Radiometric and Photo Metric Units

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Radiometric and Photometric units

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Mar5-07, 11:17 PM #1

Claude Bile

Posts: 1,330

Recognitions:Science Advisor

There seem to plenty of threads dealing withquestions on topics such as "brightness" andhow the human eye perceives objects undercertain circumstances, so I've written up a mini-tutorial on how physicists quantify theseconcepts.

1. Radiometry and Photometry

Radiometryis the measurement of the entireenergy content in the electromagnetic spectrum


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from THz frequencies up to the deep UV (3 x10^11 to 3 x 10^16 Hz). Light measured onthe radiometric scale is measured in watts.

Photometryis the measurement of energy thatis perceived by the human eye as light. Not onlydoes Photometry measure light over a muchsmaller frequency band than Radiometry, the

relative of contribution of each frequency isweighted to reflect the fact that the human eyeperceives some frequencies to be brighter thanothers. Light measured on the photometric scaleis measured in units called lumens (lm). Theresponse of the human eye is approximatelyGaussian and peaks at a wavelength of around550 nm, and cuts off at wavelengths of 400 nmto 700 nm.

As an example, if you placed 2 mW red, blue andyellow LEDs next to one another, the yellowdiode would appear brighter, in other words theyellow diode would emit more lumens worth ofradiation than the red or yellow LEDs.

2. Irradiance and Illuminance

Often we are not concerned with the absoluteamount of light being emitted or absorbed by anobject, but rather the amount of light per unit

area. Radiometrically, we term this quantityIrradiance and has units of Watts per metresquared (W/m^2). The Photometric equivalent iscalled Illuminance and has units of luminous flux(lux), which is equivalent to lumens per squaremetre (lm/m^2). (Light emitted from a surfaceis sometimes called the emittance rather thanthe irradiance).

Physicists often refer to W/m^2 as intensity,however this terminology is incorrect when

referring to opticalpower, despite the fact it maybe correct when talking about other forms ofpower! (So please, make a habit of callingW/m^2 irradiance and not intensity when talkingabout light! Okay, I'll get off my high horsenow).

Many material/light interactions depend onirradiance, for example skin burning under amagnifying glass in the sun - the higher irradiance


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causes the skin to burn, despite the fact the totalamount of power incident on whoever owns theskin is the same. With regard to light sources,fluorescent lights look dimmer than LEDs, despitethe fact they emit the same number of lumens,because the area over which the light is emittedis much smaller for an LED (i.e. the LED has ahigher lux).

3. Solid Angle, Intensity and Luminous Intensity

The problem with using Irradiance andIlluminance to characterise a light source is thatthis quantity falls as 1/r^2. Ideally, we would liketo use units that do not vary as 1/r^2.

This is where the concept ofsolid angle comesin, and is best thought of as the 3D equivalent ofthe more familiar 2D concept of angle. Where anangle in 2D (in radians) is the subtended arcdivided by the radius (i.e. theta = s/r), solidangle is the subtended surface divided by theradius squared, i.e. SA = A/r^2. (we need thesquared because the subtended area falls as1/r^2 in 3D). The unit of solid angle is called thesteradian (sr).

The Intensityof a light source is W/sr (and notW/m^2). The Photometric equivalent of

Intensity is the Luminous Intensityand has unitsof lumens/steradian (lm/sr), or candelas (cd).Light sources that emit over narrow angularrange will obviously appear brighter, because agreater proportion of the emitted lumens will beincident on your eye (provided you are viewingthe source from the right angle of course).

Curiously, both illuminance or luminous intensityon their own do not tell the whole story in termsof how bright we observe something to be!

4. Radiance and Luminance

We have established that the frequency of thelight emitted determines how bright we perceiveit to be. We have established that the smaller thearea over which a light source emits makes itappear brighter. We have also established thatthe smaller the angle range over which a lightsource emits also makes it appear brighter. Thus


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in order to define a "quantity of brightness" weneed to define it in such a way as to include all ofthese things.

The "quantity of brightness" I speak of is calledLuminance and is measured in units of lumensper metre sqaured, per steradian (lm/(m^2.sr)),or equivalently candela per square metre

(cd/m^2) or luminous flux per steradian (lux/sr),or nits (nt). The radiometric equivalent is calledthe Radiance and is has units of W/(m^2.sr).

Radiance and luminance are important quantitiesbecause they are invariant in many opticalsystems. Safety standards are usually defined interms of radiance and luminance for this reason.

So to conclude, the concept of "brightness" issurprisingly complicated to define.

Claude.

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