Optimal transfer functions for bandwidth-limited imaging

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