The need for controlled illumination arises from emerging efficiency standards and increasing light pollution. When the illumination sector diverged from imaging optics finding solutions instead in nonimaging optics, the field of illumination engineering greatly evolved. Light optics can now minimize light waste, improve light quality, and enhance light aesthetics. And because illumination optics is concerned with the transferring of light, fundamental concepts in nonimaging optics lead to solutions without imposing the constraints found in imaging optics.

This dissertation is largely concerned with nonimaging optics. An overview of this field will be given, addressing topics such as edge-ray theory, strings method, \'{e}tendue, phase space, angular space, thermodynamics, and flow lines. New advances will be discussed, specifically the theoretical advances pertaining to the asymmetric compound parabolic concentrator (ACPC). Although similar to the compound parabolic concentrator, the ACPC has differing acceptance angles, making it versatile for both the fields of solar concentration and illumination. For solar concentration, its asymmetry can be utilized for areas of the world far from the equator, where more extreme seasons are experienced. Also, in regards to illumination, the ACPC offers more specialized control in non-symmetric instances.

Here, a method to determine the acceptance angles based on the design angles for the ACPC is provided. The \'{e}tendue, phase space, and angular acceptance for the ACPC is then shown. Two cases for each of these results, and a way to predict these cases will be discussed. Flow lines for this asymmetric design are also discussed, pushing the boundaries of this relatively new nonimaging optics topic.

The ACPC could potentially help in reducing light pollution once further analysis has been completed. Light pollution is a growing problem worldwide. The valley in Yosemite National Park is one example of a place in need of lighting reform. Nonimaging optics offers ways to improve the light quality there. Using a wedge design as a primary optic to transform phase space for a compound parabolic concentrator (CPC), illumination for an equipment yard was controlled to reduce stray light. This nonimaging optics solution was both quick and inexpensive to produce. Furthermore, its small size allowed for retrofitting, which is an ideal way to fix the lights in Yosemite.

Another optic that will be discussed utilizes total internal reflection (TIR) to control illumination. Nicknamed ``The Jellyfish" for its shape, this novel aplanatic lens is one of a kind. Impressively, the Jellyfish can be used as either an illuminator or a solar concentrator because its optics work in both forward and reverse scenarios. When designed on a small scale, this optic becomes useful for micro-optic scale concentrating photovoltaic (CPV) solutions. As a light source, its adjustable size, acceptance angle, and thickness can be increased to meet various lighting standards. When designed for ideal cases, emerging rays exit the surface nearly parallel to one another. In fact, high efficiencies are seen for rays to within two degrees of the optical axis. This is due in large part to the design method, which is carried out using the concepts first developed by Ernest Abbe. The Abbe Sphere offers a starting point, after which, ideas of reflection and refraction can be utilized at front and back surfaces to guid light via TIR to its exit points.

Work documented here takes the Jellyfish and optimizes it for illumination solutions. It is adjusted to work with an extended source (LED) and meet MR-16 standards. Design and simulation processes are given, along with prototyping results.

Finally, design methods in freeform optics offers solutions that can be tailored for even the most complicated illumination distributions. One method, the Supporting Quadrics Method (SQM), takes light rays and directs them to designated locations on a target. The quadrics used for these designs can be ellipsoids, hyperbolids, or parabolids. Numbers of them can used in conjunction with one another to create a desired distribution, after which an envelope is taken to generate a final surface. When the number of these quadrics increase, they must become smaller to accommodate the overall size of the lens. This leads to the question of diffraction effects. Because each quadric is its own aperture, does diffraction play a role in disrupting what should be a precise distribution? Preliminary analysis is done to address this question.

All the work completed within this dissertation falls into nonimaging optics for illumination. With the growing prevalence of energy standards, optical design is important for controlling the light emitted from LEDs. This relatively new field provides the fundamental concepts necessary to design solutions for preventing light pollution, creating prescribed distributions, and achieving high efficiencies.