Dissertation Defense: Alex Erstad

    Thursday, November 21, 2019 - 3:00pm
    Meinel 647

    Dissertation Title: Applications of Eikonals in Optical Design


    Dr. John Koshel (chair)
    Dr. Russell Chipman
    Dr. Rongguang Liang


    The polynomial fit eikonal can characterize any complex surface by converting a ray trace of the system into a phase space transformation. This phase space transformation provides the information required to define the radiance throughout the system. The characterization of the radiance throughout the system means that the eikonal can be used in lieu of a conventional ray trace. The initial computation time needed to create the polynomial fit eikonal of a surface can be high and the eikonal representation is not as accurate as a real ray trace of a system. However, in contrast to real ray traces, the polynomial fit eikonal provides more flexibility. For example, if a full optical system has each of its surfaces converted into eikonals, then any polynomial fit eikonal surface can be exchanged with any other polynomial fit eikonal surface without needing to run cumbersome ray traces. Furthermore, once the surface is fully characterized, the eikonal does not need to be recreated as the system changes. Computation time is thus faster overall for eikonal surfaces than for real ray traces. The eikonal becomes more accurate as more terms are included. This increase in accuracy is due to higher order terms of the eikonal fitting higher order optical aberrations.

    This dissertation explores how various optical factors, such as curvature and refractive index, affect the accuracy of the eikonal fit. Whenever an eikonal fit is performed, it is not guaranteed to be accurate enough for the application at hand, so error reduction is an important factor when building eikonal surfaces. As the system’s étendue increases, it becomes harder to fit the system to a single eikonal with reasonable error. In this case, it can be advantageous to split the system’s étendue into smaller, more manageable sections to reduce the error of the eikonal. For systems with complex sources, the source can be compiled into a probability density function. This probability density function allows for the characterization of a source into a continuous function using a ray set as the basis. Rays can then be interpolated by a random weighted drawing of new rays from the probability density function and then propagated through the optical system using the eikonal.