Maximum Acceptable Tilt Angle for Point Autofocus Microscopy.

The complete and accurate acquisition of geometric information forms the bedrock of maintaining high-end instrument performance and monitoring product quality. It is also a prerequisite for achieving the 'precision' and 'intelligence' that the manufacturing industry aspires to achieve. Industrial microscopes, known for their high accuracy and resolution, have become invaluable tools in the precision measurement of small components. However, these industrial microscopes often struggle to demonstrate their advantages when dealing with complex shapes or large tilt angles. This paper introduces a ray-tracing model for point autofocus microscopy, and it provides the quantified relationship formula between the maximum acceptable tilt angle and the beam offset accepted in point autofocus microscopy, then analyzing the maximum acceptable tilt angle of the objects being measured. This novel approach uses the geometric features of a high-precision reference sphere to simulate the tilt angle and displacement of the surface under investigation. The research findings show that the maximum acceptable tilt angles of a point autofocus microscope vary across different measured directions. Additionally, the extent to which the maximum acceptable tilt angles are affected by the distances of the beam offset also varies. Finally, the difference between the experiment results and the theoretical results is less than 0.5°.

Reporting likelihood ratio for casework in firearm evidence identification.

Likelihood ratio (LR) plays an important role in estimating the weight of evidence in firearm evidence identifications. LR is computed from a statistical model including the distribution of the known-matching (KM or within) and known-nonmatching (KNM or between) comparison scores. Current LR procedures rely on KM/KNM scores from existing reference firearm toolmark data sets or alternatively from generating a set of test fires using multiple firearms. Both procedures may contain theoretical or practical issues which may hinder the LR procedures from reporting an unbiased LR estimation in casework. In this paper, a reference data set was established from a set of firearms, each test-fired two cartridge cases, resulting in a basic data set and a control data set. The congruent matching cells (CMC) method was used to generate CMC scores that are used to fit in the KM/KNM statistical distributions for LR estimation. In the initial test, 130 firearms from eight manufacturers were used for generating a reference data set consisting of 260 cartridge cases representing 130 KM and 8385 KNM pairwise breech face images. Test results showed that the KM and KNM distribution intersect at CMC = 2, which is equivalent to LR = 1 (equally to support both the prosecutor and the defense propositions). When the CMC threshold is increased to 6 or more, the LR values are higher than a million, which can provide extremely strong support to the conclusion of the same firearm (or the prosecutor's proposition) in the casework of firearm evidence identification.

Virtual image standard (VIS) for performance evaluation of the congruent matching cells (CMC) algorithms in firearm evidence identifications.

The congruent matching cells (CMC) method was invented at the National Institute of Standards and Technology (NIST) in 2012 for automatic and objective firearm evidence identifications and estimation of the weight of evidence in firearm evidence identifications. Since 2013, five CMC algorithms have been developed at NIST. In this paper, the virtual image standard (VIS) is proposed through trimming and stitching KNM images for quantitative performance evaluations of different CMC algorithms. The evaluation criteria include the correlation accuracy (both the CMC numbers and distribution pattern), correlation efficiency, false positive (FP) error rate, and the maximum separation of known matching (KM) and known non-matching (KNM) image pairs. The VIS composes correlation cells from different KNM images, which can provide a ground truth for verifying the CMC numbers, distribution patterns, and FP errors. By identifying three groups of VIS, the Convergence CMC algorithm showed superior performances for the future casework in firearm evidence identifications. Lastly, the success of this study suggests that the VIS could also be used to optimize the correlation parameters, to develop and test new CMC algorithms, and evaluate the performance before it is put into use for firearm examiner's casework.