Correlation-based smoothing model for optical polishing

Abstract

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.

Generalized numerical pressure distribution model for smoothing polishing of irregular midspatial frequency errors

“…The bridging model was further applied to the aspheric surface polished by Burge et al [9] and Tuell et al [10]. Kim et al [11] developed the normalized smoothing factor based on the simplified bridging model and conducted a contrast experiment on pitch lap and rigid conformal lap, which is verified by Shu et al [12] with the help of a correlation-based smoothing model. However, in practice, the irregular MSFR may be a superposition of innumerable sinusoidal errors with different frequencies and amplitudes.…”

“…The pressure of every frequency component is different. Consequently, it is very hard to calculate the pressure distribution between the pad and the irregular processed surface using Mehta's bridging model [12].…”

Improved the laser-induced damage threshold of fused silica by atmospheric pressure plasma processing

“…The conformal polishing process removes the deposition layer and pit microstructures on the surface of the workpiece to improve the surface quality under the condition of not destroying the surface. The surface figure and material removal difference at the peak-valley position can be expressed respectively [17]. 0 ()…”

Research on stable convergence technology of transmitted wavefront mid-spatial-frequency errors of large square spherical lens

“…The corresponding spatial frequency bands are shown in Figure 1 . For large spatial filter lenses, the power spectral density (PSD) is usually used to evaluate the MSF errors of the transmitted wavefront [4][5][6][7] , and the one-dimensional (1D) PSD curve of the transmitted wavefront errors must not exceed the cut-off line (The oblique line shown in Figure 1) [1] . The integral of the 1D PSD curve to the spatial frequency in the mid-frequency band can comprehensively reflect the severity of the MSF errors, which is expressed as the RMS value of the transmitted wavefront errors in the mid-frequency band.…”