270 



Fishery Bulletin 98(2) 



but the errors are negligible for the depth distribu- 

 tions offish used in our study. 



The signal and noise levels can be defined at any 

 one of a number of points in the receiver, including 

 optical power on the detector, current out of the detec- 

 tor, the voltage generated by that current through 

 a standard 50-Q resistance, the output of the log- 

 amplifier, or the integer value that this produces 

 when digitized. We consistently used the voltage 

 across 50 Q, which is the input voltage to the log- 

 amplifier. For an infinitesimally short laser pulse, 

 this signal varies in time as the pulse propagates 

 through the water. We could relate this time to the 

 depth at which the light was scattered back to the 

 receiver because we knew the speed at which light 

 travels through water. Therefore, we could write the 

 signal as a function of depth as for a nadir-pointing: 



S'{z} 



P(z)nd-RIHn) 

 4(z + nh)~ 



exp(-2oz). 



(8) 



where S'= the received signal per unit depth at 

 depth z; 



P = the laser power; 



R = the responsivity of the detector and load 

 inVAV; 

 (Hit) = the backscatter coefficient of the water 

 plus any fish present at that depth; 



h = the height of the aircraft above the sur- 

 face; 



n = the index of refraction of water (1.33); 

 and 



a = the lidar attenuation coefficient. 



To get the actual signal voltage, we had to inte- 

 grate Equation 8 over the finite duration of the laser 

 pulse. To get the short pulses desired, it was nec- 

 essary to use Q-switching. With this technique, the 

 laser resonator is blocked electro-optically while the 

 energy is stored in the lasing medium. The cavity 

 is then quickly opened. Lasing begins rapidly, and 

 the output power quickly builds to a high value. As 

 the energy in the lasing medium is depleted, the 

 output power decreases back to zero. This technique 

 produces a characteristic pulse shape that can be 

 approximated by 



Pit}- 



^exp[-|j- 



(9) 



where E = the total pulse energy; and 



r = 0.408 times the full width of the pulse at 

 one half of its maximum value. 



We converted this time to distance through the speed 

 of light, and integrated Equation 8 over depth. 



Two water types were used. These were Jerlov 

 ( 1968) types IB and III. These specify only the diffuse 

 attenuation coefficient K[j. To obtain an estimate of 

 lidar attenuation we needed to have an estimate 

 of the volume scattering function /3( i^), where i^ is 

 the scattering angle. We used the general functional 

 form of Petzhold (Petzhold, 1972; Mobley, 1995) with 

 the exact values scaled by the value of the scattering 

 coefficient inferred from the different values for K^^. 

 We first noted that 



Kr, = a + 2Kb 



■piO) 



sin{e)de, 



(10) 



where a = the absorption coefficient of sea water; 

 b = the scattering coefficient; and 

 PiiJ)lb = the normalized scattering function of 

 Petzhold. 



