A digital filtering system for decoding in-line holograms

A system of digital filters is presented, which is applied directly to the in-line hologram and maps the hologram into an image of the boundaries (edges) of the objects encoded in it provided that the object distribution function is real. The first stage is an approximate inverse filter in the form of a truncated series expansion in the Fourier transform domain, having basis functions coskb (u²+v²). The first term in the expansion corresponds to conventional optical reconstruction which is contaminated by the twin-image; and the twin-image is suppressed by the successive terms. The non-linear post filtering consists of a covariance filter which replaces each input pixel by the estimate of the local covariance. A thresholding may be added prior to the covariance filtering if the edges of the reconstructed objects are not sharp enough.