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No description available.

No description available.

No description available.

The object of this Ph.D work is to evaluate fidelity in surface measurements in nanometric metrology for both contact and non-contact methods, namely stylus instruments and scanning tunnelling microscopy. Fidelity is defined, in this thesis, as a measure to which an instrument system reproduces the surface features and thus the parameters of interest. High fidelity measurement has two meanings; less distortion in the measured result and less disturbance to the surface being measured. Interaction at the interface between the probe and the surface is the source of failure to achieve high fidelity. No instrument measures surface topography alone: all instruments measure a convolution of topography and the geometrical and physical interaction of the measured probe and the surface. In the case of a mechanical stylus, factors extraneous to the topography include (a) the shape and size of the stylus, (b) mechanical properties of the stylus and the specimen such as elastic moduli and hardness, (c) frictional force of the sliding pair. and (d) dynamic interaction forces during the sliding. For the scanning tunnelling microscope, factors which affect measurement in addition to topography include the geometry of the tip, the electronic properties of the surface and mechanical deformation due to electrostatic forces and contamination. 'These factors have been investigated in great detail, particularly for the stylus instruments. A specially designed electro-magnetic force actuator has been developed to give a better control on loading force during the experiments. Tracking force effects were evaluated by profiling statistical parameters, and scanning electron microscopy. Friction between a stylus and specimen has been measured for different loading force, sliding speed, material and surface finish. Improvement on dynamic characteristics of a stylus system has been achieved by active damping control. An optimal damping ratio for stylus instruments is found to be within 0.5-0.7. Through the study, the tracking force and traversing speed are found to be the crucial factors to be tackled so that high fidelity measurement can be obtained. A similar investigation has been also made on two home-built scanning tunnelling microscopes to explore the potential applications of STM on nanometric metrology.

This work was canied out between October 1986 and February 1989 at the School of Engineering, University of Warwick. The thesis begins with a review of the configurations of coordinate measuring machines in common use and an investigation into the types and magnitudes of the errors incurred due to various phenomena associated with the design, deformation or misalignment of the machine components. Some of the more significant of these errors are then measured and tabulated with a view to using them as a comparison to further work. Methods by which these errors can be rectified are then briefly reviewed. Chapter 2 is concerned with the inadequacies associated with current coordinate measuring machine software algorithm design. Measurement practices are reviewed and sources of inconsistency or potential misinterpretation are identified. Sampling error is singled out as being of particular significance. Chapter 3 reviews geometric element fitting procedures and the errors that can result from ill advised measuring practice. Systematic and random error analyses of the errors incurred in the estimates of geometric parameters are reviewed and an original investigation is performed into the errors incurred in parameters due to not considering all possible data (sampling error.) Chapter 4 presents an assessment of the nature of the problem of sampling error and outlines the way in which a robust algorithm for the formal quantification of these errors should be formulated. Chapter 5 then identifies the criteria that would maximise the implementability of an algorithm of this type. An algorithm satisfying these particular requirements is duly developed. Finally, chapter 6 consists of an investigation into the effect of probe geometry on the phenomenon of sampling errors. A method is then developed whereby the probe geometry that will minimise sampling error can be readily selected.

This thesis describes an investigation into the measurement and the characterisation of spherical and aspheric surfaces. The reliability of the nonlinear least-squares sphere fitting algorithm has been investigated. The study is focused on spherical surfaces, superimposed with random surface irregularities, within small surface segment angles. A new method based on Box’s estimation has been developed to calculate the bias of estimated parameters. The method is significantly faster and more convenient than a computer simulation process. By combining this estimate with the calculation of the uncertainty, a comprehensive understanding of the nonlinear least-squares sphere fitting algorithm has been achieved. Aspheric surface fitting algorithms are also of interest. Two methods have been developed to fit aspheric surfaces. The advantage of these two methods is that they both estimate the complete surface parameters which can then be compared with the design parameters. The first one is an indirect method. The calculation of surface parameters is based on the estimation of vertex radius, and errors in this estimate will influence all other parameters. To overcome this disadvantage, a direct method has been proposed. The method uses the nonlinear least-squares technique in which all parameters can be estimated simultaneously. The fitting algorithm has been tested on both computer simulated surfaces and measured surfaces. Issues regarding applying this method to measured surfaces have also been discussed. In addition to these theoretical studies, experimental work is presented. The dominant systematic errors have been studied in a white light confocal scanning system, which suggests that non-contact optical scanning system can be used for precision surface measurements.

Methods for the assessment of curved, rotationally symmetric surfaces in three dimensions are developed and outlined in this thesis. The assessment of electrical switching contacts, contact lens moulds and aspherical leps surfaces is demonstrated. Discrete data for surface assessment is obtained by surface measurement with a profilometer. Hence, surface measurement refers to simultaneous measurement of surface form and surface irregularity. The data is defined in a Cartesian co-ordinate system, and a data set consists of up to 27,000 discrete points on an uniform grid. The grid spacing in x and y is typically between 25um and 125um. The resolution of the data in the vertical axis is lOnm (Inm = 10"9 metre). The key aspects of the research are as follows: A method for data interpretation is proposed. The method is primarily intended to simplify surface assessment of aspherical surfaces. It consists of three key elements: pre-processing, form characterisation and data decomposition into error types. Pre-processing detects the position and orientation of a surface. The surface is then aligned and a separation of surface geometry from position and orientation is achieved. For pre-processing four algorithms are developed, outlined and compared. Form characterisation of rotationally symmetric, aspherical surfaces is then considered. A least squares method is used to fit discrete data to a general solution function in explicit notation. Various problems related to form characterisation with explicit functions are addressed and solutions are presented. Finally, methods for data decomposition into error types are presented. A standardised decomposition method (BS-ISO 10110-5) is compared with an alternative method that is developed in this research. General recommendations for the measurement and the assessment of aspherical surfaces are given. A method for the selection of a form characterisation algorithm for the assessment of nominally spherical surfaces is proposed. Many different sphere fitting algorithms are reported in literature and the best-fit parameters, centre co-ordinates and radius, vary on the same set of discrete data with the algorithm that is used for form characterisation. Five sphere fitting algorithms are investigated in this research: linear and non-linear least squares sphere fit, minimum zone sphere fit, four-point sphere fit and sphere fit by error curve analysis. In conclusion to the investigation it is proposed to use the surface irregularity distribution as a criteria for the selection of a sphere fitting algorithm. The data sampling strategy, distribution of discrete points within a segment and size and location of a segment on a surface, is also investigated. General recommendations for the measurement and the assessment of nominally spherical surfaces are given. The idea of computer aided surface assessment (CASA) is evolved. In CASA, data visualisation and data interpretation are combined for processing of discrete data from the measurement of a surface. Software for computer aided surface assessment is developed and outlined in this thesis.

Two original applications of laser speckle metrology are presented. First, a portable Laser Speckle Interferometer is described which allows the Engineer to simply point a laser beam at target surface in order to measure its vibration velocity amplitude and phase. This non-contacting capability complements an accelerometer where use of the latter is precluded; i.e. hot, light or rotating surfaces. The mechanisms which determine the noise floor of the interferometer are examined and minimisation procedures are defined. A prototype instrument is described which has a dynamic range of 60 dB over a frequency range of d.c. - 20 kHz which is adequate for general purpose use. Three applications are reported which exploit the non-contact capability of the instrument. Second, the application of Laser Speckle Photography to fluid flows is described and the development of an entirely new technique is introduced which is more appropriately named Particle Image Velocimetry (PIV). In PIV, the instantaneous two-dimensional velocity of a fluid flow is measured by taking a double-exposure photograph of a thin sheet of light within a seeded flow. Pointwise processing of the resulting transparency with a laser beam produces Young's fringes in the far field diffraction pattern whose spacing and orientation are measured to find the local fluid velocity within the illuminated region. It is shown both theoretically and by experiment, that the signal to noise ratio of these fringes and hence measurement accuracy, is significantly improved by using a two-step photographic process. In addition, it is shown that this process allows the use of more sensitive photographic films which reduce the laser power requirement and hence the cost of a PIV system. Two methods of fringe analysis are examined and it is shown that, by preprocessing the fringe pattern to remove the low frequency pedestal component, fringe spacing errors of less than 1% are achieved. It is also shown that this method significantly decreases the time required to measure fringe spacing when compared with conventional Fourier methods. In addition, a method of decreasing the overall time required to analyse an entire PIV transparency based on detection of the presence of particle images within the illuminated region is described.

This thesis presents three-dimensional surface metrology techniques suitable for the appraisal 'of curved surfaces. Instrument requirements for measuring 3-D curved surfaces are discussed and four instruments selected which meet these requirements. These instruments are a Laser Radius-scope, Fizeau Interferometer, Laser Ranging Probe and a Stylus Profilometer. Numerical algorithms for assessing the data from these instruments are then considered, with particular emphasis being placed on the evaluation of the radius of curvature of the surface, removal of this best-fit sphere from the data and visualisation of the resulting errors of form. New circle and sphere-fitting algorithms are presented for radius of curvature analysis. These numerical methods, together with a number of standard, well documented routines (least-squares circle and sphere) are then tested for their sensitivity to a number of sample parameters on ideal, computer generated data sets. The parameters tested are sample length/area, radius of curvature, centre offset and surface roughness. The new techniques show a considerable improvement in estimating the radius of the test data; in the presence of + I0.00/*m peak-to-valley surface roughness, the new circle-fit routine produced a radius error of 0.32/xm as opposed to -0.85/*m for the least-squares circle routine, whilst the new sphere-fit had a radius error of 2.29jum compared to the least-squares sphere's error of -3.64/xm. The new sphere-fit also reduces the computation times on a 66MHz. 486DX2 Personal Computer from 14.89 seconds for least-squares sphere to 0.66 seconds. Four studies are then carried out on nominally spherical samples of varying dimensions, radius of curvature and surface finish. The studies assess the radius of curvature of the samples, either directly for the Laser Radius-scope and Fizeau Interferometer or, in the case of the Laser Ranging Probe and the Stylus Profilometer, by the application of the numerical routines previously tested. The advantages, limitations and faults of each instrument are discussed and it is concluded that despite the stylus profiler's instrumentational flaws, it offers the most flexible method of measuring the three-dimensional surface profiles of curved surfaces.