NBS

PUBLICATIONS

NBSIR 81-2286

The Characterization of Auto

Headlight Glass by Refractive

Index and Density

A1110Q ^4403

Prepared by the

Law Enforcement Standards Laboratory

National Engineering Laboratory

Washington, DC 20234

October 1981

Prepared for the

National Institute of Justice

QO i.s. Department of Justice

lUO i/ashington, DC 20531

.U56

31-2286

1981

c. 2
ABOUT THE TECHNOLOGY ASSESSMENT PROGRAM

The Technology Assessment Program is sponsored by the Office of

Development, Testing, and Dissemination of the National Institute of Justice

(NIJ) , U.S. Department of Justice. The program responds to the mandate of

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to encourage research and development to improve the criminal justice system

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determines the technological needs of justice system agencies, sets minimum

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The Technology Assessment Program Advisory Council (TAPAC) consisting of

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For further information, or to register with NCJRS, write to the National

Institute of Justice, National Criminal Justice Reference Service,

Washington, DC 20531.

Paul Cascarano, Assistant Director

National Institute of Justice
nowAL BUMAD

OF 8TANDAKI>«

LIBRA AT NOV 2 3 1961

NBSIR 81-2286

*** (Jit (00

THE CHARACTERIZATION OF AUTO

HEADLIGHT GLASS BY REFRACTIVE

INDEX AND DENSITY IW

Prepared by the

Law Enforcement Standards Laboratory

National Engineering Laboratory

Washington, DC 20234

October 1 981

Prepared for the

National Institute of Justice

U.S. Department of Justice

Washington, DC 20531

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
* i» - "v ; Uf SKISUm-faY 't

r . f

; V $
ACKNOWLEDGMENTS

This report was prepared by the Law Enforcement Standards Laboratory

(LESL) of the National Bureau of Standards, under the direction of Pobert M.

Mills, former Program Manager for Investigative Aids, and Jacob J. Diamond

and Lawrence K. Eliason, successive Chiefs of LESL. The document was revised

by Paul H. Krupenie of LESL. Refractive index measurements were made by

Irving Malitson, Marilyn J. Dodge, and Warren K. Gladden. Density

measurements were made by Susan A. Mills. James A. Lechner did the

statistical analysis for this paper. Henry L. Mason assisted in the drafting

of the paper. Harold L. Steinberg collected the headlight samples and

assisted in the coordination of the project. Michael Thomas cut the

headlight glass into test pieces. The preparation of this document was

sponsored by the National Institute of Justice, Lester D. Shubin, Standards

Program Manager.

ii

FOREWORD

The Law Enforcement Standards Laboratory (LESL) of the National Bureau of

Standards (NBS ) furnishes technical support to the National Institute of

Justice (NIJ) , formerly the National Institute of Law Enforcement and

Criminal Justice, program to strengthen research that will assist law

enforcement and criminal justice agencies in the selection and procurement of

quality equipment.

LESL is: (1) Subjecting existing equipment to laboratory testing and

evaluation, and (2) conducting research leading to the development of several

series of documents, including national voluntary equipment standards, user

guides, and technical reports.

This document is a law enforcement technology report developed by LESL

under the sponsorship of NIJ as part of the Technology Assessment Program,

which is described on the inside front cover of this report. Additional

reports as well as other documents are being issued under the LESL program in

the areas of protective equipment, communications equipment, security

systems, weapons, emergency equipment, investigative aids, vehicles, and

clothing

Technical comments and suggestions concerning this report are invited

from all interested parties. They may be addressed to the author or to the

Law Enforcement Standards Laboratory, National Bureau of Standards,

Washington, DC 20234.

Lawrence K. Eliason, Chief

Law Enforcement Standards Laboratory

iii

CONTENTS

I*rl Foreword . x

1 . Summary

2. Glasses in Auto Headlights

3. Testing Reliability of Evidence . . 4 . Methods for Measuring Refractive Index ........

5. Refractive Index Measurements for this Study ....

6. Analysis of Refractive Index Data ...

6.1 Classification by Subpopulation ........ ...

6.2 Individualization ..........

6.2.1 Resolution = 10 ^ 6. 2. 1.1 Calculation of 3 ...............

6. 2. 1.2 Calculation of a ......

6.2.2 Better Resolution . 6.3 Position Effect . 6.4 Annealing .....................

6.5 Dispersion ........

6.6 Temperature Coefficient of Refractive Index and Thermal

Coefficient of Expansion ...................

7. Density Measurements . . 8. Analysis of Density Data

9. Conclusions and Update .... ........

Appendix A—"Trial by Mathematics" ..... . Appendix B —Allowance for Differences Between General Electric and

Early Corning Lenses ... ......

Appendix C —References .

ii

1

23

67

9

9

10

11

13

14

15

20

21

21

21

22

24

25

27

29

31

v

THE CHARACTERIZATION OF AUTO HEADLIGHT GLASS

BY REFRACTIVE INDEX AND DENSITY

Law Enforcement Standards Laboratory

National Bureau of Standards

Washington , DC 20234

1 . SUMMARY

By measurement of some physical property of headlight glass fragments

found at the scene of an auto accident, forensic scientists have sometimes

found it possible to infer that the glass was molded by a specific

manufacturer. From an examination of the physical appearance of fragments it

has sometimes been found possible to infer that the glass came from a broken

headlight on a specific car. The glass used in auto headlights is now made

by only two U.S. firms. The refractive index (RI) and density of the

specimens are the most common parameters of interest to forensic scientists.

This study was designed to evaluate the potential usefulness of

measurements of RI and/or density for forensic purposes. Automotive

headlights were obtained from several sources. As of the time the analytic

work was performed it appeared that there were three subpopulations of

headlight glass: General Electric (GE) , Corning manufactured before 1971,

and Corning manufactured after 1971. The distributions of RI (and density)

for the first two subpopulations overlapped considerably, so that one could

not reliably determine to which of these a candidate piece of glass belonged.

However, the latter population was different enough that one could reliably

classify a fragment as belonging either to one of the first two or to the

third. Furthermore, since headlights on the road at that time were about

equally split between the three groups, the performance of both RI and

density for individualization (i.e., the matching of an unknown fragment with

a specific lens) was evaluated using the fact of an even split. Since the

analytical work was done , the composition of glass has been changed several

times by both manufacturers (and a significant number of lenses not made in

the United States have appeared on the road) . Without another comprehensive

sampling of lenses, it is not possible to know how different the lenses on

the road today really are. However, one may obtain a conservative figure by

acting as though there is only one population, and this is done in section 9 (which updates the report to January 1981)

Certain conclusions remain valid with regard to individualization: 1)

Measurement of density is likely to be more effective than measurement of RI

2) the technique is capable of eliminating a large fraction of suspect lenses

with only a small chance of rejecting the true match; 3) the technique is

less satisfactory in confirming a true match; and 4) the effectiveness is not

increased appreciably by taking more than a few repeated measurements, by

annealing, the specimens, by measuring RI at several wavelengths, or by

measuring both RI and density.

-'-The original manuscript of this report was prepared in 1976. Final editing

and publication was delayed as a consequence of personnel changes. The

experimental techniques, methods of analysis, and data, although dated,

combined with the present update provide a useful reference for the forensic

science community.

2 The three subpopulations of headlight glass will be referred to in the text

and tables as GE , early Corning, and late Corning, respectively.

1
This report is divided as follows. Section 2 briefly describes the

manufacture of headlamp glass and the construction of a lamp. Section 3 discusses the reliability of using headlight fragments as evidence and the

two types of possible error. Section 4 describes RI measurement procedures,

including references to earlier studies of headlamp glass. Section 5 describes the NBS procedure in more detail. Section 6 contains the bulk of

the statistical analysis of the RI data, the analytical approach used, and

the conclusions reached (with a more detailed listing of its contents at the

beginning of the section) . Section 7 discusses the NBS density measurement

method, and section 8 presents an analysis of these measurements, comparing

density and RI as individualizers . Section 9 has been added to update and

summarize the results. Two short appendices and a list of references

conclude the report.

2 . GLASSES IN AUTO HEADLIGHTS

The sealed-beam headlight generally used on automobiles in this countrv

has a lens of borosilicate glass molded in one piece. Until recently only

three firms were producing this glass —Corning Glass Works, General Electric

Glass Works, and Anchor-Hocking Glass Co. In mid 1972 Anchor-Hocking

discontinued production. In 1975 Corning produced about 60 percent of the

total output, and General Electric the remainder. In chemical composition,

glasses made by these firms are believed to be quite similar, except that the

Corning mix was modified in the fall of 1971 (see par. 2 of sec. 1).

Headlight glass is made by a continuous flow process in a very long tank

furnace operating at about 1500°C. Batches of raw materials are charged into

the melting chamber. After melting, the viscous mass flows under a fireclay

float and is continuously drawn off from the working end to be fed to forming

machines which press it into the lens or reflector configurations needed.

The process is apt to leave striations, bubbles, or bits of foreign material

in the qlass, so that the molded piece may well be nonuniform in its

physical and optical properties. Figure 1 shows an example of striations in

a headlight lens; the refractive index is evidently different from point to

point

Figure 1. Striations in auto headlamp glass.

2
After a lens and a reflector are fused together to form the sealed

headlight, the assembly is given a minimal anneal by heating it to about

500°C, to remove internal stress. However, an internal stress pattern may h< expected to result from the subsequent tempering process which cools the

surface more rapidly than the interior of the material. A headlight lens

viewed through a polariscope (i.e., with polarized light) would then show

bright and dark areas indicative of the stress distribution and the variation

of refractive index across the lens.

The standard reference material (SRM 1820) , with refractive index

certified for 13 wavelengths, has been produced by the NBS for use by

forensic scientists. Its RI varies from 1.48398 at 0.70652 Hm to 1.49994 at

0.40466 ym, with uncertainties within 5xl0-6

. Its temperature coefficient of

refractive index dn/dT over a temperature range of 20-80° C is approximately

4.0xl0~ 6 /°C at 0.58926 pm, the sodium Di , D2 line. Its density is 2.292+0.001

g/cm3 at 24° C, 50 percent relative humidity, and a pressure of 99,442 Pa (746

mm Hg)

3. TESTING RELIABILITY OF EVIDENCE

The forensic scientist may be asked for a quantitative estimate of the

reliability of statements characterizing a headlight glass offered as evidence. If the scientist can produce a photograph showing a perfect match

between the fracture surfaces of a referral piece and a suspected broken

lens, that is as close to absolute certainty as one can hope to come.

However , measurements of physical properties —such as refractive index or

density —are subject to uncertainties which are dependent on the property

chosen for study, the instruments used, the number of readings taken, and the

precision of those readings. If the data are adequate, the scientist may

hope to individualize the specimen, i.e., to say with a stated degree of

confidence that a physical property measured for the referral piece will

match (have the same value as) one and only one lens from the population of

headlights on the road. Alternatively, the scientist may hope to classify

the specimen, e.g., to say that it is not window glass, bottle glass, or

spectacle glass, and to say with a stated degree of confidence that one or

more of its properties falls within the range that is representative of the

headlight glass population.

In the report sections which follow, statistical techniques are applied

to data actually taken at the NBS , and to hypothetical data which might

result if some of the operative circumstances were changed. These techniques

provide a performance test for forensic reliability. Measurements of

reliability can be useful in three ways. First, they can be useful in

determining the relative utility of various physical properties (e.g.,

refractive index and density) for making individualizations and

classifications. Secondly, they can be useful in determining the relative

merits of alternative methods for measuring these physical properties. And

thirdly, they can be useful as one indication of the weight with which

various types of physical evidence should be considered once introduced into

courtroom testimony; that is, physical evidence which has a greater degree of

uncertainty associated with it probably should not enjoy as much weight as does a more reliable type of physical evidence.

In addition to reliability, there are other performance attributes (e.g.,

the time required to make the analysis, the cost of the procedure, and the

degree of preservation of destructible evidence) which are important to

forensic scientists. However, these other attributes were not within the

scope of this study.

Since many of the techniques in this report are statistical in nature, it

is prudent to acknowledge the concern of some legal authorities concerning

the use of statistical methods in the trial process. Appendix A, quoting

3
from the published literature, supports the appropriateness of the kind of

statistical investigation reported in this paper.

For classification according to manufacturer to be reliable, the

distribution of values of some lens property--such as refractive index or

density--must not overlap among lenses molded by different manufacturers.

For individualization to be reliable, the distribution-width (i.e., standard

deviation) of property values within any one lens must be small in comparison

with the distribution-width of property values among all headlights on the

road. Otherwise, there would be no discriminatory power.

The hypothesis that two glass fragments are from the same headlight is

subject to two possible kinds of error; a nonmatch may be declared, when a match actually exists (known as false rejection) , and a match may be declared

when it does not actually exist (known as a false match) . The probability of

a false rejection is denoted by a , and the probability of a false match (or

false acceptance) by g

In aeneral, probabilities can be computed by calculating the area under a section of the appropriate normalized frequency-distribution curve. Clearly,

it is important to select the correct section from the correct distribution.

To compute a , the distribution of interest represents the property values

found within any individual lens, as shown in figure 2. The section

representing the a-error probability is the area under this frequencydistribution curve which is outside the range of ’’matching" property values,

i.e., outside the shaded band in figure 2.

Figure 2. Illustration of a-error.

4
The referral piece may have any value of RI within this population range,

but is more likely to have a value near the center of the range (the "lens

mean"). An "x" appears in figure 2 somewhat off center to indicate a possible value for this referral RI . Another piece will be said to match

this referral piece if its measured RI is sufficiently close to the referral

RI . The range of "matching" RI values for a hypothetical match criterion is

shown in figure 2 as a shaded band. Any RI values outside the shaded, area

will erroneously be declared "nonmatching." The area outside the shaded

band, representing the a -error, depends on the width of the band v/hich is

twice the criterion value C; it also depends on the position of the "x" in

figure 2 relative to the lens mean.

On the other hand, for B, interest centers on the distribution of the

property across the remainder of the appropriate lens subpopulation , as shown

in figure 3. The area of interest is the area under this frequencydistribution curve which is within the shaded band. Here too, an "x"

indicates the PI of the referral fragment. But with the scale chanced to

accommodate the much larger spread of PI values across the population, the

shaded area appears as a very narrow slice out of the population. Only the

small fraction of the population which is within the shaded area would, if

selected, be declared (falsely) matching. Thus g, the probability of a false

match, is given by the area under the probability curve within the shaded

recion. Again, it matters where the referral fragment falls with respect to

the population mean; an average 3 is therefore calculated.

For measurements made in the field, the uncertainties resulting from

inadequate equipment or lack of operative skill are likely to be greater than

those made under ideal laboratory conditions such as those reported herein.

Thus, values of a and 3 based on data taken at the NBS will be "best case"

results; the probability of error corresponding to actual investigative

situations will be no less than that reported here, and may be greater.

DISTRIBU

RI FOR Gl

1 .<

Figure 3. Illustration of 3-error.

5
4. METHODS FOR MEASURING REFRACTIVE INDEX

Refractive index is defined as the ratio, n, of the velocity of light in

air to its velocity in a transparent medium. Generally measurements are made

with monochromatic light. Measurements of RI may be made by any one of

several methods. These fall into two general classes: (a) measurement of

the change of angle suffered by a light ray as it passes through a geometrically regular sample, and (b) observation of a (possibly) irregular

fragment while immersed in a liquid of known RI . The first class is used for

precise measurements. It requires a refractometer . An Abbe refractometer

was used by Greene and Burd [1]3 in 1949 in measuring the RI of glass from 50

headlamps, with a claimed accuracy of +1x10“^. The RI of these glasses ranged

from 1.5072 to 1.5101, which is substantially higher than the RI of glass

made more recently.

The second class requires a transparent container which can be mounted on

a microscope stage. In the simple Becke line method [2] the test fragment is

immersed in one or another of a series of liquids graded in RI and observed

through a microscope with systematic reduction of illumination. If the

fragment has an RI slightly lower or slightly higher than that of the liquid,

and the focusing depth of the microscope is changed slightly, a bright line

will appear at an edge of the specimen. When a liquid is found that renders

the fragment invisible, the RI of the solid is known to be the same as that

of the liquid. Under favorable conditions, readings can be made to 5x1 0 -4 t according to Allen [2],

A comparative study of methods of illuminating the immersed specimen was

made by Saylor [3]. He compared central illumination, as used by Becke, with

oblique illumination and with a double-diaphragm method. His tests on crushed borosilicate glass showed that a matching of indices could be

obtained with much better consistency using the double diaphragm and a lowpower objective. This technique yielded an average error of 2x10*"^ with a maximum error of 5x10"^ for ri of macro-specimens in work by Faick and

Foronoff [4]

Use of a single immersion liquid whose temperature can be increased at a slow regular rate on a "hot stage" is an alternative to a graded series of RI

liquids. This method was used by Dabbs and Pearson [5] and by Dixon [6]

Ojena and DeForest [7,8] added the use of phase microscopy, and found the

internal variation within a lens to be about 6xl0~5. The overall range for

1970 headlamp glass was 1.47713 to 1.47934 with a claimed standard deviation

of 3.4xl0 -5

. They concluded that "the bulk of these variations could not

have been measured with the simple Becke line technique (accuracy +0.001)."

The F, D, and C lines were used by McCrone [9] for observation of the

Becke line with specimens on a heated stage. His collaborative study [10] , adopted as an interim official first action by the Association of Official

Analytical Chemists (AOAC) , reported an overall laboratory average error of

33x10 -

5 in their results on two standard specimens. The technique uses a liquid with RI exceeding that of the specimen at all wavelengths- precise

data on the liquid dn/dT is required.

3 Numbers in brackets refer to references appearing in appendix C.
5. REFRACTIVE INDEX MEASUREMENTS FOR THIS STUDY

For the NBS study, the 71 headlights were obtained from sources listed in

table 1. The fused joint between a lens and its reflector was ground away,

and the lens was cut into 13 pieces (as shown in fig. 4) with a diamond-faced

saw. This provided a total of 923 specimens. The four edges of each piece

were smoothed on a surface grinder, and each of its 90°-corners was assigned

a number from one to four, as shown in the figure.

Conceptually, t:he internal stresses within headlight lenses could be

relieved to a different degree, depending on whether a lens is cut up using

the diamond-faced saw, or smashed as in an actual vehicle collision. If

difference existed, our RI data would not be representative of RI values

encountered by law enforcement investigators. To check this, two lenses were

smashed, and the resulting pieces were then cut into regular shapes.

Comparing these pieces with those cut from the figure 4 pattern, no

significant differences were found in either average RI values or w.ithin-lens

RI variation.

Measurements of RI were made on about 600 rectangles using a precision

vee-block ref ractometer capable of readings to within 2xl0 -5 for glass of

optical quality. The test corner of the rectangle was fitted into the 90°

vee-block as shown in figure 5. The test sample was sealed to the vee-block

with a contact liquid of similar RI , in this case a mixture of ethylene

glycol and benzyl alcohol. An important feature of this method is that the

average index through the body of the test piece is measured, not just the

surface value. The latter value is what is observed with the grazing

incidence method using an Abbe refractometer . Readings were taken on one or

more corners of each rectangle by four different observers on different

occasions. Each RI value reported was the average of five, computed from

measurements of the angle between the successive emergent rays. All readings

were made at a controlled room temperature near 20°C.

Table 1. Sources of headlight glass for NBS study

General Electric Early Corning Late Corning

9 a

7 a 12 a

7 b

8 b3

b

5 d

2 0

C

a Purchased new in 1973-74.

b Used between 1965 and 1973 by NBS colleagues.

c Production line on four days in April 1974.

a Production line.

7
Figure 5. Schematic representation of Vee-block refractometer

no = RI of reference prism (Vee-Block) ; n = RI of glass sample;

6= angular deviation of light beam. The following expression holds:

+ sin 0 (n

2 n -

8

. 0

\ 1/2 1 1/2 sin 0 >

|
6. ANALYSIS OF REFRACTIVE INDEX DATA

This section is subdivided as follows: section 6.1 considers tin

classification of a piece of headlamp glass--i.e., the determination of which

of the three subpopulations it belongs to. Section 6.2 covers

individualization to the specific lens from which the piece originated--with

coarse measurements considered in section 6.2.1, and finer measurements in

section 6.2.2. Miscellaneous questions are covered in the remainder of the

section: whether RI varies consistently with position within a lens, in 6.3;

effects of annealing, 6.4; dispersion, 6.5; and temperature effects, 6.6.

6.1 Classification by Subpopulation

Measurements of RI on 71 lenses indicated that there are three

subpopulations to be considered as shown graphically in figure 6 and listed

in table 2 (for the sodium Di , D2 doublet) . As mentioned in section 3, the

reliability of classifications hinges on the degree of overlap of the various

subpopulations of auto headlights on the road. Since the 25 lenses obtained

directly from production lines (see table 1) were manufactured within very

short periods of time, they would be expected to be (and in fact were found

to be) considerably more alike than other lenses. The use of these lenses in

the analyses to follow would distort the results, so they were not used, and

are not represented in the data summarized in table 2

The table is based on an average RI value for each lens, which is in turn

based on five readings at each of about 13 locations on that lens. Thus each

lens? contributed one x-value. The average of these 15 or 16 values, denoted

by x, and the group standard deviation, denoted by s, are estimates of the

mean and standard deviation of the population of possible lens-averages for

the given group. The range given is the range of the 15 or 16 x-values.

Finally, the confidence limits which have been computed for the median of the

population are valid regardless of the shape of that population distribution.

The meaning of the confidence coefficient is as follows (taking the GF column

as an example) : In at least 96 percent of the (independent) cases where a confidence interval is calculated in the manner used here, that confidence

interval will bracket the true median.

GENERAL ELECTRIC ""I » i

LATE CORNING -+•"+“

EARLY CORNING

I • I

—I 1 1 1 I I ^ 4 5 6 7 8 1.479 REFRACTIVE INDEX

Figure 6. Measured refractive index values for different groups of headlamp

lenses. Each bar indicates the spread of lens averages for the group;

the vertical ticks indicate the confidence limits for the medians of the

underlying populations; and the heavy dots indicate the average of all

measured lenses in the group. (See also table 1.)

9
Table 2. Refractive indexes of automotive headlights

Population

statistics

General

Electric

Corning

before

11/1971

Corning

after

11/1971

Number of lenses 15 16 15

X (average3 RI

all lenses)

for 1.47835 1.47749 1.47476

s (estimate of

dev. within

subpopulation)

std0.00051 0.00046 0.00030

Range (of lens

averages)

1.47743 to

1.47899

1.47697 to

1.47837

1.47430 to

1.47528

Confidence limits

for the median

1.47801 and

1.47875

1.47720 and

1.47787

1.47456 and

1.47497

Confidence

coefficient

.96 .98 .96

aThe value for each lens is the average of five readings (for the

sodium , D 2 doublet) at each of 13 locations on the lens.

The results show that the average RI of each subpopulation of lenses (GE,

early Corning, and late Corning! differs significantly from the other two in

the third decimal place. The difference between late Corning and the other

two is about 3xl0 -3

. Since this difference is many times larger than the

standard deviations found within the subpopulations, late Corning glass

should be distinguishable, even by the simple Becke line method often used in

crime laboratories for RI determinations. However, a piece of glass from one

of the other two groups cannot be assigned unambiguously to either one of the

two, because the distributions of RI values for those two groups overlap

considerably (see fig. 6) .

6.2 Individualization

Individualization involves being able to show that the variability of RI

within a lens is small compared with the variability among lenses on the

road. The data used to compute table 2 cover all three manufacturers and a representative range of manufacturing dates. For 46 of these lenses, one at

a time, the standard deviation was calculated for the set of RI values

measured for the different rectangles. These 46 standard deviations were

combined to give an estimate of 6.8xl0 -5 for ol, the standard deviation for a measurement made at a random point on a lens. (The 95% confidence limits for

o L are 6.3xl0~ 5 and 7.3xl0~ 5 ). From table 2, the estimates of o p

, the

standard deviation of RI values across a given subpopulation, range between

30xl0~5 and 51x10“ 5

10
The standard deviation across a lens, o L , results from two sources of

variation—the measurement process (cr m ) , and the inhomogeneity of RI within

the lens ( oi ) . The measurement component can be estimated from repeated

readings on individual corners. A total of 89 pairs of such readings were

made by one operator from eight representative lenses, yielding an estimate

of 3.8xl0 -5 for the standard deviation attributable to measurement error.

Thus , the estimated standard deviation due to the inhomogeneity of RI within

the lens is 5.6xl0 -5

, i.e., [ (6 . 8) 2 - ( 3 . 8) 2 = (5 . 6

2

]

. This indicates that it

would not be reasonable to expect any method of RI measurement to achieve a standard deviation, for measurements across a lens, of less than about 6xl0~ 5 for a glass as inhomogeneous as that used in headlamp lenses. For

convenience the estimated values of the various standard deviations are

tabulated in table 3.

There is no significant evidence of non-Normality for any of the three

subpopulations, nor for the values within a single lens. Therefore,

throughout the remainder of this report, calculations are based on a Normal

(Gaussian) distribution of RI values for each of the three subpopulations,

with the standard deviation o p different for each subpopulation.

A Normal distribution is also assumed for the RI values within an individual lens, with standard deviation which does not depend on the

subpopulation

6.2.1 Resolution = 10 4

The RI measurements at NBS were made by experienced observers usina a ref ractometer under optimum laboratory conditions. RI measurements in the

field are likely to be made to only lxlO-3

, or perhaps 1x10” 4

. When the

reading scale is this coarse, how large are the error probabilities, a and 6?

Table 3. Estimated standard deviations for refractive index

Symbol Type of variability Estimated value

o L

°i

°m

°1

o 2

Measurements at

random positions

across a lens

Inhomogeneity in a lens

Due to the NBS

measurement process

Among late Corning

lenses on the road

Among GE and early

Corning lenses on

the road

6.8x10 5

5.6xl0~ 5

3.8xl0" 5

30xl0~ 5

Average of 51xl0“5 and

46xl0- 5 = 48x10-5
Suppose that readings are taken with no measurement error on a scale of

uniformly-spaced values with interval 9=lxl0~ 4

. Since actual measurements are

not perfectly accurate, and since many laboratories have a measurement

resolution which is closer to 10 3 rather than 10-4

, an optimistic case is

being considered here.

The results are given in table 4. The remainder of section 6.2.1

contains the statistical derivations and calculations which produce table 4

and may be skipped by readers so inclined without interfering with the

remainder of the report.

It has been assumed that the true RI values across any one lens

constitute a Normal population, with mean values varying from lens to lens,

and with a standard deviation independent of which subpopulation is being

considered. Since is relatively small compared to the subpopulation

standard deviation, ap , the position of the mean for a given lens can be

thought of as uniformly distributed over the interval between some two

adjacent readout values.

Denote readout RI values by x, and true RI values by y. Any sensible

rule for deciding whether a referral fragment matches a sample from the

population must be of the following form: If xj is the readout value for the

referral fragment, and X 2 is a readout value for some suspected source lens

in the population, a match is declared when and only when |xi~X 2 | is at most

k0 . We are free to choose the integer k.

It is easy to see that k=0 will not be very satisfactory, because if the

true mean RI value, y, is midway between two readout values, the probability

is approximately 0.5 that two samples from that lens will give different

readout values. False rejection would be declared about 50 percent of the

time. a has also been found to be about 50 percent for other values of y

when k=0 . The larger we make k, the smaller will be a, the probability for a false rejection, and the larger will be 0, the probability for a false match.

Table 4. Reliability of headlight glass individualization--low resolution

RI measurements

Assumptions (both optimistic)

1 . No measurement errors

2. Resolution of measurements, 6 = 1x10

A match is declared if Ix^-^l ± k9

k

Average

a Weighted average

of 6

0 0.56 0.037

1 0.078 0.11

2 0.0031 0.17

12
6. 2. 1.1 Calculation of B Under the optimistic assumption of no measurement errors, Xj will be the

nearest possible readout value to y x

; x

L and can differ by no more than

6/2. The same holds for x 2 and y 2

.

If x 2 is to be within k0 of x^-and thereby be a false match--y2 must be

between x 1 -(k+l/2)6 and x,+(k+l/2)0. For a lens randomly drawn from the

population of lenses on the road, the chance that y 2 is within this interval

depends on where the interval lies with respect to the mean up of the

subpopulation, i.e., on the difference Xj-Up. This probability is maximized

when that difference is zero. Denote this maximum value by B*. It is the

area under the Normal distribution (yp =x 1

, o=aD ) bounded by x 1 -(k+l/2)0 and

x

1 +(k+l/2)6: v

0* =

* [(k+l/2)0/o

p

]-*[-(k+l/2)0/Cp]

where $ is the integral of (2ir ) _1 / 2 exp (-t 2 /2) from -oo to the argument within

the brackets. In the above case, the central area of interest is symmetrical

about the distribution mean, and can be written as:

B* = 2$ [(k+1/2) e/°p]-l.

Since the average height of a Normal distribution is l/y/2 times the

maximum height (at the mean) , multiply B* by 1/V2~ to allow for Xj — values

different from the mean.

Account must also be taken of the fact that there are three

subpopulations of lens glass: late Corning, early Corning, and GE . We will

denote the B corresponding to the late Corning subpopulation by B

t

, and the 0

corresponding to the early Corning and GE subpopulations by B

2

. Assume, for example, that each of the three contains a third of all

lenses on the road. If the referral fragment happens to be from a late

Corning lens, only one-third of all the other lenses on the road will have a chance of false acceptance. Thus:

Bl = b 1 */(3 VT ).

Or, if the referral fragment happens to be from an early Corning or GE

lens, only two-thirds of all the other lenses on the road will have a chance

of false acceptance so that:

B

2 = 2 B 2 * / (3 \Z~2~ ).

The first situation will occur about one-third of the time, the second about

two-thirds of the time. Thus for the entire population the average is:

(e.vVT)

(|) (|)

(0 2 */vT) . B

13
For the late Corning subpopulation, with © =1x10 4

, o =o 1= 3 x 10 4

, and k=l

\ (j)

= H0 * 5 ] = 0.6915;

thus

B i = 3V2 - 2 (0.6915) - l] = 0 . 0903.

For the other subpopulation, ° ^

=a

2 =4 „ 8xl0~ 4

;

2 (4.8)

= $[0.3125] = 0.6227;

and

B 2 = —?— 2 (0.6227) - 1 = 0.1157.

2\f2 L J

The weighted average & (i.e., the chance of a false match) for k=l, 0=lxlO~ 4

, and no measurement error is thus:

4

B = 0.1072.

6 . 2. 1.2 Calculation of a

To determine a with the same assumptions for 0 , 0p , and k, suppose that

the two pieces of glass to be compared are from the same lens. Denote by Xj

a readout value on the referral fragment, and by Y\ the true (but unknown) RI

value for that fragment. Since we are assuming x

1 to be the nearest possible

readout value to y^ , x^ and yi cannot differ by more than 0/2. At the other

extreme, y t might exactly coincide with a readout value. We will calculate a for each of these extreme cases. Suppose y 2 is the true RI value for the

other fragment. Then Y2 ~Yi will have a Normal distribution with mean zero and

standard deviation \fT~ oi . If Y\ =x i

r the probability that another X 2 will

differ from x x by more than k 6 is the probability that y 2 will differ from Y\

by more than (k+l/ 2 ) 0 , i.e.,:

For k=l

a a

2 $ (k+1/2 ) 0/(o

i VT)j .

a a .89401 0.0582.

However, if y^Xj+0/2, the probability that another x 2 will differ from xi by

more than k 0 is the probability that y 2 will be greater than y! +k0 or less

than y-j-tk+DO, i.e..

By expanding the model (and complicating the derivation) to account for the

difference between GE and early Corning, this value can be further reduced,

to about .086. Details are in appendix B.

14
a b

= $[-ke/(o iV^j] + $ [- (k+1) 6 / (

i

-x/2

-

) ]

.

Again for k=l

= $[-1.2627] + $[-2.5254]

= 0.1034 + 0.0058 = 0.1092.

In fact, « was calculated also for other intermediate cases, because the

dependence of a on yj-Xj is not smooth. The result was (for k=l)

a = 0.078.

These results for k=l and similar ones for k=0 and k=2 are tabulated in

table 4, and plotted in figure 7 as three points. It should be remembered

that these results were obtained using two optimistic assumptions; realistic

measurement errors and measurement resolution of 0>lxlO~ 4 will degrade this

performance

6.2.2 Better Resolution

Suppose that more precise RI data are obtained. It will be shown in this

section that under certain conditions, slightly improved values for a and 6 can be obtained. These results are presented in figure 7 and tables 5a-5d.

Whether the improved reliability is worth the added cost and time is a question forensic scientists will have to answer. Readers not interested in

the statistical derivations can refer to the figure and tables , and then skip

to section 6.3 without loss of continuity.

Assume that RI data is taken to five decimal places with the standard

deviation due to the measurement process, am , equaling 3.8xl0 -5

. The standard

deviation corresponding to the inherent variability within a headlight,

is 5.6xl0 -5

, as before (see table 3)

If a match is to be declared correctly, then referral fragment and

suspected source must actually be pieces from a single lens. In such a situation, let:

mr = number of locations measured on the referral fragment,

ms = number of locations measured on the suspected source,

nr = number of independent measurements at each point of the referral

fragment

n s number of independent measurements at each point of the

suspected source , and

a D = standard deviation of the difference |x 1 -x2

l of RI values for

two sets of measurements on one lens; that difference will

be normally distributed with a mean of zero. Then

o D

2 m n

r r

_1

msn s

J m

2

15
REFRACTIVE

INDEX:

m

r

=1, ms

=1, n

r

=1, n$

=lo

0=9.6

*

10

H31VW 3S1VJ V 30 AllUSVaOHd - d 33VH3AV

X

CD 'Oc

•H

<D>

•H

X>O

SiU

IK

<D

>1

XIw

<D

VIc

0)

4JX!

Cr> •H

i—

T3

fd0) X3 • W

0) 4J >

•H

+Jo

E

O

4J3

RJ 0)E

«nO

co

e H

P

4J•HW

c

<1) td fd N

•H <T3 •H C

fd id 3dH

>

•Hc

•H

«WO

•P •H

i—

•H

X3

(d

CD (X

0)p

3

Cr "H

16
Table 5a. Refractive index reliability

One location of referral piece measured one time.

One location of suspect piece measured one time.

o D = 9.57xl0 -5

a CxlO 5

6 16 28

0.001 31.5 0.166 0.230 0.209

0.004 27.6 0.151 0.205 0.187

0.008 25.4 0.142 0.190 0.174

0.010 24.7 0.139 0.185 0.170

0.020 22.3 0.128 0.168 0.155

0.040 19.7 0.115 0.150 0.138

0.050 18.8 0.110 0.143 0.132

0.060 18.0 0.106 0.138 0.127

0.080 16.8 0.100 0.129 0.119

0.10 15.7 0.0944 0.121 0.112

0.20 12.3 0.0748 0.0952 0.0884

0.40 8.0 0.0498 0.0629 0.0585

0.50 6.5 0.0401 0.0503 0.0469

0.60 5.0 0.0313 0.0390 0.0364

0.80 2.4 0.0152 0.0188 0.0176

Table 5b. Refractive index reliability

One location of referral piece measured four times.

Four locations of suspect piece measured four times.

o D = 6.61xl0' 5

a CxlO 5

B 1

e 2

8

0.001 21.8 0.125 0.165 0.152

0.004 19.0 0.112 0.145 0.134

0.008 17.5 0.104 0.134 0 . 124

0.010 17.0 0.101 0.131 0.121

0.020 15.4 0.0924 0.118 0.109

0.040 13.6 0.0824 0.105 0.0975

0.050 13.0 0.0788 0.100 0.0929

0.060 12.4 0.0757 0.0963 0.0894

0.080 11.6 0.0708 0.0898 0.0835

0.10 10.9 0.0666 0.0847 0.0787

0.20 8.5 0.0523 0.0662 0.0616

0.40 5.6 0.0346 0.0435 0.0405

0.50 4.5 0.0279 0.0349 0.0326

0.60 3.5 0.0216 0 . 0271 0.0253

0.80 1.7 0.0105 0.0132 0.0123

17
Table 5c. Refractive index reliability

Four locations of referral piece measured four times.

Four locations of suspect piece measured four times.

o D = 4 . 18x1

-5

a CxlO 5

B 1b 2

B

0.001 13.8 0.0834 0.106 0.0985

0 o 004 12.0 0.0734 0.0934 0.0867

0.008 11.1 0.0680 0.0861 0.0801

0.010 10.8 0.0661 0.0836 0.0778

0.020 9.7 0.0599 0.0758 0.0705

0.040 8.6 0.0531 0.0670 0.0624

0.050 8.2 0.0507 0.0640 0.0596

0.060 7.9 0.0487 0.0614 0.0572

0.080 7.4 0.0454 0.0570 0.0531

0.10 6.9 0.0427 0.0536 0.0500

0.20 5.4 0.0334 0.0419 0.0391

0.40 3.5 0.0220 0.0275 0.0257

0.50 2.8 0.0176 0.0221 0.0206

0.60 2.2 0.0137 0.0172 0.0160

0.80 1.1 0.0066 0.0083 0.0077

Table 5d. Refractive index

Four locations of referral piece

Eight locations of suspect piece

o D

= 3 .51x10“

: reliability

measured 10

measured 10

-5

times

times

a CxlO 5

B 1 02 B

0.001 11.5 0.0707 0.0896 0.0833

0.004 10.1 0.0622 0.0786 0.0731

0.008 9.3 0.0574 0.0725 0.0675

0.010 9.0 0.0558 0.0704 0.0655

0.020 8.2 0.0506 0.0637 0.0593

0.040 7.2 0.0448 0.0563 0.0525

0.050 6.9 0.0428 0.0538 0.0501

0.060 6.6 0.0411 0.0516 0.0481

0.080 6.1 0.0383 0.0480 0.0448

0.10 5.8 0.0359 0.0451 0.0420

0.20 4.5 0.0281 0.0352 0.0328

0.40 3.0 0.0185 0.0231 0.0216

0.50 2.4 0.0148 0.0185 0.0173

0.60 1.8 0.0115 0.0144 0.0134

0.80 0.9 0.00556 0.00696 0.0065

18
We next determine a criterion, C, which the difference |xj-x

2

| must not

exceed if the two pieces are to be declared matching. Assuming a Normally

distributed population, we do this by finding the value for z for which

l-Mz)=a/2. where, as before, 4>(z) is the area under the Normal density curve

from — oo to z. For example, if a is taken to be 0.05, z=+1.96. The criterion

C is then equal to zo D>

o D can be reduced by making more measurements at more locations on both

the referral and suspect fragments. However, as can be seen from table 6,

there is a limit to this reduction.

Table 6. Dependence of o D on the number of measurements

a. = 5.6xl0 -5

= 3 . 8xl0 -5

l m

RI measurements taken to fifth decimal place

m

r ms nr ns

o Dxl0 5

1 1 1 1 9.57

1 4 4 4 6.61

4 4 4 4 4.18

4 8 5 5 3.58

4 8 10 10 3.51

There will be a false match if a match is declared between the referral

fragment and a fragment from any other lens. For simplicity, consider first

only the late Corning subpopulation. Its mean RI is 1.47476. There will be

more lenses with RI's close to that value, say within ±lxlO~ 5

, than will be

chat close to any other value. Hence 6 will be a maximum if the referral

fragment RI should measure 1.47476.

To calculate P exactly , an integration must be made over the distribution

of late Corning lenses, but approximations correct to two decimal places can

be computed by calculating the probability that a randomly selected lens from

the late Corning population will have a true mean RI within C of the true

mean RI of the referral fragment. For a fragment with mean RI equal to the population mean, this probability is the two-sided value $ (C/a p

) -$ (~C/a n ) =

2$ (C/ Op) -1 = . B* say. Since the average height of a Normal density function

is V V2 times the maximum height (at the mean) , we multiply 6* by l/\jr2 ~ to

allow for RI's different from the mean.

19
Account is taken of the fact that there are three subpopulations in the

same way as in section 6 . 2. 1.1. If the referral fragment happens to be from

a late Corning lens, only one-third of all the lenses on the road will have a chance of false acceptance so that */ Ox/T) . Or if the referral fragment

happens to be from an early Corning or GE lens, only two-thirds of all the

lenses on the road will have a chance of false acceptance so that B 2 = 2B 2 */

(3V2) . The first situation will occur about one-third of the time, the second

about two-thirds of the time. Then, for the entire population, the average

is

B = j BjVoVT) + |VTb 2 */3.

Tables 5a through 5d show a and 6 values , together with corresponding values

of C, for the four cases plotted in figure 7 .* Table 7 summarizes the steps

used to calculate B for a specified a .

6.3 Position Effect

To check for the possibility that the process of molding the lens

configuration might affect the RI variability from point to point within the

lenses, RI's of corners of 17 rectangles from two different lenses were

measured by one operator. The values were analyzed by angular position and

by their radial distance from the lens center. No correlation was found for

either set and it was concluded that the position of a specimen within the

lens has no significant effect on its RI value.

Table 7. Summary of steps to find 6 for given a

RI data measured to fifth decimal place.

Refer to text for definitions of symbols.

1. Find z such that 1-<1> (z) - a/2

2 . C = z a D

3. = 2*(C/o 1 )-l

B 2

* = 2$ (C/a 2

) -1

4. = Q 1 */3VJ

Z 2 = 2 B 2 */3 y/2

r 1 2 „ 5. B - 3

B]_ + 3

B 2

As in section 6.2.1, differences between GE and early Corning lenses allow

a slight reduction in the 3 values calculated here. Details are in appendix B.

20
6.4

Annealing

Preliminary results of RI measurements on the 71 lenses showed a spread

of about 20x10

5 (o L=6 . 8x10“ 5

) in RI values across any single lens. It was

hoped that heating the specimens to about 500 °C followed by slow cooling

would reduce this spread, presumably by equalizing internal stresses. A

group of pieces from 21 lenses selected to cover the range of spreads found

earlier were subjected to such annealing. For some pieces there were changes

in the fifth decimal place, but no statistically significant improvement was

found. The presence of striations with RI differing from the rest of the

piece may account for these results.

Pieces from 11 lenses in this group were annealed again at a higher

temperature for a longer time. The RI values were markedly reduced, but with

increase of spread. Examination with an electron microscope indicated there

had been a separation into silica-rich and boron-rich phases. In view of the

unpredictability of annealing effects, the treatment is not recommended for

characterization studies of headlamp glass.

6.5

Dispersion

Because light of different colors (wavelengths) travels at different

velocities in a transparent medium, the refractive index n will be found to

have lower values for the longer wavelengths in the red region of the

spectrum than for the shorter wavelengths in the blue. The effect is called

dispersion. It is known that various types of glass differ significantly in

this regard, and measurements made with red, yellow, and blue light will

serve to distinguish headlamp glass from window glass, bottle glass, or

optical glass.

Dispersion measurements made at NBS were based on illumination sources

preferred for their spectral purity: cadmium red C' (0.6438 m m) , sodium

yellow doublet D (0.5893 Mm), and cadmium blue F' (0.4800 pm). Dispersion is

often expressed in terms of differences in refractive index values measured

at several wavelengths. In this study, these RI differences did not vary

appreciably from headlight to headlight. More specifically, at least 18

measurements were made of both n^ and n^ ' for each of 12 different lenses.

The average range of measurements within a lens for C' was 20x10“ 5

, and for

D, 17xl0“ 5

; the range over all 12 lenses was 468xl0“ 5 and 464xl0-5

respectively, allowing some discrimination between lenses. On the other hand,

the average range within a lens of the difference nc _nD was 10xl0" 5

; the

range over all lenses was only 22xl0~ 5

. Thus the difference nc -nD varies

within a lens by an amount that is almost half its total population

variation. Therefore, dispersion is not a sensitive parameter for either

classifying or individualizing auto headlight glasses. That is, dispersion

cannot be used effectively to distinguish one auto headlight from another.

The measured RI differences were typically 182xl0“ 5 for n(D-C'), 734xl0" 5 for n (F ' -C '

, and 553xl0“ 5 for n(F'-D). The Abbe number, defined as

v =

is about 65.

6.6

Temperature Coefficient of Refractive Index and Thermal

Coefficient of Expansion

The temperature coefficient of refractive index and the thermal

coefficient of expansion must be known when using a ''hot stage" method of

measuring refractive index and density. It is known that the RI of

borosilicate glass changes with temperature, partly because of the chance in

density, and partly because of a shift in the ultraviolet absorption band

which is characteristic of the chemical composition.

21
The NBS automatic fringe-recording interferograph developed by Saunders

[11] can measure simultaneously both dn/dT and the thermal coefficient of

expansion. For one piece of the headlamp samples, the latter was found to be

3.88x10~6/°C over a broad range of temperature, and dn/dT was found to be

5.3x10~ 6 /°C at 0.5893 ym between 20° and 80°C. This positive coefficient

disagrees with the estimated -6 . 5xlO~6/°C reported for 0.589 ym between 20

and 40°C by Ojena and DeForest [8]

7. DENSITY MEASUREMENTS

In addition to RI , another physical property widely used to characterize

glass is its density. The NBS refractive index standard reference glass No.

1820 has a density of 2.292+0.001 g/cm3 at 24 °C, 50 percent relative

humidity, and a pressure of 99,442 Pa (746 mm Hg)

That there is strong correlation between density and RI , both at room

temperature and at annealing temperatures, was indicated for optical glass

by Tool, Tilton and Saunders [ 12]

Density was one of the properties measured

by Nelson [13] in an individualization study of 50 Lucas 700 headlamp

fragments. He obtained a standard deviation of 0.001 g/cm 3 for six repeated

determinations, estimating an accuracy of +0.002 g/cm 3

. However, when two

pieces had nearly the same density he made comparative measurements (with a sensitivity of 0.0005 g/cm3 ), which succeeded in distinguishing all but two

pairs out of the 50.

Figure 8. Sink-float density apparatus.

22
The density measurements for the NBS study were obtained by the

sink/float method. The density liquid was made by combining STetrabromethane and Isopropyl Salicylate acid, in proportions designed to

match the density of the sample at about 20° C. A mixture of 64 mL of STetrabromethane and 3.86 mL of Isopropyl Salicylate acid was found suitable.

The density liquid was calibrated at higher temperatures with a series of

density standards, before and during the actual test runs.

The density liquid was held in a U-tube as shown in figure 8; the U-tube,

in turn, was mounted in a temperature-controlled water bath. The temperature

of the liquid was monitored by a resistance thermometer which was held in one

arm of the U-tube. The sample was held in a wire cage in the other arm of

the U-tube and observed for change in position via a traveling cathetometer

The test procedure was to raise the temperature of the bath at a rate of

approximately 0.0035 ° C/min until the sample changed from a floating to a sinking condition.

Two pieces of glass from each of 12 headlamp lenses were measured,

covering all three subpopulations (late Corning, early Corning, and GE)

Lenses were selected having a range of standard deviations for RI ; these had

been subjected to various amounts of annealing, and covered the range of RI

values found. These were arranged in an appropriate order such that any

effects due to time (e.g., instrument drift) would not be mixed with effects

due to manufacturer, annealing, etc. Values of density and RI are shown in

table 8

Table 8. Data on first 24 density measurements and four repeats.

Order of

measurement Lens Piece Mfr . a Refractive

index

Density/repeat

g/cm^

1 11 a 1 1.47498 2.25226/2. 25448

2 151 E 2 545 5264

3 12 D 3 147 2952/ 2918

4 129 a 2 664 6358

5 27 J 3 264 3689

6 149 e 1 665 6606

7 5 E 1 733 6844

8 3 D 3 354 3884

9 104 U 2 604 5788

10 8 a 3 249 3438

11 39 J 1 630 6189

12 145 E 2 463 5233

13 145 R 2 469 5245

14 39 L 1 613 6073

15 8 A 3 240 3381

16 104 e 2 610 5761

17 3 L 3 355 3884

18 5 V 1 724 6841

19 149 A 1 658 6584

20 27 P 3 260 3720

21 129 u 2 673 6384

22 12 J 3 155 2746/ 2705

23 151 L 2 557 5378

24 11 6 1 517 5507/ 5456

Note: Mfr . 1 = General Electric

Mfr. 2 = Early Corning

Mfr . 3 = Late Corning

23
8. ANALYSIS OF DENSITY DATA

Various plots and analyses of the data of table 8 were performed,

revealing no discernible instrument drift, but casting suspicion on a few of

the values. Accordingly, four measurements were repeated. Based upon the

estimated measurement-error s.d. of 15xl0~ 5 g/cm3 for a single measurement,

three of these repeat measurements agreed (at the 5% significance level) with

the initial readings. The repeat value of the measurement labeled #1 was

significantly different (at the 0.02% significance level) from the initial

value; the remeasured value (2.25448) was used in place of the original value

(2.25226) .

The correlation between RI and density was found to be 0.99. This high

correlation obviated the necessity for an independent population study of

density, since density values for the purpose of determining population

parameters can be predicted quite adequately from RI values.

Because of this high correlation, forensic scientists should not consider

refractive index and density measurements as independent types of physical

evidence when characterizing auto headlight glass. That is, assuming for the

moment that RI and density measurements have comparable inherent

reliabilities, m RI measurements and n density measurements on a single lens

are equivalent to (m+n) of either refractive index or density measurements.

The regression equation is

Density Value = -8 .09+7 . Olx (RI Value).

For classification of headlamp glasses, density and refractive index are

equivalent

For individualization, however, density could be a more useful property

than RI if the inhomogeneity of the lens, as represented by o^ , was less for

density; if the standard deviation of the measurement error (% was smaller;

or if readings could be taken easily to more decimal places. To estimate the

standard deviation for density measurements across a lens, seven pieces of

glass from each of the four lenses were measured to the nearest 0.3xl0 -5. The

resulting estimate of o L was 26.7xl0~ 5

, with 90 percent confidence limits at

33.4xl0“ 5 and 20.0xl0“ 5

. Also, there were five repeat measurements made at

different times, from which the measurement error component was estimated

to be 15x10" 5

. Since (26. 7) 2 -(15) 2 - (22) 2

, an estimate of the standard

deviation ( ) due to inhomogeneity of a lens is 22xl0“5

. (This discussion

parallels the discussion for RI in section 6.2.)

To compare fairly the relative sizes of the lens standard deviations

corresponding to refractive index and density, the RI standard deviation

should be multiplied by 7.01 (because it is the ratio °l/°P that counts, and

the population standard deviation is 7.01 times larger for density than for

RI ; see the regression equation above). This multiplication and comparison

is shown in table 9. It will be seen that the standard deviation due to

inhomogeneity of density is about 55 percent of the product 7.01 x the

standard deviation for RI ; the same ratio holds for the measurement error

standard deviation. Thus, it appears worthwhile to apply the reliability

analysis of section 6.2 to these data for density, coupled with population

estimates of o j =7 . 01x30xl0"5 for late Corning glass, and o

2 =7 . 01x48x10"^ for

the other subpopulation

24
Table 9. Comparisons of refractive index and density standard deviations

Refractive

index at

0.58926 um

RI value

x7 . 01

Density

measurement

g/cnr

of measurements at

across a lens, o L

-5 -5 -5

Est. std. dev.

random points

6.8x10 48x10 26.7x10

Est. std. dev.

error, o m

of measurement 3.8xl0

-5

-5

27xl0" 5

-5

15xl0~ 5

-5

Est. std. dev.

in a lens,

due to inhomogeneity 5.6x10 39x10 22x10

For one density measurement of both the hypothetical referral fragment

and its suspected source, we may write as before:

° D

2 =2(22xl(T 5

) 2 +2 (15x10-5

) 2

= (37 . 66xl0-5

) 2

.

Computed a and 8 values —comparable with those in table 5a —are tabulated in

table 10 and plotted in figure 7. There appears to be significant improvement

in the reliability of density measurements compared to the reliability of

corresponding refractive index measurements.

9. CONCLUSIONS AND UPDATE

This section presents conclusions in terms of the defined average error

probabilities a (the chance that the lens which does in fact match the

referral piece will falsely be declared nonmatching) and 6 (the chance that

a randomly-selected, nonmatching lens will falsely be declared matching).

Either of these two error probabilities can be decreased, at the expense of

increasing the other, by changing the criterion for a match. Furthermore,

both can be decreased (up to a point) by taking more measurements on more

pieces of glass; however, since the referral piece is often small, we have

not considered multiple referral pieces.

The top curve in figure 7 represents the available (a, 6) -pairs using RI

with one piece from the suspect lens and one measurement on it (and one

measurement on the referral piece) , as of the time the analyses were

originally done. Representative (a, 6) values from this curve are (.001,. 21);

(.025 , .15); (0.5;. 13); (.11, .11); and (.48, .05). It is seen that decreasing 8 costs dearly in terms of a. Changes due to more samples and/or measurements,

to using density instead of RI , and to changes in the basic population of

lenses on the road, are most conveniently expressed in terms of factors which

modify 8 for any given a (i.e., which raise or lower the top curve in figure

7, since the scales are logarithmic) . Such a representation is close to

exact, as long as both errors are below (say) 50 percent.

25
Table 10. Density reliability.

One location of referral piece measured one time.

One location of suspect piece measured one time.

o D = 37.66x10 5 g/cm3

a CxlO 5 (g/cm3

)

6 i

6 28

0.001 123.9 0.105 0.135 0.125

0.004 108.4 0.0928 0.119 0.110

0.008 99.9 0.0861 0.110 0.102

0.010 97.0 0.0838 0.107 0.0991

0.020 87.6 0.0762 0.0969 0.0900

0.040 77.4 0.0677 0.0857 0.0797

0.050 73.8 0.0647 0.0819 0.0762

0.060 70.8 0.0622 0.0786 0.0731

0.080 65.9 0.0580 0.0732 0.0681

0.10 62.0 0.0546 0.0689 0.0641

0.20 48.3 0.0428 0.0538 0.0501

0.40 31.7 0.0282 0.0354 0.0354

0.50 25.4 0.0226 0.0284 0.0265

0.60 19.7 0.0176 0.0220 0.0205

0.80 9.5 0.00851 0.0106 0.00990

Taking four measurements on each of four pieces from the suspect lens and

on the referral piece results in decreasing 6 by a factor 0.71. Using density

instead of RI decreases 6 by a factor of 0.55. Finally, if the variation

within a lens and the variation across a subpopulation both remain at the

values observed in this study, but the subpopulations are shifted till they

coincide (a conservative assumption) , then 6 -values are increased by at most

a factor of 1.8. These factors can be applied sequentially. Thus, since it

happens that 0.55 x 1.8 = 1.0, the top two curves in figure 7 represent not

only the (a, 8) pairs available in 1975 , using RI , but also (upper bounds on)

the values available today using density.

Finally, it should be noted that conclusions regarding the reliability of

refractive index and density measurements to characterize auto headlight

glass should not be made on the basis of measurements of % at NBS . may

be quite different for measurements made in forensic laboratories under the

pressures of producing evidence for actual criminal investigations.

Meaningful values of om for this purpose, for both refractive index and

density, can best be measured in forensic laboratory proficiency tests. The

omvalues computed in this study, again for both refractive index and density,

are of interest as "best case" values. Larger values of o m , which are

probably encountered in real criminal investigations, will degrade the

reliability that can be expected.

26
APPENDIX A—"TRIAL BY MATHEMATICS

This appendix quotes from a paper by Laurence H. Tribe, "Trial by

Mathematics: Precision and Retrial in the Legal Process" [14] concerning the

wisdom of the use of statistical methods in the trial process. The first two

quotations are representative of the concerns expressed: "...the very system

that surrounds mathematical arguments--the relative obscurity that makes them

at once impenetrable by the layman and impressive to him--creates a continuing risk that he will give such arguments a credence they may not

deserve and a weight they cannot logically claim" [15] . "...in at least some

contexts, permitting any use of certain mathematical methods entails a sufficiently high risk of misuse sufficiently costly to avoid, that it would

be irrational not to take such misuse into account when deciding whether to

permit the methods to be employed at all." [16] . Continuing to quote Tribe,

"With the possible exception ... of using evidence as to frequencies in order

to negate a misleading impression of unequalness that expert opinion might

otherwise convey, I think it fair to say that the costs of attempting to

integrate mathematics into the factfinding process of a legal trial outweigh

the benefits" [17] . The exception mentioned here is the use to which the

statistics used in this report are applied. In a footnote, Tribe writes,

"...the most common defensive use (of mathematical methods) would probably be

the translation into quantitative form of an expert's damaging opinion that a certain physical trace or combination of traces must 'almost certainly' have

been left by the accused. ...Courts otherwise hostile to probabilistic proof

have at times allowed such quantification of expert opinion about trace

evidence even at the prosecutor's initiation. ...And, once such

quantification has been initiated by the defense, the case for allowing the

prosecution to rebut in mathematical terms becomes quite persuasive." [18]

27

APPENDIX B—ALLOWANCE FOR DIFFERENCES BETWEEN

GENERAL ELECTRIC AND EARLY CORNING LENSES

The derivations in the body of this report were performed using a model

which said that the distributions for GE lenses and for early Corning lenses

were identical. Actually, although there is a good deal of overlap, the two

means are significantly different. (The standard deviations are not

significantly different.) Thus the number of lenses that are candidates for

false match is smaller than assumed. To account for this fact, we need to

take a more complicated approach than that used before.

Let x be the RI of the referral piece. x is a random variable with a Normal distribution Fj , with given mean Mi and variance o

2

. Let y 2 represent

the mean of another (overlapping) distribution F2 with the same variance. For

a given value of x, the probability of drawing a matching piece from F x is

Fj (x+c) -F j (x-c) , where c is the criterion for a match. We can replace this

expression by 2cfl (x) , where (x) is the probability density function, since

c is small with respect to o. Similarly, 2cf2 (x) is the probability that a random piece from F2 will match. Since the two subpopulations are each

assumed to contain one-third of the existing lenses, the total probability of

drawing a (false) match is l/3(2cf 1 (x) ) +1/3 (2cf2 (x) )

we must average this

expression over the possible values of x. Thus we have

x-y ! Substituting t = , we obtain

0

29
“ 1/2 where ( t ) = (

tt ) exp(-t2 /2) is the standardized Normal density function

„ 2 c* With y! = p 2 ' we 9et B 2 = —— . 3\/V

Thus the 6

2 values we had should be multiplied by a factor

1+exp- .79 _ = 0.727.

Now does not change, so the change in B

2 affects 6 as follows:

1

B - 3

6 1+ e

2

which becomes

8 = jBj + J

(* 727 B 2

)

4 Since $2 = j

(approximately) , B is changed from

2 / 4

3

B i + t (3 ^ 1

to

1 2 4 - B, + - (.727) — B 1 . 3

1 3 3

Thus the correction factor to be applied to the 6 values already calculated

is

" 1 2 , 4

"

’ 1 2 / 4\"

2 +3

( .727) j _ 3 +

3 ( 3/_ = 0.80

30
APPENDIX C —REFERENCES

[ 1] Greene, R. S.; Burd, D. Q. Headlight glass as evidence. J. Crim.

Law, Criminol. Police Sci. 40: 85; 1949.

[2] Allen, R. M. Practical refractometry by means of the microscope.

1962. Available from Cargille Laboratories, Minneapolis, MN 55440.

[3] Saylor, C. P. Accuracy of microscopical methods for determining

refractive index by immersion. J. Res. Nat. Bur. Stand. (U.S.). 15:

277; 1935.

[4] Faick, C. A.; Foronoff, B. A precision apparatus for the rapid

determination of indices of refraction and dispersion by immersion.

J. Res. Nat. Bur. Stand. (U.S.). 32: 67; 1944.

[5] Dabbs, M. D. G.; Pearson, E. F. The hot stage microscope. Central

Research Establishment Report No. 26; 1969. Available from the Home

Office, Central Research Establishment, Reading, Berkshire, England,

R974PN.

[6]

Dixon, B. M. Use of the Mettler FP-2 for RI determinations. J. Can.

Soc . Forensic Sci. 9: 115; 1970 .

[7] Ojena, S. M.; DeForest, P. R. Precise refractive index determinations

by the immersion method using phase contrast microscopy and the

Mettler hot stage. J. Forensic Sci. 17: 315; 1972.

[8] Ojena, S. M.; DeForest, P. R. A study of the refractive index

variations within and between sealed beam headlights using a precise

method. J. Forensic Sci. 17: 409; 1972.

[9] McCrone, W. C. Microscopical characterization of glass fragments. J.

Assoc. Off. Anal. Chem . 55: 834; 1972.

[10] McCrone, W. C. Collaborative study of the microscopical

characterization of glass fragments. J. Assoc. Off. Anal. Chem. 56:

1223; 1973.

[11] Saunders, J. B. An apparatus for photographing interference

phenomena. J. Res. Nat. Bur. Stand. (U.S.). 35: 157; 1945.

[12] Tool, A. Q.; Tilton, H. W.; Saunders, J. B. Changes caused in the

refractivity and density of glass by annealing. J. Res. Nat. Bur.

Stand. (U.S.). 38: 519; 1947.

[13]

Nelson, D. F. The identification of Lucas 700 headlamp glass

fragments by their physical properties. Analyst. 84(999): 388-392;

1959 .

[14] Tribe, L

process

. H.

Harv

[15] Ibid , P- 1334 .

[16] Ibid

P. 1331.

[17] Ibid

P- 1377 .

[18 ] Ibid

P. 1377 .

31
NBS°114A (rev j-eo

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

1. PUBLICATION OR

REPORT NO.

NBSIR 81-2286

2. Performing Organ. Report NoJ 3. Publication Date October 1981

The Characterization of Auto Headlight Glass by

Refractive Index and Density

5. AUTHOR(S)

Law Enforcement Standards Laboratory

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7 . Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

8

.

Type of Report & Period Covered

Final

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State . ZIP)

National Institute of Justice

U.S. Department of Justice

Washington, DC 20531

10.

SUPPLEMENTARY NOTES

3] Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnifi cant bibliography or literature survey, mention it here) By measurement of some physical property of headlight glass

fragments found at the scene of an auto accident, forensic scientists

have sometimes found it possible to infer that the glass was molded by

a specific manufacturer, or even that it came from a broken headlamp

on a specific car. The refractive index (RI) and density of the

representative specimens are the most common parameters of interest to

forensic scientists. In this study, performed in 1975, automotive

headlights were obtained from several sources , From RI and density

measurements, it is concluded that partial classification (by manufacturer and/or age) could be reliably achieved. There is less likelihood

that an unknown fragment can be reliably individualized to a specific

headlamp lens because of the inhomogeneity within each lens . The

probability is not increased appreciably by taking repeated measurements , by annealing the specimens, by measuring RI at several

wavelengths, or by measuring both RI apd density.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

auto headlight glass; classification; density; forensic science;

individualization; population statistics; refractive index

13. AVAILABILITY

[X] Unlimited

| | For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

[X] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

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15. Price

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