In lensless digital in-line holographic microscopy, currently applied fast reconstruction techniques use approximations limiting the usable NA for optical resolution. The computational effort for an exact scalar reconstruction with straightforward algorithms depends on the relation between the desired resolution and the given pixel pitch of the detector. So there is a trade-off between achievable image resolution and required computation time. We present an exact reconstruction algorithm that guaranties optimum resolution with affordable computation time. Experimental results show a realized NA of at least 0.62. A 1 megapixel hologram was reconstructed in about .
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