Beyond the conventional information limit: the relevant coherence function

The theory of partial coherence functions as applied to a super-resolution reconstruction algorithm is developed in detail, taking into account the phase gradients across the aperture function, the source and detector sizes, and temporal coherence. Experimental examples demonstrate the main properties of the relevant coherence envelopes, and why they need not limit the total band-pass of the microscope. It is demonstrated that finite detector size in the STEM configuration can facilitate a simpler reconstruction algorithm by creating a virtual objective aperture which obviates the need for a physical objective aperture. These results are also relevant to the question of uniquely deconvolving shadow images.

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