Restoration of three-dimensional correlation function and structure factor from two-dimensional observations

TL;DR

This paper presents a method to reconstruct three-dimensional correlation functions and structure factors from two-dimensional observational data in homogeneous isotropic systems, using an expansion based on slab thickness.

Contribution

It introduces a novel expansion approach to recover 3D correlation functions from 2D data, applicable to critical density fluctuations.

Findings

Successfully reconstructs 3D correlation functions from 2D observations.

Provides explicit formulas for the expansion based on slab thickness.

Demonstrates applicability to critical density fluctuation analysis.

Abstract

The static pair correlation (distribution) function and the structure factor of particle distributions in three-dimensional homogeneous isotropic systems are explicitly restored from two-dimensional data observed in a thin slab sliced out from original systems. The result is given as an expansion with respect to the thickness of the slab and applied to the critical density fluctuations.