Depth Measurement Bias in Pulsed Airborne Laser Hydrography Induced by Chromatic Dispersion

Abstract

In contrast to topographic laser scanning, laser hydrography must take into account the presence of two media. A pulsed laser beam, which enters the water from the air at an oblique angle, is refracted at the air–water boundary in the direction of the plumb line. This change in the direction described by Snellius’ law is caused by a slower speed of the light wave in the water, i.e., the phase velocity. Light scattering caused by turbidity gives rise to further deviations from the straight path. Together, the slower speed and the turbidity-induced path extension cause a longer pulse round trip time in the water than in the air. For an accurate measurement, it is important to correct this propagation time extension. It is a common practice to assume the phase velocity as the velocity for the laser pulses in water. In a dispersive medium, however, the phase velocity is only an approximation of the velocity of a pulse. In media with chromatic dispersion, the pulses propagate with a different velocity, i.e., the group velocity. In water, using the group velocity instead of the phase velocity reduces the range dependent bias of the depth measurement at a laser wavelength of 532 nm by more than 1.5%. We present an easy to perform an experiment, which shows that the group velocity differs so much from the phase velocity that this difference should be taken into account. We further discuss the use of group velocity to explain the depth bias using examples from the literature.