Light-sheet microscopy facilitates rapid, high-contrast, volumetric imaging with minimal sample exposure. However, the rapid divergence of a traditional Gaussian light sheet restricts the field of view (FOV) that provides innate subcellular resolution. We show that the Airy beam innately yields high contrast and resolution up to a tenfold larger FOV. In contrast to the Bessel beam, which also provides an increased FOV, the Airy beam's characteristic asymmetric excitation pattern results in all fluorescence contributing positively to the contrast, enabling a step change for light-sheet microscopy.

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In a similar fashion to diffusers or other highly scattering media, multimode fibres deliver coherent light signals in the form of apparently random speckled patterns. In contrast to other optically random environments, multimode fibres feature remarkably faithful cylindrical symmetry. Our experimental studies challenge the commonly held notion that classifies multimode fibres as unpredictable optical systems. Instead, we demonstrate that commercially available multimode fibres are capable of performing as extremely precise optical components. We show that, with a sufficiently accurate theoretical model, light propagation within straight or even significantly deformed segments of multimode fibres may be predicted up to distances in excess of hundreds of millimetres. Harnessing this newly discovered predictability in imaging, we demonstrate the unparalleled power of multimode fibre-based endoscopes, which offer exceptional performance both in terms of resolution and instrument footprint. These results thus pave the way for numerous exciting applications, including high-quality imaging deep inside motile organisms.T he theoretical description of light transport processes within ideal multimode fibres (MMFs) has been developed for over half a century 1-4 . This elaborate theoretical model is, however, frequently considered inadequate to describe real-life MMFs, which are manufactured by drawing melted silica preforms. Such fibres are commonly seen as unreliable, and the inherent randomization of light propagating through them is typically attributed to undetectable deviations from the ideal fibre structure. It is a commonly held belief that this additional chaos is unpredictable and that its influence grows with the length of the fibre. Despite this, light transport through MMFs remains deterministic.The prospect of deterministic light propagation within MMFs has only recently been used through methods of digital holography and by adopting the concept of empirical measurement of the transformation matrix (TM) 5-11 . This technique, developed in studies of light propagation through highly turbid media 12-17 , has opened a new window of opportunity for MMFs to become extremely narrow and minimally invasive endoscopes, allowing sub-micrometre resolution imaging in deep regions of sensitive tissues 9,18 .However attractive, this technology suffers from several major limitations, the most critical being the lack of flexible operation. Any bending or looping of the fibre results in changes to its TM, rendering the imaging heavily impaired. All current methods exploiting MMFs for imaging require open optical access to the distal end of the fibre during the time-consuming measurement of the TM. Furthermore, this characterization must be repeated upfront for every intended configuration (deformation) and any axial distance of the focal plane behind the fibre before the system can be used for imaging 7,19 . The necessity to determine the TM empirically is therefore a major bottleneck of the technology, and it would be immense...

There has been an immense drive in modern microscopy towards miniaturization and fibre-based technology. This has been necessitated by the need to access hostile or difficult environments in situ and in vivo. Strategies to date have included the use of specialist fibres and miniaturized scanning systems accompanied by ingenious microfabricated lenses. Here we present a novel approach for this field by utilizing disordered light within a standard multimode optical fibre for lensless microscopy and optical mode conversion. We demonstrate the modalities of bright- and dark-field imaging and scanning fluorescence microscopy at acquisition rates that allow observation of dynamic processes such as Brownian motion of mesoscopic particles. Furthermore, we show how such control can realize a new form of mode converter and generate various types of advanced light fields such as propagation-invariant beams and optical vortices. These may be useful for future fibre-based implementations of super-resolution or light-sheet microscopy.

We present a powerful approach towards full understanding of laser light propagation through multimode optical fibres and control of the light at the fibre output. Transmission of light within a multimode fibre introduces randomization of laser beam amplitude, phase and polarization. We discuss the importance of each of these factors and introduce an experimental geometry allowing full analysis of the light transmission through the multimode fibre and subsequent beam-shaping using a single spatial light modulator. We show that using this approach one can generate an arbitrary output optical field within the accessible field of view and range of spatial frequencies given by fibre core diameter and numerical aperture, respectively, that contains over 80% of the total available power. We also show that this technology has applications in biophotonics. As an example, we demonstrate the manipulation of colloidal microparticles.