Conventional approaches to microscopy record essentially two-dimensional images with a trade between transverse resolution and depth of field. Advances in computational imaging, using engineered point-spread functions have enabled an increase in depth of field, but generally with poor image quality arising from axial variations in the point-spread function. We report how the axial variations in Airy beams can be exploited to enable diffraction-limited, aberration-free 3D microscopy in a single snapshot for imaging of both 3D surfaces and 3D volumes. Localisation microscopy of point emitters enables microscopy with nanoscale nanoscale resolution and when implemented with various exotic point-spread functions this can be extended to 3D imaging. We will show how 3D locational microscopy based on Airy beams can enable much higher emitter densities, which enables the essential high-speed 3D measurement required in applications ranging through fluid dynamics, cardio-vascular monitoring and single-molecule imaging.

Extreme ultraviolet (XUV) light applications are still a very promising field that was heavily enlivened by the definition of the new wavelength for semiconductor lithography within the XUV range. But the detection of XUV light is also important for the exploration in the field of space science (i.e., monitoring the formation and evolution of solar storms) and high-energy physics (i.e., dark matter detection). The advancement of this technology mainly depends on the performance optimization of XUV sources, optical systems and related photodetectors. In this work, the optical design of a high flux XUV setup was simulated and defined to optimise the beam path which is the backbone of the initial evaluation process for the characterisation of luminescent materials under XUV irradiation. Additionally, the paper focused on the conceptualisation and realisation of the experimental setup as well as the alignment of the optical components and the detector calibration.

Concatenated backward ray mapping is an alternative for ray tracing in 2D. It is based on the phase space description of an optical system. Phase space is the set of position and direction coordinates of rays intersecting an optical line. The original algorithm is limited to optical systems consisting of only straight line segments; we extend it to accommodate curved segments. The algorithm is applied to the compound parabolic concentrator, a standard optical system that collects parallel light and reshapes it to a focused beam. We compare the accuracy and speed of the extended algorithm to the original algorithm and Monte Carlo ray tracing. The results show that the extended algorithm outperforms both methods.

We present a novel approach to computing reflectors with a scattering surface in illumination optics. A scattering model governed by a Fredholm integral equation is derived. Solving this integral relation yields a virtual specular target distribution, which we insert into a Monge-Ampère least-squares numerical solver to get a scattering reflector that yields the desired illumination.

We present a novel approach to minimize aberrations in imaging systems. The energy distributions at the source and target of an optical system play a crucial role in designing freeform surfaces through illumination optics methodologies. We quantify the on-axis and off-axis aberrations using a merit function that depends on the energy distributions. The minimization of the merit function yields optimal energy distributions, which subsequently enable us to design freeform reflector surfaces that cause the least aberrations. We validate our method by testing it for two configurations, a single-reflector system with a parallel source to a near-field target, and a double-reflector system with a parallel source to a point target.