Deconvolution of differential OTF (dOTF) to measure high-resolution wavefront structure

Differential OTF uses two images taken with a telescope pupil modification between them to measure the complex field over most of the pupil. If the pupil modification involves a non-negligible region of the pupil, the dOTF field is blurred by convolution with the complex conjugate of the pupil field change. In some cases, the convolution kernel, or difference field, can cause significant blurring. We explore using deconvolution to recover a highresolution measurement of the complex pupil field. In particular, by assuming we know something about the area and nature of the difference field, we can construct a Wiener filter that increases the resolution of the complex pupil field estimate in the presence of noise. By introducing a controllable pupil modification, such as actuating a telescope primary mirror segment in piston-tip-tilt to make the measurement, we explain added features to the difference field which can be used to increase the signal-to-noise ratio for information in arbitrary ranges of spatial frequency. We will present theory and numerical simulations to discuss key features of the difference field which lead to its utility for deconvolution of dOTF measurements.