Modeling LiDAR return waveform for variable characteristics ofalbedo, roughness, and geometry within a footprint

The laser altimetry systems (LiDAR) are being used in ever increasing number of applications taking advantage of their dense sampling, high accuracy, and the direct generation of 3D surface points. Full waveform digitization is a technique which digitizes total backscattered laser signal with a high sampling rate. This is a relatively new technique and algorithms are being developed to obtain maximum amount of information from the return waveform.This paper presents a mathematical model to simulate the return waveform at receiver. The simulator can be used for spaceborne altimetric system (e.g., LLRI (Lunar Laser Ranging Instrument) onboard Chandrayan) or airborne laser altimetry system (e.g., ALTM waveform digitization) to compare the influence of geometry, roughness and albedo on the received
waveform. To realise this, a mathematical model is employed to generate footprints that vary in their characteristics in terms albedo, geometry, and roughness. The footprint is divided into small bins such that each bin has uniform albedo, roughness, and geometry. Energy distribution in the transmitted pulse is considered gaussian. The energy distribution of the pulse falling onto the footprint is approximated using assumed distribution. For each bin the energy incident is computed and accordingly the reflected energy is determined. The final waveform is generated by integrating the energy returned from the bins according to their time of arrival.