Imaging astronomical objects, such as stars, planets and galaxies, with ground-based telescopes, is challenging due to the blurring effects of Earth’s time-varying atmosphere. Beyond a certain diameter, the resolution of a telescope is limited by atmospheric turbulence.

There are three ways in which the limitations of imaging through Earth’s atmosphere can be addressed: put the telescope in space, real-time adaptive optics (AO), and computer post-processing. This thesis deals with real-time AO only.

An AO system consists of three major components: The deformable mirror (DM), the wavefront sensor (WFS) and the wavefront controller (WFC). A DM is a mirror where the shape of the mirror surface can be electronically controlled. The DM is placed in the telescope light path. The WFS is used to estimate the wavefront of the incoming light. The WFC takes the wavefront estimate from the WFS and drives the shape of the mirror, such that the wavefront is as close to planar as possible. This thesis focuses on the WFS and wavefront estimation.

The next generation of ground-based telescopes will have mirror diameters on the order of 25 m to 40 m. These so-called extremely large telescope (ELT)s will all make extensive use of AO systems, with the deformable mirror forming a key component in the telescopes’ optical design. The preferred WFS for ELTs is the pyramid WFS. The pyramid WFS provides higher sensitivity and dynamic range in closed-loop than the Shack-Hartmann WFS commonly used in current AO systems.

The pyramid WFS consists of a 4-sided glass prism placed at the focal plane of the telescope and relay optics which re-image the pupil through the pyramid onto the WFS detector. The image formed on the detector consists of four pupil images, from which the slope of the wavefront at each position in the pupil can be found. The pyramid WFS can be generalised to an N-sided prism. This thesis explores the 2-sided roofs, 3-sided, pyramid, 6-sided and cone (infinite sides) prism WFSs in end-to-end numerical simulations using Octopus. In a high photon flux scenario, the pyramid WFS achieves the best performance, with the worst sensor within 2.5%. In a low photon flux scenario, with a high readout noise, the 3-sided WFS performs 8.6% better than the pyramid WFS.

For ELTs, and more specifically the European Extremely Large Telescope (EELT), the support structure, or spider, which supports the secondary mirror, is large enough to obstruct entire rows of WFS subapertures. The spider arms are on the order of 50 cm thick, which is larger than the expected r0 at the observatory site. The effect of the large spider is to sub-divide the pupil into discontinuous segments, resulting in each segment having a different mean phase (piston). Segment piston modes are poorly sensed by a pyramid WFS, but the DM can easily produce them. Segment piston can also be introduced by the wavefront reconstructor if not properly optimised. In simulation, an 8 m telescope, without a spider, achieves a closed-loop long exposure Strehl of 96% in K-band at high flux. Introducing a thick spider and keeping the AO parameters the same, the Strehl drops to 0.8%. By optimising the illumination threshold for active subaperture selection, the amount of regularisation used in the wavefront estimation and the AO loop gain, the closed-loop long exposure Strehl is significantly improved, at 94.7%.

Using the EELT 6-fold spider geometry, the pupil is divided into six segments. Using the eigenmodes of the segment piston modes, the sensitivity of the pyramid WFS to segment piston modes at different modulation radii is evaluated. The unmodulated pyramid WFS is shown to be the most sensitive to segment piston modes.

This thesis presents a new modulation technique for the pyramid WFS, the flip-flop method, which combines the increased linearity and dynamic range of the modulated pyramid, with the sensitivity to segment piston modes of the unmodulated pyramid. The flip-flop method is able to run in closed-loop and control segment piston errors, even in R-band. The flip-flop method uses a single pyramid WFS, with two modulation states, modulated and unmodulated. The modulated loop runs at 1 kHz and controls the bulk of atmospheric turbulence. The unmodulated loop has a specialised reconstructor which is optimised for controlling the segment piston modes and runs at 100 Hz. For a high flux case, with an r0 of 15 cm, an improvement of 8.3% and 12.1% is shown for K and R-band respectively over a modulated pyramid.