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.     

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.     

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.     

平板玻璃受热后折射率的变化规律初探

目的探索平板玻璃受热后折射率的变化规律。方法首先采用差示扫描量热仪测定玻璃样品的转变温度Tg,将样品加热至不同的温度(温度范围从室温到Tg以上),自然冷却至室温后再用GRIM3测量折射率。结果加热温度在Tg以下时,玻璃的折射率基本不变,加热温度在Tg以上时,折射率有明显变化。结论对于从火灾和爆炸现场提取的玻璃,在进行折射率比对时应当考虑现场高温对测量值的影响,并进行必要的修正。     

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.     

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.     

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。     

Elemental analysis of glass fragments by ICP-MS as evidence of association: analysis of a case

Inductively coupled plasma mass spectrometry (ICP-MS) was used to analyze glass evidence from a case in which a person broke a window in each of 15 vehicles in a parking lot in order to gain entry into the vehicles. The results of the analysis by traditional methods, which measure the properties of color, thickness, density, and refractive index, are also reported. A total of 15 known samples representing the windows on the cars and 42 questioned glass fragments recovered from the suspect and the police vehicle where the suspect was sitting were submitted for analysis. Density comparisons separated one of the known samples into three samples, increasing the number of known samples from 15 to 17. The concentrations of 16 elements were measured for all but three of the samples using an external calibration ICP-MS method with internal standardization. Color assessment (non-instrumental) separated the 17 known samples into two groups, and refractive index measurements resulted in six groups when the Emmons double variation method was used and ten groups when the Glass Refractive Index Measurement 2 (GRIM2) system was used. Elemental analysis, by itself, differentiated all of the known samples from each other and associated four of the known sample fragments with several of the questioned sample fragments. The informing power of RI, density, and elemental analysis comparisons is evaluated and a summary of the case results is reported.     

A study of the performance and utility of annealing in forensic glass analysis

The use of annealing in forensic glass casework is reviewed. New data is presented that suggests a continuous approach to the interpretation of such data may be superior to the classification approach. Data are presented supporting the previously observed relationship between change in refractive index (RI) and the thickness of the glass pane. An examination of the possible assumption of independence between RI and change in RI is undertaken.     

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.     

Application of false discovery rate procedure to pairwise comparisons of refractive index of glass fragments

This study was undertaken to apply a new method of controlling type I error when performing pairwise comparisons. The Benjamini and Hochberg false discovery rate (FDR) controlling procedures have proved to be very powerful tools in solving many practical problems but have not yet been applied to pairwise comparisons of refractive index of glass samples. Students t-test and Welch test (unequal variance Student's t-test) were applied to all possible pairwise comparisons. The comparisons were made on the basis of refractive index values of 72 glass fragments from different car windows and 69 different fragments from one windscreen. The type I error was controlled by the use of Benjamini and Hochberg false discovery rate (FDR) controlling procedure. To illustrate the importance of controlling type I error when using pairwise comparisons, results of pairwise comparisons with the FDR controlling procedure were compared to those comparisons made without any controlling procedure. Significantly fewer false negative results (false rejection of H0) were found during the use of FDR procedure in the comparison of refractive indices from the same windscreen than when comparing without controlling type I error. The results of application of FDR method were also compared to the results of other post-hoc tests, such as Tukey HSD test and Bonfferoni test. The FDR method has higher power than Bonferroni method and Tukey HSD method and control errors better than comparing without controlling type I error. The method of choice, for pairwise comparison of glass fragments on the basis of refractive index is Welch test with FDR adjustment. The method gave type I errors at level about 5.3% and type II error at about 3.7%.     

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.     

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。     

An investigation into the relationship between edge counts and the variability of the refractive index of glass. Part I: Edge morphology

The effect of glass fragment morphology on the variability of refractive index values in five different glass objects was investigated. Data are presented that suggest that the variability of refractive index values is increased when fragment edge morphology becomes unsuitable for phase contrast microscopy.     

An investigation into the spatial elemental distribution within a pane of glass by time of flight secondary ion mass spectrometry

Advances in the technology employed for the manufacture of glass have resulted in a final glass product with little variability in terms of its physical and optical properties. For example, the refractive index of Australian float glass tends to lie between 1.5189 and 1.5194. It has therefore become necessary to complement physical and optical methods for forensic glass comparison with instrumental elemental analyses. In a previous study, time-of-flight secondary ion mass spectrometry has been shown to offer potential for the analysis of glass particles as small as a few tens of microns across. In this study, the three-dimensional homogeneity of a sheet of float glass is described, and consequences for forensic elemental analysis of glass particles of such size are explored. Variation in Si, Ca, Mg, and Na levels immediately under the nonfloat surface was observed, with the variance accompanied by a decrease in refractive index.     

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.     

油浸法测定玻璃折射率的不确定度评定

目的建立油浸法测定玻璃折射率不确定度的评定方法。方法按照不确定度的A类和B类评定方法,对未知玻璃折射率测定过程中不确定度分量进行计算,最终确定扩展部不确定度。结果油浸法测定玻璃折射率的扩展不确定度约为4×10-5。结论根据不确定度计算出来的折射率的变化范围与实际分析中折射率的变化范围完全吻合。     

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.     

Employing glass refractive index measurement (GRIM) in fiber analysis: a simple method for evaluating the crystallinity of acrylics

The refractive index (RI) of 40 colorless acrylic fiber samples was determined by the immersion oil and Mettler hot stage method, implemented in the glass refractive index measurement (GRIM) instrument by Foster and Freeman. Low standard deviations for nearly all the samples were obtained and differentiation of fibers even with the same trade name was possible just on the basis of RI. Wide angle X-ray scattering (WAXS) and differential scanning calorimetry (DSC) were employed to establish a linear correlation between RI and the degree of crystallinity. Insights on the structural order of this group of fibers is then obtainable by a quick and easy technique, adding value to casework comparisons.     

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.