This dissertation, "Use of the Richardson-Lucy Algorithm in Analyzing Positron Annihilation Spectroscopy Data" by Dapeng, Yu, 于大鵬, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled USE OF THE RICHARDSON-LUCY ALGORITHM IN ANALYZING POSITRON ANNIHILATION SPECTROSCOPY DATA submitted by Yu Da Peng for the Degree of Master of Philosophy at The University of Hong Kong in December 2006 Positron annihilation spectroscopy (PAS) is a popular technique for studying defect structures of materials. It includes positron annihilation lifetime spectroscopy (PALS), Doppler broadening spectroscopy (DBS) and coincidence Doppler broadening spectroscopy (CDBS) techniques. A common phenomenon found in the spectra of all these techniques is the 'blurring' that results from the instrumental resolution function and stochastic noise, both of which lead to an 'ill-posed' problem on recovering the original data. Other specific characteristics of the PAS data make this inverse problem more complicated. For example, one-dimensional experimental DBS spectra have a long exponential tail on the low energy side of the annihilation peak and a constant background noise on the high energy side. On the other hand, CDBS spectra have the form of two-dimensional images with a cross shape noise centralized on the vertical and horizontal annihilation peaks resulting from random coincidences. Analysis of PALS data includes a reverse Laplace transform of the positron decay spectrum which is technically difficult. Although many researchers have applied different methods to this field for a long time, there is as yet no common and effective method which can be used for data analysis of all these three positron annihilation experimental techniques. For this work, the Richardson-Lucy deconvolution algorithm has been employed for studying both Monte Carlo simulated PAS spectra and experimental PAS data. Not only can it successfully remove the long low energy exponential tail found in DBS spectra and deal with the vertical and horizontal cross pieces and background noise found in CDBS spectra, its computational time in retrieving the underlying momentum density distribution is much less than other techniques. With regard to the PALS spectra, it was shown that after introducing the Gardner method to transform the Laplace integral into a convolution, the lifetime component distribution may be extracted through two successive Richardson-Lucy deconvolutions. Although the resulting lifetime component distribution was not perfectly extracted, it was found to be equally as good as other inversion techniques with the added advantage that more data points are used to describe the information of the lifetime and intensity distribution. All these results suggest that the Richardson-Lucy deconvolution method is not only accurate, but is the most effective and efficient method of analysis. As such, it is expected to become the most popular algorithm used in this field of research. DOI: 10.5353/th_b3861799 Subjects: Convolutions (Mathematics) Algorithms Positron annihilation Spectrum analysis