Ghost diffraction by ghost imaging

Ghost imaging (GI) is a technique to retrieve images of a remote object through space-momentum correlation of light beams. Ghost diffraction (GD) is its relative where diffraction patterns of an object are retrieved. Recently, GI was extended to time domain, which makes temporal GD (TGD) relevant now. However, GD is not readily applicable to time domain. This is because GD dwells on the Fourier transform (FT) of electric fields, for which three degrees of freedom of a wavevector are critical while only one is available in time domain. Here we report a successful TGD experiment by using a proper TGI setup, which defies our notion of GD. The time-domain diffraction was made available through the inverse-FT of the transmission spectra. Spatio-temporarily correlated beams were created by splitting pseudorandomized light. One (R) propagates along an optic fiber while the other (O) passed through an interferometer with a built-in frequency upconverter. We retrieved beats by taking the covariance between the intensity fluctuation of R and the integrated output of O. Diffraction patterns due to a "two slit" in frequency domain were in fact retrieved by applying TGI, viz., TGD. Possible extension to space-momentum domain will be discussed.