Coherent use of opposing lenses for axial resolution increase in fluorescence microscopy I Comparative study of concepts

We study the use of coherent counterpropagating interfering waves to increase threefold to sevenfold the optical bandwidth and the resolution of fluorescence microscopy along the optic axis. Systematic comparison of the point-spread function and the optical transfer function (OTF) for the standing-wave microscope (SWM), the incoherent illumination interference image interference microscope $({\mathrm{I}}^5\mathrm{M}),$ and the 4Pi confocal microscope reveals essential differences among their resolution capabilities. It is shown that the OTF’s of these microscopes differ strongly in contiguity and amplitude within the enlarged range of transferred frequencies, and therefore they also differ in their ability to provide data from which interference artifacts can be removed. We demonstrate that for practical aperture angles the production of an interference pattern is insufficient for improving the axial resolution by the expected factor of 3–7. Conditions of the OTF for unambiguous improvement of axial resolution of arbitrary objects are fulfilled not at all in the SWM, partially in the ${\mathrm{I}}^5\mathrm{M},$ and fully in the two-photon 4Pi confocal microscope.