400 TYLER AND PREISENDORFER [CHAP. 8 



some fixed reference system. Then the scalar irradiance, h{p), at point p is 

 defined as : 



h{p) = r r N{p, d, cf>) dQ, (5) 



Je=o J0=o 

 where 



dQ = sin e dd d(f>. 



We can obtain an analytic expression for spherical irradiance, h4n{p), in the 

 following way : consider a small spherical collector of radius r with center at p. 

 Then the amount P{p, 6, (f>) of radiant flux intercepted by the spherical surface 

 from a unit solid angle in the direction {d, (f)) is (using the cosine law) 



Pip,d,cf>) = N{p,d,cf>) ( cosi/jdA, 



J hemisphere 



(6) 



where the hemisphere of integration is determined by the plane of the great 

 circle which is perpendicular to the direction {d, cf)). The integral is easy to 

 evaluate because it simply represents the projected area of the hemisphere on 

 the plane of its great circle, so that 



P{p, d, cf>) = rrr'^Nip, d, 0). (7) 



The amount P{p) of flux intercepted by the sphere from all directions is : 



Pip) = r r p(P' ^' */•) ^^ = ^r^Mp)- 



J 6=0 J<p=0 



(8) 



Finally, the average flux per unit area on the collecting sphere is, by deflnition, 



hUp) = P(^)/477r2 = lh{p). (9) 



The distinction between scalar and spherical irradiance can be stated as 

 follows : scalar irradiance arises naturally in theoretical analyses and has a 

 simple analytic definition in terms of the angular distribution of field radiance 

 about a point in space ; spherical irradiance is the associated quantity measured 

 by a small spherical collecting surface which exhibits the properties of a cosine 

 collector at every point of its surface. 



The passage of light through the sea is here considered on a macroscopic 

 level in which the main tools are the radiometric concepts and the simple 

 devices used to measure them, namely the radiance tube (Gershun, 1939), 

 irradiance collector, and spherical irradiance collector. 



The optical properties of the sea can be divided quite naturally into two 

 classes : one class consisting of the inherent optical properties of the medium, 

 and the other class consisting of the apparent optical properties of the medium. 

 The former class includes such quantities as the volume attenuation function, 

 the volume scattering function and the absorption function. These summarize 

 certain intrinsic physical actions of the medium on a given beam of light as 

 the beam passes through the medium. This action is generally independent of 



