The interpretation of refractive index measurements. III

The question of whether or not to group recovered glass fragments before comparison with a control sample is fundamental to the interpretation of refractive index measurements. A computer program has been written to perform the grouping and explore the consequences. Grouping the fragments is shown to increase the chances of finding all recovered fragments similar when they have in fact come from the same source as the control, and to give enhanced discrimination when the recovered glass has come from a different source. When the recovered fragments have come from two different sources the consequences of the grouping procedure are preferable to non-grouping.     

The interpretation of refractive index measurements V.

An approach to the interpretation of glass refractive index measurements in forensic science casework which has been developed in four previous papers is extended to deal with the calculation of coincidence probabilities in cases which involve multiple control and recovered samples. Examples of the calculations are given and there is a discussion of the possible limitations of the method.     

The interpretation of refractive index measurements. IV

An approach to the interpretation of glass refractive index measurements in forensic science casework which has been described in three previous papers is developed further. Three methods of calculating a coincidence probability to assist in the assessment of evidential significance are described and compared. An interactive computer program RUNG has been written which incorporates the results of previous work and also a program for estimating coincidence probabilities. Examples of its operation are given.     

The statistical interpretation of refractive index measurements II: The multiple source problem

The method proposed by Grove [1] for comparing measurements made on control and recovered fragments is extended to deal with the possibility that the recovered fragments may originally have come from more than one source. The cases of two and four recovered fragments are examined in detail. Simulation results are given which show that the discriminatory power of the method varies with the number of sources and with the distribution of the fragments over those sources. It is greatest when the recovered fragments come from one source.     

The use of interference filters in refractive index measurements

Interference filters were investigated as alternatives to sodium vapour lamps to establish their suitability for making refractive index measurements using a hot stage microscope. It was found that variations in the characteristics of filters and in their method of mounting could give rise to systematic errors unless adequate precautions were taken.     

The effect of annealing on the variation of glass refractive index

The variation of refractive index (RI) over a non-toughened, float pane of glass and a toughened, float pane of glass was investigated. The two panes of colourless, float glass were cut into 150 5 cm × 5 cm squares. The pre- and post-annealing RI values from three random areas from each square were measured. Bayesian statistical hierarchical modelling of the results showed that for the non-toughened, float glass pane annealing increased the variability in RI by a factor of 1.29-1.58, with a mean of 1.43 (with 95% probability); and for the toughened, float pane of glass annealing decreased the variability in RI by a factor of 0.63-0.76, with a mean of 0.69 (with 95% probability). In addition it was found that although there were no systematic differences in ΔRI across either pane of glass, there were observable differences across both panes of glass. These results provide information regarding the expected RI variation over entire panes of both non-toughened and toughened float window glass for both pre- and post-annealing RI measurements.     

Spatial variation of refractive index in a pane of float glass.

In the statistical interpretation of forensic glass evidence it is standard practice to make the assumption of homogeneity of the refractive index (RI) of the source glass, or of localized homogeneity. However, the work of Locke and Hayes showed that, for toughened windscreen glass, this assumption might not be true. This work is well cited, but there appears to have been little follow-on published research. Furthermore, the toughening process is something known to affect the refractive index, and is a process that float glass does not undergo. Float glass is a major component of casework in New Zealand and for that reason it would be interesting to know whether the findings of Locke and Hayes apply when dealing with float glass. In this paper we describe an experiment similar to that of Locke and Hayes, systematically examining the variation of RI in a pane of float window glass. It was found that, although there were no systematic differences in refractive index, there were observable differences across the pane.     

玻璃折射率数据处理方法初探

目的探讨玻璃折射率数据处理方法。方法将案件中收集到的45个玻璃样品和同一个车灯不同部位的45块玻璃样品进行折射率测定。用独立样本Student’st检验、welch检验以及方差分析（ANOVA）对数据进行成对检验。结果方差分析法中Dunnett’s C法处理玻璃折射率数据,有效控制了第一类和第二类错误。当α=0．05时,犯第一类错误的概率约为4．44％,犯第二类错误的概率约为3．54％。     

The interpretation of elemental composition measurements from forensic glass evidence III

In this paper we introduce a permutation testing approach to the interpretation of evidence which consists of elemental composition measurements, with glass evidence as an example. This work extends previous work of Curran et al. [J.M. Curran, C.M. Triggs, J.R. Almirall, J.S. Buckleton and K.A.J. Walsh, The interpretation of elemental composition measurements from forensic glass evidence, Science and Justice 37 (1997) 241–244.] and shows how we may remove some of the constraints that limited the applicability of the previous results. We provide the reader with tools for evidence pre-screening that may aid in the direction of further analyses of the data, rather than for the presentation of evidence interpretation in a court case.     

Bayesian mixture modelling for glass refractive index measurement

Glass is a common type of physical evidence in forensic science. Broken glass recovered from a suspect may have similar physical characteristics to glass collected at a crime scene and therefore can be used as evidence. Statistical treatment of this evidence involves computing a measure of the weight of evidence. This may be done in a Bayesian framework that incorporates information from the circumstances of the crime. One of the most crucial quantities in this calculation is the assessment of the relative rarity of the characteristics of the glass, essentially the probability distribution used to model the physical characteristics of recovered glass. Typical characteristics used in casework are the elemental composition of glass and the refractive index measurement. There is a considerable body of scientific literature devoted to the modelling of this information. For example a kernel density estimation has been used to model the background population of glass based on the refractive index measurement and a multivariate Gaussian finite mixture model has been used to model the elemental composition of glass. In this paper, we present an alternative approach, the Dirichlet Process Mixture Model, to model the glass refractive index measurement in a Bayesian methodology. A key advantage is that using this method allows us to model the probability density distribution of refractive index measurements in a more flexible way.     

The use of melting point and refractive index determination to compare colourless polyester fibres

The incidence of polyesters encountered in forensic fibre examinations continues to increase. To meet different consumer needs such fibres can be subjected to many physical and chemical variations during production. Some of these variations are discussed. Accurate comparison of these fibres presents a particular problem to the forensic scientist. Melting point and refractive index determinations were made on various samples of colourless polyesters provided by different manufacturers to assess the comparative value of such information and to find out the possibility of relating it to modifications of the basic polymer. Melting points alone were found to be of little comparative value, but determination of both refractive indices n_∥ and n_⊥ does allow discrimination between samples. Consideration of both melting point and refractive index together may help to provide an insight into polymer variation, though this remains somewhat speculative.     

汽车风挡玻璃的鉴别方法研究

目的研究油浸法和X射线荧光光谱法对汽车风挡玻璃的鉴别能力。方法应用油浸法对30个风挡玻璃样品进行折射率测试，并将所得数据进行t检验分析。对不能区分的样品再用X射线荧光光谱进行元素成分分析。结果30个样品共组成的435对中，折射率t检验在置信度959／5时区分427对，其余8对通过元素成分实现区分。结论折射率测试和元素分析相结合，可对常见汽车风挡玻璃进行有效区分。     

Evaluation of match criteria used for the comparison of refractive index of glass fragments

For comparative glass examinations, the refractive indices (RIs) of recovered glass fragments are often compared to a test interval defined by measurements from a broken glass object. RI measurements from five modern float glasses were used via resampling to assess the frequencies of false exclusion errors for eight test criteria as functions of the number of measurements. The test criteria were based on ranges, fixed intervals, and multiples of standard deviations of the known source measurements. The observed error rates for the eight tests studied are between zero and c. 35%, depending upon the match criteria, the number of measurements, and the RI distribution for a glass source. The results of this study can be used to predict the false exclusion rate for a test criterion under a given set of conditions or to select test criteria that result in a desired error rate for these typical sheet glasses.     

An investigation of refractive index anomalies at the surfaces of glass objects and windows

Results obtained using GRIM equipment show that the refractive index (RI) of surface layers of float and non-float flat glass, glass containers and tableware can vary significantly from that of the bulk glass. The results also suggest that, using the oil immersion method with GRIM, it is not possible to obtain surface RI measurements which are useful for discrimination. Instead, a range of values is obtained for each sample, the individual results probably being dependent upon the thickness and geometry of the particular edge under examination.