414 TYLER AND PREISENDORFER [CHAP. 8 



Then it follows from (40) that 



^„ = l--''\-> . (66) 



Property {%) shows that the depth-dependence of radiant density, or scalar 

 irradiance in a natural hydrosol, eventually becomes exactly exponential in 

 behavior. The value A;oo is uniquely determined by a and a. Property (u ) states 

 that the radiance distribution eventually assumes a fixed angular structure 

 (the asymptotic radiance distribution) at great depths. This limiting angular 

 structure is readily found in principle ; it is independent of the external lighting 

 conditions and depends only on the angular structure of u. Property {iv) is an 

 equivalent assertion to (u), but now phrased in terms of the distribution 

 functions. The quantities D{ + ) and D{ — ) are readily obtained from the 

 limiting form of the radiance distribution functions. Properties {Hi) and {i) 

 show that the logarithmic derivatives of irradiance and scalar irradiance 

 eventually coincide as depth increases indefinitely. It may easily be shown 

 that the logarithmic derivatives of h{Z, + ) and h{Z, — ) also approach A:oo as 

 Z ^ 00. (Of course, then so do the logarithmic derivatives of A477, and h^„{Z, + ) 

 approach A;oo as Z ^ 00.) Finally, property {v) states that R{Z, — ) approaches 

 a fixed value as Z ^ 00, and this value is characterized in terms of koo, D{± ) 

 and a as shown in (56). 



2. Instrumentation for the Measurement of the Underwater Light Field 

 and the Determination of the Optical Properties of the Sea 



In the application of radiometry to light measurements in the sea^ there are 

 five important parameters which must be always kept in mind. 



1. The directional distribution of the light being measured. 



2. The bandwidth or wavelength range included in the measurement. 



3. The state of polarization of the radiation. 



4. The magnitude of the radiant quantity measured. 



5. The direction of propogation of the radiant quantity being measured. 



The measurement of some optical properties like the attenuation coefficient 

 and the volume scattering function requires artificial light which is strictly 

 limited in its distribution, i.e. a collimated beam of light. Other quantities, like 

 irradiance or spherical irradiance, and optical properties, like the diffuse 

 attenuation function K, are determined for the light field as it exists in nature. 

 Directional distribution is, therefore, under the control of the experimentalist 

 only to the extent that in building instruments he must conform to the 

 strict requirements of the defined quantities. 



Bandwidth, on the other hand, is left almost entirely to the discretion of the 

 experimentalist. The selection of bandwidth has been a vexing problem because 

 it is not always clear what bandwidth should be used for a specific application. 



