A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Abrasive fine-finishing technology is often applied as a final finishing process, and the selection of the right technology is crucial to obtaining the desired performance of functions such as fatigue life. This paper begins with classifications of the technology along with fundamentals and brief histories of the individual methods. The material removal mechanisms, specific energies, and finishing characteristics of the various technologies are summarized giving assessments of the surfaces created by them. Guidelines developed for selecting the appropriate methods, and case studies illustrate the effectiveness of various methods. This paper ends with a discussion of the future prospects of the technology. (C) 2016

Abrasive fine-finishing technology

A method for null-testing fast convex aspheric optical surfaces is presented The method consists of using a cylindrical screen with a set of lines drawn on it in such a way that its image, which is formed by reflection on a perfect surface, yields a perfect square grid Departures from this geometry are due to imperfections of the surface, allowing one to know if the surface is close to the design shape Tests conducted with a full hemisphere and with the parabolic surface of a lens show the feasibility of the method Numerical simulations show that it is possible to detect surface departures as small as 5 microm

Null-screen testing of fast convex aspheric surfaces.

High Energy Fluid Jet Machining (HEFJet-Mach): From scientific and technological advances to niche industrial applications

Computer controlled polishing requires accurate knowledge of the tool influence function (TIF) for the polishing tool (i.e. lap). While a linear Preston's model for material removal allows the TIF to be determined for most cases, nonlinear removal behavior as the tool runs over the edge of the part introduces a difficulty in modeling the edge TIF. We provide a new parametric model that fits 5 parameters to measured data to accurately predict the edge TIF for cases of a polishing tool that is either spinning or orbiting over the edge of the workpiece.

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Parametric modeling of edge effects for polishing tool influence functions.

In a polishing process the wear is greater at the edge when the tool extends beyond the border of the workpiece. To explain this effect, we propose a new model in which the pressure is higher at the edge. This model is applied to the case of a circular tool that polishes a circular workpiece. Our model correctly predicts that a greater amount of material is removed from the edge of the workpiece.

Edge effects with the Preston equation for a circular tool and workpiece

A common mathematical model is established for the Ronchi and Hartmann tests and for interpretation of the Ronchigrams as level curves of the components of the transversal aberrations. With the same point of view, a Hartmanngram is regarded as two 90° crossed null Ronchi gratings. A simple and direct method is also developed for calculating Ronchigrams for the cases of centered and off-axis conic sections with the point light source at any location.

Ronchi and Hartmann tests with the same mathematical theory

In the polishing process, the wear tends to be greater when the tool extends beyond the edge of the workpiece. A linear pressure distribution (between the tool and the workpiece) has been used to explain this effect, however, this model also can predict negative pressures. This could mean that material is deposited instead of being removed. We present a new pressure distribution proposal, which presents like a skin effect. This means that the pressure is significantly higher at the border points than at internal points of the glass. With this model the material removal at the border points is increased considerably since, according to Preston, the wear is proportional to the pressure. This pressure distribution model is applied to calculate the wear produced by a square tool on a glass border moving along straight lines.

Edge effects with Preston equation

To help in the fabrication of off-axis conic sections, we present a method to approximate this off-axis section by an on-axis conic centered on the portion desired. This method is based on the method of continuum least squares to obtain the vertex’s curvature and conic constant of the fitted conic on-axis, given the curvature at the vertex and the conic constant of the parent conic from where we want the section and the size of that section. Simple analytic expressions for the curvature and conic constant are derived in terms of the parameters of the off-axis section.

Conic that best fits an off-axis conic section.

Assuming the Ronchi and the Hartmann tests to be null tests, we were able to design special screens for each test that produce aligned straight fringes and a square array for the observed patterns. It also became clear that the screen filter and observing planes for both tests can be interchanged.

Alberto Cordero-Dávila

Papers

Edge effects with the Preston equation for a circular tool and workpiece

Ronchi and Hartmann tests with the same mathematical theory

Edge effects with Preston equation

Conic that best fits an off-axis conic section.

Null Hartmann and Ronchi-Hartmann tests