Exponential Decomposition with Implicit Deconvolution of Lidar Backscatter from the Water Column

Abstract

Bathymetric laser scanning is a powerful tool to obtain information about the morphology of coastal, river, and inland waters. Laser scanning in general is a method to sense the shape of remote objects by sweeping a laser beam across the objects while measuring the distance to every surface point. In bathymetric applications, the electromagnetic light wave also needs to penetrate the water column resulting in a spread reflection from below the surface of the water body complicating the interpretation of the received wave. As the signal seen by the sensor’s receiver is the result of a convolution of the system waveform with the differential backscatter cross section, one approach is to use a deconvolution method to recover the object shape. An alternative approach is to fit a parameterised model to the measured receiver signal. While deconvolution methods are not capable to directly deliver object parameters such as distance to water surface or bottom, modelling methods suffer from neglecting the system waveform. We present a new waveform decomposition method that avoids current shortcomings. The proposed method uses a model composed of segments of exponential functions, which is motivated by the physics of the backscatter process in the water column, and a record of the system waveform which is stored as part of the sensor’s calibration data. The method further consists of an algorithm which evaluates the parameters of the exponential model while, at the same time, performing a deconvolution from the system waveform in an implicit manner. The effectiveness of the method is exemplified using real data from a nearshore airborne LIDAR data acquisition.