T is imulus Weigh Func ions To Calcula e Mus s Colo Coo dina es
F om 10-nm Bandwid h Spec al Da a
C. Mon es a Campos h A. Pons b F.J. He edia a
aA ea de Nu iciOn y B o na ologla. F. Fa macia. Uni e sidad de Se illa. 41012 Se illa.
b Ins i u o de FIsica Aplicada (CSIC). 28006 Mad id.
ABSTRACT
Colo measu emen o ed mus s is a ec ed by e o s due o he ins umen a chi ec u e. The in luence o
bandwid h in colo coo dina es e o s is s udied and a se o weigh ing unc ions o he colo coo dina es calcula ion, om
10 n n spec al da a, is p oposed.
Keywo ds: mus s colo , spec al bandwid h, weigh ing unc ions
1. INTRODUCTION
Mus colo measu emen can be o g ea alue du ing wine elabo a ion, bo h o e alua ing g ape ma u a ion and
o p edic ing colo and chemical composi ion o wines. T is i nulus colo esul s depend on measu e condi ions. Mos o
hese measu emen s a e done unde di e en ci cums ances (indus ial, coun y, labo a o y en i onmen ) and, in many
cases. la ge bandwid h ins umen s a e used.
Al hough s anda d condi ions ha e been de ined o hose pa ame e s which in luence he colo measu e esul ,
such as obse e , illu ninan . illumina ion-obse a ion geome y, bandpass and spec al measu e in e al, p ac ical
ealiza ions di e om each o he , so e o s a ise in calcula ing is imulus alues. These e o s depend on he ype o
measu e ins umen and i s cha ac e is ics o cons uc ion (Be ns & Pe e sen, 1988; Fai child & Reni , T99; Be ns &
Reni , 1997 Bu ns & Be ns. 997). Fu he mo e, ac o s as empe a u e o ela i e humidi y mus be con olled o ob ain
single and epea able measu emen s. because hey inay e ec samples.
Colo e o as a unc ion o measu emen bandwid h has been s udied o many sample ypes in se e al
labo a o ies. In pa icula . colo e o in se e al ypes o ood has been s udied by ou g oup, a ising he conclusion ha
bandwid hs la ge han 5 nm p oduce a no iceable colo e o on many o hem. Mus s we e one o hose s udied oods wi h
a no iceable e o in colo coo dina es o bandwid h la ge han S n n.
Wi hin mus s. colo di e ence be ween measu emen s o he same objec , wi h di e en ins umen s, a e mainly
due o he di e ence in measu emen geome y and ins Llmen bandwid h, since mos ins umen s ge spec al da a a he
han is imulus colo measu emen p ope ly. Di e ences in measu emen geome y a e no so impo an in his case
because ansmi ance is he quan i y used o de e nine colo and he mus is e y anspa en .
2. EXPERIMENTAL PROCEDURE
Twen y se en ed mus samples. co esponding o di e en s ages along he g ape ma u a ion, and belonging o
ou ha es (1996-1999) ha e been s udied. F om hem. i e ep esen a i e samples we e selec ed o es he bandpass
e o elimina ion me hodology. The es o samples we e used o ob ain weigh ing unc ions.
A Hewle -Packa d HP8452 UV diode a ay spec opho o ne e was used o scan he spec a o he samples.
T is i nulus alues we e ob ained om he isible ansmi ance alues and ch oma ic coo dina es we e calcula ed o he
CIE 1976 (L*a*b*)uniJo,in co/o space. CIELAB (CIE, 1986). The me hod was applied o e he whole isible spec um,
380-780 nm, a 2 n n in e als, ollowing he weigh ed-o dina e me hod. CIE s anda d illuminan A and CIE s anda d
9 h Cong ess o he In e na ional Colou Associa ion, P oceedings
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obse e 1931 ( ield<4°) we e used in he colo calcula ion. Iii o de o s udy he bandwid h e ec wi hou in luences o
o he expe imen al condi ions, e ec i e ansmi ance alues we e calcula ed by using he ollowing equa ion:
J T(2)B(2)d2
nLii)
' iii • B(2)dA
Cii)
whe e T(X) is he sample's ansmi ance as measu ed by he spec opho o ne e ; B(X) is he sli unc ion ( iangula o m is
assumed) and cib is he ex ension o he measu e spec al in e al. T ansmi ance alues o a I 0 n n bandpass ha e been
calcula ed o all he samples and hen colo coo dina es ha e been calcula ed using illu ninan A and he CIE 1931
s anda d obse e (2°) om 380 o 780 nm using a 10 nm summa ion in e al.
The e a e mainly wo app oaches in he li e a u e o a oid he bandwid h e o in he calcula ion o colo
coo dina es: Calcula ing weigh ing unc ions o he is i nulus unc ions o ge ing he 1-nm adiance alues om he
expe imen al da a. In he i s case. ASTM (1995) ecommends weigh ing ac o s Wx, Wy, Wz, de ined di e en ly o 10
and 20 n n bandpass. These weigh ing ac o s al eady con ain he p oduc o illu ninan A and he CIE 1931 s anda d
obse e (2°) o he espec i e in e al and hey ha e been p epa ed o co ec spec al measu emen s e o s due o
bandpass e ec . Colo coo dina es o ou mus samples ha e been calcula ed acco ding o he ASTM p ocedu e o a 10 im
bandwid h.
A me hod o co ec ing adiance da a o bandpass e o is p oposed by S ea ns and S ea ns (1988). By applying
his me hod o he samples, he calcula ed colo coo dina es should coincide wi h he I-nm coo dina es. The model
es ima es he ze o bandwid h adiance da a om he measu ed adiance, conside ing a 10 nm iangula and symme ical
bandpass and a measu emen in e al equal o he bandwid h. This me hod has been applied o ou mus samples o
calcula e colo coo dina es.
3. RESULTS AND DISCUSSION
To al colo di e ence in (L*a*b*) as well as di e ence in ligh ness and ch o na be ween 2-nm ini ial da a and
he coo dina es calcula ed om he 10 n n bandpass alues ha e been ob ained, conside ing o he 10 n n bandwid h:
unco ec ed alues, ASTM co ec ed alues and alues co ec ed by he S ea ns & S ea ns me hod.
The ASTM weigh ing unc ions esul s a e no sa is ac o y, because hey p oduce an imp o emen o oughly 0.1
CIELAB uni in colo di e ence wi h espec o he unco ec ed alue, and in many cases colo di e ences in mus samples
a e s ill highe han 0.5 CIELAB uni s a e co ec ion.
The S ea ns & S ea ns me hod gi es a be e co ec ion han he ASTM o mos o he samples conside ed,
p oducing a educ ion o 0.2 o 0.3 CIELAB uni s in colo di e ence. bu he co ec ion is s ill insu icien and again many
di e ences a e la ge han 0.5 CIELAB LIlli s.
To ge a no iceable educ ion in bandpass colo e o , di e en weigh ing unc ions we e calcula ed acco ding o
he ollowing c i e ion:
x (X, AX1 n n) =x(X, nm) x p(x)
y (X, AXI nm) =y(X, n n) x p(y)
z (X. AXI nm) =z(X, nm) x p(z)
The weigh ing unc ions a e hen de ined as se s o alues, one o e e y is i nulus unc ion. The simples
exp essions o calcula e indi idual alues o each a e:
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* p(x) gene a
H —p(y} gene a'
x(,)* T(A)* E(2*
(x)- %
p1O*x()*E()*TA(2)*AO
y()* T(,)* E(,%)*
()— )
py -
z(A,)* T(A)*E(A)* A1
(z) A2
p1O*z()*E()*TA()*jo
whe e AX is he spec al in e al in which he sli unc ion is de ined; x(2), y(?), z(X) a e he is i nulus unc ions, E(X) is
he illu ninan and T(X) is he sample ansmi ance.
These h ee eqLla ions we e applied o he 1-nm and 10-nm spec al da a o mus samples, om he ou ha es s.
Fo each ha es . a i hme ic media was calcula ed, and, since no la ge di e ence was ound om ha es o ha es , he
a i hme ic media o he ou alues was calcula ed again. The s anda d de ia ion o hese a e aged alues was in he o de
o 2 pa s pe housand. So, h ee sui able weigh ing unc ions we e ob ained o apply o gene al mus samples (Fig. 1).
Fig. I. Veigh ing Func ions
The h ee weigh ing unc ions, p(x). p(y). p(z) we e analyzed, and each o hem had a spec al zone whe e he
co ec ing ac ion is highe .
The unc ion p(x) has go a maximum alue in 500-600 nm ( ed-o ange zone). This zone coincide wi h he x(X)
peak. The unc ion has go ano he high alue in he blue zone (390-450 nm) o co ec he coo dina e b*.
On he o he hand, unc ion p(y) is no iceable only in he blue zone (380-480 nm). The weigh ing unc ion p(z) had
a maximum o co ec ing blue wa eleng hs in he same zone han p(x).
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The h ee unc ions had a plane spec al zone (580-780 nm) whe e no co ec ions we e necessa y.
Colo coo dina es ob ained by applying hese eigh ing unc ions o a se o 5 samples o 10 nm ansmi ance
alues a e much close o he 2 u n alues han hose ob ained by he o he app oxima ions (ASTM, S ea ns). These
samples, as men ioned be o e, we e no used o de i e he p e ious weigh ing unc ions
4. CONCLUSIONS
When bandpass is di e en om 1 nm, e o s a ise in calcula ing colo coo dina es, al hough hose e o s a e no
no iceable when he bandwid h is lowe han 5 nm. The e a e wo me hods in he li e a u e o y o co ec hose e o s.
Bo h ha e been es ed in his wo k o mus samples. Howe e , by using ASTM weigh ing unc ions o applying he S ea ns
& S ea ns me hod he e was no imp o emen in he highe bandpass alues wi h espec o 1-nm bandpass.
To elimina e bandpass e ec in is imulus alues i is necessa y o calcula e sui able weigh ing unc ions. A
c i e ion o calcula ing hese unc ions has been p oposed. By applying hese weigh ing unc ion o mus samples, i is
possible o compa e colo coo dina es ob ained oni -n n spec al da a o hose ob ained om TO-nm expe imen al alues.
REFERENCES
ASTM. Annual book o ASTMsiaiida ds, ol 06.01, 1995.
R.S. Be ns, L. Reni , An ab idged echnique o diagnose spec opho ome ic e o s', Colo Res. App!. 22, pp 51-60, 1997.
R.S. Be ns. K.H. Pe e sen. Empi ical modeling o sys ema ic spec opho ome ic e o s," Colo Res. App!. 13, pp 243-
256. 1988.
PD. Bu ns, R.S. Be ns, 'E o p opaga ion analysis in colo measu emen s and imaging", Colo Res. App!. 22, pp 280-289,
1997.
CIE. Colo ime y Pub. CIE 15.2 Viena, Aus ia, 1986.
M.D. Fai child, L. Reni P opaga ion o andom e o s in spec opho ome ic colo ime y", Colo Res. App!. 16, pp 360-
367, 1991.
El. S ea ns. "In luence o spec opho ome e sli s on is imulus calcula ions", Colo Res. App!. 6, pp 79-84, 1981.
El. S ea ns, RE. S ea ns, An example o a me hod o co ec ing adiance da a o bandpass e o ", Colo Res. App!. 13,
pp25'7-259, 1988.
W.H. Venable, "Accu a e is imulus alues om spec al da a", Colo Res. App!. 14, pp 26 1-267, 1989.
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