Since the time of Lord Rayleigh, the usual approach to find the power spectral density of the reflected electric field from a rough surface has been to represent the surface as a Fourier series, and then find the Fourier transform of the autocorrelation of this reflected E-field. This can be viewed as a correlogram approach to finding the power spectral density. In the present work, we instead use a periodogram-based approach, which calculates the power spectral density directly in the frequency domain. From the calculated power spectral density, an alternative form of the first-order radar cross section per unit area of the ocean surface is found. In this paper, the derivation of this new first-order radar cross section per unit area will be detailed, and compared to those from the traditional correlogram approach.
