The ability to form images through hair-thin optical fibres promises to open up new applications from biomedical imaging to industrial inspection. Unfortunately, their deployment has been limited because small changes in mechanical deformation (e.g. bending) and temperature can completely scramble optical information, which distorts the resulting images. Since such changes are dynamic, correcting them requires measurement of the fibre transmission matrix in situ immediately before imaging. Transmission matrix calibration typically requires access to both the proximal and distal facets of the fibre simultaneously, which is not feasible during most realistic usage scenarios without compromising the thin form factor with bulky distal optics. Here, we introduce a new approach to determine the transmission matrix of multi-mode or multi-core optical fibre in a reflection-mode configuration without requiring access to the distal facet. A thin stack of structured metasurface reflectors is used at the distal facet of the fibre to introduce wavelength-dependent, spatially heterogeneous reflectance profiles. We derive a first-order fibre model that compensates these wavelength-dependent changes in the fibre transmission matrix and show that, consequently, the reflected data at 3 wavelengths can be used to unambiguously reconstruct the full transmission matrix by an iterative optimisation algorithm. We then present a method for sample illumination and imaging following reconstruction of the transmission matrix. Unlike previous approaches, our method does not require the fibre matrix to be unitary making it applicable to physically realistic fibre systems that have non-negligible power loss. We demonstrate the transmission matrix reconstruction and imaging method first using simulated non-unitary fibres and noisy reflection matrices, then using much larger experimentally-measured transmission matrices of a densely-packed multicore fibre. Finally, we demonstrate the method on an experimentally-measured multi-wavelength set of transmission matrices recorded from a step-index multimode fibre. Our findings pave the way for online transmission matrix calibration in situ in hair-thin optical fibres.

Imaging through optical fibres has recently emerged as a promising method of micro-scale optical imaging within a hair-thin form factor. This has significant applications in endoscopy and may enable minimally invasive imaging deep within live tissue for improved diagnosis of disease. Multi-mode fibres (MMF) are the most common choice because of their high resolution but multicore fibres (MCF) offer a number of advantages such as widespread clinical use, ability to form approximate images without correction and an inherently sparse transmission matrix (TM) enabling simple and fast characterisation. We present a novel experimental investigation into properties of MCF important for imaging, specifically: a new method to upsample and downsample measured TMs with minimal information loss, the first experimental measurement of MCF spatial eigenmodes, a novel statistical treatment of behaviour under bending based on a wireless fading model, and an experimental observation of TM drift due to self-heating effects and discussion of how to compensate this. We next present practical techniques for imaging through MCFs, including alignment, how to parallelise TM characterisation measurements to improve speed and how to use non-interferometric phase and polarisation recovery for improved stability. Finally, we present two recent applications of MCF imaging: polarimetric imaging using a robust Bayesian inference approach, and entropic imaging for imaging early-stage tumours.

Computer-generated holography (CGH) is a technique to generate holographic interference patterns. One of the major issues related to computer hologram generation is the massive computational power required. Hardware accelerators are used to accelerate this process. Previous publications targeting hardware platforms lack performance comparisons between different architectures and do not provide enough information for the evaluation of the suitability of recent hardware platforms for CGH algorithms. We aim to address these limitations and present a comprehensive review of CGH-related hardware implementations.

This work describes a novel approach to time-multiplexed holographic projection on binary phase devices. Unlike other time-multiplexed algorithms where each frame is the inverse transform of independently modified target images, Single-Transform Time-Multiplexed (STTM) hologram generation produces multiple sub-frames from a single inverse transform. Uniformly spacing complex rotations on the diffraction field then allows the emulation of devices containing 2 N modulation levels on binary devices by using N sub-frames. In comparison to One-Step Phase Retrieval (OSPR), STTM produces lower mean squared error for up to N = 5 than the equivalent number of OSPR sub-frames with a generation time of 1 /N of the equivalent OSPR frame. A mathematical justification of the STTM approach is presented and a hybrid approach is introduced allowing STTM to be used in conjunction with OSPR in order to combine performance benefits.

The fluorescent detection of proteins without labels or stains, which affect their behaviour and require additional genetic or chemical preparation, has broad applications to biological research. However, standard approaches require large sample volumes or analyse only a small fraction of the sample. Here we use optofluidic hollow-core photonic crystal fibres to detect and quantify sub-microlitre volumes of unmodified bovine serum albumin (BSA) protein down to 100 nM concentrations. The optofluidic fibre's waveguiding properties are optimised for guidance at the (auto)fluorescence emission wavelength, enabling fluorescence collection from a 10 cm long excitation region, increasing sensitivity. The observed spectra agree with spectra taken from a conventional cuvette-based fluorimeter, corrected for the guidance properties of the fibre. The BSA fluorescence depended linearly on BSA concentration, while only a small hysteresis effect was observed, suggesting limited biofouling of the fibre sensor. Finally, we briefly discuss how this method could be used to study aggregation kinetics. With small sample volumes, the ability to use unlabelled proteins, and continuous flow, the method will be of interest to a broad range of protein-related research.