Holography with extended reference by autocorrelation linear differential operation.

We introduce a generalization of Fourier transform holography that allows the use of the boundary waves of an extended object to act as a holographic-like reference. By applying a linear differential operator on the field autocorrelation, we use a sharp feature on the extended reference to reconstruct a complex-valued image of the object of interest in a single-step computation. We generalize the approach of Podorov et al. [Opt. Express 15, 9954 (2007)] to a much wider class of extended reference objects. Effects of apertures in Fourier domain and imperfections in the reference object are analyzed. Realistic numerical simulations show the feasibility of our approach and its robustness against noise.