Adaptive optics for corrections of phase and polarisation state aberrations in microscopes
Keywords: microscopy
vectorial aberrations
adaptive optics

Phase and polarization aberrations can affect the focus of optical systems and thus cause image distortion and quality reduction. Adaptive optics (AO) such as objective lens correction collars, spatial light modulators (SLM) and deformable mirrors (DM) are used in microscopy imaging systems to modulate and correct phase and polarization state errors. Different adaptive elements have special properties which make them suitable for different systems. In certain applications such as laser machining or microscopic imaging through an interface between mismatched refractive indices, spherical aberration is the major factor that affects the focal spot quality; the correction collar attached to the objective lens is a suitable and simple form of adaptive elements for correcting spherical aberration. In some microscopes, system misalignment and sample induced phase aberrations, especially in deep imaging, greatly affect image quality; a DM can be a good option when correcting phase aberrations of both the input and output beam while a SLM can be used if only the input laser beam requires correction. In certain systems, such as gradient index (GRIN) lens and stimulated emission depletion (STED) microscopy imaging systems, the image quality is also affected by polarization aberrations which can potentially be corrected by SLM devices.
Despite years of development, the operations of these adaptive elements to fulfil different correction tasks effectively and efficiently remain challenging. The spherical compensations of objective lens correction collars will introduce extra defocus at the same time, which makes it difficult to operate. In the cases when the fluorescence signal level is low, wavefront sensor-based operations of adaptive elements become infeasible so wavefront sensorless methods are used; yet there was no systematic comparison for various sensorless based methods to help people understand them better and advice people on method selections. Conventional sensorless based correction methods, which normally require multiple exposures per aberration mode and multiple rounds of corrections, are not the most efficient ways of operation. Polarisation states have a total of three degrees of freedom; corrections of polarisation states are more complex compared to phase aberrations, for which there is only one degree of freedom. Polarisation state conversion will induce extra geometric phase error which makes corrections more difficult.
In this thesis, I discussed and presented results trying to resolve the problems mentioned above. I first presented an automated control system for both spherical and defocus compensation using a motorised objective lens correction collar and an axially movable sample mounting stage. I then presented a universal framework for sensorless AO method to provide a better understanding of various sensorless approaches; this framework also allowed a systematic comparisons of various aberration representations used in different methods. I then presented a machine learning based sensorless AO method which shows promise to be more versatile than conventional sensor-less AO methods. Finally I presented theoretical analysis of vectorial state conversions (which includes both polarisation state and phase properties of light) and complex retarder compensations using a series of adaptive elements.