where c can range from 1 to 6 depending upon the ratio a/b. For example, 

 if a/b > 2, c may be in the range 1 < c < 3, and if a/b < 1/3, c may 

 range from 3 < c < 6. With most of the fluorescence power reaching the 

 receiver being emitted within two attenuation lengths of the surface and with 

 a > b for most cases, the optical depth due to scattering is less than 1. 

 From data presented in reference 18 on the propagation of light from a spheri- 

 cal lamp, it can be reasoned that for scattering optical depths less than 1 

 the value of c falls in the range 1 < c < 2. Since the effective attenua- 

 tion coefficient varies with depth and turbidity, its form can only be roughly 

 approximated by 



Yf ~ a f + — 



1 l 1.5 



Combining equations (1), (2), and (3) yields 



; -( YS/ +Yf)z 

 (z + mR) 2 



dP r = K dz (4) 



where 



K = 



P<£A r AX d (1 - p £ )(1 - p f )e" (6 ^ +6f)R an 



Utt AX f 

 The total power received by the telescope is obtained by integration of 



dP r over all values of z. Thus, 



00 P - ( YJ, + Yf) z 



(z + mR) 2 



P r = K \ dz 



mR + z 



Making the transformation w = yields 



mR 



P - L e ( ^W )raR f ! 

 r mR J i ,,2 



°o -(Y£+Yf)roR w 



dw 



1 w< 



