Study on the energy conservation of the small perturbation method

The small perturbation method (SPM) for rough surface scattering has been studied extensively in many fields such as optics, remote sensing and propagation, while the energy conservation for SPM is not clear. In this paper, based on Huygens' Principle and the extinction theorem, the SPM is used to derive the second order transmitted field. By calculating the reflectivity and transmittance of SPM to the first order and the second order, we can study the region of validity for the small perturbation method. It is shown that the first order SPM violates the conservation of energy, while the second order solutions conform to the energy conservation. This is particularly important for the calculation of transmittance or emissivity.