Accuracy of Shack-Hartmann wavefront sensor using a coherent wound fibre image bundle.

Shack-Hartmann wavefront sensors using wound fibre bundles are desired for multi-object adaptive optical systems to provide large multiplex positioned by Starbugs. The use of the large-sized wound fibre bundle provides the exibility to use more sub-apertures wavefront sensor for ELTs. These compact wavefront sensors take advantage of large focal surfaces such as the Giant Magellan Telescope. The focus of this paper is to study the wound fibre image bundle structure defects effect on the centroid measurement accuracy of a Shack-Hartmann wavefront sensor. We use the first moment centroid method to estimate the centroid of a focused Gaussian beam sampled by a simulated bundle. Spot estimation accuracy with wound fibre image bundle and its structure impact on wavefront measurement accuracy statistics are addressed. Our results show that when the measurement signal to noise ratio is high, the centroid measurement accuracy is dominated by the wound fibre image bundle structure, e.g. tile angle and gap spacing. For the measurement with low signal to noise ratio, its accuracy is influenced by the read noise of the detector instead of the wound fibre image bundle structure defects. We demonstrate this both with simulation and experimentally. We provide a statistical model of the centroid and wavefront error of a wound fibre image bundle found through experiment.