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.     

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.     

The consequences of potentially differing distributions of the refractive indices of glass fragments from control and recovered sources

In forensic cases involving glass evidence, the variance of the recovered glass refractive index (RI) has been observed to be larger than the variance of the control glass RI. This has consequences for subsequent interpretation. To investigate this phenomenon, a study was made of the probable distributions of refractive indices of the recovered glass given a range of casework type scenarios involving breakage and backscatter. An investigation of the consequences of any distribution differences with regard to casework was also made. It was discovered that the inclusion of surface fragments from the float surface of the glass can have a profound effect on the comparison of recovered and control glass samples. The effect was largest when a breaker was striking the float surface of a window. In particular, it was found that the inclusion of a few surface fragments even post grouping is sufficient by itself to explain the observed differences in variance of RI between control and recovered groups. Surface fragments, if present, are very likely to be treated as outliers and to be deemed as non-matching. The findings of this paper challenge routine glass examination procedure and suggest that knowledge of which surface is facing the striker is valuable information in interpretation.     

Elemental analysis by energy dispersive x-ray: a significant factor in the forensic analysis of glass.

Eighty-one glass samples were analyzed by EDX; two were indistinguishable. However, when the physical properties of the glass samples were considered, all glass samples were distinguishable from each other. The need to examine glass with respect not only to physical properties but also to elemental composition has been demonstrated. The authors believe that if glass is examined only by density and refractive indexes it is quite possible to conclude incorrectly that glass samples with the same physical qualities could have originated from the same source. To confirm that the glass specimens may have in fact originated from the same source their elemental compositions in addition to density and refractive indexes must be determined. The analysis by EDX of glass samples can selectively eliminate most specimens on the basis of elemental differences. If this step is performed prior to refractive index or density measurements considerable time savings can be realized in casework situations.     

Analysis of glass fragments by laser ablation-inductively coupled plasma-mass spectrometry and principal component analysis

Laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS) is used to differentiate glass samples with similar optical and physical properties based on trace elemental composition. Laser ablation increases the number of elements that can be used for differentiation by eliminating problems commonly associated with dissolution and contamination. In this study, standard residential window and tempered glass samples that could not be differentiated by refractive index or density were successfully differentiated by LA-ICP-MS. The primary analysis approach used is Principal Component Analysis (PCA) of the complete mass spectrum. PCA, a multivariate analysis technique, provides rapid analysis of samples without time-consuming pair-wise comparison of calibrated analyses or prior knowledge of the elements present in the samples. Probabilities for positive association of the individual samples are derived from PCA. Utilization of the Q-statistic with PCA allowed us to distinguish all samples within the set to a certainty greater than the 99% confidence interval.     

An investigation of bulk and surface refractive indices for flat window glasses,patterned window glasses and windscreen glasses

The bulk and surface refractive indices have been measured for 20 float window glasses, 20 non-float window glasses, 20 patterned window glasses and 20 toughened float windscreen glasses.The refractive index of the tin-contact surface of the float glasses was always greater than that of the bulk, typically by 0.002 (range 0.00053–0.00307). In contrast the refractive indices of the two surfaces and the bulk of the sheet window glasses were in agreement within accepted experimental error in each case. A number of patterned window glasses showed significantly different refractive indices between the plain and patterned surfaces, the largest difference obtained (0.00021) being an order of magnitude smaller than that found for a typical float glass.Nine of the 40 float glasses examined yielded abnormal fragments from the upper surface in the sense that they did not disappear at the match temperature of the bulk glass. The refractive index measured from these abnormal fragments for two of these glasses was lower than the refractive index from the bulk glass.The variation in the bulk refractive index for the sheet and float window glasses produced an estimated standard deviation (E.S.D.) of 1.2 × 10^?5. However, the patterned glasses were nearly three times as variable (E.S.D. = 3.3 × 10^?5) and the toughened float glasses were, on average, almost seven times as variable (E.S.D. = 8.0 × 10^?5).The value of making surface as well as bulk refractive index measurements in routine casework is discussed in the light of the above results.     

Elemental analysis of glass by laser ablation inductively coupled plasma optical emission spectrometry (LA-ICP-OES)

The elemental analysis of glass evidence has been established as a powerful discrimination tool for forensic analysts. Laser ablation inductively coupled plasma optical emission spectrometry (LA-ICP-OES) has been compared to laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) and energy dispersive micro X-ray fluorescence spectroscopy (μXRF/EDS) as competing instrumentation for the elemental analysis of glass. The development of a method for the forensic analysis of glass coupling laser ablation to ICP-OES is presented for the first time. LA-ICP-OES has demonstrated comparable analytical performance to LA-ICP-MS based on the use of the element menu, Al (Al I 396.15 nm), Ba (Ba II 455.40 nm), Ca (Ca II 315.88 nm), Fe (Fe II 238.20 nm), Li (Li I 670.78 nm), Mg (Mg I 285.21 nm), Sr (Sr II 407.77 nm), Ti (Ti II 368.51 nm), and Zr (Zr II 343.82 nm). The relevant figures of merit, such as precision, accuracy and sensitivity, are presented and compared to LA-ICP-MS. A set of 41 glass samples was used to assess the discrimination power of the LA-ICP-OES method in comparison to other elemental analysis techniques. This sample set consisted of several vehicle glass samples that originated from the same source (inside and outside windshield panes) and several glass samples that originated from different vehicles. Different match criteria were used and compared to determine the potential for Type I and Type II errors. It was determined that broader match criteria is more applicable to the forensic comparison of glass analysis because it can reduce the affect that micro-heterogeneity inherent in the glass fragments and a less than ideal sampling strategy can have on the interpretation of the results. Based on the test set reported here, a plus or minus four standard deviation (± 4s) match criterion yielded the lowest possibility of Type I and Type II errors. The developed LA-ICP-OES method has been shown to perform similarly to LA-ICP-MS in the discrimination among different sources of glass while offering the advantages of a lower cost of acquisition and operation of analytical instrumentation making ICP-OES a possible alternative elemental analysis method for the forensic laboratory.     

The effect of re-annealing on the distribution of refractive index in a windscreen and a windowpane classification of glass samples

Tiny glass fragments of two typical objects being of interest in forensic investigations: car windscreen and windowpane were examined from the point of view of their importance as crime evidence. Both examined objects were made from float glass and were toughened. The present paper concerns examination of refractive index distribution across the objects under investigation before and after the glass fragments were annealed according to previously chosen procedure. The annealing procedure was carried out in order to increase discrimination power of refractive index (RI). The following conclusions can be drawn from the results obtained. For both examined objects the mean RI was significantly higher after annealing and, at the same time, standard deviations in RI were smaller. The distributions of RI for both examined objects appeared not to be normal; the deviations from normality were observed at both sides of RI distributions. It was found that the difference in the values DeltaRI (difference between mean values of RI after annealing and before annealing) for both examined object was not significant and thus it would be not a good parameter to differentiate between two heat strengthen objects. The attempt to classify 181 glass samples on the basis of theirs RI and DeltaRI was performed. Increased discrimination of glass samples was observed.     

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.     

3.9. Attempts at typing ABO blood groups in individual human hairs of less than 4 cm length

Approximately 350 glass samples of known origin, encompassing most of the types of glass likely to be encountered in forensic science casework, have been analysed by inductively coupled plasma-atomic-emission spectrometry. The samples included 123 window glasses, 56 vehicle glasses, 91 container glasses and 58 tableware glasses. The analytical procedure provided the quantitative levels of manganese, iron, magnesium, aluminium and barium in the samples. The data for the elemental concentrations, together with refractive index, are presented in histogram form.     

油浸法鉴别汽车后视镜玻璃的研究

目的研究油浸法对汽车后视镜玻璃的鉴别能力。方法应用油浸法对20种汽车后视镜玻璃进行折射率值测定并用t检验法对数据进行处理。结果在置信度为95％时，20个后视镜玻璃样品的区分率为97．9％。结论油浸法对汽车后视镜玻璃有很好的区分能力，而且使用样品量少，可以达到微克级，是一种鉴别后视镜玻璃的有效方法。     

A survey of glass fragments recovered from clothing of persons suspected of involvement in crime

The refractive indices (RI) of over 2000 glass fragments recovered from items of clothing submitted to the Birmingham and Wetherby Home Office forensic science laboratories in connection with crimes involving broken glass have been measured. The glass fragments have been classified according to their location on the clothing, and a grouping algorithm has been applied to the data.The refractive index distribution was found to be dependent on the location of the glass on the clothing. The significance of the results in the interpretation of glass evidence is discussed.     

Quantitative analysis of glasses used within Australia

An initial 134 glasses have been collected from eleven classifications of glass used within Australia. These include both local and imported glasses. Quantitative elemental analyses of the glasses have been determined using a scanning electron microscope equipped with an energy dispersive X-ray spectrometer. The current program provides for an elemental analysis for Na, Mg, Al, Si, P, S or Pb, Cl, K, Ca, Ba or Ti, V, Cr, Fe, Mn and Zn expressed as oxides, and has a sensitivity down to approximately 0.1%. The data for the six most commonly occurring elements, namely, Na, Mg, Al, Si, K and Ca, together with the refractive index are presented for each class of glass in terms of their mean value and standard deviation from the mean, and also in histogram form.     

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.     

Development and evaluation of a standard method for the quantitative determination of elements in float glass samples by LA-ICP-MS

Forensic analysis of glass samples was performed in different laboratories within the NITE-CRIME (Natural Isotopes and Trace Elements in Criminalistics and Environmental Forensics) European Network, using a variety of Laser Ablation Inductively Coupled Plasma Mass Spectrometry (LA-ICP-MS) systems. The main objective of the interlaboratory tests was to cross-validate the different combinations of laser ablation systems with different ICP-MS instruments. A first study using widely available samples, such as the NIST SRM 610 and NIST SRM 612 reference glasses, led to deviations in the determined concentrations for trace elements amongst the laboratories up to 60%. Extensive discussion among the laboratories and the production of new glass reference standards (FGS 1 and FGS 2) established an improved analytical protocol, which was tested on a well-characterized float glass sample (FG 10-1 from the BKA Wiesbaden collection). Subsequently, interlaboratory tests produced improved results for nearly all elements with a deviation of < 10%, demonstrating that LA-ICP-MS can deliver absolute quantitative measurements on major, minor and trace elements in float glass samples for forensic and other purposes.     

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.     

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。     

Classification of Glass Fragments Based on Elemental Composition and Refractive Index*

Abstract: The aim of this study was to assess the efficiency of likelihood ratio (LR)‐based measures when they are applied to solving various classification problems for glass objects which are described by elemental composition, and refractive index (RI) values, and compare LR‐based methods to other classification methods such as support vector machines (SVM) and naïve Bayes classifiers (NBC). One hundred and fifty‐three glass objects (23 building windows, 25 bulbs, 32 car windows, 57 containers, and 16 headlamps) were analyzed by scanning electron microscopy coupled with an energy dispersive X‐ray spectrometer. Refractive indices for building and car windows were measured before (RI_b), and after (RI_a) an annealing process. The proposed scheme for glass fragment(s) classification demonstrates some efficiency, although the classification of car windows (c) and building windows (w) must be treated carefully. This is because of their very similar elemental content. However, a combination of elemental content and information on the change in RI during annealing (ΔRI = RI_a?RI_b) gave very promising results. A LR model for the classification of glass fragments into use‐type categories for forensic purposes gives slightly higher misclassification rates than SVM and NBC. However, the observed differences between results obtained by all three approaches were very similar, especially when applied to the car window and building window classification problem. Therefore, the LR model can be recommended because of the ease of interpretation of LR‐based measures of certainty.     

The classification and discrimination of glass fragments using non destructive energy dispersive X-ray microfluorescence

Frequency of analytical characteristics is best estimated on glass recovered at random. However, as such data were not available to us, we decided to use control windows for this estimation. In order to use such a database, one has to establish that the recovered fragment comes from a window. Therefore, elemental analysis was used both for classification and discrimination of glass fragments. Several articles have been published on the subject, but most methods alter the glass sample. The use of non destructive energy dispersive X-ray microfluorescence (microXRF) for the analysis of small glass fragments has been evaluated in this context. The refractive index (RI) has also been measured in order to evaluate the complementarity of techniques. Classification of fragments has been achieved using Fisher's linear discriminant analysis (LDA) and neural networks (NN). Discrimination was based on Hotelling's T2 test. Only pairs that were not differentiated by RI followed by the Welch test were studied. The results show that neural network and linear discriminant analysis using qualitative and semi-quantitative data establishes a classification of glass specimens with a high degree of reliability. For discrimination, 119 windows collected from crime scene were compared: using RI it was possible to distinguish 6892 pairs. Out of 129 remaining pairs, 112 were distinguished by microXRF.     

Comparison of glass fragments using particle-induced X-ray emission (PIXE) spectrometry

A procedure has been developed to analyze the trace element concentrations in glass fragments using particle-induced X-ray emission (PIXE) spectrometry. This method involves using accelerated protons to excite inner-shell electronic transitions of target atoms and recording the resultant X-rays to characterize the trace element concentrations. The protocol was able to identify those glass fragments that originated from different sources based on their elemental analyses. The protocol includes specific approaches to calculating uncertainties and handling measurements below the level of detection. The results indicate that this approach has increased sensitivity for several elements with higher atomic number compared with X-ray fluorescence methods. While not as sensitive as laser-ablation or inductively coupled plasma mass spectrometry methods of dissolved samples, it is entirely nondestructive and entails a much simpler sample preparation process that may be used to presort glass fragments for more comprehensive elemental analysis. As such, the technique described may have a niche role in forensic glass analysis.