The Effect of Surface Roughness on Reflected Intensity

We desire to quantitatively characterize the effect surface roughness has on extreme ultraviolet radiation. This was done by taking the ratio of the reflectance of a surface with random roughness and the reflectance from a perfectly smooth surface of the same composition and size. The reflectance was calculated by numerically solving the exact integral equations for the electric and magnetic fields. The reflectance for the rough surface was averaged from many different random surfaces. In order to determine the parameters that affect this ratio, we varied angle of incidence, rms height of the roughness, thickness of the substance, real and imaginary parts of the index of reflection, and frequency cut-off for the random noise on the surface. We determined that in the extreme ultraviolet only the angle and rms height mattered. We did a fit to create a correction factor and compared it to Debye-Waller and Nevot-Croce correction factors.