Finding model parameters for the system waveform of a full-wave lidar: a pragmatic solution

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Abstract
The system waveform (SWFM) of a pulsed LiDAR is obtained from the pulse shape received when pointing the sensor towards a flat, extended target with the surface normal equal to the laser beam direction. The SWFM is determined by the shape of the outgoing laser pulse and the transfer characteristics of the receiver. Knowing the SWFM is essential for performing highly accurate range measurements, for interpreting the LiDAR waveforms correctly, and to derive additional attributes for detected target returns. Often the actual SWFM is not known explicitly, and a Gaussian pulse shape is used in lieu thereof. However, the Gaussian pulse, despite its advantageous properties, does not properly address asymmetries and ringing effects typically present in real-life SWFMs. We present a model of the SWFM composed of harmonic and exponential terms which is able to account for these effects while at the same time being mathematically easy to handle. Unfortunately, the approximation of data by a sum of harmonics and exponentials belongs to the class of ill-posed problems. Nevertheless, we present a pragmatic solution to the problem and demonstrate the versatility of the resulting model.

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