Optimal threshold condition for conditional correlation measurements

Determine a rigorously proven theoretical criterion for selecting the optimal threshold condition in the post-selection scheme based on the intensity difference between the two bucket signals, with the aim of maximizing the quality or contrast-to-noise ratio of the induced positive or negative spatial correlation patterns.

Background

The post-selection scheme constructs conditional intensity correlation functions by retaining measurements according to whether the bucket-intensity difference satisfies a threshold condition, such as $|\Delta I|\leq s\sigma$ or $|\Delta I|>s\sigma$. The authors show experimentally and numerically that different thresholds produce either anti-bunching-like correlation dips or bunching-type correlation peaks and that suitable thresholds can substantially reduce the number of measurements required.

Although the experiments identify threshold ranges that yield favorable contrast-to-noise ratios, the optimal thresholds for positive and negative correlation patterns are not symmetric and appear to depend on the experimental conditions and, in ghost-imaging applications, on the object itself. The paper therefore leaves unresolved the derivation of a rigorous theoretical rule for determining the optimal threshold condition.