The effect of object shape and laser beam shape on LIDAR system resolution

In a LIDAR system, a pulsed laser beam is propagated to a scene, and then reflected back by objects. Ideally if the beam diameter and the pulse width are close to zero, then the reflected beam in time domain is similar to a delta function, which can accurately locate an object's position. However, in a practical system, the beam has finite size. Therefore, even if the pulse width is small, an object shape will make the reflected beam stretched along the time axis, then affect system resolution. In this paper, we assume the beam with Gaussian shape. The beam can be formulated as a delta function convolved with a shape function, such as a rectangular function, in time domain. Then the reflected beam can be defined as a system response function convolved with the shape function. We use symmetric objects to analyze the reflected beam. Corn, sphere, and cylinder objects are used to find a LIDAR system's response function. The case for large beam size is discussed. We assume the beam shape is similar to a plane wave. With this assumption, we get the simplified LIDAR system response functions for the three kinds of objects. Then we use tiny spheres to emulate an arbitrary object, and study its effect to the returned beam.