Wavefront sensing with the differential optical transfer function

Recently a new technique for estimating the complex field in the pupil of a telescope from image-plane intensity measurements has been introduced by Codona.1, 2 The simplest form of the method uses two images of a point source, one with a small modification introduced in the pupil. The algorithm to recover the pupil field uses a functional derivative of the optical transfer function (OTF), and is simple and non-iterative. The derivative is approximated empirically by the difference between the Fourier transforms of the two PSFs: the differential OTF or dOTF. In keeping with the Hermitian symmetry of the OTF, the dOTF includes two conjugate copies of the pupil field overlapping at the point of modification. By placing the modification near the edge of the pupil, the overlap region can be kept small. It can be eliminated altogether by using a second modification and a third image. The technique can be used in broadband light, at the cost of blurring in the recovered phase that is proportional to the fractional bandwidth. Although the dOTF is unlikely to find application in high frame rate astronomical adaptive optics, it has many potential uses such as optical shop testing, non-common-path wavefront error estimation, segmented telescope phasing and general imaging system diagnostics. In this paper, we review the dOTF concept, theory, and initial experiments to demonstrate the technique.