Friday, September 19, 2014

Lumens, Candelas, Lux, and Nits

In Chapter 14 (Atoms and Light) of the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss photometry, the measurement of electromagnetic radiation and its ability to produce a human visual sensation. I find photometry interesting mainly because of all the unusual units.

Let’s start by assuming you have a source of light emitting a certain amount of energy per second, or in other words with a certain power in watts. This is called the radiant power or radiant flux, and is a fundamental concept in radiometry. But how do we perceive such a source of light? That is a question in photometry. Our perception will depend on the wavelength of light. If the light is all in the infrared or ultraviolet, we won’t see anything. If in the visible spectrum, our perception depends on the wavelength. In fact, the situation is even more complicated than this, because our perception depends on if we are using the cones in the retina of our eye to see bright light in color (photopic vision), or we are using rods to see dim light in black and white (scotopic vision). Moreover, our ability to see varies among individuals. The usual convention is to assume we are using photopic vision, and to say that a source radiating a power of one watt of light at a wavelength of 555 nm (green light, the wavelength that the eye is most sensitive to) has a luminous flux of 683 lumens.

The light source may emit different amounts of light in different directions. In radiometry, the radiant intensity is the power emitted per solid angle, in units of watt per steradian. We can define an analogous photometric unit for the luminous intensity to be the luman per steradian, or the candela. The candela is one of seven “SI base units” (the others are the kilogram, meter, second, ampere, mole, and kelvin). Russ and I mention the candela in Table 14.6, which is a large table that compares radiometric, photometric and actinometric quantities. We also define it in the text, using the old-fashioned name “candle” rather than candela.

Often you want to know the intensity of light per unit area, or irradiance. In radiometry, irradiance is measured in watts per square meter. In photometry, the illuminance is measured in lumens per square meter, also called the lux.

Finally, the radiance of a surface is the radiant power per solid angle per unit surface area (W sr-1 m-2). The analogous photometric quantity is the luminance, which is measured in units of lumen sr-1 m-2, or candela m-2, or lux sr-1, or nit. The brightness of a computer display is measured in nits.

In summary, below is an abbreviated version of Table 14.6 in IPMB

Radiometry Photometry
Radiant power (W) Luminous flux (lumen)
Radiant Intensity (W sr-1) Luminous intensity (candela)
Irradiance (W m-2) Illuminance (lux)
Radiance (W sr-1 m-2) Luminance (nit)

Where did the relationship between 1 W and 683 lumens come from? Before electric lights, a candle was a major source of light. A typical candle emits about 1 candela of light. The relationship between the watt and the lumen is somewhat analogous to the relationship between absolute temperature and thermal energy, and the relationship between a mole and the number of molecules. This would put the conversion factor of 683 lumens per watt in the same class as Boltzmann's constant (1.38 x 10-23 J per K) and Avogadro's number (6.02 x 1023 molecules per mole).

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