Recen Inno a ions in Mecha onics (RIiM) Vol. 2. (2015). No. 1-2.
DOI: 10.17667/ iim.2015.1-2/8.
1
Measu emen o he e ec o ch oma ici y and
in ensi y on colou ep esen a ion pa ame e s o a
CRT display
D . Klá a Wenzel
Depa men o Mecha onics, Op ics and Mechanical
Enginee ing In o ma ics
Budapes Uni e si y o Technology and Economics
Budapes , Hunga y
[email p o ec ed]me.hu
Ágnes U bin
Depa men o Mecha onics, Op ics and Mechanical
Enginee ing In o ma ics
Budapes Uni e si y o Technology and Economics
Budapes , Hunga y
[email p o ec ed]me.hu
Abs ac —The aim o he measu emen de ailed in his pape
was o measu e he jus -no icable s imuli o he pa icipa ing
subjec s. The s imuli we e de ined by ch oma ici y and in ensi y
as he main pa ame e s o he ma hema ical model. The esul s
show co elance be ween in ensi y and he jus -no icable s imuli,
as desc ibed in he Webe -F echne Law bu a con adic ion was
shown a e he analysis in he unc ion o ch oma ici y. This
con adic ion can be explained by he di e ence be ween he
sensi i i y o he h ee cones o he eye.
Keywo ds—Webe -F echne law; jus -no icable s imuli;
ch oma ici y; in ensi y; CRT display
I. INTRODUCTION
The measu emen de ailed in his pape is he pa o a
esea ch aiming o obse e he in luence o colou ed lenses on
colou ision using es s on displays. Al hough du ing his
measu emen no glasses we e used. Since he esul s o es s
c ea ed o displays signi ican ly depend on he pa ame e s o
he display, in o de o be able o ocus on he in luence o he
glasses i s we need o know how and which pa ame e s o
he display do eac o he change o he ac o s se in he
measu emen s.
II. CONDITIONS
Du ing he design p ocess o he expe imen he main aim
was o a oid he in luence o he ac o s non-de ined by us as
much as possible.
The main ac o s o he measu emen s we e in ensi y and
ch oma ici y in o de o co espond wi h he colou
ep esen a ion pa ame e s o he display. The ac ual objec o
he measu emen s was o ind he jus -no icable di e ence
be ween wo colou s imuli.
A. Loca ion
Each measu emen was held in he Visual Sys em
Labo a o y a he Depa men o Mecha onics, Op ics and
Mechanical Enginee ing In o ma ics a he Budapes
Uni e si y o Technology and Economics. The en i onmen al
ligh ing was shaded and homogeneous illuminance o 400 lux
was p o ided.
B. Exe cise
The measu emen s a ed wi h a neu al g ey sc een,
subjec s had o change he colou o a do in he middle o he
sc een un il hey could no ice he di e ence be ween he
backg ound and he do . The subjec s had o si o a posi ion
ha p o ided ha he do was seen in 5° angle o iew.
C. Subjec s
In he expe imen 6 subjec s pa icipa ed. Each o hem
was good colou obse e wi hou any colou ision
de iciency. The subjec s we e in no mal men al s a e, elaxed
and hey could easily ocus on he exce cise. The du a ion o
he measu emen was se o a oid ha he subjec s become
i ed: i ook 10 minu es.
D. Ch oma ici y
The ch oma ici y o he s imuli we e he plain R, G and B
p ime s o he display in o de o minimize he in luence o he
noise caused by mixing colou s and also in o de o be able o
calcula e wi h he in luence la e by mixing any o he colou s
om he p ime s.
E. In ensi y
In o de o se he ac o le els o in ensi y he
cha ac e is ics o he display was needed. Fig. 1. Fig. 2. and
Fig. 3. each show bo h he measu ed in ensi y o he p ime s
and a quad a ic polynomial app oxima ion depending on DAC
alues.
Recen Inno a ions in Mecha onics (RIiM) Vol. 2. (2015). No. 1-2.
DOI: 10.17667/ iim.2015.1-2/8.
2
Fig. 1. Measu ed and app oxima ed in ensi y o he R p ime o he display
Fig. 2. Measu ed and app oxima ed in ensi y o he G p ime o he display
Fig. 3. Measu ed and app oxima ed in ensi y o he B p ime o he display
The equa ions o he app oxima ion polynomials a e he
ollowing:
      
      
      
As i can be seen, only he cons an coe icien s o he
unc ions a e di e en which means ha he cha ac e is ics o
p ime s o he display a e qui e simila .
The le els o in ensi y we e selec ed om he egion whe e
he slope o he unc ion is big enough o a oid he in luence
o high noise.
III. THE MATHEMATICAL MODEL
In o de o be able o desc ibe he expe imen and he
esul s in an exac , compac mode, a ma hema ical model was
se . Since his measu emen is a pa o a esea ch he
ma hema ical model was c ea ed conside ing u he
pa ame e s and ac o le els so i is basically mo e
complica ed han as i was needed o his ac ual measu emen
Fi s de ine wo ec o s ha con ain he alues o he 2
main pa ame e s o he measu emen .
Le BDG be he se o (R,G,B) alues ha de ine he colou
o he backg ound and DOT ha con ains he (R,G,B) alues
o he colou o he jus -no icable do .
BDGi(R,G,B), whe e i=1..n 
DOTj(R,G,B), whe e j=1..m 
The expe ience is se up o n ypes o backg ounds and m
ypes o do s. Fo u he calcula ions use he ollowing uni
ma ix and uni ec o s:
  
  
  
  
Wi h hese he jus -no icable s imuli can be de ined in he
ollowing o m:
  
whe e STIM is a ma ix wi h m˙n elemen s o (R,G,B) alues.
Recen Inno a ions in Mecha onics (RIiM) Vol. 2. (2015). No. 1-2.
DOI: 10.17667/ iim.2015.1-2/8.
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The ac ual alues o he measu emen can be seen in he
ollowing o mulas:
  
The do s we e se in o de o gene a e s imuli ha con ain
only one p ime o he display so always one componen was
inc eased om he backg ound. Table 1. shows he a e age
esul o he measu emen s.
TABLE I. THE JUST-NOTICABLE COLOUR STIMULI DEPENDING ON THE
BACKGROUND AND THE COLOUR OF THE DOT
(125,125,125)
(185,185,185)
(245,245,245)
R
(3,0,0)
(4,0,0)
(4,0,0)
G
(0,2,0)
(0,2,0)
(0,3,0)
B
(0,0,4)
(0,0,5)
(0,0,6)
IV. ANALYSIS
The Webe -Fechne law [1] s a es he ela ionship be ween
he magni ude o a s imulus and he in ensi y o he e e ence
can be desc ibed in he o m:
  
whe e dI is he di e ence be ween he wo s imuli, I is he
e e ence and k is a cons an . In o de o calcula e he ac ual k
cons an s he cha ac e is ics and he app oxima ed unc ions
IR, IG and IB de ailed abo e we e used.
  
  
  
  
The esul s o he measu emen s we e analysed depending on
bo h ac o s o he expe imen .
A. The e ec o in ensi y
k˙,j alues (see Table 2.) show exac ly wha we expec ed om
he Webe -Fechne law: he s anda d de ia ions a e one
magni ude smalle han he a e ages and he highe
backg ound-in ensi y equi es bigge s imuli.
TABLE II. THE AVERAGE VALUES AND STANDARD DEVIATION OF
CONSTANT K
a e age
s anda d de ia ion
R
0,0212
0,0069
G
0,0112
0,0024
B
0,0274
0,0058
B. The e ec o colou
Table 2. gi es ano he poin o iew as i shows he k
cons an s depending on he colou o he s imuli. Acco ding o
his we could say ha he Blue p ime gi es he mos in ensi e
sign since he highes k alue belongs o ha .
In o de o unde s and his e ec de ine BRL, BRM and BRS
as he b igh ness o he R, G and B p ime s pe cei ed by he
human eye.
  
  
  
whe e R(

), G(

) and B(

) a e he spec al in ensi y unc ions
o he p ime s o he display and V(

) is he CIE luminosi y
unc ion.
Table 3. shows he B igh ness alues in pe cen age a e.
TABLE III. RATE OF PERCEPTED BRIGHTNESS OF THE PRIME CHANNELS
OF THE DISPLAY
BRR
BRG
BRB
44,08%
100%
13,77%
The alues show ha he G een channel sends he b igh es
pe cei ed sign. Acco ding o he Webe -Fechne law he
highes jus -no icable s imuli should belong o ha howe e
he esul s o he measu emen show he opposi e.
Recen Inno a ions in Mecha onics (RIiM) Vol. 2. (2015). No. 1-2.
DOI: 10.17667/ iim.2015.1-2/8.
4
The conclusion o he Webe -Fechne law abo e assumes
ha he sensi i i y o he ecep o s a e he same du ing he
measu emen s and don’ depend on he colou o he s imuli.
Fig. 4. shows he spec al sensi i i y o he cones and he
spec al in ensi y o he p ime s o he display.
Fig. 4. Spec al sensi i i y o he L, M and S ecep o s and spec al in ensi y
o R, G and B p ime s o he display
I can be seen ha each p ime has a spec al in ensi y
co esponding o he sensi i i y o a cone so basically each
cone can see one o he p ime channels
Di e en s imuli a e mainly pe cei ed by di e en cones
(neglec ing he o e laps) so he k cons an s a e no compa able
wi hou knowing he a io o he sensi i i y o he cones.
Con e sely, his con ex does no only explain he
con adic ion be ween he Webe -Fechne law and ou esul s
bu i also gi es in o ma ion o he sensi i i y o he cones.
Since he smalles jus -no icable s imuli belongs o he
channel o which also belongs he highes pe cei ed
b igh ness, assuming ha he s imuli gene a ed by he G
p ime a e pe cei ed by he cone deu e os, i can be said ha
he deu e os has he bes esolu ion among i os and p o os.
V. CONCLUSION
Since he da a o he measu emen s was analysed
conside ing bo h main ac o s wo conclusions can be s a ed.
The main esul we shall es ablish is ha he con adic ion
be ween he Webe -Fechne law and he da a o he
measu emen s was caused by he di e ence be ween he
sensi i i y o he cones depending on colou s. Addi ional
esul is ha he sensi i i y depending on in ensi y o he
pe cei ed ligh did co espond wi h he Webe -Fechne law.
Re e ences
[1] Selig Hech , The isual disc imina ion o in ensi y and he Webe -
Fechne law, 1924
[2] D . Ákos An al, D . K isz ián Samu, A moni o os színlá ás izsgála hazai
el e jedése, OPTIKAI MAGAZIN 16:(2) pp. 54-55., 2012
[3] D . Klá a Wenzel, Áb ahám Gy., Kucse a I., Ko ács G., So e ius M.:
Possibili ies o colou adap a ion, CIE Symposium ’99, Budapes , 1999.
[4] D . Klá a Wenzel: Op ics o Colo s, Womenomics, GE Women’s
Ne wo k Ligh ing Hunga y, Budapes , 2010.07.02.
[5] D . Klá a Wenzel: Indi idual Cha ac e is ics o Colou Vision, Colou
Dynamics ‘88, Budapes , No embe 2-6, 1988