Fractional-order correlation imaging with thermal light

TL;DR

This paper explores fractional-order correlation moments in thermal light ghost imaging, revealing new ways to generate ghost images with adjustable visibility and noise characteristics, supported by theoretical analysis and experiments.

Contribution

It introduces the use of fractional-order moments in ghost imaging, expanding the correlation order beyond integers and analyzing their effects on image quality.

Findings

Negative correlation orders produce negative ghost images

Fractional orders improve image visibility and noise control

Experimental results validate the theoretical probability model

Abstract

In thermal light ghost imaging, the correlation orders were usually positive integers in previous studies. In this paper, we examine the fractional-order moments, whose correlation order are fractional numbers, between the bucket and reference signals in the ghost imaging system. The crucial step in theory is to determine the precise relation between the bucket signals and reference signals. We deduce the joint probability density function between the bucket and reference signals by regarding the reference signals as an array of independent stochastic variables. In calculating the fractional-order moments, the correlation order for the reference signals must be positive to avoid infinity. While the correlation order for the bucket signals can be positive or negative numbers. Negative (positive) ghost images are obtained with negative (positive) orders of the bucket signals. The visibility degree and signal-to-noise ratio of ghost images from the fractional-order moments are analysed. The experimental results and numerical simulations meet our analysis based on probability theory.