Measurement of the effect of chromaticity and intensity on colour representation parameters of a CRT display

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. 3 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