  One of the fundamental limits of classical optical microscopy is the
diffraction limit of optical resolution. It results from the finite bandwidth
of the optical transfer function (or OTF) of an optical microscope, which
restricts the maximum spatial frequencies that are transmitted by a microscope.
However, given the frequency support of the OTF, which is fully determined by
the used optical hardware, an open and unsolved question is what is the optimal
amplitude and phase distribution of spatial frequencies across this support
that delivers the "sharpest" possible image. In this paper, we will answer this
question and present a general rule how to find the optimal OTF for any given
imaging system. We discuss our result in the context of optical microscopy, by
considering in particular the cases of wide-field microscopy, confocal Image
Scanning Microscopy (ISM), 4pi microscopy, and Structured Illumination
Microscopy (SIM). Our results are important for finding optimal deconvolution
algorithms for microscopy images, and we demonstrate this experimentally on the
example of ISM. Our results can also serve as a guideline for designing optical
systems that deliver best possible images, and they can be easily generalized
to non-optical imaging such as telescopic imaging, ultrasound imaging, or
magnetic resonance imaging.
