This paper presents a new method to model X-ray scattering on random rough surfaces. It combines the approaches we presented in two previous papers -PZ&LVS 1 & PZ. 2 An actual rough surface is (incompletely) described by its Power Spectral Density (PSD). For a given PSD, model surfaces with the same roughness as the actual surface are constructed by preserving the PSD amplitudes and assigning a random phase to each spectral component. Rays representing the incident wave are reflected from the model surface and projected onto a flat plane, which is the first order approximation of the model surface, as outgoing rays and corrected for phase delays. The projected outgoing rays are then corrected for wave densities and redistributed onto an uniform grid where the model surface is constructed. The scattering is then calculated using the Fourier Transform of the resulting distribution. This method provides the exact solutions for scattering in all directions, without small angle approximation. It is generally applicable to any wave scatterings on random rough surfaces and is not limited to small scattering angles. Examples are given for the Chandra X-ray Observatory optics. This method is also useful for the future generation X-ray astronomy missions. any given wave, there is no clear distinction between "smooth" and "rough" surfaces (see Section 2), therefore it is impossible to separate scattered wave into coherently reflected and incoherently scattered waves.The novelty of our new method is that it treats the reflected wave and scattered wave together (e.g. every ray is treated as scattered, even in the specular direction) as coherent scattering, and consequently both depend upon the surface roughness. It does not require any assumptions in order to separate the wave into reflected and scattered waves, and does not require the small angle approximation so that all the scattered rays can be traced accurately.This new study of the century old problem is motivated by our direct involvement of the evaluation of the X-ray mirror performance aboard the Chandra X-ray Observatory (CXO) -the NASA's third great space observatories, which has been successfully operated since July 23, 1999. It is the first, and so far the only, X-ray telescope achieving sub-arcsec angular resolution (< 0.5 ′′ FWHM), which let us see the X-ray Universe we had never seen before. Chandra's spectacular success owes to the genius design and superb manufacture of its X-ray mirrors. These mirrors are the largest and the most precise grazing incidence optics ever built. At 0.84-m long and 0.6 -1.2-m in diameters, the surface area of each mirror ranging from 1.6 to 3.2 square meters. They were polished to the highest quality ever achieved for any X-ray mirrors of this size. The surface roughness of these mirrors is comparable to or less than the X-ray wavelengths in the 0.1-10 keV band over most of the mirror surfaces. However, the mirrors are still not perfect, and consequently there are still small amount of scattered X-rays. We need an accurate model...