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\title{Adaptive optics correction for bent multimode fibres for use in biological imaging}
\author{Eusebiu Sutu\\[1cm]{Supervisors: Martin Booth, Nigel Emptage}}
\date{October 2024}

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Multimode optical fibres show great promise for \textit{in vivo} imaging due to their thin profile, limiting
invasiveness. However, propagation through such a fibre leads to scrambling of the light, which
requires adaptive optics for compensation in order to create a focus at or near the output facet.
Furthermore, changes in conformation due to bending lead to a change in transmission properties, limiting the ability to generate a focus at the output facet without recalibration. Hence, a requirement for effective imaging though an optical fibre is that one can adaptively change the calibration as the fibre conformation changes.

The thesis proposes an approach to correct for such changes in transmission and regain the ability to focus through a bent fibre, without access to the distal facet, as the system is intended for use during imaging. The method presented in this report uses a sensorless adaptive optics approach in concomitance with a Walsh mode representation of the modulated input optical field to correct for a bent fibre and increase the intensity of a desired focus. Then, with the use of memory effect, the area in which the correction is achievable is increased. However, the area in which a desired correction of at least $70\%$ of the focus intensity generated with a fully calibrated fibre is limited. Thus, the approach shows that by using multiple correction targets, the entire facet of the fibre can be accounted for. Furthermore, the focus plane is not limited to only the distal facet, but it can be set at different axial depths, through the use of free-space propagation.

The correction procedure is dependent on the use of reflectors for the sensorless adaptive optics optimisation step. Thus, the thesis also proposes a novel approach for the simulation of Bragg gratings in multimode optical fibres, which can provide a tool in choosing the desired reflector to be used with the correction approach.    

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I would like to start by underlining my gratefulness to Prof. Martin Booth and Prof. Nigel Emptage, my two supervisors, for their guidance and support throughout my studies.

I am also grateful to Dr. Patrick Salter and Dr. David Phillips for their ideas and advice.

I am also grateful to Maike Lenz for her ideas and discussions.

Finally, I am also grateful to the Biotechnology and Biological Sciences Research Council and the Doctoral Training Centre for the financial support provided.
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% Section 1 - Introduction
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% Section 2 - General Background
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% Section 3 - REfocussing using Sensorless Adaptive Optics
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% Section 4 - Memory Effect
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% Section 5 - Correction Procedure
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% Section 6 - Bragg Gratings
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% Section 7 - Discussion and Conclusion
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