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Based on truncated inverse filtering, a theory for deconvolution of complex fields is studied. The validity of the theory is verified by comparing with experimental data from digital holographic microscopy (DHM) using a high-NA system (NA=0.95). Comparison with standard intensity deconvolution reveals that only complex deconvolution deals correctly with coherent cross-talk. With improved image resolution, complex deconvolution is demonstrated to exceed the Rayleigh limit. Gain in resolution arises by accessing the objects complex field - containing the information encoded in the phase - and deconvolving it with the reconstructed complex transfer function (CTF). Synthetic (based on Debye theory modeled with experimental parameters of MO) and experimental amplitude point spread functions (APSF) are used for the CTF reconstruction and compared. Thus, the optical system used for microscopy is characterized quantitatively by its APSF. The role of noise is discussed in the context of complex field deconvolution. As further results, we demonstrate that complex deconvolution does not require any additional optics in the DHM setup while extending the limit of resolution with coherent illumination by a factor of at least 1.64.

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We present a novel technique for three-dimensional (3D) image processing of complex fields. It consists in inverting the coherent image formation by filtering the complex spectrum with a realistic 3D coherent transfer function (CTF) of a high-NA digital holographic microscope. By combining scattering theory and signal processing, the method is demonstrated to yield the reconstruction of a scattering object field. Experimental reconstructions in phase and amplitude are presented under non-design imaging conditions. The suggested technique is best suited for an implementation in high-resolution diffraction tomography based on sample or illumination rotation.

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