We study how finite-window sampling (random spatial truncation) and reciprocal-space radial binning influence the detection of hyperuniformity in disordered systems. Starting from thirteen representative two-dimensional simulation systems and two experimental biological systems, we apply random spatial truncation and then rescale the cropped systems to a fixed number density. We then compute the structure factor S(k) and the local number variance σN2R to determine whether cropped configurations preserve the salient structural properties of the original ones. We find that moderate random spatial truncation does not change qualitatively the hyperuniformity classification of the systems, despite a reduction in measured hyperuniformity exponent α for α>1. Since spatial truncations exacerbate fluctuations in measured S(k) at small k, we show that modest reciprocal-space radial binning (controlled by a binning parameter m) effectively smooths out such fluctuations without changing the hyperuniformity class. Practical guidelines for choosing m and cross-checking S(k) fits with σN2R scaling are provided. Our research provides a concrete, low-cost, and effective methodology for robust detection and classification of hyperuniformity in finite and truncated datasets, which are prevalent in experimental systems.
Liu et al. (Mon,) studied this question.