Three-dimensional optical transfer function in a fiber-optical confocal fluorescence microscope using annular lenses

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Abstract
Three-dimensional fluorescent image formation is analyzed for a fiber-optical confocal scanning microscope that uses annular lenses. The three-dimensional optical transfer function is derived, including the effects of the central obstruction radius and of the fiber spot size. Numerical calculations of the three-dimensional optical transfer functions have been performed for various cases. No negative values exist in the transfer functions, and no missing cone of spatial frequencies appears if the illumination fiber is identical to the collection fiber. It is found that using annular lenses in a system with optical fibers can result in improved resolution in both transverse and axial directions.