Evaluation of image-shift measurement algorithms for solar Shack-Hartmann wavefront sensors

TL;DR

This paper evaluates various image-shift measurement algorithms for solar Shack-Hartmann wavefront sensors, identifying the most accurate methods and clarifying whether they measure Z-tilts or G-tilts, considering factors like noise and blurring.

Contribution

It provides a comprehensive assessment of shift measurement algorithms, highlighting the superior methods based on difference functions and their tilt measurement characteristics.

Findings

Square difference function and absolute difference squared are the best methods.

Subpixel accuracy achieved with 2D quadratic interpolation.

Algorithms measure Z-tilts rather than G-tilts.

Abstract

Context. Solar Shack-Hartmann wavefront sensors measure differential wavefront tilts as the relative shift between images from different subapertures. There are several methods in use for measuring these shifts. Aims. We evaluate the inherent accuracy of the methods and the effects of various sources of error, such as noise, bias mismatch, and blurring. We investigate whether Z-tilts or G-tilts are measured. Methods. We test the algorithms on two kinds of artificial data sets, one corresponding to images with known shifts and one corresponding to seeing with different r_0. Results. Our results show that the best methods for shift measurements are based on the square difference function and the absolute difference function squared, with subpixel accuracy accomplished by use of two-dimensional quadratic interpolation. These methods measure Z-tilts rather than G-tilts.