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A polishing pad can smooth out mid-to-high spatial frequency errors automatically due to its rigidity and modeling of the smoothing effect is important. The relationship between surface error and polishing time is built here based on the Bridging model and Preston's equation. A series of smoothing experiments using pitch tools under different motion manners were performed and the results verified exponential decay between surface error and smoothing time. At the same time, parameters describing smoothing efficiency and smoothing limit were also fitted from the results. This method can be applied to predict the smoothing effect, estimate the smoothing time and compare smoothing rates of different runs.

A generalized model is developed to quantitatively describe the smoothing effects from different polishing tools used for optical surfaces. The smoothing effect naturally corrects mid-to-high spatial frequency errors that have features small compared to the size of the polishing lap. The original parametric smoothing model provided a convenient way to compare smoothing efficiency of different polishing tools for the case of sinusoidal surface irregularity, providing the ratio of surface improvement via smoothing to the bulk material removal. A new correlation-based smoothing model expands the capability to quantify smoothing using general surface data with complex irregularity. For this case, we define smoothing as a band-limited correlated component of the change in the surface and original surface. Various concepts and methods, such as correlation screening, have been developed and verified to manipulate the data for the calculation of smoothing factor. Data from two actual polishing runs from the Giant Magellan Telescope off-axis segment and the Large Synoptic Survey Telescope monolithic primary-tertiary mirror were processed, and a quantitative evaluation for the smoothing efficiency of a large pitch lap and a conformal lap with polishing pads is provided.

Aspheric surfaces are often measured using interferometers with null correctors, either refractive or diffractive. The use of null correctors allows high accuracy in the measurement, but also introduces imaging aberrations, such as mapping distortion and field curvature. These imaging aberrations couple with diffraction effects and limit the accuracy of the measurements, causing high frequency features in the surface under test to be filtered out and creating artifacts near boundaries, especially at edges. We provide a concise methodology for analyzing these effects using the astigmatic field curves to define the aberration, and showing how this couples with diffraction as represented by the Talbot effect and Fresnel edge diffraction. The resulting relationships are validated with both computer simulations and direct measurements from an interferometer with CGH null corrector.

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