SECT. 4] LIGHT 399 



proportional to the measured radiances. Such a display is called a radiance 

 distribution solid. The shape of this solid will vary with depth, approaching a 

 prolate spheroid whose major and minor axes depend uniquely on the values 

 of a and s for the medium. Preisendorfer (1959) has shown in theory that, in 

 a medium containing only scattering centers, the limiting shape is a sphere, 

 whereas in a medium exhibiting only absorption the limiting shape is a vertical 

 line. 



It is common practice to illustrate the radiance-distribution solid by showing 

 only those vectors lying in a particular plane of interest, for example, the plane 

 parallel to the sun's rays. Typical radiance-distribution diagrams of this latter 

 type are shown in Fig. 2. 



B. Irradiance 



A second important construct, also borrowed from radiometry, is irradiance, 

 or flux per unit area. The definition of irradiance is given in the equation 



H = PjA. (2) 



If we consider not the gross flux P but the parcels of flux dP arriving from the 

 various solid angles da> we can write 



dH = dPjA 

 but from equation (1) 



N = dPI{A cos e do)) 

 so that 



dH = N cos e doj . (3) 



Thus irradiance H can be obtained from radiance distribution by summation, 

 that is 



H = 21N cose Aoj. (4) 



C. Scalar and Spherical Irradiance 



Scalar and spherical irradiance are the last two of the major radiometric 

 concepts to be discussed here. Scalar irradiance gives a quantitative measure 

 of the total radiant flux arriving at a point from all directions about the point. 

 Scalar irradiance, in essence, is a measure of the amount of radiant energy per 

 unit volume of space at a given point ; the individual amount coming in 

 from each direction about the point is unimportant, only the total is of 

 interest. 



Scalar irradiance can be determined if the radiance distribution is known for 

 all directions around the point of interest. Let N{p, 6, (j>) be the field radiance 

 at point p, arriving from the direction {d, <j)), where 6 and <f> are measured from 



