Linearizing the vertical scale of an interferometric microscope and its effect on step-height measurement.

The vertical scale calibration of an interferometric microscope is important for establishing traceability of surface topography measurements to the International System of Units (SI) unit of length, the meter. Building on the calibration procedure for the amplification coefficient developed by de Groot and Beverage [Proc. SPIE 9526, 952610 (2015)], this paper describes a calibration procedure that yields the response curve for the entire vertical scan motion of a coherent scanning interferometric microscope. The method requires only a flat mirror as an artifact, a narrow band spectral filter, an aperture to reduce the effective numerical aperture, and the ability to raise and lower the microscope head so that the center of the interferogram can be varied within the scan range. The local frequency of the interferogram is determined by fitting sections of the interferogram to a sinusoidal function. The nonlinearity determined from the local frequency data can be used to estimate the uncertainty in uncorrected vertical height measurements. We describe how optical profile data can be corrected for nonlinearity due to dynamic effects in the scan motion and show that the correction improves the reproducibility of step height measurements by at least a factor of three and close to that of the repeatability.

Automated interpretation of comparison scores for firearm toolmarks on cartridge case primers.

An automated approach for evaluating the strength of the evidence of firearm toolmark comparison results is presented for a common source scenario. First, comparison scores are derived describing the similarity of marks typically encountered on the primer of fired cartridge cases: aperture shear striations as well as breechface and firing pin impressions. Subsequently, these scores are interpreted using reference distributions of comparison scores obtained for representative known matching (KM) and known non-matching (KNM) ballistic samples in a common source, score-based likelihood ratio (LR) system. We study various alternatives to set up such an LR system and compare them using qualitative and quantitative criteria known from the literature. As an example, results are applied to establish a system suitable for a firearm-ammunition combination often encountered in casework: Glock firearms with Fiocchi nickel primer ammunition. The system outputs an LR and a measure of LR uncertainty. The range of possible LR-values is limited to a minimum and maximum value in areas of the score domain with little reference data. Finally, the feasibility of combining LRs of different mark types into one LR for the entire primer is assessed. For the distribution models considered in this paper, different modeling approaches are optimal for different types of similarity scores. For the chosen firearm-ammunition combination, non-parametric Kernel Density Estimation (KDE) models perform best for similarity scores based on the correlation coefficient, whereas parametric models perform best for the Congruent Matching Cells (CMC) scores, assuming binomial and beta-binomial models for KM and KNM score distributions respectively. Finally, it is demonstrated that individual LRs of different mark types can be combined into one LR, to interpret a set of different marks on the primer as a whole.

Firearm examination: Examiner judgments and computer-based comparisons.

Forensic firearm examination provides the court of law with information about the source of fired cartridge cases. We assessed the validity of source decisions of a computer-based method and of 73 firearm examiners who compared breechface and firing pin impressions of 48 comparison sets. We also compared the computer-based method's comparison scores with the examiners' degree-of-support judgments and assessed the validity of the latter. The true-positive rate (sensitivity) and true-negative rate (specificity) of the computer-based method (for the comparison of both the breechface and firing pin impressions) were 94.4% and at least 91.7%, respectively. For the examiners, the true-positive rate was at least 95.3% and the true-negative rate was at least 86.2%. The validity of the source decisions improved when the evaluations of breechface and firing pin impressions were combined and for the examiners also when the perceived difficulty of the comparison decreased. The examiners were reluctant to provide source decisions for "difficult" comparisons even though their source decisions were mostly correct. The correlation between the computer-based method's comparison scores and the examiners' degree-of-support judgments was low for the same-source comparisons to negligible for the different-source comparisons. Combining the outcomes of computer-based methods with the judgments of examiners could increase the validity of firearm examinations. The examiners' numerical degree-of-support judgments for their source decisions were not well-calibrated and showed clear signs of overconfidence. We suggest studying the merits of performance feedback to calibrate these judgments.

Evaluating Likelihood Ratio (LR) for firearm evidence identifications in forensic science based on the Congruent Matching Cells (CMC) method.

Firearm evidence identification has been challenged by the 2008 and 2009 National Research Council (NRC) reports and by legal proceedings on its fundamental assumptions, its procedure involving subjective interpretations, and the lack of a statistical foundation for evaluation of error rates or other measures for the weight of evidence. To address these challenges, researchers of the National Institute of Standards and Technology (NIST) recently developed a Congruent Matching Cells (CMC) method for automatic and objective firearm evidence identification and quantitative error rate evaluation. Based on the CMC method, a likelihood ratio (LR) procedure is proposed in this paper aiming to provide a scientific basis for firearm evidence identification and a method for evaluation of the weight of evidence. The initial LR evaluations using two sets of 9mm cartridge cases' breech face impression images with different sample sizes, imaging methods and ammunition showed that for all the declared identifications of the tested 2D and 3D image pairs, the evaluated LRs for the least favorable scenario were well above an order of 106, which provides Extremely Strong Support for a prosecution proposition (e.g. a same-source proposition) in a Bayesian frame. The LR evaluations also showed that for all the declared exclusions of the tested 3D image pairs, the evaluated LRs for the least favorable scenario were above an order of 102, which provides Moderately Strong Support for a defense proposition (e.g. a different-source proposition) in a Bayesian frame.

Pilot study on deformed bullet correlation.

Most studies on bullet identification address test fired bullets that have near pristine striated marks on the land engraved areas (LEAs). However, in case work, bullets found at a crime scene may be severely deformed or fragmented. The resulting missing, expanded, or distorted LEA striations can cause challenges in toolmark comparisons performed by examiners or algorithms. In this paper, an image reconstruction procedure is proposed that, in combination with the Congruent Matching Profile Segments (CMPS) profile comparison method, facilitates the algorithmic correlation of deformed bullets. Initial validation tests were conducted using 57 bullets, with varying degrees of fragmentation or deformation, that were fired from the same 9mm Luger caliber Luger pistol. The bullets spanned 7 different ammunition brands. The CMPS method was applied to correlate the LEA striation profiles extracted from LEA topography images that were corrected for pattern distortion. 15 bullet LEAs, out of 250 bullet LEAs that could be measured, had major distortions. Two sets of comparison tests were conducted, corresponding to a same source and specific source scenario: 1) comparison of the severely distorted LEAs with a near-pristine reference bullet, before and after image reconstruction, and 2) inter comparisons of distorted LEAs, before and after reconstruction. The reconstruction process significantly improved the correlation results when dealing with distorted bullet LEAs. In general, the improvement was larger for samples with relatively large deformation and good striation visibility. Samples with approximately parallel striations tend to have less improvement of CMPS results after profile reconstruction since the CMPS method itself can correct certain scale errors.

Fired bullet signature correlation using the Congruent Matching Profile Segments (CMPS) method.

We introduce the Congruent Matching Profile Segments (CMPS) method for objective comparison of striated tool marks and apply it to bullet signature correlations. The method is derived from the congruent matching cell (CMC) method developed for the comparison of impressed tool marks. The proposed method is designed to increase comparison accuracy by addressing the comparison challenges caused by striae profiles with different lateral scales, varying vertical (height) scales, and sections that are poorly marked or have little to no similarity. Instead of correlating the entire profiles extracted from striated tool marks, the method divides one of the compared profiles into segments. Each segment is then correlated with the other profile. The CMPS method uses the normalized cross-correlation function with multiple correlation peak inspection to determine the number of profile segments that have both significant topography similarity and a congruent registration position. Initial tests were performed on the land engraved areas (LEAs) of 35 bullets fired from 10 consecutively manufactured pistol barrels. The results show clear separation between the CMPS scores of the 549 known non-matching (KNM) LEA profiles and the 46 known matching (KM) LEA profiles. These results are an improvement over those obtained using the correlation coefficient score of whole profiles. The large number of CMPS segment correlations may facilitate a statistical approach to error rate estimations.

Sensing fabrication errors in diffraction gratings using high dynamic range imaging.

We describe the design of a simple instrument for the identification and characterization of fabrication errors in diffraction gratings. The instrument uses an uncooled charge-coupled device (CCD) camera and a high dynamic range imaging process to detect the light scattered off a grating under test in the focal plane of a lens. We demonstrate that the instrument can achieve a dynamic range around nine orders of magnitude and we show that we are able to clearly identify small, periodic fabrication errors in two test gratings that could not be detected with microscopic techniques.

Estimating error rates for firearm evidence identifications in forensic science.

Estimating error rates for firearm evidence identification is a fundamental challenge in forensic science. This paper describes the recently developed congruent matching cells (CMC) method for image comparisons, its application to firearm evidence identification, and its usage and initial tests for error rate estimation. The CMC method divides compared topography images into correlation cells. Four identification parameters are defined for quantifying both the topography similarity of the correlated cell pairs and the pattern congruency of the registered cell locations. A declared match requires a significant number of CMCs, i.e., cell pairs that meet all similarity and congruency requirements. Initial testing on breech face impressions of a set of 40 cartridge cases fired with consecutively manufactured pistol slides showed wide separation between the distributions of CMC numbers observed for known matching and known non-matching image pairs. Another test on 95 cartridge cases from a different set of slides manufactured by the same process also yielded widely separated distributions. The test results were used to develop two statistical models for the probability mass function of CMC correlation scores. The models were applied to develop a framework for estimating cumulative false positive and false negative error rates and individual error rates of declared matches and non-matches for this population of breech face impressions. The prospect for applying the models to large populations and realistic case work is also discussed. The CMC method can provide a statistical foundation for estimating error rates in firearm evidence identifications, thus emulating methods used for forensic identification of DNA evidence.

A convergence algorithm for correlation of breech face images based on the congruent matching cells (CMC) method.

The Congruent Matching Cells (CMC) method was invented at the National Institute of Standards and Technology (NIST) for accurate firearm evidence identification and error rate estimation. The CMC method is based on the principle of discretization. The toolmark image of the reference sample is divided into correlation cells. Each cell is registered to the cell-sized area of the compared image that has maximum surface topography similarity. For each resulting cell pair, one parameter quantifies the similarity of the cell surface topography and three parameters quantify the pattern congruency of the registration position and orientation. An identification (declared match) requires a significant number of CMCs, that is, cell pairs that meet both similarity and pattern congruency requirements. The use of cell correlations reduces the effects of "invalid regions" in the compared image pairs and increases the correlation accuracy. The identification accuracy of the CMC method can be further improved by considering a feature named "convergence," that is, the tendency of the x-y registration positions of the correlated cell pairs to converge at the correct registration angle when comparing same-source samples at different relative orientations. In this paper, the difference of the convergence feature between known matching (KM) and known non-matching (KNM) image pairs is characterized, based on which an improved algorithm is developed for breech face image correlations using the CMC method. Its advantage is demonstrated by comparison with three existing CMC algorithms using four datasets. The datasets address three different brands of consecutively manufactured pistol slides, with significant differences in the distribution overlap of cell pair topography similarity for KM and KNM image pairs. For the same CMC threshold values, the convergence algorithm demonstrates noticeably improved results by reducing the number of false-positive or false-negative CMCs in a comparison.

Identifying persistent and characteristic features in firearm tool marks on cartridge cases.

Recent concerns about subjectivity in forensic firearm identification have motivated the development of algorithms to compare firearm tool marks that are imparted on ammunition and to generate quantitative measures of similarity. In this paper, we describe an algorithm that identifies impressed tool marks on a cartridge case that are both consistent between firings and contribute strongly to a surface similarity metric. The result is a representation of the tool mark topography that emphasizes both significant and persistent features across firings. This characteristic surface map is useful for understanding the variability and persistence of the tool marks created by a firearm and can provide improved discrimination between the comparison scores of samples fired from the same firearm and the scores of samples fired from different firearms. The algorithm also provides a convenient method for visualizing areas of similarity that may be useful in providing quantitative support for visual comparisons by trained examiners.

Holographic radius test plates for spherical surfaces with large radius of curvature.

We describe a novel interferometric method, based on nested Fresnel zone lenses or photon sieves, for testing and measuring the radius of curvature of precision spherical surfaces that have radii in a range between several meters and a few hundred meters. We illustrate the measurement concept with radius measurements of a spherical mirror with a radius of about 10 m. The measured radius is 9877 mm±10 mm for a coverage factor k=2. Our measurements also demonstrate, for the first time to the best of our knowledge, the utility of photon sieves for precision surface metrology because they diffuse higher diffraction orders of computer generated holograms, which reduces coherent noise.

Deformation-free form error measurement of thin, plane-parallel optics floated on a heavy liquid.

We describe a novel method for measuring the unconstrained flatness error of thin, plane-parallel precision optics. Test parts are floated on high-density aqueous metatungstate solutions while measuring the flatness error with an interferometer. The support of the flat optics by the uniform hydrostatic pressure at the submerged face of the flat optic eliminates flatness errors caused by mounting forces. A small, well characterized flatness error results from the bending of the floating flat by the hydrostatic pressure gradient at the edges. An equation describing the bending of thin, flat plates floating on a liquid is derived, which can be used to correct the flatness measurements of arbitrarily shaped plates. The method can be used to measure flatness errors of both nontransparent and transparent parts, and it is illustrated with flatness measurements of photomask blanks and substrates for extreme ultraviolet lithography. The refractive index of a saturated aqueous lithium metatungstate solution was measured at 632.8 nm and was found to be close to the refractive indices of several low thermal expansion optical materials.

Form-Profiling of Optics Using the Geometry Measuring Machine and the M-48 CMM at NIST.

We are developing an instrument, the Geometry Measuring Machine (GEMM), to measure the profile errors of aspheric and free form optical surfaces, with measurement uncertainties near 1 nm. Using GEMM, an optical profile is reconstructed from local curvatures of a surface, which are measured at points on the optic's surface. We will describe a prototype version of GEMM, its repeatability with time, a measurements registry practice, and the calibration practice needed to make nanometer resolution comparisons with other instruments. Over three months, the repeatability of GEMM is 3 nm rms, and is based on the constancy of the measured profile of an elliptical mirror with a radius of curvature of about 83 m. As a demonstration of GEMM's capabilities for curvature measurement, profiles of that same mirror were measured with GEMM and the NIST Moore M-48 coordinate measuring machine. Although the methods are far different, two reconstructed profiles differ by 22 nm peak-to-valley, or 6 nm rms. This comparability clearly demonstrates that with appropriate calibration, our prototype of the GEMM can measure complex-shaped optics.