The Photometric System
	Light flux, for the purposes of illumination engineering, is measured 
in lumens.  A lumen of light, no matter what its wavelength (color), 
appears equally bright to the human eye.  The human eye has a stronger 
response to some wavelengths of light than to other wavelengths.  The 
strongest response for the light-adapted eye (when scene luminance >/= .001 
Lambert) comes at a wavelength of 555 nm.  A light-adapted eye is said to 
be operating in the photopic region.  A dark-adapted eye is operating in the 
scotopic region (scene luminance </= 10^-8 Lambert).  In between is the 
mesopic region.  The peak response of the eye shifts from 555 nm to 510 
nm as scene luminance is decreased from the photopic region to the 
scotopic region.  The standard lumen is approximately 1/680 of a watt of 
radiant energy at 555 nm.  Standard values for other wavelengths are 
based on the photopic response curve and are given with two-place 
accuracy by the table below.  The values are correct no matter what region 
you're operating in - they're based only on the photopic region.  If you're 
operating in a different region, there are corrections to apply to obtain 
the eye's relative response, but this doesn't change the standard values 
given below.  

Wavelength, nm   Lumens/watt         Wavelength, nm  Lumens/watt
      400           0.27                600              430
      450          26                   650               73
      500        220                    700                2.8
      550        680

	Following are the standard units used in photometry with their 
definitions and symbols.

	Luminous flux, F, is measured in lumens.
	Quantity of light, Q, is measured in lumen-hours or lumen-seconds.  
It is the time integral of luminous flux.
	Luminous Intensity, I, is measured in candles, candlepower, or 
candela (all the same thing).  It is a measure of how much flux is flowing 
through a solid angle.  A lumen per steradian is a candle.  There are 4 pi 
steradians to a complete solid angle.  A unit area at unit distance from a 
point source covers a steradian.  This follows from the fact that the 
surface area of a sphere is 4 pi r^2.  
	Lamps are measured in MSCP, mean spherical candlepower.  If you 
multiply MSCP by 4 pi, you have the lumen output of the lamp.  In the case of 
an ordinary lamp which has a horizontal filament when it is burning base 
down, roughly 3 steradians are ineffectual: one is wiped out by inter- 
ference from the base and two more are very low intensity since not much 
light comes off either end of the filament.  So figure the MSCP should be 
multiplied by 4/3 to get the candles coming off perpendicular to the lamp 
filament.  Incidentally, the number of lumens coming from an incandescent 
lamp varies approximately as the 3.6 power of the voltage.  This can be 
really important if you are using a lamp of known candlepower to 
calibrate a photometer.
	Illumination (illuminance), E, is the _areal density_ of incident 
luminous flux: how many lumens per unit area.  A lumen per square foot is 
a foot-candle; a one square foot area on the surface of a sphere of radius 
one foot and having a one candle point source centered in it would 
therefore have an illumination of one foot-candle due to the one lumen 
falling on it.  If you substitute meter for candle you have a meter-candle 
or lux.  In this case you still have the flux of one steradian but now it's 
spread out over one square meter.  Multiply an illumination level in lux by 
.0929 to convert it to foot-candles.  (footÖ/meter)^2= .0929.  A centimeter-
candle is a phot.  Illumination from a point source falls off as the square 
of the distance.  So if you divide the intensity of a point source in candles 
by the distance from it in feet squared, you have the illumination in foot 
candles at that distance.
	Luminance, B, is the _areal intensity_ of an extended diffuse source 
or an extended diffuse reflector.  If a perfectly diffuse, perfectly 
reflecting surface has one foot-candle (one lumen per square foot) of 
illumination falling on it, its luminance is one foot-Lambert or 1/pi
candles per square foot.  The total amount of flux coming off this 
perfectly diffuse, perfectly reflecting surface is, of course, one lumen per 
square foot.  Looking at it another way, if you have a one square foot 
diffuse source that has a luminance of one candle per square foot (pi times 
as much intensity as in the previous example), then the total output of 
this source is pi lumens.  If you travel out a good distance along the 
normal to the center of this one square foot surface, it will look like a 
point source with an  intensity of one candle.  
	To contrast: Intensity in candles is for a point source while 
luminance in candles per square foot is for an extended source - luminance 
is intensity per unit area.  If it's a perfectly diffuse but not perfectly 
reflecting surface, you have to multiply by the reflectance, k, to find the 
luminance.  
	Also to contrast: Illumination, E, is for the incident or incoming 
flux's areal _density_; luminance, B, is for reflected or outgoing flux's 
areal _intensity_.  In the ideal case of illumination, incoming flux is more 
or less  perpendicular to the surface being illuminated.  But an extended 
source emits light according to the cosine law and a diffuse reflecting 
surface reflects according to the cosine law: the amount of flux emitted 
per unit surface area is proportional to the cosine of the angle between 
the direction in which the flux is being emitted and the normal to the 
emitting surface.  A consequence of this law is that no matter from what 
direction you look at a perfectly diffuse reflecting or emitting surface, 
the luminance on the basis of _projected_ area is the same.  So if you have 
a light meter looking at a perfectly diffuse surface, it doesn't matter 
what the angle between the axis of the light meter and the normal to the 
surface is as long as all the light meter can see is the surface: in any case 
the reading will be the same.
	There are a number of luminance units, but they are in categories:  
two of the categories are those using English units and those using metric 
units.  Another two categories are those which have the constant1/¹ built 
into them and those that do not.  The latter stems from the fact that the 
formula to calculate luminance (photometric Brightness), B, from 
illumination (illuminance), E,  contains the factor 1/¹.  To illustrate:

		B = (k*E)(1/pi) 
		Bfl = k*E 

where:	B = luminance, candles/foot^2
	Bfl = luminance, foot-Lamberts
	k = reflectivity   	    0<k<1
	E = illuminance in foot-candles (lumens/ foot^2)

	Obviously, if you divide a luminance expressed in 
foot-Lamberts by pi you then have the luminance expressed in 
candles /foot^2.  (Bfl/pi=B)

Other luminance units are:
                stilb = 1 candle/square centimeter      sb
                apostilb = stilb/(pi X 10^4)=10^-4 L    asb
                nit = 1 candle/ square meter            nt
                Lambert = (1/pi) candle/square cm       L

	Below is a table of photometric units with short definitions.

  Symbol      Term                 Unit              Unit Definition

    Q      light quantity       lumen-hour          radiant energy 
                                lumen-second        as corrected for
                                                    eye's spectral response

    F      luminous flux        lumen               radiant energy flux 	
                                                    as corrected for
                                                    eye's spectral response

    I      luminous intensity   candle              one lumen per steradian
                                candela             one lumen per steradian
                                candlepower         one lumen per steradian

    E      illumination	        foot-candle         lumen/foot^2
                                lux                 lumen/meter^2
                                phot                lumen/centimeter^2

    B      luminance            candle/foot^2       see unit def's. above
                                foot-Lambert   =    (1/pi) candles/foot^2
                                Lambert        =    (1/pi) candles/centimeter^2
                                stilb          =    1 candle/centimeter^2
                                nit            =    1 candle/meter^2

Note: A lumen-second is sometimes known as a Talbot.

To review:

	Quantity of light, Q, is akin to a quantity of photons except that here 
the number of photons is pro-rated according to how bright they appear to the 
eye.
	Luminous flux, F, is akin to the time rate of flow of photons except 
that the photons are not given a value based on their wavelength or energy 
but rather on how bright they apppear to the eye.
	Luminous intensity, I, is the solid-angular density of luminous flux.  
Applies primarily to point sources.
	Illumination, E, is the areal density of incident luminous flux.
	Luminance, B, is the areal intensity of an extended source.


	           Photometry with a Photographic Light Meter
	The first caveat to keep in mind is that the average unfiltered light 
meter doesn't have the same spectral sensitivity curve that the human eye 
does.  Each type of sensor used has its own curve.  Silicon blue cells aren't 
too bad.  The overall sensitivity of a cell is usually measured with a 
2856K or 2870K incandescent lamp.  Less commonly it is measured with 
6000K sunlight.
	The basis of using a light meter is the fact that a light meter uses 
the Additive Photographic Exposure System, the system which uses 
Exposure Values:

         Ev = Av + Tv = Sv + Bv

where:   Ev = Exposure Value
         Av = Aperture Value = ln N^2/ln 2    where N = f/no.
         Tv = Time Value = ln (t^-1)/ln 2     where t = time in sec.s
         Sv = Speed Value = ln (0.3 S)/ln 2   where S = ASA speed
         Bv = Brightness Value = ln Bfl/ln 2

from which, for example:
	    Av(N=f/1) = 0
	    Tv(t=1 sec) = 0
	    Sv(S=ASA 3.125) Å 
	    Bv( Bfl = 1 foot-Lambert) = 0

and therefore:
	    Bfl = 2^Bv
	    Ev (Sv = 0) = Bv

	From the preceeding two equations you can see that if you set the 
meter dial to an ASA speed of approximately 3.1 (same as Sv = 0), when 
you read a scene luminance level the Ev reading will be Bv from which you 
can calculate Bfl.  If you don't have an ASA setting of 3.1 on your dial, just 
use ASA 100 and subtract 5 from the Ev reading to get Bv.  
(Sv@ASA100=5)

 		                Image Illumination
	If you know the object luminance (photometric brightness), the 
f-number of the lens, and the image magnification, you can calculate the 
image illumination.  The image magnification is the quotient of any linear 
dimension in the image divided by the corresponding linear dimension on 
the object.  It is, in the usual photographic case, a number less than one.  
The f-number is the f-number for the lens when focussed at infinity - this 
is what's written on the lens.  The formula that relates these quantities is 
given below:

		Eimage = (t pi B)/[4 N^2 (1+m)^2]
or:		Eimage = (t Bfl)/[4 N^2 (1+m)^2]
where:	Eimage is in foot-candles  (divide by .0929 to get lux)
           t   is the transmittance of the lens (usually .9 to .95 but lower 
                  for more surfaces in the lens or lack of anti-reflection    
                   coatings)
           B   is the object luminance in candles/square foot
           Bfl is the object luminance in foot-Lamberts
           N   is the f-number of the lens
           m   is the image magnification

References:
G.E. Miniature Lamp Catalog
Gilway Technical Lamp Catalog
"Lenses in Photography" Rudolph Kingslake Rev.Ed.c1963 A.S.Barnes
"Applied Optics & Optical Engr." Ed. by Kingslake c1965 Academic Press
"The Lighting Primer" Bernard Boylan c1987 Iowa State Univ.
"University Physics" Sears & Zemansky c1955 Addison-Wesley