The pages of this dissertation detail the development of an advanced metrology instrument for measuring large optical surfaces. The system is designed to accurately guide the fabrication of the Giant Magellan Telescope and future telescopes through loose-abrasive grinding. The instrument couples a commercial laser tracker with an advanced calibration technique and a set of external references to mitigate a number of error sources. The system is also required to work as a verification test for the GMT principal optical interferometric test of the polished mirror segment to corroborate the measurements in several low-order aberrations. A set of system performance goals were developed to ensure that the system will achieve these purposes. The design, analysis, calibration results, and measurement performance of the Laser Tracker Plus system are presented in this dissertation.

In the aberration analysis of a wavefront over a certain domain, the polynomials that are orthogonal over and represent balanced wave aberrations for this domain are used. For example, Zernike circle polynomials are used for the analysis of a circular wavefront. Similarly, the annular polynomials are used to analyze the annular wavefronts for systems with annular pupils, as in a rotationally symmetric two-mirror system, such as the Hubble space telescope. However, when the data available for analysis are the slopes of a wavefront, as, for example, in a Shack-Hartmann sensor, we can integrate the slope data to obtain the wavefront data, and then use the orthogonal polynomials to obtain the aberration coefficients. An alternative is to find vector functions that are orthogonal to the gradients of the wavefront polynomials, and obtain the aberration coefficients directly as the inner products of these functions with the slope data. In this paper, we show that an infinite number of vector functions can be obtained in this manner. We show further that the vector functions that are irrotational are unique and propagate minimum uncorrelated additive random noise from the slope data to the aberration coefficients.

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The use of optical input/output (I/O) interconnects, in addition to electrical I/Os, is a promising approach for achieving high-bandwidth, chip-to-board communications required for future high-performance gigascale chip-based systems. While numerous efforts are underway to investigate the integration of optoelectronics and silicon microelectronics, virtually no work has been reported relating to testing of such chips. The objective of this research is to explore methods that enable wafer-level testing of gigascale chips having electrical and optical I/O interconnects. A major challenge in achieving this is to develop probe modules which would allow high-precision, temporary interconnection of a multitude of electrical and optical I/Os, in a chip-size area, to automated test equipment. A probe module would need to do this in a rapid, step-and-repeat manner across all the chips on the wafer. In this work, two candidate probe modules were devised, batch-fabricated on Si using microfabrication techniques, and successfully demonstrated. The first probe module consists of compliant electrical probes (10^3 probes/cm^2) fabricated alongside grating-in-waveguide optical probes. The second module consists of micro-opto-electro-mechanical-systems (MOEMS)-based microsocket probes (10^4 probes/cm^2) to interface a chip with polymer pillar-based electrical and optical I/Os. High-density through-wafer interconnects are an essential attribute in both probe substrates for transferring electrical and optical signals to the substrate back-side. Fabrication and characterization of metal-clad, metal-filled, and polymer-filled through-wafer interconnects as well as process integration with probe substrate fabrication are described and numerous possible redistribution schemes are explicated. Chips with optical and electrical I/Os are an emerging technology, and one that test engineers are likely to encounter in the near future. The contributions of this thesis are to help understand and address the issues relating to joint electrical and optical testing during manufacturing.