Arnab
Sarkar
,
Suresh K.
Aggarwal
* and
D.
Alamelu
Fuel Chemistry Division, Bhabha Atomic Research Centre, Trombay, Mumbai, 400 085, India. E-mail: skaggr@barc.gov.in; skaggr2002@rediffmail.com; Fax: +91-22-25505151; Tel: +91-22-25593740
First published on 11th November 2009
The goal of this work was to examine the probability of instant identification of confidential documents for forensic application by comparison with a spectral library generated using laser induced breakdown spectroscopy (LIBS). The library consisted of representative spectra from different types of papers used for official (governmental) work. Statistical methods using linear and rank correlations were applied to identify the unknown paper. Both correlation methods yielded probabilities of correct identification close to unity for all the studied samples. The approach would have applications in forensic science.
In governmental confidential documents, replacing one of the pages of the document is the easiest forgery case. Currently, important government documents rely on special paper, ink and water marking to prevent forgery. The elemental profile of paper of the same quality varies from company to company and even with the time of production. This is because of variation in the soil quality as well as environment in the forests from where trees are used by the paper producing company. During confidential document printing, all the pages will generally belong to paper from a single company and same production time. Hence if a few particular pages are replaced by the forger at a later stage, it should be possible to identify the forgery by elemental profiling. Neutron activation analysis (NAA) has been used to obtain elemental profiling.1 Laser induced breakdown spectroscopy (LIBS) is a promising alternative technique for rapid identification of forged document instead of NAA which is time consuming and depends upon the availability of a nuclear reactor or a neutron source.
Gornushkin et al.2,3 have shown that simple statistical correlation methods, such as linear and rank correlations, can be successfully applied for the identification of solid and particulate materials without trace or bulk quantifications. A near 100% reliable identification was achieved based on the use of thousands of data points (pixels) representing the sample spectrum in a relatively large spectral window. Anzano et al.4 employed this methodology for characterization of post-consumer commercial plastic waste widely used for household and industrial purposes. Jurado-López et al.5 used a rank correlation method for the rapid identification of alloys used in the manufacture of jewellery. Mateo et al.6 showed the capability of linear correlation method for depth profiling by LIBS. Rodriguez-Celis et al.7 compared glass spectra from car windows using linear and rank correlation methods and showed effective discrimination at a 95% confidence level. In this paper, we demonstrate the application of parametric (linear) and non-parametric (rank) correlations for identification of several confidential papers using LIBS.
Sample No. | Year of use | Watermark |
---|---|---|
L1 | 1999 | RAJAMANI |
L2 | 2000 | CARD |
L3 | 2001 | SYMBOLIC |
L4 | 2002 | ASHOK |
L5 | 2003 | BALLARPURI |
L6 | 2004 | CENPULP |
L7 | 2005 | ANDHRA |
L8 | 2006 | SIRPUR |
L9 | 2007 | SIMPLEX LEDGER |
L10 | 2008 | SUDARSHAN CHKRA |
Sample No. | Year of use |
---|---|
X1 | 1999 |
X2 | 2000 |
X3 | 2001 |
X4 | 2002 |
X5 | 2003 |
X6 | 2004 |
X7 | 2005 |
X8 | 2006 |
X9 | 2007 |
X10 | 2008 |
For each of the unknown paper samples, similar to the library samples, LIBS spectra were recorded on 10 different pieces of paper, obtained by cutting each unknown YCR paper at random positions.
An inbuilt program for correlation analysis in Microsoft Excel 2003 was used for computation of correlation coefficients between the LIBS spectrum of unknown and library spectra.
Each channel consisted of 2048 pixels. Hence from two channels, 4096 data points were available, which are enough to permit statistical analysis like linear correlation and non-parametric rank correlation. Linear correlation measures the similarity in trend and the correlation coefficient “r” is expressed as,
![]() | (1) |
![]() | (2) |
As before, xi (or its corresponding rank Ri) stands for the intensity of light detected by pixel i in the detector spectrum for stored library YCR paper, whereas yi (or its corresponding rank Si) stands for the intensity at the same pixel i of the unknown spectrum. The ranks are numbers 1, 2, 3, …, N, where N is the total number of data points (or pixels in the present case, 4096), which replaces the true values of x and y in accordance with their magnitudes. For example, the most intense pixel in the spectrum obtained in the present study was assigned the number 4096 with number 1 assigned to the least intense pixel, i.e., the rank increases with increase in intensity. It is important to emphasize that if a correlation is proven non-parametrically, then it really exists.11
We applied both the correlation methods for the identification of the unknown YCR papers. Typical correlation plots for the above mentioned two correlation methods are shown in Fig. 2. All the 10 LIBS spectra of each of the 10 unknown YCR papers were correlated with 10 library spectra and the average correlation coefficient values are shown in Fig. 3a for linear correlation and in Fig. 3b for rank correlation. Table 3 shows results obtained when library paper L4 was linearly correlated with spectra of unknown YCR papers X1, X2, X3 and X4. From Figs. 3(a) and (b), it is clear that the identical pair of samples are (L1–X1), (L2–X2), (L3–X3), (L4–X4), (L5–X5), (L6–X6), (L7–X7), (L8–X8), (L9–X9) and (L10–X10). From Tables 1 and 2, it is evident that the observed identical pair of paper actually belongs to the same year YCR paper branch, i.e., 100% identification is achieved.
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Fig. 2 Linear and rank correlation plots for the sample LI (library) vs. unknown X1. |
![]() | ||
Fig. 3 Linear (a) and rank (b) correlation coefficients for the YCR papers. Arrows indicate samples showing the best correlation coefficients. If identification is correct, the indicated sample is the same as the library sample given on the x-axis. |
Sample No. | Linear correlation coefficient (r) | |||
---|---|---|---|---|
L4 vs. X1 | L4 vs. X2 | L4 vs. X3 | L4 vs. X4 | |
1 | 0.9642 | 0.9683 | 0.9629 | 0.9901 |
2 | 0.9517 | 0.9696 | 0.9497 | 0.9956 |
3 | 0.9388 | 0.9693 | 0.9515 | 0.9934 |
4 | 0.9396 | 0.9617 | 0.9473 | 0.9938 |
5 | 0.9441 | 0.9682 | 0.9277 | 0.9962 |
6 | 0.9550 | 0.9658 | 0.9248 | 0.9941 |
7 | 0.9414 | 0.9539 | 0.8997 | 0.9948 |
8 | 0.9381 | 0.9781 | 0.9318 | 0.9836 |
9 | 0.9488 | 0.9732 | 0.9185 | 0.9959 |
10 | 0.9539 | 0.9592 | 0.9230 | 0.9944 |
Mean | 0.9476 | 0.9667 | 0.9337 | 0.9932 |
Standard deviation | 0.0086 | 0.0070 | 0.0190 | 0.0038 |
Apart from the difference in the average values of correlation coefficients, other statistical tests were also performed. Initially an F-test was done between the distributions of correlation coefficient values and the significance of the F-test was calculated. When the calculated significance of F was less than 0.1, the difference in variances was considered as significant and the Student t-test was applied assuming unequal variance from which the probability that two distributions of correlation coefficients had different means was calculated. For the other scenario, the Student's t-test was performed assuming equal variance performed. Tables 4 and 5 show the probability of the two distributions of correlation coefficients had different means.
Unknown paper samples↓ | Library paper sample → | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 | L9 | L10 | |
X1 | 0 | 0.9998 | 1 | 1 | 1 | 1 | 0.9997 | 1 | 1 | 1 |
X2 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
X3 | 1 | 1 | 0 | 1 | 0.9999 | 1 | 1 | 1 | 0.9999 | 1 |
X4 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0.9998 | 1 | 1 |
X5 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
X6 | 1 | 1 | 0.9997 | 1 | 1 | 0 | 1 | 1 | 1 | 0.9998 |
X7 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 |
X8 | 1 | 1 | 1 | 0.9998 | 1 | 1 | 1 | 0 | 1 | 1 |
X9 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
X10 | 0.9997 | 1 | 1 | 1 | 1 | 0.9996 | 1 | 1 | 1 | 0 |
Unknown paper samples ↓ | Library paper sample → | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 | L9 | L10 | |
X1 | 0 | 1 | 0.9999 | 1 | 0.9999 | 1 | 0.9999 | 1 | 0.9999 | 0.9999 |
X2 | 1 | 0 | 0.9963 | 1 | 0.9963 | 0.9963 | 0.9963 | 0.9963 | 1 | 1 |
X3 | 1 | 0.9998 | 0 | 0.9995 | 1 | 1 | 1 | 1 | 1 | 1 |
X4 | 0.9999 | 1 | 1 | 0 | 0.9999 | 0.9999 | 1 | 1 | 0.9999 | 1 |
X5 | 1 | 1 | 1 | 1 | 0 | 0.9963 | 0.9963 | 0.9963 | 0.9963 | 0.9963 |
X6 | 1 | 0.9999 | 1 | 0.9999 | 1 | 0 | 1 | 1 | 1 | 1 |
X7 | 0.9963 | 1 | 0.9963 | 1 | 0.9999 | 1 | 0 | 0.9999 | 1 | 0.9979 |
X8 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0.9963 | 0.9963 |
X9 | 1 | 0.9999 | 0.9999 | 0.9999 | 1 | 0.9963 | 0.9999 | 1 | 0 | 1 |
X10 | 0.9963 | 0.9963 | 0.9963 | 1 | 0.9999 | 1 | 0.9963 | 0.9999 | 1 | 0 |
The diagonal elements in Table 4 correspond to the correlation (using linear correlation coefficient) of the sample with itself, all exhibiting a zero probability of difference. The same is also given in Table 5 using rank correlation coefficient. All the probabilities given in Tables 4 and 5 as 1.0, differ from 1.0 by a negligibly small value, less than 10−8. As can be seen from Tables 4 and 5, almost 100% matching is achieved using both the linear and rank correlations. It is well known that if a correlation is proven non-parametrically, i.e., by rank correlation, then it really exists.11 For the application and methodology discussed in this work, there was no significant difference between the two approaches i.e. linear and rank correlation.
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