Generation of 3D random topography datasets with periodic boundaries for surface metrology algorithms and measurement standards

A procedure is presented to generate three-dimensional (3D) random topography datasets with periodic boundaries for the evaluation of surface metrology algorithms and original data for measurement standards. A non-causal two-dimensional (2D) autoregressive (AR) model, which expresses the surface as a linear weighted summation of AR parameters and topography data in addition to a random noise component, is applied to computationally generate 3D random topography data. By the use of an extension that assumes periodic boundaries, the edges of the generated data become continuous across the boundaries. It has been verified that the spectral properties are not affected by this extension. This technique offers advantages for the evaluation of computational techniques for surface metrology, such as filtrations and spectral analysis since the edge effect can be avoided by assuming periodic boundaries, and inherent effects of the techniques can be evaluated. In addition, for use as a random measurement standard for instrument calibration, it is possible to simply arrange the generated data repeatedly in the measuring window similarly to floor tiles without introducing discontinuous edges at the boundaries of the data.