Three-dimensional Coherent Transfer Function in Reflection-mode Confocal Microscopy Using Annular Lenses

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Abstract
The three-dimensional (3D) coherent transfer function (CTF) in a reflection-mode confocal scanning microscope using two equal annular lenses has been derived analytically under the paraxial approximation. This analytic 3D CTF is then generalized to a confocal system using optical fibres as an illumination source and a signal collector. Various 3D- and two-dimensional (2D) numerical plots are presented to reveal the dependence of the 3D CTF on the size of the central obstruction and on the fibre spot size. As expected, using annular lenses may result in improved transverse resolution but poorer axial resolution compared with those for circular lenses, and using optical fibres of finite cross-section may result in degraded resolution in both axial and transverse directions. The relationship of the 3D CTF to the 2D in-focus CTF is discussed.