P r (Xj.) 



P (Xi) £A r AX d 



4ir(Yf + y i )m 2 R 2 AX f j = 1 



J2 °j( X i) "j (i = 1.2,3,4) 



(8) 



where subscript i denotes the laser excitation wavelength, and subscript j 

 denotes the algal color group. It should be noted that these equations are 

 different from the equations derived in references 8, 13, and 14 (which are all 

 by the same authors) for a multiple-wavelength laser fluorosensor system. The 

 matrix elements for equation (8) can be written as 



x i = E a iJ n J 

 j=1 



(i = 1,2,3,4) 



(9) 



where 



P r (Xj.) 4ir(Yf + Yi)m 2 R 2 AX f 



PoW 



a r A\i 



(10) 



and 



ffij = aj(Xi) 



Thus the matrix form of equation (8) is 



E N 



The concentration matrix N can then be determined from 



z-1 X 



(11) 



where Z~1 is the inverse matrix of £. The matrix derivation of equation (11) 

 is similar to that given in references 8, 13, and 14. In order for the concen- 

 trations of chlorophyll a for each algal color group to be determined from 

 equation (11), the fluorescence cross sections of the algae aj(X^) must be 

 known for each measurement, and the parameters P r (Xj_), P (Xj_), Yf, & nd Yi 

 must be determined for each laser firing. In the initial experiments which 

 were conducted with the ALOPE system, only the power received by the detection 

 system P r (Xj_) was recorded for each laser shot. It was assumed that the 

 power output of each laser was predictable and that the attenuation coeffi- 

 cients Yf and Yi would be determined by in situ measurement techniques. 



The first field test of the ALOPE system was conducted from the George P. 

 Coleman Bridge 30 m above the surface of the York River at Yorktown, Virginia. 



13 



