**3. Inversion of** *σ***(***ω***) to Measure the Directional Wave Spectrum**

The aim of inversion is to obtain the ocean wave directional spectrum, *S*( *k*), from the power spectrum of the measured radar cross section, *σ*(*ω*) using Equations (24) and (28). The power spectrum of the backscattered radar signal is proportional to *σ*(*ω*) and therefore in principle needs to be calibrated to account for antenna gains, propagation losses and other factors. To avoid this the problem is usually framed in terms of the ratio of the second and first order backscatter power spectra. A number of inversion methods have been published e.g., [6,8,9,15,16,30]. Here we use the method of Wyatt [10,11] which is referred to in this paper as the Seaview inversion method since Seaview Sensing Ltd has an exclusive license from the University of Sheffield to commercialise the software package and continue its development.
