| Polarization encoded heterodyne interferometry forms the basis of measurement and control in numerous high precision applications. While electronic fringe sub-division has led to sub-nanometer resolution, the accuracy of these systems is limited by subtle cyclical nonlinearities to approximately 5 nm p-p. This dissertation concerns itself with the modeling, experimental measurement and compensation of these cyclical errors. Analytical models are developed for a two-retroreflector displacement measuring interferometer. These models explore the contributions of various error sources (input beam rotation, ellipticity, non-orthogonality, analyzer alignment and beamsplitter leakage) to both the first and second harmonic nonlinearity. Interactions between input beam errors (rotation and ellipticity) and beamsplitter leakage are investigated and used as a basis for developing compensation strategies. Two experimental techniques are described---pressure and velocity scanning. The technique of pressure scanning is used to measure the nonlinearities and experimentally validate the cancellation of the second-harmonic nonlinearity, while velocity scanning is used to validate the cancellation of the first-harmonic nonlinearity. It is shown that the contribution of input beam ellipticity and rotational misalignment to the first-harmonic can be minimized by aligning the analyzer at 45°. It is further shown that the error contribution due to input beam errors may be used to cancel the contribution due to beamsplitter leakage. Compensation strategies are verified experimentally, and cancellation of the first and second harmonic errors to the 0.03 nm and 0.5 nm p-p level respectively are demonstrated. |
