Advancements in null corrector design and certification

The dissertation addresses advancements in null corrector design. The Rayces zero-index concept is validated and used to design null correctors in single pass. By using a doublet field lens in the standard Offner null corrector, the overall length and size of the null corrector are reduced. The Multi-Object Double Spectrograph (MODS) blue corrector study outlines the process associated with designing and producing a null corrector. A novel ghost image analysis technique is used to evaluate candidate MODS blue null corrector designs. Tolerance analysis is performed and manufacturing specifications are defined for the MODS blue null corrector. Several off-axis null corrector designs are investigated as potential solutions to test 8.4 m off-axis elements of a 25 m diameter parabola.; The dissertation also addresses advancements in null corrector certification. Truncated-series solutions for diamond turned mirrors and computer generated hologram certifiers for aspheric surfaces that can be modeled in lens design code are derived. The truncated-series solutions are general and can be applied to most aspheric surfaces with only simple changes in coefficients. These equations are implemented in lens design code via the user defined surface (UDS). The process of implementing a UDS is outlined in the dissertation. Once a UDS is identified, a two-step design process is used to create the certifier. First, the corresponding Shack surface of the aspheric surface or surfaces under test must be defined. Second, a point source illuminates the mirrored Shack surface and a certifier is placed at, in, or outside the center of curvature of the Shack surface. Because the rays go back to a point source after reflection from the Shack surface, a standard merit function that minimizes RMS spot radius can be used to find the coefficients. Certifier surface solutions are presented at the center of curvature and inside the center of curvature of the Shack surface for a broad range of aspheric optics. The solution for a certifier outside of the center of curvature of a parabola's Shack surface is also provided.