Refraction angle calculation in multi-layered ice for wide-beam airborne radar

We propose an algorithm to calculate the refraction path travelled by a signal from a source to a remote scatterer, through a horizontally parallel multilayer medium with vertical-varying refractive index. The exact solution in a simple two-layered medium requires solving a degree-4 polynomial according to Snell's law, meaning a time-demanding solution. For narrow-beam sources a small-angle approximation is commonly used. In this new technique, we transformed the governing equations until the system can be solved by intersection of two curves. As these are monotonic with opposite slope, the crossing point can be estimated by iteration, with a minimum search algorithm. This method has been applied to focus synthetic aperture radar images of the Antarctic bedrock, improving the detected response in the wide-beam case, and reducing time regarding to compute the polynomial solution.