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Adaptive optics (AO) is a powerful tool used in a wide range of research areas spanning from aerospace to microscopy. To date, AO has largely been applied to optical phase aberration correction, with recent advances extending to include the vectorial properties of light. However, intensity errors widely exist in optical systems, yet their associated correction methods are still very much in their infancy. Here, we propose a new adaptive optics method that is termed intensity adaptive optics (I-AO), which features a dual-feedback loop for intensity aberration correction that addresses both intensity uniformity and the overall intensity. We demonstrate that I-AO can operate in both sensor-based and sensorless regimes and validate its feasibility by quantitatively analysing the quality of the focus of an aberrated optical system. This technique expands the AO toolkit, broadens its scope of application, and opens a new avenue for next-generation AO innovations.

The resolution and contrast of microscope imaging is often affected by aberrations introduced by imperfect optical systems and inhomogeneous refractive structures in specimens. Adaptive optics (AO) compensates these aberrations and restores diffraction limited performance. A wide range of AO solutions have been introduced, often tailored to a specific microscope type or application. Until now, a universal AO solution -- one that can be readily transferred between microscope modalities -- has not been deployed. We propose versatile and fast aberration correction using a physics-based machine learning (ML) assisted wavefront-sensorless AO control method. Unlike previous ML methods, we used a bespoke neural network (NN) architecture, designed using physical understanding of image formation, that was embedded in the control loop of the microscope. The approach means that not only is the resulting NN orders of magnitude simpler than previous NN methods, but the concept is translatable across microscope modalities. We demonstrated the method on a two-photon, a three-photon and a widefield three-dimensional (3D) structured illumination microscope. Results showed that the method outperformed commonly-used modal-based sensorless AO methods. We also showed that our ML-based method was robust in a range of challenging imaging conditions, such as extended 3D sample structures, specimen motion, low signal to noise ratio and activity-induced fluorescence fluctuations. Moreover, as the bespoke architecture encapsulated physical understanding of the imaging process, the internal NN configuration was no-longer a ``black box'', but provided physical insights on internal workings, which could influence future designs., Comment: 27 pages, 12 figures

Adaptive optics normally concerns the feedback correction of phase aberrations. Such correction has been of benefit in various optical systems, with applications ranging in scale from astronomical telescopes to super-resolution microscopes. Here we extend this powerful tool into the vectorial domain, encompassing higher-dimensional feedback correction of both polarisation and phase. This technique is termed vectorial adaptive optics (V-AO). We show that V-AO can be implemented using sensor feedback, indirectly using sensorless AO, or in hybrid form combining aspects of both. We validate improvements in both vector field state and the focal quality of an optical system, through correction for commonplace vectorial aberration sources, ranging from objective lenses to biological samples. This technique pushes the boundaries of traditional scalar beam shaping by providing feedback control of extra vectorial degrees of freedom. This paves the way for next generation AO functionality by manipulating the complex vectorial field.

Advances in vectorial polarisation-resolved imaging are bringing new capabilities to applications ranging from fundamental physics through to clinical diagnosis. Imaging polarimetry requires determination of the Mueller matrix (MM) at every point, providing a complete description of an object's vectorial properties. Despite forming a comprehensive representation, the MM does not usually provide easily-interpretable information about the object's internal structure. Certain simpler vectorial metrics are derived from subsets of the MM elements. These metrics permit extraction of signatures that provide direct indicators of hidden optical properties of complex systems, while featuring an intriguing asymmetry about what information can or cannot be inferred via these metrics. We harness such characteristics to reveal the spin-Hall effect of light, infer microscopic structure within laser-written photonic waveguides, and conduct rapid pathological diagnosis through analysis of healthy and cancerous tissue. This provides new insight for the broader usage of such asymmetric inferred vectorial information.

While polarisation sensing is vital in many areas of research, with applications spanning from microscopy to aerospace, traditional approaches are limited by method-related error amplification or accumulation, placing fundamental limitations on precision and accuracy in single-shot polarimetry. Here, we put forward a new measurement paradigm to circumvent this, introducing the notion of a universal full Poincar\'e generator to map all polarisation analyser states into a single vectorially structured light field, allowing all vector components to be analysed in a single-shot with theoretically user-defined precision. To demonstrate the advantage of our approach, we use a common GRIN optic as our mapping device and show mean errors of <1% for each vector component, enhancing the sensitivity by around three times, allowing us to sense weak polarisation aberrations not measurable by traditional single-shot techniques. Our work paves the way for next-generation polarimetry, impacting a wide variety of applications relying on weak vector measurement.

Graded index (GRIN) lenses are commonly used for compact imaging systems. It is not widely appreciated that the ion-exchange process that creates the rotationally symmetric GRIN lens index profile also causes a symmetric birefringence variation. This property is usually considered a nuisance, such that manufacturing processes are optimized to keep it to a minimum. Here, rather than avoiding this birefringence, we understand and harness it by using GRIN lenses in cascade with other optical components to enable extra functionality in commonplace GRIN lens systems. We show how birefringence in the GRIN cascades can generate vector vortex beams and foci, and how it can be used advantageously to improve axial resolution. Through using the birefringence for analysis, we show that the GRIN cascades form the basis of a new single-shot Mueller matrix polarimeter with potential for endoscopic label-free cancer diagnostics. The versatility of these cascades opens up new technological directions.