Recognitions:

There seem to plenty of threads dealing with questions on topics such as "brightness" and how the human eye perceives objects under certain circumstances, so I've written up a mini-tutorial on how physicists quantify these concepts.

Radiometry is the measurement of the entire energy content in the electromagnetic spectrum from THz frequencies up to the deep UV (3 x 10^11 to 3 x 10^16 Hz). Light measured on the radiometric scale is measured in watts.

Photometry is the measurement of energy that is perceived by the human eye as light. Not only does Photometry measure light over a much smaller frequency band than Radiometry, the relative of contribution of each frequency is weighted to reflect the fact that the human eye perceives some frequencies to be brighter than others. Light measured on the photometric scale is measured in units called lumens (lm). The response of the human eye is approximately Gaussian and peaks at a wavelength of around 550 nm, and cuts off at wavelengths of 400 nm to 700 nm.

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

Often we are not concerned with the absolute amount of light being emitted or absorbed by an object, but rather the amount of light per unit area. Radiometrically, we term this quantity Irradiance and has units of Watts per metre squared (W/m^2). The Photometric equivalent is called Illuminance and has units of luminous flux (lux), which is equivalent to lumens per square metre (lm/m^2). (Light emitted from a surface is sometimes called the emittance rather than the irradiance).

Physicists often refer to W/m^2 as intensity, however this terminology is incorrect when referring to optical power, despite the fact it may be correct when talking about other forms of power! (So please, make a habit of calling W/m^2 irradiance and not intensity when talking about light! Okay, I'll get off my high horse now).

Many material/light interactions depend on irradiance, for example skin burning under a magnifying glass in the sun - the higher irradiance causes the skin to burn, despite the fact the total amount of power incident on whoever owns the skin is the same. With regard to light sources, fluorescent lights look dimmer than LEDs, despite the fact they emit the same number of lumens, because the area over which the light is emitted is much smaller for an LED (i.e. the LED has a higher lux).

3. Solid Angle, Intensity and Luminous Intensity

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

This is where the concept of solid angle comes in, and is best thought of as the 3D equivalent of the more familiar 2D concept of angle. Where an angle in 2D (in radians) is the subtended arc divided by the radius (i.e. theta = s/r), solid angle is the subtended surface divided by the radius squared, i.e. SA = A/r^2. (we need the squared because the subtended area falls as 1/r^2 in 3D). The unit of solid angle is called the steradian (sr).

The Intensity of a light source is W/sr (and not W/m^2). The Photometric equivalent of Intensity is the Luminous Intensity and has units of lumens/steradian (lm/sr), or candelas (cd). Light sources that emit over narrow angular range will obviously appear brighter, because a greater proportion of the emitted lumens will be incident on your eye (provided you are viewing the source from the right angle of course).

Curiously, both illuminance or luminous intensity on their own do not tell the whole story in terms of how bright we observe something to be!

We have established that the frequency of the light emitted determines how bright we perceive it to be. We have established that the smaller the area over which a light source emits makes it appear brighter. We have also established that the smaller the angle range over which a light source emits also makes it appear brighter. Thus in order to define a "quantity of brightness" we need to define it in such a way as to include all of these things.

The "quantity of brightness" I speak of is called Luminance and is measured in units of lumens per 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 called the Radiance and is has units of W/(m^2.sr).

Radiance and luminance are important quantities because they are invariant in many optical systems. Safety standards are usually defined in terms of radiance and luminance for this reason.

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

Claude.

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