Spectral Density of Spatial Noise of a Laser Beam Upon Reflection from a Non-Ideal Surface

We have studied the spectral properties of the inhomogeneities in the surface profile of a quartz plate in the spatial range from 10 μm to 100 mm on the basis of precision interferometric measurements. Analytical integral relations connecting one- and two-dimensional spectral densities of an isotropic random function, such as surface profile or spatial phase distribution of the laser beam, were obtained. It is shown that if the one-dimensional spectral density in a certain range of spatial frequencies decreases in a power-law manner, then the two-dimensional spectral density in the same range also decreases in a power-law manner with an exponent greater by one. The experimental data are in good agreement with the theoretical ones.