Within the optics industry, there is a continuous drive to reduce the size, weight, power consumption and cost of optical systems (known as SWAP-C). A new generation of fabrication technologies for GRadient-INdex (GRIN) materials promise the capability to manufacture GRIN media of arbitrary refractive index distribution (within index variation and spatial resolution limits). This represents an opportunity to further optimise the SWAP-C of lens systems, yet also presents challenges for the optical designer. The necessary optical design tools for arbitary GRINs are not widely implemented, and the potential applications where arbitrary GRINs provide a benefit are not widely explored.

This work addresses these design challenges via two routes. In the first body of work we explore the necessary design tools for generalised GRIN lenses, including efficient mathematical representations for GRIN distributions and tools for the generation of starting points for further optimisation. A powerful new tool is devised that can convert conventional homogeneous lens constructions to generalised GRIN media, which allows the GRIN lens designer to leverage the vast archive available of homogeneous lens solutions as starting points. We also address the aberration correction potential of GRIN lenses with planar surfaces.

In the second body of work we explore the applications that directly benefit from GRIN optics. We demonstrate that layered polymer GRIN lenses of spherical distribution enabled by new extrusion-based manufacture technologies can show comparable performance to conventional cemented doublets and hybrid refractive-diffractive lenses. We also explore the application of a freeform-GRIN distribution to the design of a head-mounted display (HMD), showing that GRIN can significantly reduce the optical complexity of a baseline homogeneous HMD design. Finally, we demonstrate that GRIN can be a powerful tool in the optical design of optical systems with very wide, multispectral infrared wavebands. A short-wave to long-wave (SWIR-LWIR) infrared design study shows a GRIN-based solution can dramatically reduce lens count, size and mass while reducing sensitivity to manufacturing tolerances.

We conclude that the required design infrastructure for arbitrary GRIN lenses is feasible and emerging, and that there are technological challenges in modern optical design that justify ongoing research into GRIN optics. Progress in the optical design of generalised GRINs must be accompanied by refinement in manufacture, metrology, and environmental qualification to enable widespread adoption and deployment.

In this thesis we try to provide novel solutions to key problems related to imaging and imaging system. Imaging is usually referred to as the technique for reproducing the information of the object. In optics, we usually refer the object information to the light field in the object plane due to the interaction of the illumination field and the object. Imaging technique allows the reproduced object information to be recorded by detectors such as human eye, photo resist, or CCD/CMOS sensor. In order to image an object, there must be light. We consider only un polarized quasi-monochromatic light illuminating the object and we approximate the field in the object plane by the multiplication of the transmittance / reflectance of the object and the illumination field (the first Born approximation). However, the results in this thesis can also be generalized to situations beyond the above scope. Here we mainly focus on two aspects: the aberrations, the errors of the imaging system, and the spatial coherence of the light field. In a typical imaging scenario, we consider the object plane field as a source consisting a series of point sources. The field generated by each point source propagates independently to the image plane through the imaging system. Ideally, these fields should all identically have the correct distribution and be centered at the correct location. However, this is not the case in presence of the aberrations. As a result, the image will become blurred.

This thesis focusses on two aspects of tunable optics: Fabry-Pérot interferometers with a variable distance between their mirrors and electrowetting liquid lenses. The need for a device to detect child abuse has motivated us to design and build a camera that can detect the chemical composition of the upper skin layers of a bruise using a self-made Fabry-Pérot interferometer. The research described in the first part of this thesis has shown that wide-angle spectral imaging can be achieved with compact and cost-effective cameras using Fabry-Pérot interferometers. Designs with a full field of 90◦ in which the Fabry-Pérot interferometer is mounted either in front of an imaging system or behind a telecentric lens system are presented and analysed. The dependency of the spectral resolution on the numerical aperture of the lens system is derived and its value as a design criterion is shown. It is shown that the telecentric camera design is preferable over the collimated design for bruise imaging with a Fabry-Pérot interferometer.
The idea to use a liquid lens for spectral imaging has directed the research towards a new concept of controlling surface waves on the surface of a liquid lens. We investigate and model surface waves because they decrease the imaging quality during fast focal switching. We propose a model that describes the surface modes appearing on a liquid lens and that predicts the resonance frequencies. The effects of those surface modes on a laser beam are simulated using geometrical optics and Fresnel propagation, and the model is verified experimentally. The model of the surface oscillations is used to develop a technique to create aspheric surface shapes on commercially available electrowetting liquid lenses. The surface waves on the liquid lens are described by Bessel functions of which a linear combination can be used to create any circularly symmetrical aspheric lens shape at an instant of time. With these surface profiles, one can realise a large set of circularly symmetrical wavefronts and hence intensity distributions of beams transmitted by the lens. The necessary liquid lens actuation to achieve a desired shape is calculated via a Hankel transform and confirmed experimentally. The voltage signal can be repeated at video rate. Measurements taken with a Mach-Zehnder interferometer confirm the model of the surface waves. The capabilities and limitations of the proposed method are demonstrated using the examples of a Bessel surface, spherical aberration, an axicon, and a top hat structure.