela/cm2

Scot ꟷ 1 scot = 1/10−3 .π candela/m2

Bril ꟷ 1 bril = 1/10−7 .π candela/m2

Foot-lambert ꟷ 1 foot-lambert = 1/π candela per square foot

Foot-candle ꟷ 1 foot-candle = lm/ft2

The image sensors field is baffled with all these units, some of which are still in use today. A possible explanation for why we have so many photometric units, compated to a single sharp one for electric current, is that we as humans naturally have light detectors, but not electric current ones (well, sort of). Each of us owning such receptors can create the perfect environment for speculation. This, combined with the vigorous victorian age pride is possibly the cause for the creation all those weird units. What do you think?

Lastly, here, if somebody asks you, this is one foot-candle!

One foot-candle

One foot-candle, courtesy of General Electric