Traditional optical instrumentation typically requires a controlled, stable environment, and this limits systems to a laboratory setting. For in-situ metrology applications and outdoor measurements, novel methods that are compact and stable are required. The focus of this thesis is to numerically evaluate, build, and test multiple interferometric holography setups to identify potential candidates for these applications. All setups used specialized geometric phase (GP) elements to perform a common-path, self-referenced measurement technique. The setups used a polarized camera sensor, consisting of a four-polarizer array of pixels, capturing high-speed measurements, otherwise known as single-shot phase shifting. The application was taken one step further, in which the complex wavefield was captured as well, which enabled digital holographic postprocessing such as numerical refocusing. In this work, the angular spectrum (AS) method was employed to refocus the wavefield numerically. Advantages of this ability are overcoming the tradeoff between depth of focus and resolution, along with diminishing the components' mechanical movement. Two different GP elements, GP lenses and GP gratings, were used to realize different shearing interferometric methods. The GP lens in the first incoherent system behaves as a concave or convex lens, based on the incoming polarization, resulting in two separate beams that interfere. All other experimental setups used incoherent and coherent light with GP gratings to spatially shear the object wavefield, enabling interference. Objects were digitally reconstructed, and parameters were evaluated to compare systems.
