Quantities and units used in photometry

They are basically the same as the radiometric units except that they are weighted for the spectral response of the human eye and have funny names. A few additional units have been introduced to deal with the amount of light reflected from diffuse (matte) surfaces. The symbols used are identical to those radiometric units, except that a subscript "v" is added to denote "visual". The following chart compares them.

QUANTITY	RADIOMETRIC	PHOTOMETRIC
power	watt (W)	lumen (lm)
power per unit area	W/m2	lm/m2 = lux (lx)
power per unit solid angle	W/sr	lm/sr = candela (cd)
power per area per solid angle	W/m2-sr	lm/m2-sr = cd/m2 = nit

Now we can get more specific about the details.

The candela is one of the seven base units of the SI system. It is defined as follows:

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 10¹² hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

The candela is abbreviated as cd and its symbol is Iv. The above definition was adopted by the 16th CGPM in 1979.

The candela was formerly defined as the luminous intensity, in the perpendicular direction, of a surface of 1/600 000 square metre of a black body at the temperature of freezing platinum under a pressure of 101 325 newtons per square metre. This earlier definition was initially adopted in 1946 and later modified by the 13th CGPM (1967). It was abrogated in 1979 and replaced by the current definition.

The current definition was adopted because of several reasons. First, the freezing point of platinum (» 2042K) was tied to another base unit, the kelvin. If the best estimate of this point were changed, it would then impact the candela. The uncertainty of the thermodynamic temperature of this fixed point created an unacceptable uncertainty in the value of the candela. Second, the realization of the Pt blackbody was extraordinarily difficult; only a few were ever built. Third, if the temperature were slightly off, possibly because of temperature gradients or contamination, the freezing point might change or the temperature of the cavity might differ. The sensitivity of the candela to a slight change in temperature is significant. At a wavelength 555 nm, a change in temperature of only 1K results in a luminance change approaching 1%. Fourth, the relative spectral radiance of blackbody radiation changes drastically (some three orders of magnitude) over the visible range. Finally, recent advances in radiometry offered a host of new possibilities for the realization of the candela.

The value 683 lm/W was selected based upon the best measurements with existing platinum freezing point blackbodies. It has varied over time from 620 to nearly 700 lm/W, depending largely upon the assigned value of the freezing point of platinum.   The value of 1/600 000 square metre was chosen to maintain consistency with prior standards. Note that neither the old nor the new definition say anything about the spectral response of the human eye. There are additional definitions that include the characteristics of the eye, but the base unit (candela) and those SI units derived from it are "eyeless."

Also note that in the definition there is no specification for the spatial distribution of intensity. Luminous intensity, while often associated with an isotropic point source, is a valid specification for characterizing highly directional light sources such as spotlights and LEDs.

One other issue before we press on. Since the candela is now defined in terms of other SI derived quantities, there is really no need to retain it as an SI base quantity. It remains so for reasons of history and continuity.

The lumen is an SI derived unit for luminous flux. The abbreviation is lm and the symbol is Fv. The lumen is derived from the candela and is the luminous flux emitted into unit solid angle (1 sr) by an isotropic point source having a luminous intensity of 1 candela.   The lumen is the product of luminous intensity and solid angle, cd-sr. It is analogous to the unit of radiant flux (watt), differing only in the eye response weighting. If a light source is isotropic, the relationship between lumens and candelas is 1 cd = 4p lm. In other words, an isotropic source having a luminous intensity of 1 candela emits 4p lumens into space, which just happens to be 4p steradians. We can also state that 1 cd = 1 lm/sr, analogous to the equivalent radiometric definition.

If a source is not isotropic, the relationship between candelas and lumens is empirical. A fundamental method used to determine the total flux (lumens) is to measure Later on, we can use this "calibrated" lamp as a reference in an integrating sphere for routine measurements of luminous flux.

Lumens are what we get from the hardware store when we purchase a light bulb. We want a high number of lumens with a minimum of power consumption and a reasonable lifetime. Projection devices are also characterized by lumens to indicate how much luminous flux they can deliver to a screen.

Illuminance is another SI derived quantity which denotes luminous flux density . It has a special name, lux, and is lumens per square metre, or lm/m2. The symbol is Ev. Most light meters measure this quantity, as it is of great importance in illuminating engineering. The IESNA Lighting Handbook has some sixteen pages of recommended illuminances for various activities and locales, ranging from morgues to museums. Typical values range from 100 000 lx for direct sunlight to 20-50 lx for hospital corridors at night. Luminance should probably be included on the official list of derived SI quantities, but is not. It is analogous to radiance, differentiating the lumen with respect to both area and direction. It also has a special name, nit, and is cd/m2 or lm/m2-sr if you prefer. The symbol is Lv.  It is most often used to characterize the "brightness" of flat emitting or reflecting surfaces.  A typical use would be the luminance of your laptop computer screen.  They have between 100 and 250 nits, and the sunlight readable ones have more than 1000 nits. Typical CRT monitors have between 50 and 125 nits.

Other photometric units

We have other photometric units (boy, do we have some strange ones). Photometric quantities should be reported in SI units as given above. However, the literature is filled with now obsolete terminology and we must be able to interpret it. So here are a few terms that have been used in the past.

Illuminance :

1 metre-candle = 1 lux

1 phot = 1 lm/cm2 = 104 lux

1 foot-candle = 1 lumen/ft2 = 10.76 lux

1 milliphot = 10 lux

Luminance : Here we have two classes of units. The first is conventional, easily related to the SI unit, the cd/m2 (nit).

1 stilb = 1 cd/cm2 = 104 cd/m2 = 104 nit

1 cd/ft2 = 10.76 cd/m2 = 10.76 nit

The second class was designed to "simplify" characterization of light reflected from diffuse surfaces by including in the definitions the concept of a perfect diffuse reflector (lambertian, reflectance r = 1). If one unit of illuminance falls upon this hypothetical reflector, then 1 unit of luminance is reflected. The perfect diffuse reflector emits 1/p units of luminance per unit illuminance. If the reflectance is r, then the luminance is r times the illuminance. Consequently, these units all have a factor of (1/p) built in.

1 lambert = (1/p) cd/cm2 = (104/p) cd/m2

1 apostilb = (1/p) cd/m2

1 foot-lambert = (1/p) cd/ft2 = 3.426 cd/m2

1 millilambert = (10/p) cd/m2

1 skot = 1 milliblondel = (10-3/p) cd/m2

Photometric quantities are already the result of an integration over wavelength. It therefore makes no sense to speak of spectral luminance or the like.