DERIVATION OF POWER RECEIVED BY LASER FLUOROSENSOR SYSTEM 



Unexplained assumptions by many authors (refs. 8 to 14) in deriving the 

 governing equation for the power received by a laser fluorosensor system have 

 resulted in various relationships which differ by as much as a factor of 2tt. 

 A thorough derivation of this equation with justified assumptions is needed to 

 establish the appropriate form of the equation. 



The general configuration used in this derivation is given in figure 6. 

 A common assumption in all derivations is that the algae and all scattering 

 material are uniform with depth in the water. The laser irradiance in W/m 2 -nm 

 which reaches a depth of z in the water is given by 



P e * (1 - Pj,)e 



H z = (D 



where 



P Q laser output power, W 



gg, atmospheric extinction coefficient at laser wavelength, m~' 



R distance from laser fluorescence system to water, m 



P^ water surface reflectivity at laser wavelength 



Y^ effective attenuation coefficient of water at laser wavelength, m" 1 



z water depth of differential volume under examination, m 



AXj, wavelength bandwidth of laser energy, nm 



A z area illuminated by laser at a depth of z, m 2 



The effective water attenuation coefficient may vary with depth (ref. 15) 

 because of changes in the angular distribution of laser light as it is multiply 

 scattered and deviated from collimated light at the surface to relatively dif- 

 fuse light several attenuation lengths underwater (ref. 16). The single- 

 scattering attenuation coefficient for a collimated beam is 



a = a + b 



where a is the absorption coefficient and b is the scattering coefficient. 

 It is assumed in the derivation of a that if a photon is scattered it is lost 

 to the beam, and the energy in the unscattered beam is exponentially reduced 

 by the amount e" ar where r is the distance traveled in the water (ref. 16). 

 Since the laser excitation wavelengths for algae are between 400 and 650 nm, 



