Three-dimensional coherent transfer function for reflection confocal microscopy in the presence of refractive-index mismatch

The three-dimensional (3-D) coherent transfer function for reflection confocal microscopy of high-numerical-aperture objectives is derived and calculated in the presence of refractive-index mismatch when a laser beam is focused into a medium of refractive index different from its immersion medium. This aberrated coherent transfer function is then used to estimate the readout efficiency of 3-D data bits recorded in a thick medium. It is shown that the readout efficiency of confocal microscopy for 3-D bit data storage is decreased with the focal depth of an objective in a recording medium. However, a high readout efficiency can be maintained if the tube length of a reading objective is linearly altered to compensate for the spherical aberration caused by the refractive-index mismatch.