The University of Southampton
University of Southampton Institutional Repository

Precision measurement and characterisation of spherical and aspheric surfaces

Precision measurement and characterisation of spherical and aspheric surfaces
Precision measurement and characterisation of spherical and aspheric surfaces
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.
Sun, Wenjuan
85a2b297-f55f-48a7-9059-a769aade3b89
Sun, Wenjuan
85a2b297-f55f-48a7-9059-a769aade3b89

Sun, Wenjuan (2007) Precision measurement and characterisation of spherical and aspheric surfaces. University of Southampton, School of Engineering Sciences, Doctoral Thesis, 159pp.

Record type: Thesis (Doctoral)

Abstract

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.

Text
Thesis-final_version.pdf - Other
Restricted to Repository staff only

More information

Published date: May 2007
Organisations: University of Southampton

Identifiers

Local EPrints ID: 65594
URI: http://eprints.soton.ac.uk/id/eprint/65594
PURE UUID: 859677f0-87be-4450-b114-5f6403ee0459

Catalogue record

Date deposited: 24 Mar 2009
Last modified: 13 Mar 2024 17:47

Export record

Contributors

Author: Wenjuan Sun

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×