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Science and Justice 47 (2007) 9–1

An investigation into the use of calculating the first derivative of absorbancespectra as a tool for forensic fibre analysis

K. Wiggins a,1, R. Palmer b,⁎, W. Hutchinson b, P. Drummond a

a The Forensic Science Service, 109 Lambeth Road, London, SE1 7LP, United Kingdomb The Forensic Science Service, Hinchingbrooke Park, Huntingdon, Cambridgeshire, PE29 6NU, United Kingdom

Received 2 November 2005; accepted 21 November 2006

Abstract

A range of fibre samples was measured using J&M MSP400 and J&M MSP800 microspectrophotometers across the visible and UV/visiblewavelength ranges respectively. The first derivative of the absorbance spectra was then calculated and studied. When the absorbance spectraproduced for some samples were broad and featureless, the first derivative spectra provided more points of comparison that facilitateddiscrimination. For many of the samples, calculating the first derivative did not result in any additional discrimination due to the high number ofpoints of comparison present in the absorbance spectra. However, for the samples that exhibited a high level of intra-sample colour variation (e.g.through uneven dye uptake common in cotton and wool, etc.), which was evident in the absorbance spectra, the associated first derivative spectrahighlighted this variation between the fibres and could potentially have resulted in false exclusions. The results show that whilst calculating firstderivative can be a useful aid in the comparison of spectra, a high degree of caution is required when applying this method to fibres which exhibita large intra-sample variation in colour.© 2007 Forensic Science Society. Published by Elsevier Ireland Ltd. All rights reserved.

Keywords: First derivative; Fibres; Microspectrophotometry; Spectra; Comparison

1. Introduction

Since microspectrophotometry has been used as part of theanalysis of coloured textile fibres in forensic fibre examination,the results have been generated in the form of transmission andabsorbance spectra. Comparison of spectra routinely involvesoverlaying these to determine whether they match with respectto peak positions and general spectral shape.

Absorbance spectra that have multiple points of identifica-tion, comprising peaks, troughs and shoulders, can besuccessfully compared using this method. However, when anabsorbance spectrum has little detail (e.g. only a single broadpeak such as that obtained from an almost opaque fibre), thismethod is more problematic and less discriminating.

This study aimed to identify whether calculating the firstderivative of absorbance spectra could provide a means of

⁎ Corresponding author.E-mail address: ray.palmer@fss.pnn.police.uk (R. Palmer).

1 Retired January 2006.

1355-0306/$ - see front matter © 2007 Forensic Science Society. Published by Elsdoi:10.1016/j.scijus.2006.11.001

additional discrimination for fibre comparison and to determineunder what circumstances it could bemost effectively employed.

Derivative spectroscopy provides a means for presentingspectral data in a potentially more useful form than the zeroorder, untreated data. The technique has been used for manyyears in branches of analytical spectroscopy such as finding theend point for titration plots. Derivative spectra are usuallyobtained by differentiating the recorded signal with respect towavelength as the spectrum is scanned. First, second and higherderivatives can now easily be generated using the softwaresupplied with currently available instrumentation.

Analytical applications of derivative spectroscopy arenumerous and generally owe their popularity to the apparenthigher resolution of the differential data compared to theoriginal spectrum. This can result in broad, apparentlyfeatureless peaks in the original spectrum being resolved toshow distinct, measurable components. To date this techniquehas not been widely employed in the field of forensic fibreanalysis and comparison and this is reflected in the limitedamount of published data [1,2].

evier Ireland Ltd. All rights reserved.

Fig. 1. Absorbance spectrum (left) and associated first derivative spectrum (right) of a red acrylic fibre.

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Fig. 1 shows a visible wavelength range microspectro-photometry spectrum measured from a red acrylic fibre. Theoriginal absorbance plotted against wavelength spectrum showsa peak maximum at around 535 nm. This is the point at whichthere is no change in the peak gradient, and as such, this pointappears at zero on the first derivative plot. Also, a subtleshoulder on the leading edge of the original peak at around450 nm is displayed as a more distinctive feature on the firstderivative plot, thus providing an aid to comparison.

Various mathematical procedures may be employed todifferentiate spectral data. When data is recorded at evenlyspaced intervals along the wavelength (λ), or other x-axis, thesimplest method to produce the first derivative spectrum is bycalculating the difference between two points, i and i+1.

ByBk

¼ yiþ1 � yikiþ1 � ki

where y represents the spectral intensity.A first derivative spectrum is produced when the results of

such a calculation are plotted. This can emphasise differencesbetween spectra, but will also enhance any noise present in theoriginal spectrum. Subsequently, this can result in a noisy firstderivative spectrum which will be difficult to interpret. Due tothis observation, a polynomial line of best fit is plotted over aselected number of data points, to smooth the data before it isdifferentiated. This process is applied to all the data in steps untilthe entire spectrum has been processed. This was first used bySavitzky and Golay [3] based on the following equation:

ByBk

¼ 110Dk

�2yi�2 � yi�1 þ yiþ1 þ 2yiþ2ð Þ

2. Experimental

2.1. Samples

A range of fibre types and colours reflecting those commonlyencountered in casework, were used in this study.

Man-made fibre samples

• Red acrylic• Orange polyester,• Black polyester,• Blue nylon,• Blue “tigertail” acrylic,• Blue polyester.

Natural fibre samples

• Dark grey lambswool,• Yellow cashmere,• Black cotton,• Pink wool.

Dye batch fibre samples

• Brown acrylic (10 batches),• Red acrylic (7 batches),• Red acrylic (9 batches),• Navy blue acrylic (10 batches).

2.2. Equipment

The microspectrophotometry was performed using twodifferent instruments, both using Spectralys v1.82 software.One instrument – the J&M MSP400 microspectrophotometer –measured across the visible wavelength range (380–710 nm); thesecond instrument – the J&M MSP800 microspectrophoto-meter –measured across the UV/Visible wavelength range (250–710 nm). All measuring parameters used are given in Table 1.

3. Method

The Spectralys v1.82 software has the capability to calcu-late the first (and second) derivative of spectra (absorbance ortransmittance) using the Savitzky–Golay smoothing algorithm

Table 1Measuring parameters used for microspectrophotometry

Instrument Visible range UV/visible range

J&M MSP400microspectrophotometer

J&M MSP800microspectrophotometer a

J&M MSP800microspectrophotometer

Wavelength range (nm) 380–710 380–710 380–710 250–710Integration time (ms) 50 50 50 120Number of accumulations 1 10 b 1 10a The J&MMSP800 microspectrophotometer was used in the visible wavelength range for the preliminary consistency check detailed in “Section One—Man-made

Fibres”.b Used for the dye batch fibre samples.

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[3], with the option of 5, 7, 9, 11, 13, 15, 17, 19 or 21 smoothingpoints. A series of calculations were carried out using thedifferent smoothing point values. Absorbance spectra were usedfor these calculations which contained minute details such asslight shoulders; this allowed determination of whether thesewould be “lost” if higher numbers of smoothing points wereused. These calculations showed that an acceptable level ofsmoothing, with no apparent loss of spectral detail, wasproduced using a high number of smoothing points with astep size of 1 nm. On the basis of these experiments 21 pointswere chosen as the optimum smoothing parameter for thesecalculations, and was therefore used throughout the study.Although previous literature [2] discusses the risks of using ahigh number of smoothing points, this is when a step size of2.5 nm is employed. The use of a step size of 1 nm thereforeappears to solve this problem.

The main experiment comprised of three sections.

3.1. Section One—man-made fibres

The aim of Section One was to test the technique using theleast problematic samples from a casework perspective. Ingeneral, the absorbance spectra produced for a sample of man-made fibres exhibit minimal intra-sample variation becausethese are usually homogenous in terms of dye uptake andtherefore colour within a single sample. Because absorbancespectra produced from these fibres were expected to showminimal variation, it was anticipated that this would be reflectedin the associated first derivative spectra.

Following the Forensic Science Service (FSS) microspec-trophotometry protocol, five fibres from each sample weremeasured and output on a single set of absorbance plottedagainst wavelength axes. The five fibres were selected toencompass the observed range of variation within the sample,i.e. the palest through to the darkest fibres.

In order to demonstrate whether both instruments generatedsimilar results in the visible wavelength range, a consistencycheck was performed by comparing spectra generated by eachinstrument, using the tungsten light source, from the samefibres.

3.2. Section Two—natural fibres

As already stated, natural fibres have a much higher level ofintra-sample variation than man-made fibres, which influences

the uptake and retention of dye. The variation in colour that thiscauses within a sample is reflected in the associated absorbancespectra. The purpose of this section of the study was todetermine if the higher levels of intra-sample variation observedin the absorbance spectra (with respect to absorbance level andminor spectral detail) would be reflected in the resultant firstderivative spectra.

Ten fibres were selected to encompass the observed range ofvariation within each sample, i.e. the palest through to thedarkest fibres.

3.3. Section Three—dye batch fibre samples

The aim of Section Three was to determine to what degreecalculating the first derivative allowed differentiation betweensamples with very similar absorbance spectra [4,5]. Thesamples used for this section of the study consisted of betweenseven and ten dye batches of the same fibre type. Some of thesets of samples had slight differences in their absorbancespectra; it was anticipated that this would cause slightdifferences in the first derivative spectra. ‘Dye batch variation’is a phenomenon often encountered in casework [4–6], andone of the causes is that components of the dye ‘recipe’ mayhave been changed slightly from batch to batch duringproduction.

All of the dye batch fibre samples were acrylic and thereforefive fibres from each batch were measured.

4. Results

4.1. Section One—man-made fibres

4.1.1. Visible wavelength rangeThe consistency check performed to compare the visible

range output from the two instruments produced someinteresting results.

BLACK POLYESTER: Fig. 2 shows that the 420–470 nmregion of the absorbance spectra had extremely differentgradients when the two sets were compared; a differencewhich was evident in the associated first derivative spectra. Thisregion in the two sets of first derivative spectra is approximatelythe same shape, but the MSP400 spectra cross the 0.00 Abs/nmline (which depicts an extreme of gradient-in this case a peakand a trough), whereas the MSP800 results do not (thusshowing no gradient extremes, i.e. no peaks or troughs).

Fig. 2. Black polyester fibres measured on MSP400 and MSP800, with the associated first derivative spectra.

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This difference between the two sets of results can beattributed to the different models of instrument and thisconclusion is based on personal experience. In general practiceresults produced on different models of instrument, particularly

with different software packages, should not be compared. Thisis true when comparing standard absorbance spectra and firstderivative spectra. In the FSS, where the software packages areidentical, spectra produced on the J&M MSP400 are still not

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compared with those obtained from the J&M MSP800.However, since the instruments in this study were used fordifferent purposes (i.e. one to measure in the visible wavelengthrange and the other for the UV/visible wavelength range), thisobservation was not considered to be a problem.

RED ACRYLIC: The two sets of absorbance spectramatched and the associated first derivative spectra were withinrange of each other.

BLUE NYLON: The two sets of absorbance spectra differedslightly with regard to the gradient of the spectra in the 400 nmregion. This difference could be seen in the first derivativespectra.

BLUE POLYESTER: Differences were seen in the lowerregion of the spectra (380–410 nm) between both the sets ofabsorbance spectra and first derivative spectra produced on thetwo instruments.

ORANGE POLYESTER: The two sets of absorbance andfirst derivative spectra matched.

BLUE “TIGERTAIL” ACRYLIC: The two sets of absor-bance spectra matched. The first derivative spectra, however,clearly demonstrated one of the risks of calculating the firstderivative.

Fig. 3 shows the absorbance spectra and associated firstderivative spectra for this “tigertail” sample. Of the fivefibres measured on the MSP400, two were pale and threewere dark. The first derivative spectra for these fibres showtwo distinct shapes. The five fibres measured on the MSP800graduate between the palest and the darkest fibres. Theassociated first derivative spectra also graduate between thetwo extremes.

When comparing the absorbance spectra, the five fibresin each set match each other (although they represent arange of levels of dye uptake). When the first derivativespectra are examined, those produced on the MSP400 maysuggest that there are two different populations of fibres withinthe sample — even though this is not the case. The resultsproduced on the MSP800 clearly show that the gradients of themain peaks change as the absorbance values increase — thusaltering the first derivative spectra. The progression of thischange can clearly be seen when the graduated succession ofpale to dark fibres is measured.

If the control set of fibres only included one of the extremes,i.e. pale or dark fibres, and the recovered fibre happened to be atthe other extreme, the absorbance spectra would be quite similarto each other (it is unlikely that they would differ enough tosuggest that they did not match). However, and as these resultsshow, the first derivative spectra could differ enormously. Thisdemonstrates that if the spectral comparison of the firstderivative results are not considered alongside the originalabsorbance spectra, this could result in a fibre being wronglyexcluded as a match.

4.1.2. UV/Visible Wavelength RangeORANGE POLYESTER, BLUE POLYESTER AND

BLACK POLYESTER: When measured in the UV wave-length range, polyester fibres absorb all light below 300 nm(the same is true for wool fibres). This results in a total

absorbance peak in this region of the spectrum. When the firstderivative is calculated, this peak then equates into an extremetrough (Fig. 4).

This means only a small section of the absorbance spectrumfor wool and polyester fibres in the UV wavelength range (300–380 nm) is potentially available for obtaining extra informationthrough UV microspectrophotometry. This is also true, there-fore, for the associated first derivative spectra.

BLUE NYLON, RED ACRYLIC, BLUE “TIGERTAIL”ACRYLIC: The absorbance spectra for all of these samplesshow variation in the UV region. As expected, this level ofvariation is reflected in the associated first derivative spectra.

4.2. Section Two — natural fibres

4.2.1. Visible wavelength rangePINKWOOL and BLACK COTTON: both of these samples

show little variation in the absorbance spectra. The associatedfirst derivative spectra therefore also show little variation. Inboth sets of absorbance spectra there are a number of points ofcomparison, and calculating the first derivative spectra thereforedid not add any extra value in terms of discrimination.

YELLOW CASHMERE: there is very little information inthe absorbance spectra for this sample. There are however, morepoints of comparison within the associated first derivativespectra which would therefore aid comparison. However, due tothe slight difference in gradient in one area of the absorbancespectra for some of the fibres, there is (as stipulated earlier) arisk that matching fibres might incorrectly be eliminated due tothe resultant difference that this causes in the first derivativespectra.

GREY LAMBSWOOL: this sample was found to consist ofa blend of a number of different fibre populations. This isevident when studying either the absorbance spectra or the firstderivative spectra. Due to the high level of detail in theabsorbance spectra, calculation of the first derivative did notappear to provide any further benefit.

4.2.2. UV/visible wavelength rangePINK WOOL: as detailed in the “Orange polyester, blue

polyester and black polyester UV/Visible range” section(above) wool fibres absorb all of the light below 300 nm anddisplay a total absorbance peak which is then present in the firstderivative spectra. In the region of the absorbance spectrabetween 300 and 380 nm there is a high level of variation withinthe sample which is then evident in the associated firstderivative spectra.

BLACK COTTON: there is detail in the UV wavelengthrange of the absorbance spectra, with a minimum degree ofvariation exhibited between individual fibres. The variationobserved was present in the first derivative spectra and – forsome fibres – the minor differences in the absorbance spectrawere highlighted, clarifying the differences between thefibres.

YELLOW CASHMERE: the yellow cashmere sample hadvery low absorbance levels and very broad featureless spectrain the visible wavelength range, as can be seen in Fig. 5. The

Fig. 3. Blue “Tigertail” acrylic fibres measured on MSP400 and MSP800, with the associated first derivative spectra.

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UV region of the spectra has a total absorbance peak.Therefore, the absorbance spectra of this sample have littlevalue. However, the associated first derivative spectra havesome detail in the wavelength range 320–520 nm. The first

derivative spectra also emphasises the slight variation withinthe sample, which was less obvious when studying theabsorbance spectra alone. Even though the first derivativespectra on its own provides minimal comparative detail, when

Fig. 4. Absorbance and first derivative spectra for the orange polyester sample.

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it is used in conjunction with the absorbance spectra it doesfacilitate the comparison.

GREY LAMBSWOOL: the absorbance and first derivativespectra produced for this sample showed that there are a numberof different fibre populations within it, however, neither form ofspectra provided more information than the other.

Fig. 5. Absorbance and first derivative sp

4.3. Section Three — dye batch fibre samples

4.3.1. Visible wavelength rangeBROWN ACRYLIC: Two of the batches were found to

form distinct populations from the other eight. The differ-ences were found in the 620 nm region of the spectra. These

ectra of the yellow cashmere sample.

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obvious differences in the absorbance spectra meant that calcu-lating the first derivative would not provide any further usefulinformation.

Fig. 6. Absorbance and first derivative spectra of the brow

RED ACRYLIC: all seven batches matched. The sample hada high level of variation within the absorbance spectra and thiswas reflected in the first derivative spectra. However, as with

n acrylic dye batch samples 4 (top) and 5 (bottom).

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previous samples, the associated variation in the first derivativespectra could potentially result in false exclusions due to intra-sample variation resulting in gradient changes in parts of theabsorbance spectra.

RED ACRYLIC (SET TWO): all nine batches matched,based on the absorbance and first derivative spectra. There waslittle variation in either the absorbance spectra or the associatedfirst derivative spectra.

NAVY BLUE ACRYLIC: the absorbance spectra clearlydemonstrated that all of the batches matched each other.However, when the first derivative spectra are studied, some ofthe fibres within each sample do not appear to match. Thespectra are similar to those in Fig. 3. Again, this means thatthere is a possibility that matching fibres will be wronglyeliminated.

4.3.2. UV/visible wavelength rangeBROWN ACRYLIC: comparison of the absorbance and first

derivative spectra clearly showed that two of the batches formeda different population. Although this suggested that there is noapparent benefit in calculating the first derivative, there wereother very subtle differences which although not obvious whencomparing the absorbance spectra, are clear when using the firstderivative spectra. These subtle differences can be seen in Fig.6, in the 370–390 nm region.

RED ACRYLIC: the seven samples all matched based on theabsorbance and first derivative spectra. There was little detailevident in the UV region of the absorbance spectra, however,the corresponding region of the first derivative spectra can beused to clarify any differences present.

RED ACRYLIC (SET TWO): all nine samples matched,based on the absorbance and first derivative spectra. There wassome variation in the UV region of the absorbance spectrawhich was also evident in the corresponding region of the firstderivative spectra.

NAVY BLUE ACRYLIC: all ten samples matched, based onthe absorbance spectra. However, as was seen when this samplewas measured in the visible wavelength range, the differences inabsorbance/gradient resulted in a variation within the firstderivative spectra which could potentially result in falseexclusions.

4.4. Discussion

When two fibres from the same source are dyed with thesame dye but one fibre takes up/retains more dye than theother, differences will be evident in their absorbance spectra.However, the shape of the spectra will generally be similar.When comparing a matching recovered fibre with the controlfibre spectra, the recovered fibre will fall within the spectralrange of the controls. However, when the first derivative ofthe recovered and control fibre spectra is calculated, thedifferent gradients caused by the high intra-sample variationlevels may mean that the calculation of the first derivativespectra results in the recovered fibres appearing to bedifferent to the control. If due care is not exercised in suchcircumstances, it is possible to conclude that the recovered

fibre does not match. This risks valuable fibre evidence beingdismissed.

Whilst it is possible to calculate error rates for falseexclusions, in terms of this study such an exercise would bemeaningless. Such error rates will differ according to the fibretype and dye type/recipe used and the very specific intra-samplevariation occurring for each (almost infinite) combination. Toquote such rates based on the fibre type/dye combinationsemployed in this study would therefore be misleading.However, the data clearly exemplify the need for caution inthe circumstances cited.

The majority of the samples in this study had enough pointsof comparison in the absorbance spectra to allow confidentcomparisons to be made. Whilst in these instances calculatingthe first derivative spectrum would not appear to add any value,experience in casework suggests that subtle differences canoccur even in multi-peak spectra and therefore use of firstderivative may be of great benefit in these circumstances andshould not be immediately disregarded.

This study illustrates that calculation of the first derivativeis most beneficial when the absorbance spectra are tightlygrouped with regard to absorbance level but broad andlacking in detail. An example of this is the yellow cashmeresample used in this project. The lack of detail in both the UV/visible and visible only absorbance spectra meant that itwould be difficult to make any meaningful comparisons fromthese results, however, when the first derivative spectra iscalculated it is possible to visualise more points of comparisonwhich can allow the comparison to be reported with greaterconfidence.

5. Conclusion

When absorbance spectra are broad and featureless,calculating the first derivative can provide extra points ofcomparison which aid the interpretation of results. This wouldbe beneficial when thin layer chromatography cannot be used(due to the dye not extracting or insufficient sample beingavailable).

There is a risk that the first derivative spectra could showdifferences between fibres that match. This is because twoabsorbance spectra at different absorbance levels, i.e. from apale and a dark fibre, may have very different gradients. Thesegradient differences would translate to huge differences in thefirst derivative spectra, once again illustrating the need for arepresentative control sample. There is less risk involved whenthe absorbance spectra are tightly grouped and show littlevariation with regard to the absorbance level.

Care should be taken at all times when calculating thefirst derivative and interpreting first derivative data. Suchdata should never be considered in isolation from the originalabsorbance spectrum.

Acknowledgement

The authors would like to thank Gary Polwarth for carryingout the visible range MSP work.

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