All airborne lidar bathymeter (ALB) systems locate the bottom of a water body by tracking the progression of a short light pulse from its initial contact with the water surface through its interaction with the bottom. The detected signal is the light backscattered by the water column, or reflected by the water surface or the bottom as represented by the waveform - a time-series of the return intensity. All systems share a common set of design elements, face a similar set of design constraints, and ultimately rely on an analysis of a series of detected waveforms to produce a map of the bathymetry. The characteristics of the waveform depend both on the environmental optical properties - especially the water inherent optical properties (IOPs, see Chap. 2) - and on system design. A major purpose of this chapter is to present a mathematical description of the process, incorporating realistic representations of the system elements and pulse propagation geometry. Using a special implementation of the small-angle approximation, a closed form expression for the waveform is presented. This solution is then used to explore contributions to the observed waveform following adjustments in ALB system design and to examine implications of the model for calibration. The chapter closes with consideration of eye-safety requirements and a discussion of the optimization and technical constraints and tradeoffs on system design.