A fast algorithm is proposed for the reconstruction of digital holograms that are recorded at high numerical aperture. The method directly evaluates the Rayleigh-Sommerfeld diffraction integral by use of a fast convolution algorithm. A shift parameter that accounts for the coordinate system's transverse displacement of the object plane and the hologram plane is introduced in a discrete representation of the diffraction kernel. Combination of the samplings reconstructed with different shift values yields diffraction-limited resolution over the full field of view. The algorithm is suitable for various applications such as holographic microscopy and metrology. Simulation and experimental results are presented.
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