Defocus optical transfer function: fast evaluation and lightweight storage based on cubic spline interpolation.

Abstract

Certain problems of image processing and 3D optical sectioning require the knowledge of defocus optical transfer function (OTF) with high resolution but its computation is not trivial: the OTF is an oscillatory integral. To efficiently compute the defocus OTF of a linear isoplanatic imaging system in incoherent illumination with a given accuracy on a fine grid, we suggest using cubic spline interpolation. The approximation error analysis of the splines shows that our method requires fewer OTF point evaluations than the direct evaluation at each grid point. The cubic spline also is a compact representation of the OTF and can be used to resolve data transfer bottlenecks and the lack of storage difficulties.