Focus detection from digital in-line holograms based on spectral l_1 norms

A rapid focus-detection technique based directly on the spectral content of digital holograms is developed. It differs from previous approaches in that it does not need a full reconstruction of the image. The technique uses l1 norms of object spectral components associated with the real and imaginary parts of the reconstruction kernel. Further, the l1 norms can be computed efficiently in the spatial frequency domain using a polar coordinate system, yielding a drastic speedup of ∼2 orders of magnitude compared with image-based focus detection. Significant computational savings are achieved when subsequent image reconstructions are done selectively over the detected focus distances. Focus-detection results from holograms of plankton are demonstrated that show the technique is both accurate and robust.