Some features of temporal ghost imaging with classical light

Temporal ghost imaging with classical pulsed light is described as a temporal counterpart of conventional ghost imaging with thermal light. A temporal object to be imaged is located in the test arm while the reference arm consists of some simple temporal optical elements. The incident light is assumed to be temporally incoherent, classical pulsed light. We first show that the correlation between intensity fluctuations in these two arms is given by a fractional Fourier transform of the temporal object. In special cases, the fractional Fourier transform reduces to the ordinary Fourier transform and the image of the object. We then derive explicit expressions for the resultant ghost image under two different conditions, with a view to examining the effect of the incident pulse. As a result, it is found that the resultant temporal ghost image depends only on the single temporal variable in the reference arm though the light in this arm never interacts with the object, and that it is generally distorted by the effect of the incident pulse.