formance. As a result, more accurate depth estimates 
can be obtained. In addition, the LIDAR bathymeter 
can be used for non-bathymetric purposes such as in 
the measurement of sea water turbidity. A quantitative 
measure of turbidity is the rate of attenuation of the 
laser beam in water and this rate is dependent on the 
degree of scattering and absorption of the laser light in 
water. 
4 CONCLUSIONS 
The mathematical characterization of the surface and 
bottom reflections in laser bathymetry has been exam 
ined. The bottom reflection can be represented by a 
Gaussian function and by adjusting parameter a, dif 
ferent possible reflection widths can be obtained. The 
surface reflection, on the other hand, can be represented 
by the EMG function and by adjusting S T , a variety of 
asymmetric reflection profiles can be obtained. Exten 
sive test results with real life data have shown that the 
application of the proposed characterization to LARSEN 
waveforms is indeed reasonable. 
A nonlinear least-squares optimization technique has 
been applied to facilitate the decomposition of each 
LARSEN waveform into the surface and bottom reflec 
tions. By using the Levenberg-Marquardt minimization 
method in conjunction with an initialization scheme, 
reliable depth estimates can be obtained for a diverse 
range of circumstances. 
ACKNOWLEDGEMENT 
The authors are grateful to the Natural Sciences and 
Engineering Research Council of Canada for supporting 
this research. 
certain nonlinear problems in least squares. J. Appl. 
Math., 2: 164-168. 
Marquardt, D.W., 1963. An algorithm for least-squares 
estimation of nonlinear parameters. J. SIAM, 11(2): 
431-441. 
Muirhead, Iv. and A.P. Cracknell, 1986. Airborne lidar 
bathvmetry: review article. Int. J. Remote Sensing, 
7(5): 597-614. 
O’Neil, R.A., V. Thomson, J.N. deVilliers, and J.R. 
Gibson, 1978. The Aerial Hydrography Program at 
CCRS. Proc. Coastal Mapping Symp., 125-132. 
O’Neil, R.A., 1980. Field trials of a lidar bathymeter 
in the Magdalen Islands. Proc. 4th Laser Hydrography 
Symp., 56-S4. 
Penny, M.F., R.H. Abbot, D.M. Philips, B. Billard, 
D. Rees, D.W. Faulkner, 1986. Airborne laser hydrog 
raphy in Australia. Appl. Opt., 25(13): 2046-2058. 
Phillips, D.M. and B.W. Koerber, 1984. A theoretical 
study of an airborne laser technique for determining sea 
water turbidity. Australian J. Phys., 37(35): 2046-2058. 
Svanberg, S., 1981. Lasers as probes for air and sea. 
Contemp. Phys., 21: 541-577. 
Wong, H. and A. Antoniou, 1990. Signal Processing 
Techniques for Airborne Laser Bathymetry. Proc. 13th 
Canadian Symp. Remote Sensing. 
REFERENCES 
Abramowitz, M., and I.A. Stegun, eds., 1964. Hand 
book of mathematical functions. Applied Mathematics 
Series, vol. 55, National Bureau of Standards, Wash 
ington, D.C., pp. 299. 
Banic, J., S. Sizgoric and R.A. O’Neil, 1986. Scanning 
lidar bathymeter for water depth measurement. Proc. 
SPIE, Laser Radar Technology and Applications, 663: 
187-195. 
Bressel, C'., I. Itzkan, J.E. Nunes and F. Hoge, 1977. 
Airborne oceanographic lidar system. Proc. 11th Int. 
Symp. Remote Sensing Environ., II: 1259-1269. 
Casey, M.J., 1984. Deploying the lidar on hydrographic 
surveys. Proc. 9th Canadian Symp. Remote Sensing, 
165-175. 
Foley, J.P. and J.G. Dorsey, 1983. Equations for calcu 
lation of chromatographic figures of merit for ideal and 
skewed peaks. Anal. Chem., 55(4): 730-737. 
Hickman G.D., and J.E. Hogg, 1969. Application of an 
airborne pulsed laser for near shore bathymetry mea 
surements. Remote Sensing Environ., 1: 47-58. 
Hoge, F.E. and N. Swift., 1983. Airborne detection 
of oceanic turbidity cell structure using depth-resolved 
laser-induced water raman backscattering. Appl. Opt., 
22(23): 3778-3786. 
Lee, H.S. and N.T. O’Neill, 1984. LIDAR return pulse 
profile and its relationship to water optical parameters. 
Proc. 7th SPIE Conf. Ocean Opt., 297-305. 
Levenberg, Iv., 1944. A method for the solution of 
93