Sixth-order coincidence fractional Fourier transform implemented with partially coherent light

The sixth-order coincidence fractional Fourier transform (FRT) with incoherent and partially coherent light is introduced as an extension of the recently introduced fourth-order coincidence FRT. An optical system for implementing sixth-order coincidence FRT is designed. It is found that the visibility of the sixth-order coincidence FRT pattern of an object is always much higher than that of the fourth-order coincidence FRT pattern. The visibility is closely related to the transverse width and the transverse coherence length of the light source and also depends on the fractional order of the optical system.