The images of space objects, such as stars and artificial satellites, are blurred by atmospheric turbulence. Adaptive optics (AO) is traditionally used to mitigate the blurring effect of atmospheric turbulence. A typical AO control system employs a wavefront sensor (WFS) to estimate the phase aberration induced by atmospheric turbulence. In recent years, there has been a significant tendency toward wavefront sensorless (WFSL) AO, in which intensity images instead of WFSs are used for estimating the phase aberration. The WFSL AO has traditionally been utilised in fields of AO, such as microscopy and free-space optical communications. Such methods, however, have rarely been used for astronomical applications due to the fact that atmospheric turbulence varies at a high rate.

This research attempts to make WFSL AO possible for astronomical imaging. Overall, WFSL methods are classified into model-free and model-based. Model-free methods are based on iterative global optimisation algorithms. Such methods do not model the search space (here atmospheric turbulence) and intensity-based objective function. However, they have low computational complexity and do not require to calibrate the deformable mirror (DM). Therefore, these methods can be implemented using a general-purpose PC for real-time calculation. Model-based methods, on the other hand, parametrically model the search space and/or the objective function to deterministically find the optimum of the objective function using a few intensity measurements. Typically, such methods are computationally intractable and thus need a high-performance computer to efficiently correct the phase aberration in real time. In this thesis, several model-free and model-based WFSL meth- ods are proposed and simulated.

The two first aberration modes, tip and tilt, collectively contain the largest share of atmospheric turbulence. Thus, correcting these two modes would notably improve the image quality. In this thesis, three model-free WFSL methods based on hill-climbing algorithm variants are developed for removing tip and tilt. Utilising the statistics of tip and tilt in atmospheric turbulence along with some mathematical techniques, the number of intensity measurements needed is reduced to the maximum possible number, which is calculated using the highest resonant frequency of a typical tip/tilt mirror existing in the market and a reasonable tilt frequency of 80 Hz. These methods can improve the fractional encircled energy (EE) from about 26% to 54%, 45% and 58% using 29, 38 and 48 intensity measurements, respectively.

For larger magnitudes of the aberration, the impact of higher modes in- creases. Therefore, removing the first two modes alone does not significantly help improve the image quality. Two model-based WFSL methods using Gaussian radial surrogate functions are developed for removing the eight aberration modes after tip and tilt. To reduce the number of required measurements, the search space of atmospheric turbulence is modelled by deriving the probable maximum magnitude of each aberration mode. To decrease the number of measurements to the maximum possible number, which is calculated using the highest frame rate of the University of Canterbury’s Electrical and Computer Engineering Optics laboratory’s deformable mirror and the worst atmospheric turbulence’s evolution frequency at the University of Canterbury Mount John Observatory site, a few techniques including space-filling sampling plans are employed. The first method is designed for small and medium aberration magnitudes (less than 3 [rad]) and the second one is for larger aberrations. Examining the first method using 100 random Kolmogorov phase screens shows the improvement of the average fractional EE by 20%. The number of measurements for the second method, however, exceeds the maximum possible number.

In situations where a high-performance computer or a GPU is accessible, a general model-based method can be developed such that it extracts the input aberration deterministically using a significantly small number of intensity measurements. The light phase can be approximated to be composed of rectangular segments of piston elements. Using this approximation, it is demonstrated that an intensity image corresponding to a phase divided by that corresponding to a single segment yields a function, which is indeed a Fourier series. Extracting the coefficients of this series using the acquired intensity image leads to a number of non-linear equations. Two general model-based WFSL methods are developed based on this mathematical relation. These methods need two intensity measurements for aberrations with magnitudes less than 1 [rad] RMS, six measurements for magnitudes between 1 and 3 [rad] RMS, and ten measurements for magnitudes between 3 and 5 [rad] RMS. These methods surpass the previous works in terms of the number of intensity measurements needed. The main advantage of the proposed methods over the preceding ones is that our proposed methods are zonal and require a fixed number of intensity measurements. In contrast, existing model- based methods are modal and the least number of measurements reported thus far is N + 1 for correcting N modes. In other words, as opposed to existing model-based methods, the proposed methods are independent of the number of modes contained in a phase aberration. Moreover, the trade-off between the accuracy and computational complexity in the proposed methods is tunable as well.

Note that all the results in this thesis are obtained through computer simulations, as opposed to laboratory experiments.