Identifying and Characterizing Micro-machining Signatures on Freeform Surfaces Using Morphological Methods

Freeform surfaces are replacing traditional surfaces and have significantly reduced volume and weight and highly improved performance in modern complex optic systems, bio-systems and other disciplines [1]. These high-precision freeform components are enabled by state-of-the-art micro-machining technologies, compromising mechanical methods (diamond turning and polishing etc.), physical methods (laser beam and ion beam machining), and chemical methods (lithography, electro-chemical machining etc.). However, a fundamental pre-requisite to achieve the potential growth to these high-added value freeform components is to measure and characterize these components with the required accuracy such that their manufacturing quality can be controlled. The surface topography is a fingerprint of all process stages of the manufacturing process. Thus identifying and evaluating these topographical features on freeform surfaces left by production techniques are critically important in that they could present an indication of the manufacturing quality and offer feedback to the process control

HOW TOUGH IS IT TO REPEATEDLY HIT THE BALL IN GOLF?

Golf is an increasingly popular sport, whose most challenging skill is the driver swing. There have been a large number of studies characterizing golf swings, yielding insightful instructions on how to successfully structure the swing. Achieving a sub 18 handicap is no longer the primary concern for golfers. Instead, players are now most troubled by a lack of consistency during swing execution. The goal of this study is to determine how to consistently execute repeated quality golf swings. By characterizing both successful and failed swings of 22 experienced golfers, we aim to identify swing parameters that are most sensitive and/or prone to motor control variations. We specifically report on five distinct problem areas, as well as provide suggestions for how to address these problems

A theoretical insight into morphological operations in surface measurement by introducing the slope transform

As one of the tools for surface analysis, morphological operations, although not as popular as linear convolution operations (e.g. the Gaussian filter), are really useful in mechanical surface reconstruction, surface filtration, functional simulation etc. By introducing the slope transform originally developed for signal processing into the field of surface metrology, an analytic capability is gained for morphological operations, paralleling that of the Fourier transform in the context of linear convolution. Using the slope transform, the tangential dilation is converted into the addition in the slope domain, just as by the Fourier transform, the convolution switches into the multiplication in the frequency domain. Under the theory of the slope transform, the slope and curvature changes of the structuring element to the operated surface can be obtained, offering a deeper understanding of morphological operations in surface measurement. The derivation of the analytical solutions to the tangential dilation of a sine wave and a disk by a disk are presented respectively. An example of the discretized tangential dilation of a sine wave by the disks with two different radii is illustrated to show the consistency and distinction between the tangential dilation and the classical dilation