Fourier domain compression techniques in resolving spatial characteristics of surfaces

It is often desirable to zoom-in on a particular region of the image of a surface. The techniques of replication and interpolation are well known for magnifying images in the spatial domain. However if the information is in the spatial frequency domain such as the optical Fourier transform of a surface reflectance profile, frequency compression techniques could be used to resolve the spatial characteristics of a surface on a magnified scale. The Fourier transform of a surface reflectance function is the signature of various spatial features which are present in the surface. It maps spatial structures into the spatial frequency domain and their physical dimensions are encoded into this space via reciprocal relationships. If the object exhibits large periodic structures as well as small, the Fourier domain will map such structures into its low frequency and high frequency regions respectively. It is the high spatial frequency regions which contain the fine surface details and to resolve such structures demands very fine sampling intervals in the frequency domain