Light-sheet fluorescence microscopy enables rapid 3D imaging of biological samples. Unlike confocal and two-photon microscopes, a light-sheet microscope illuminates the focal plane with an objective orthogonal to the detection axis and images it in a single snapshot. Its combination of height contrast and minimal sample exposure make it ideal to image thick samples with sub-cellular resolution. To uniformly illuminate a wide field-of-view without compromising axial resolution, propagation-invariant light-fields such as Bessel and Airy beams have been put forward. These beams do however irradiate the sample with a relatively broad transversal structure. The fluorescence excited by the side lobes of Bessel beams can be blocked physically during recording, at the cost of increased sample exposure. In contrast, the Airy beam has a fine transversal structure that is both curved and asymmetric. Its fine structure captures all the high-frequency components that enable high axial resolution without the need to discard useful fluorescence. This advantage does not carry over naturally to two-photon excitation where the fine transversal structure is suppressed. We demonstrate a symmetric and planar Airy light-sheet that can be used with two-photon excitation and that does not rely on deconvolution.

To increase the irradiance generated by an illumination system, multiple sub-systems, each generating their own irradiance distribution can be used. We propose a method using B-spline refinement to find the irradiance distribution that a single sub-system produces, so a desired irradiance distribution is obtained using multiple sub-systems.

We present a method for designing freeform optical surfaces for illumination optics. By the laws of reflection, refraction and conservation of energy, a fully nonlinear PDE, the Monge-Ampère quation, is derived for the optical surface. By the edge ray principle a transport boundary condition is obtained. We solve the hyperbolic variant of the PDE using a least-squares method, resulting in optical saddle surfaces for a parallel source and far-field target.

We present an inverse method for optical design that compensates local Fresnel reflections. We elaborate this method for a point source and far-field target. We modify an existing design algorithm based on the least-squares method. This is done in such a way that the shape of the transmitted intensity is as desired.

We present an alternative method to ray tracing that is based on a phase space description of light propagation. Liouville's equation of geometrical optics describes the evolution of the basic luminance on phase space. At an optical interface, the laws of optics describe non-local boundary conditions for the basic luminance. A discontinuous Galerkin method is employed to solve Liouville's equation for a dielectric total internal reflection concentrator.