j. Cosmet.
Sci.,55, 81-93 (January/February
2004)
Analyzingthe laser-lightreflectionfrom humanhair fibers.
II. Derivinga measureof hair luster
F.-J. WORTMANN, E. SCHULZEZURWIESCHE, and
B. BOURCEAU, DWI, GermanWoolResearch
Institute,Veltmanplatz
8, 52062 Aachen(F.-J.W.), Schwarzkopf
GmbH, Hohenzollernring
127-129, 22763 Hambz/rg(E.S.z.W.), and FiantecGmbH,
Technologiezentrz/m,
Ez/ropaplatz,
52068 Aachen(B.B.), Germany.
Accepted
for publication
October
8, 2003.
Synopsis
Hair shineor lusterisperceived
asanimportant,thoughanalytically
somewhat
elusive,
attributeof beauty,
primarilyassociated
with cleanandhealthyhair.Principles
for theassessment
of hairlusteraredeveloped
that are consistent
with the practicalsituation.Theseprinciplesare relatedto the components
of light,
specularly
anddiffuselyreflected
fromsinglehairfibers,asmeasured
by laser-based,
multianglegoniophotometry,presented
in Part 1. Considering
variousdefinitions
of gloss,their tradition,practicalimplementation, and their inherentlimitationsfor testinghair, the glossindexasa physicallyconsistentmeasureof
hair lusteris derivedfrom the ratio of the integralintensitiesof the light components.
Changesof the
parameter
values
alonghairlength,namelytheirdecrease,
areanalyzed
forhairsofdifferent
colorandethnic
origin.The correlation
with shineevaluations
of hairtresses
by panels,basedon literaturedata,is analyzed
and ascertained.
INTRODUCTION
When applyinghair cosmeticproductsthe consumerexpectsperceivable,
beneficial
effects.Sinceamongour senses
visionundoubtedlyplaysa mostimportantrole, claims
for increased
hair shine(luster,gloss)arefrequentfor hair cosmeticconsumerproducts,
as well as for the raw materialsthey contain.This is due to the fact that hair shineis
perceived
asan important,thoughanalytically
somewhat
elusive,attributeof beauty,
primarilyassociated
with cleanand healthyhair.
Hair shineis generatedwhena beamof light strikesthe hair surface.Partsof the light
arespecularlyreflectedandthenperceivedat a particularangleanddirection,generating
surface
highlightsandbrightness
contrast,whileotherpartsarescattered
anddiffusely
reflected.A further fractionof light is refractedinto the hair, where it is absorbed,
scattered,
or reflected.All of the effectsdependon the geometryof the hair surface,the
Addressall correspondence
to F.-J. Wortmann.
81
82
JOURNAL OF COSMETIC SCIENCE
refractiveindex,the incidentangleof the light, the angleof observation,
andthe external
and internal
structure of the hair fiber.
Part I (1) described
the applicationof multichannellasergoniophotometry
to determine
the angulardistributionof reflectedlight from singlehairs.Analyzingthesedistributions for hairs differing in ethnic origin and color gave detailson changesof light
reflection,includinginformationon the cuticleangle.Thesewerediscussed
in termsof
changesof the hair surfacealongthe hair length.
The principlesfor the generationof hairshine,asoutlinedabove,arein ourviewdirectly
relatedto the practicalsituation.Figure 1 showsthe appearance
of an Asianblack(Fig.
1A), a medium-brown (Fig. lB), and a blonde Caucasian(Fig. 1C) clean hair tress
spotlightedundera stereomicroscope
at a magnificationof approx.20 x. Suchtresses
can
be takento represent
a freelymovinghair stylewithoutmajorfiberinteractions.
Largely
white light reflexesareobserved
on singlehairsthat contrastwith nonreflecting
adjacent
areas,which are either dark or light, dependingon hair color.
Againstthe background
of the technicalterminology(2,3), asdiscussed
in detailbelow,
the phenomenaobservedin Figure 1 areappropriatelytermed"hair luster,"because
they
are associated
with the contrastgloss(2) of dark areasadjacentto light reflexes.These
highlightsare due to specularlyreflectedlight from singlefibers,wherea high number
of intensive,white reflexes,dynamicallyappearingandvanishingwith the movementof
the hair, give "shine"and enhancethe appearance
of beauty.The overalllevel of shine
that may be achievedon the basisof a given degreeof luster stronglydependson
hairstyle(4).
Various approaches
have been describedto determine hair luster on hair tressesas a
measurablequantity, applyinggoniophotometry
(e.g., 5,6). Further approaches
have
been color measurements
(7) and image analysis(e.g., 8). In parallel, the common
laboratorypracticefor screeningproductsis to use expertor consumerpanelsto subjectivelyrank hair luster,e.g., by meansof a "shinebox"(6,9-12). Noteworthyis the
approachby Tango and Shimmoto(13) to developa methodand a devicefor the in vivo
determinationof hair shinethat is relatedto the principlesof commercial"glossmeters"
(10,14).
Morefundamental
investigations
alsoappliedgoniophotometry
to singlehairfibersand
arraysof parallel,singlefibers(5,11,13,15-17). Thoughgrosschangesin hair appearancethroughhair careproductsmay well be detectedon hair tresses,effectsrelatedto
the assemblyas suchcomplicateif not preventa detailedinterpretationof the results.
In the caseof singlefibers, this methodgives detailedinsight into the interaction
betweenlight andthe fiber surface,
anda varietyof parameters
canbe definedin terms
of the intensitiesof specularlyand diffuselyreflectedlight. In view of the conclusions
drawnfrom Figure 1, the useof goniophotometry
would appearto be an especially
promisingapproach.Problemswith this methodin the past(5,11), dueto inherentlarge
variationsbetweenindividualhairs,aswell aslong recordingtimes,havebeenovercome
through multi-angle detectionand fast data acquisitionfor the completeangularintensitydistributionof reflectedlight, asdescribedin Part I (1). On this basisa physically, practicallyplausible,and mathematicallystableparameterto describehair gloss,
luster, and shine is introduced and assessed.
MEASURE
OF HAIR
LUSTER
83
A
B
C
Figure I. Spotlightedtresses
of blackAsian(A) andbrown(B) andblonde(C) Caucasian
hair, respectively,
undera light microscope
at an initial 20x magnification.
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JOURNAL OF COSMETIC SCIENCE
DERIVING
A MEASURE
MEASUREMENT
AND
FOR
ANALYSIS
HAIR
OF LIGHT
LUSTER
REFLECTANCE
FROM
HUMAN
HAIR
The measurement
of light reflectance
from singlehumanhairs,asdescribedin detail in
Part 1 of this paper(1), is basedon the determinationof the angle-dependent
intensity
of the light from a greenlaser(X = 532 nm) scatteredfrom a singlefiber. The wave
lengthwaschosen
suchasto be in that rangewherethe daylightsensitivityof the human
eye is at its maximum.
The basisfor the investigationwasthreetypesof hair, namelyblackAsianand brown
and blondeCaucasianhair (seeFigure 1). Each samplewas taken from the head of a
femalevolunteerand exceededin all cases20 cm in length. The hairswereshampooed
(LES 15%, pH 5.5), rinsed,dried, and storedunder ambient conditionsuntil measurement.
The experimentalsetup(1) is suchthat the verticallypolarizedlaserbeam(approx.50
pW) meetsthe hair fiber, arrangedhorizontallyunder slight tensionand in ambient,
thoughstable,room conditions(approx.22øC, 50% RH), at an incidentangleof 40 ø
(beamspotdiameter100 pm). The detectionof the reflectedlight is conductedwithin
about 100 ms in the horizontalplanecontainingthe fiber and the incidentlight beam
througha rangeof 6.5ø to 173.5ø with an OpticalRlulti-ChannelAnalyzer.
The solidline in Figure2 showsthe so-calledgoniophotometric
(GP) curve,derivedby
smoothingthe angular light intensity data for the most generalcase,namely light
0,4
0,2
0,0
0
10
20
30
40
50
60
70
80
90
Receptor Angle [ø]
Figure 2. GP curvedata(
) for a light blondehair measured
at a positionnearthe tip end.Gaussian
distributionsfor specularly(.... ), diffusely(---), and internally(---) reflectedlight, as fitted to the GP
curve (seeFigure 7 in ref. 1).
MEASURE
OF HAIR
LUSTER
85
blonde,Caucasianhair measuredat a positionnearthe tip end. In this contextit is
important to note that the surfaceof hair is not smoothbut featurescuticle cells in a
tile-like arrangement,
wherethe cell scaleedgespoint towardsthe fiber tip. To ensure
a consistent
biasof light reflectiondue to the cuticleinclinationangle(1), all measurementswerecarriedout with the directionof the incidentlight towardthe tip endof the
hair.
In view of the surfaceand overallmorphologicalstructureof humanhair, the reflection
of light is subjectto a specialtype of geometrythat in turn andwith the principlesof
geometricaloptics leadsone to expectthree principal componentsof light reflection.
These are representedby the three Gaussiandistributionsfitted to the GP curve in
Figure 2. Details of the fitting procedureand the parametersderivedthereofare given
in Part 1 (1).
When the incidentbeamhits the fiber surfacein the root-to-tip (RT) directionat the
incidentangleE•(1), a first fractionof the light, S, is specularly
reflectedat the receptor
angle•/s. For the experimentalsetup,usingthe incidentangleE• = 40 ø and assuming
a tilt anglefor the cuticleof 2.5ø leadsto an expectation
valuefor the receptorangleof
the specularlyreflectedlight of •/s = 350. At this position,Figure 2 showsthe peak
describingthe intensitydistributionof specularlyreflectedlight with a width at halfheight of 9ø-10 ø.
A secondfractionof light, Ds, is diffuselyscatteredat and nearthe fiber surface,namely
at surfaceroughnesses
(18), at the variousinterfacesbetweenthe cuticlecell layersof
humanhair (19), at the interfaceof cuticleandcortex,andat opticalimperfections
of the
cortex, such as voids and inclusions.
Figure2 showsbetween40 ø and 45ø the broadGaussiandistributionfor diffusereflection. It is important to note from Figure 2 that the hair surfacecannotbe consideredas
being primarily an ideal, diffusereflectorfor which scatteringoccurssuch that the
intensityof the diffuselyreflectedlight is uniform. Though on the basisof Reich and
Robbins'analysis(11) of GP curves,the existence
of a uniformcontributionfor Ds is
assumed,its magnitudeis obviouslysmall comparedto the non-uniformeffect and
coveredby the broadGaussiandistributionfor diffusereflection.
A furtherpart of the incidentbeamis refractedinto the fiber accordingto Snell'sor
Descartes'law. Inside the hair the light is scatteredat voids and inclusions,is partly
absorbed
by hair pigmentandcolor,and is thuswavelengthfiltered,dependingon the
color and its intensity. Diffuse reflectiontakes place at structuralinhomogeneities
within the cortex.For lightly coloredhair, light may be diffuselyreflectedat or in the
medulla (4,20), a more or lesscontinuousand hollow, tube-like structure in the fiber
interior.
In very blonde or white hair a significantamount of light may be reflectedat the
backsideof the fiber, that is, from the hair/air surfaceinterfaceoppositethe point of
incidence.When this third componentof light re-emerges
from the fiber, it is experimentallyobserved,asshownin Figure2, asa separatepeak in the GP curve(5,15,17)
at anglesaround64øwith a width of 25ø(1). Thistypeof light is considered
asa specific
fractionof diffuselyreflectedlight, termedD v sinceit is relatedto the internalreflection
effect.
86
DEFINING
JOURNAL OF COSMETIC SCIENCE
HAIR
GLOSS
Surfaces
and objectsoftenshowgloss,which is attributedto specularreflectance
at the
respective
surface.Due to the diversityof surfacestructures,
differentkindsof glosscan
be observed.Hunter, as early as 1937 (2), intensivelyinvestigatedthe phenomenonof
glossand arrivedat a classification
with six differenttypesof glossthat weredefinedin
terms of measurableparameters.
Stammet •/. (5) reviewedthe semanticsof gloss,luster, shine, etc. for human hair.
Measuringby goniophotometry
light reflectedfrom singlehairsor hair strings,Bustard
and Smith (15) and Stammet •/. (5), respectively,choseone of theseclasses,
namely
"contrastgloss,"to representthe "luster"of hair. Their approachrelatesto the work by
Nickersonon the glossof cottonyarn and fabric(3), whereshefoundthis type of gloss
well applicableto test textile lusterin correspondence
with the visualassessment.
Hunter (2) definescontrastglossas "contrastbetweenspecularlyreflectingareasand
other areas."It is measuredby comparingthe intensityof the light that is specularly
reflectedwith the intensity of that which is diffuselyscattered,so that:
H
gc = s/d
(1)
H
g•. is Huntercontrast
gloss.s andd arethe intensitiesof specular
anddiffusereflection,
respectively,measuredat two positions,namely(a) at the expectedreceptorangle for
specularly
reflectedlight and (b) normalto the materialsurface.Followingthe notation
introducedby Stamm et al. (5), lower caseletters are employedto designatethese
so-calledspotvalues.SinceEquation1 goesto infinity asd approaches
zero,Nickerson
suggestedas an alternative:
N
gc : (s - d)/s
(2)
wheregff is the"Nickerson
contrast
gloss,"
considered
to represent
luster.Forcotton,
Nickerson(3) found a good correlationbetweencontrastglossvaluesand visualestimates of luster.
Nickersoncontrastglossbecomeszerowhen d equalss, unity when d equalszero,and
negativewhen d > s. In view of the complexstructuresof the GP curvesfor different
typesof hair (1), all threecasesare likely to occurin practice.
The approachapplyingspotvaluesis valid, notablyfor flat surfaces,
wherethe angleof
incidenceand the receptoranglefor specularlyreflectedlight are equaland wherethe
intensityof the scatteredlight showsno angulardependence.
However,both of these
conditionsare obviouslynot fulfilled for humanhair, implying that spotmeasurements,
asimplementedin commercialtestingdevices(10,13,14) are expectedto be at bestof
very limited use for determininghair gloss.In this view, it is not unexpected,that
Stammet a/. (5), Bustardand Smith (15), and Guiolet eta/. (17) found that the gloss
parameters
definedin equations1 and 2, basedon spotvalues,havehigh precisionbut
poor sensitivity.
Variousapproaches
havebeendevisedto determineintegralvaluesfor specularlyand
diffuselyreflectedlight (5,11,15), applyingthe principlesinherentto equation1 and
especially
equation2 in orderto deriveparameters
to describe
hairluster.The definition
of theseparameters
waseitherbasedon theoreticalconsiderations
(5,15) or on empirical
observations
(11). Inherentto the approaches
is theprinciplethat diffusereflectionfrom
hair occursuniformly.
MEASURE
OF HAIR
LUSTER
87
Dismissingthis assumptionin view of the positionsand shapesof the light intensity
distributionsunderlyingthe GP curves(seeFigure 2) and of our interpretationof Figure
1, we proposethat the effectof hair lusterand of the shineof a given hairstyleis related
to the ratio of the total amount of light reflectedspecularlyfrom single hairs to the
overall amount of reflectedlight:
G L -- S/(D + S)
(3)
D = D s + D,
(4)
with
Followingthe notationof Stammet a/. (5), capital letters are employedto mark the
integralvaluesof light intensity.Go the glossindex,is considered
to describe"specular
gloss,"as a measureof/uster, in correspondence
to earlier definitionsand subjective
descriptions
as "brillianceof specularlyreflectedlight" (2) and "brillianceof highlights"
(3).
S and the componentsof D are determinedfrom the completegoniophotometriccurves
for singlehuman hairsthroughseparatingand integratingthe intensitiesof the specularly and diffusely reflectedlight components,respectively,by fitting three Gaussian
distributions(seeFigure 2). With the exceptionof light blondeor white hair, Di can
usuallybe neglected,greatly simplifyingthe determinationof the componentsof equation 3.
The propertiesof equation3 areplausiblyconnected
with practicalobservations.
If there
is no specularlyreflectedlight, S = 0 and henceGz. -- 0. In the caseof D -- 0, there is
no diffuselyreflectedlight, and perfectluster is achievedwith Gz. -- 1. If the situation
arisesthat the integral intensitiesof specularand diffusereflectionsare equal so that S
-- D, equation3 yields 50% gloss.By darkeningor lightening hair, the diffusecomponent, due to changesin light absorptionin the fiber, will decreaseor increase,
respectively.If the specularcomponentremainsunchanged,glosswill increaseor decrease,respectively,by the coloringof the hair alone.This corresponds
to the practical
observationthat dark hair alwaystendsto appearmore lustrousthan blondehair.
RESULTS
AND
DISCUSSION
By fitting Gaussiandistributionsto the GP curves,locationsand widths for the three
typesof reflectedlight were determinedfor the different typesof hair. The parameter
valuesand their changesalongthe hair length, including cuticleangle,arepresentedand
discussedin detail in Part I of this paper (1).
By far, most GP curvescouldwell be analyzedby consideringjust S and D,, that is, by
a two-component
approach.Only for light blondehair did Di asa furthercomponentof
diffuse reflectionhave to be considered.Introducing the areasof the fitted peaksfor a
given GP curveinto equation3 yields the respectivevalue for the glossindex
All datawere checkedfor outliersprior to further analysisby assessing
them in so-called
normalprobabilityplotsas implementedin the appliedstatisticssoftware(21). In this
type of plot, cumulative data frequenciesfollow a straight line when the data are
normally distributed.On this basis,three obviousoutlierswere readily identified
< 10%) in theseplots for brown hair and removedprior to further analysisof the data.
88
JOURNAL OF COSMETIC SCIENCE
The data given in Table I representthe accepteddata for the gloss index and are
arithmetic meansfor measurements
taken at a given positionrelativeto the root end on
a numberof hairs(N) of the sametype. For a given hair type the data are summarized
in groupmeans.Data are further summarizedoverall hair typesin the form of a grand
mean.
Effectsof measurementposition and hair type on the parameterswere assessed
for
significance
by analysisof variance(ANOVA) and linearregression
(LR). In thosecases
whereANOVA indicatedinhomogeneity,
multiple comparison
of meansanalysiswas
conducted,applyingthe nonconservative
LSD test (21). Statisticalsignificance
of effects
(ANOVA: inhomogeneityof data;LSD: differences
betweendata groups;LR: slopeof
the regressionline) is characterizedthroughout by the o•-value(22), which is the
probabilityof committinga so-calledType I error,i.e., by finding an effectthat in fact
doesnot exist.In cases
whereo• < 0.05, effectsaresignificantat the usual95% leveland
beyond.
The resultsfor the three hair types are summarizedin Figure 3 in the form of a
box-and-whisker
plot. Analysisof varianceshowsthat, in agreementwith the visual
impression,the dataare inhomogeneous
well beyondthe 95 % level (o• < 0.0001), where
the LSD test identifies the o•-levelsfor the differences,as given on the horizontal
whiskersin Figure 3. Here it is shown that the gloss index showsno significant
differencebetweenblackand brown,but is decreased
ratherdramaticallyfor the blonde
hair. This effectcanbe largelyattributedto the absorption
of refractedlight for the two
dark hair types,which suppresses
diffuselight reflectionfrom the hair interiorandthus
inducesa strong and brilliant hair luster.
Table
I
Valuesfor the GlossIndex GL Derivedfrom the GP Curvesfor VariousHair Types
Hair type
Black
Position (cm)
1
12
64.1
3
53.2
10
7
59.3
15
20
3
7
59.8
57.4
32
60.2 + 3.33
1
10
66.5
10
9
54.4
20
7
55.8
25
3O
4
10
55.6
57.6
40
58.6 + 3.05
l0
31.8
Groupmean+ q
Blonde
G•_(%)
5
Groupmean + q
Brown
N
1
5
9
32.2
10
9
3O.7
15
9
14.9
20
Group mean + q
10
47
14.7
24.8 + 3.84
Grand mean + q
119
45.7 + 3.66
A numberof hairs(N) weremeasuredat variouspositionsrelativeto the root. Group andgrandmeanvalues
are given with their 95% confidencerange+ q.
MEASURE
7O
...................................
OF HAIR
LUSTER
89
0.55 .......................................................................................................
6O
<0.001
I
40
o
:30 ...............................................................................................................
I
ß Mean [---] Std.Err. -[- 95% Conf_Rg.
ß
I
black
brown
blonde
Hair Type
Fiõure 3. Box-and-whisker
plot summarizinggJossindexvaluesfor the threehair types.Data points,boxes,
and whiskersare definedby their arithmeticgroup mean (Mean), the standarderror (Std. Err.), and the
limiting valuefor the 95% confidence
range(95% Conf. Rg). The horizontalwhiskerssignifya specific
comparison
of means(LSD test), given with the (x-valueto characterize
the significanceof the difference.
There are changesin the glossindex along the hair length, as summarizedgraphically
in Figure4. Eachstraightline represents
a fit to the meanvaluesgiven.Considerations
of statisticalsignificance
relate,however,to fits of the singledata.For the blackhair, the
changeof glossalongthe hair lengthis a tendencyat best,but in fact not significantat
the chosen95% significancelevel (o• = 0.2). The level of the grand mean for the gloss
indexof the blackhair is markedin Figure4. For the brownhair, the decrease
of gloss
along the hair length is more pronouncedand the significanceof the slope of the
regression
line just missesthe 95% level (o• = 0.054). For the blondehair, glossstarts
from an alreadycomparativelylow level at the root and then decreases
stronglyand
significantlytowardsthe tip (o• < 0.001).
The decrease
in hair glossdue to a relativeincreasein the intensityof diffuselyreflected
light canbe attributedto hair colorlighteningtowardsthe fiber tip combinedwith the
formationof damage-related
structures,
suchascracksor voids,that scatterlight, which
havebeeninducedby daily hair groomingpracticesincludingheattreatments(20,23),
sunlightexposure,etc. Black and brown hair reachvaluesaround65% glossnear the
rootends,whichmaybe considered
a reasonable
estimatefor the maximumnaturalgloss
of hair.
For natural black or dark brown hair, diffuse reflection from the fiber interior will be
negligibledue to the absorptionof the refractedlight. However,for all hair types,cuticle
90
JOURNAL OF COSMETIC SCIENCE
70
black
•
y= 62.3 -0.28 x
50
-o 40
o
30
2O
10
0
5
10
15
20
25
30
35
Distance from Root [cm]
Figure 4. Meansfor the glossindexGL at variouspositionsalongthe hair, givenasdistancefrom the hair
rootfor black(O), brown(I), andblonde(•) hair, respectively.
The solidlinesarethe linearregression
linesthroughthe datafor brownand blondehair. Filled symbolsare usedfor thosecaseswherethe slope
of the regressionline has a relevantstatisticalsignificance.The equationsthat are given on the graph
specifically
relateto the individualresults.The horizontalline on the right marksthe groupmean(60.2%)
for black hair (seeTable I), wherethe decrease
alongthe hair length is not significant.
cells will as a rule not contain pigment. Light is hencerefractedinto the cuticle and
passesthrough a substantialnumber of cuticle cells with reflection,refraction,and
scatteringat the cell interfacesuntil ultimate reflectionat the cuticle/cortexinterface
generatesa major componentof what is observedas diffuselyreflectedlight.
This effectwill further be intensifiedif, throughhair damage,delaminationhasoccurred
betweencuticlecell layers(19,23) or if, moregenerally,cracks,voids,or inclusionshave
beenformed.The glossmeasurement
of hair, which due to its colordoesnot allow light
reflection from the fiber interior, thus providesthrough the diffuse componentof
reflectedlight informationon the structuralstatusof its cuticlelayer.In this contextthe
differencesin the changeof glossalongthe hair length for the blackand the brownhair
(seeFigure 4) are interestingto note.
It is importantto note that the approach,describedin this paper,for determiningthe
glossindex is equally applicablefor African hair, despiteits strong ellipticity and
curliness.However, this type of hair was not included in the study, since it was
consideredas being lesssuitablein the contextof determiningthe effectsof hair color
and along-hair changes.
MEASURE
OF HAIR
LUSTER
91
In practice,hair shineis a very complexphenomenon(16,24), which involvesphysical,
physiological,and psychophysical
considerations.
Gz., on the other hand, providesan
absolute, numerical scale.
In this view, it hasto be noted that consumerperceptioncannotbe expectedto follow
an equisense
scalein which a unit of differenceindicatesan equal sensorydifferencein
luster(3). In practice,an expertor a consumerwill generallyrank productperformance
in a contrastsituation (half-headtest, before-rs-after,product A vs product B, etc.)
relating to relative changesof appearance
(4), rather than work on the basisof ordinal
sensoryunits. As was shownin small scalepanel tests(18,25), theserank differences
appearto be closelyrelatedto thelaboratorysituationof glosstestingof singlehair fibers
described here.
However, a somewhatmore comprehensive
argument for the feasibility of the gloss
index to model the assessment
of hair luster by a consumerpanel is derivedfrom the
extensiveinvestigationsby Reich and Robbins(11). They found a linear relationship
betweenthe inverseof the width of the GP curveat half height and the luster ranking
by panels.
Applying the data given in Part I (1) for the positionsand widths of the Gaussian
distributionsdescribingspecularand diffuse reflection,theoreticalGP curveswere
calculated
on the basisof equation3, assumingthe presence
of S andD s only,for a wide
rangeof G/• values.Finally, the width at half-heightw of the theoreticalGP curveswas
0
40
60
80
100
Gloss Index in %
Figure 5. Inverseof the width at half-heightfor calculatedGP curveson the basisof a presumedvaluefor
the glossindex.The largelylinearrelationshipfor Gz.valuesbeyond25% is indicatedby the straightline.
92
JOURNAL OF COSMETIC SCIENCE
derived.Figure5 showsthe relationbetweenthe dataderivedin this mannerfor 1/w and
the presumedglossindex values.
When appreciablehair glossis generated,i.e., when the peak for specularreflection
startsto dominatethe GP curves,which occursaround GL > 20-30%, a largely linear
relationshipis observed,as marked in Figure 5, which corresponds
to Reich and Robbins'observation
(11). In thisview, the hypothesis
that the glossindexis a valid measure
for hair luster that correlateswith the consumer'sperceptionof hair shine is further
corroborated.Furthermore,more elusivefacetsrelated to hair gloss,suchas "silky" or
"greasy"hair shine,are the objectiveof currentinvestigations.
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