3-DIMENSIONAL TRANSFER-FUNCTIONS IN 4PI CONFOCAL MICROSCOPES

We investigate three-dimensional transfer functions in order to understand image formation in the recently proposed 4Pi confocal microscope [J. Opt. Soc. Am. A 9, 2159 (1992); Opt. Commun. 93, 277 (1992)]. Both nonfluorescence and fluorescence imaging methods are considered, and the effects of apodization functions are taken into account. It is shown that for a 4Pi confocal system of finite-sized aperture the cutoff spatial frequency in the axial direction is larger than that in the transverse direction; this behavior is opposite that of conventional confocal systems, explaining the observation of high axial resolution in 4Pi confocal systems. In addition, the three-dimensional optical transfer function for a conventional confocal fluorescence microscope of high aperture is presented.