Estimation of the Pair Correlation Function of Random Point Fields via Frequency Domain

Applying a Wiener-Khintchine type theorem for random point fields, the estimation of the pair correlation function via the frequency domain is presented, which offers certain advantages over conventional estimation, especially for large datasets. The discretization of the point data, i.e., its mapping onto a grid, can be viewed as a digital image, where this mapping includes regularization of the data. Using a fast Fourier transform and its co-transform, the estimation of the pair correlation is consistently embedded in the field of digital image analysis. Finally, building upon this technique, an estimator of the density of the Bartlett spectrum is derived, whose normalization is known in scattering theory as the structure factor. The suitability of the estimators is demonstrated with examples.