Estimation of the pair correlation function of random point fields via frequency domain

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