Light output – lumen, lux and the candle

Imagine the following: the SI base unit of luminous intensity (read: light output) – candela – is based on the output from a candle. Not sure whether it is one of the big fat candles or rather a thin taper type candle. But candle types is not the main concern here…

Obviously being an SI base unit, the candela (cd) is better defined than just the light output from a simple candle: the candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 Hz (~555 nm) and that has a radiant intensity in that direction of 1/683 W per steradian (sr) – en.wikipedia.org/wiki/Candela. All good and well, but what is a steradian? To be explained a little further below.

Next on the definition list is the lumen. A lumen (lm) is the SI derived unit for luminous flux, defined as 1 lm = 1 cd . sr – en.wikipedia.org/wiki/Lumen_(unit). “Luminous” refers to the amount light output that the average human perceives – per some standard – and flux refers to whatever surface the light falls on. For the sake of the exercise let’s use the CIE 1931 Luminous Efficiency function as the human perception standard, shown below. For those paying attention there appears to be no difference between a lumen and a candela – at least numerically this is correct. However note that a lumen represents the light output produced across the complete human perception range, and the fact that 1 candela = 1 lumen is a consequence of the fact that 1 candela is at the “peak” perception wavelength of 555 nm, i.e., a Dirac delta function at said wavelength (en.wikipedia.org/wiki/Dirac_delta_function).

So this is the radiant energy in the wavelength range of 400-700 nms. Hopefully it’s clear to draw the distinction between luminous flux and radiant flux, where the latter is the radiant energy for all wavelengths, i.e., not “bandwidth limited” to the average human perception of light.

Before moving onto the lux, an explanation for a steradian is now required. The steradian is to the 3D world what the radian is to the 2D world when specifying an angle. More accurately, a steradian is the SI unit of solid angle, analogous to the radian which quantifies planar angles. But what does it mean? Wikipedia of course helps out here and I’ve shamelessly poached from their image library, below. A steradian is the surface area of the cone bottom, when considering a sphere, divided by the radius of the sphere squared. In practical terms, and presuming that unit measures are used, a 1 m high light source subtends 1 steradian when the measurement area is a spherical surface of 1 m2. A little complicated and also impractical unless one is measuring a lamp in a spherical chamber.

And so finally, the lux (lx) is the SI derived unit of illuminance, equal to one lumen per square metre – en.wikipedia.org/wiki/Lux. This is the 2D practical measurement for understanding how much light – per average human visual perception don’t forget – is hitting that 1m x 1m area one may be looking at. In practice this unit of measurement is used in some instances and not in others. Go figure.

Now to a good question is: how many lumens is a lamp radiating based on spectrum and its power input. See the next post: Quantifying light output

By | 2018-05-08T21:33:39+00:00 Sunday, 18 June 2017|Lighting|1 Comment

About the Author:

Colin is the chief designer at lagrangianpoint. His interests are in (too) many areas - to name a few: the Arduino platform, LED lighting, Software Defined Radio, statistics, trying to learn French, cooking and wine. Unfortunately lagrangianpoint isn't his day job just yet - but it's the plan. In the meantime he is Clinical Operations Manager for Cochlear EMEA. (Cochlear specialises in implantable hearing solutions for adults and children who are affected by deafness or hearing loss - check out www.cochlear.com)

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  1. […] the previous two posts – How to measure light output – the question and Light output – lumen, lux and the candle – one watt of radiant power at 555 nm is by definition equal to 683 lumens. So given the CIE […]

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