Shih, YanhuaSmith, Thomas Allen2022-02-092022-02-092020-01-0112359http://hdl.handle.net/11603/24220Two-photon interference present in thermal light has been applied to various interferometers and imaging techniques. Differing from more traditional optical setups that use the measurement of intensity to observe single-photon interference, two-photon interference is observed through optical correlation measurements between a pair of detectors. This dissertations presents recent work in developing two separate applications of two-photon interference: turbulence-free interferometers and X-ray ghost microscopes. Inspired by the original Hanbury Brown-Twiss interferometer, which is insensitive to optical turbulence, the turbulence-free interferometers discussed here achieve path overlap of the two-photon amplitudes, resulting in the cancellation of the contributions of turbulence, i.e. turbulence-free. This mechanism is demonstrated here in the form of the two-photon double-slit interferometer and then proposed in a new type of turbulence-free, two-photon optical beats interferometer that will likely have practical applications such as turbulence-free gravitational-wave detection. Alongside the development of two-photon interferometers, two-photon, lensless ghost imaging has been developed. The lensless nature of the technique has made X-ray ghost imaging an intriguing possibility. Due to the ineffectiveness of traditional lenses on X rays, most X-ray imaging is projection-based. Unlike true, diffraction-limited point-to-point imaging (such as imaging with a lens), projection-based imaging is more comparable to the formation of a shadow. While still extremely useful, this type of imaging lacks the full resolving power one might expect with high-energy (short-wavelength) X rays. Presented here is the theory behind potential nanometer resolution in the form of diffraction-limited point-to-point imaging achievable with X-ray ghost imaging; namely, the X-ray ghost microscope. These contributions to the field of quantum optics provide an intriguing look into the fundamental nature of light and will allow for nontraditional, practical applications.application:pdfGhost imagingInterferometryOptical turbulenceQuantum opticsX-ray imagingAdvances in the Study of Two-photon Interferometry: From Turbulence-free Interferometers to X-ray Ghost MicroscopesText