Effects of third-order spherical aberration on the 3-D incoherent optical transfer function

We derive the expression for the 3-D incoherent optical transfer function when third-order spherical aberration is present. The normalized verision of the transfer function is numerically calculated for various amounts of spherical aberration. We find the effects of the aberration to be highly dependent on the spatial frequency in the longitudinal direction. We also calculate a structure content parameter, as a quality criterion, from the normalized transfer function. The structure content parameter dependence on spherical aberration is well-fit by a simply Cauchy curve for aberrations out to two waves at the margin.