Theory and application of differential OTF (dOTF) wavefront sensing

Abstract

A new image-based technique for measuring the complex field in the pupil of a telescope is presented. The simplest form of the method uses two point source images, one with a small modification introduced in the pupil. The processing of the images is very simple and non-iterative. The method is based on a specially-defined complex functional derivative of the OTF. This derivative is approximated empirically by the difference between the Fourier transforms of the two PSFs: the differential OTF or "dOTF." Due to the complex conjugate in the OTF, the dOTF includes two complex images of the complex pupil field overlapping at the point of pupil modification. By placing the modification near the edge of the pupil, the overlap region can be minimized. The overlap region is typically small, but can be eliminated altogether by using a second modification and a third image. The technique can use broadband light, but the result incurs a radial blurring proportional to the fractional bandwidth. This is also easily dealt with using another modification and image. Although the dOTF a poor match for high frame rate astronomical AO applications, it has many potential uses. Optical shop testing, non-common-path wavefront error estimation, alignment and vignetting, telescope segment phasing, general imaging system diagnostics and testing applications are considered. More advanced applications are possible with extensions to the theory, such as extended incoherence background scenes as sources instead of stars, and 3-D tomographic aberration and transmission mapping open up many new applications.