Ghost images reconstructed from fractional-order moments with thermal light

We present the joint probability density function (PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to examine the fractional-order moments of the bucket and the reference signals, in which the correlation orders are fractional numbers, other than positive integers in previous studies. The experimental results show that various images can be reconstructed from fractional-order moments. Negative (positive) ghost images are obtained with negative (positive) orders of the bucket signals. The visibility and peak signal-to-noise ratios of the diverse ghost images depend greatly on the fractional orders.