Sandra Olsson

Ludvig Z Csajbok

Katarina Jood

Karin Nylén

Bengt Nellgård

Christina Jern
email: christina.jern@neuro.gu.se

Association between genetic variation on chromosome 9p21 and aneurysmal subarachnoid haemorrhage

Keywords: intracranial aneurysm, subarachnoid haemorrhage, single nucleotide polymorphism

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Subarachnoid haemorrhage (SAH) is a serious condition that has a young age onset and poor outcome. The incident rate in Sweden is 12.4/100 000 person-years. [START_REF] Koffijberg | Subarachnoid haemorrhage in Sweden 1987-2002: Regional incidence and case fatality rates[END_REF] SAH is in 85% of the cases caused by the rupture of an intracranial aneurysm (IA). [START_REF] Van Gijn | Subarachnoid haemorrhage: Diagnosis, causes and management[END_REF] The most important risk factors are smoking, hypertension, and excessive alcohol intake. [START_REF] Feigin | Risk factors for subarachnoid hemorrhage: An updated systematic review of epidemiological studies[END_REF] SAH occurs more often in women. [START_REF] Linn | Incidence of subarachnoid hemorrhage: Role of region, year, and rate of computed tomography: A meta-analysis[END_REF] In addition, genetic factors have also shown to play an important role in SAH.

First-degree relatives of SAH patients have three to five times higher risk of SAH than the general population. [START_REF] Gaist | Risk of subarachnoid haemorrhage in first degree relatives of patients with subarachnoid haemorrhage: Follow up study based on national registries in Denmark[END_REF] Furthermore, it is estimated that about 9% of first degree relatives to patients suffering from SAH/IA harbour an unruptured IA, [START_REF] Brown | MR angiography and surgery for unruptured familial intracranial aneurysms in persons with a family history of cerebral aneurysms[END_REF][START_REF] Ronkainen | Familial intracranial aneurysms[END_REF] whereas the population frequency is approximately 2%. [START_REF] Rinkel | Prevalence and risk of rupture of intracranial aneurysms: A systematic review[END_REF] As there is heritability in IA, whole-genome linkage studies have been conducted and linkage has been found to several loci. In the largest whole-genome linkage study comprising 333 families possible linkage to 4q and 12p was detected [START_REF] Foroud | Genome screen in familial intracranial aneurysm[END_REF]. There is also one genome-wide association study (GWAS) on IA, on two European populations and one Japanese population, in which associations were found for 2q33, 8q11 and 9p21 [START_REF] Bilguvar | Susceptibility loci for intracranial aneurysm in european and japanese populations[END_REF]. Association between 9p21 and IA was also shown by Helgadottir et al in a candidate gene study including three different European populations [START_REF] Helgadottir | The same sequence variant on 9p21 associates with myocardial infarction, abdominal aortic aneurysm and intracranial aneurysm[END_REF]. Interestingly, 9p21 also shows association to other vascular phenotypes such as coronary artery disease (CAD), [START_REF] Helgadottir | Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls[END_REF][12][START_REF] Samani | Genomewide association analysis of coronary artery disease[END_REF][START_REF] Mcpherson | A common allele on chromosome 9 associated with coronary heart disease[END_REF][START_REF] Broadbent | Susceptibility to coronary artery disease and diabetes is encoded by distinct, tightly linked SNPs in the ANRIL locus on chromosome 9p[END_REF] ischemic stroke (IS), [START_REF] Matarin | Whole genome analyses suggest ischemic stroke and heart disease share an association with polymorphisms on chromosome 9p21[END_REF] aortic aneurysms, [START_REF] Helgadottir | The same sequence variant on 9p21 associates with myocardial infarction, abdominal aortic aneurysm and intracranial aneurysm[END_REF] and arterial stiffness. [18] The molecular mechanism underlying these associations has not yet been identified. However, the findings that 9p21 is associated with aneurysms and arterial stiffness suggest that genetic variations at this locus may influence vessel properties, thereby leading various vascular diseases susceptibility.

3

The aim of the present study was to investigate whether there is an association between genetic variants on 9p21 and ruptured IA, ie aneurysmal subarachnoid haemorrhage (aSAH), in a Swedish population, and if so, to evaluate whether this association is independent of hypertension as well as smoking.

METHODS

Study Population

Consecutive Caucasian patients presenting with SAH admitted to the Neurointensive Care Unit (NICU) at the Sahlgrenska University Hospital, between 2000 and 2004, were recruited.

During this period, out of 253 patients considered, 183 fulfilled the diagnostic criteria and were willing to participate in the study. A detailed description of the inclusion criteria has been published. [START_REF] Ladenvall | Association between factor XIII single nucleotide polymorphisms and aneurysmal subarachnoid hemorrhage[END_REF][START_REF] Nylén | Serum glial fibrillary acidic protein is related to focal brain injury and outcome after aneurysmal subarachnoid hemorrhage[END_REF] SAH was defined by symptoms suggestive of SAH combined with subarachnoid blood on computed tomography (CT). Only patients with aSAH, defined as an aneurysm visualised on intra-arterial angiography, were included. Patients were treated with neurosurgical clipping or by endovascular coiling. For each case two healthy Caucasian controls, matched for age (+/-2 years), sex, and geographical residence area, were randomly selected from a population based health survey [START_REF] Wilhelmsen | Risk factors for cardiovascular disease during the period 1985-1995 in Göteborg, Sweden. The GOT-MONICA project[END_REF] or from the Swedish Population Register.

The latter source was used to recruit controls younger than 30 years of age. All participants gave informed consent, and when patients were unable to communicate his or her next-of-kin gave informed consent. The Medical Ethics Committee at the University of Gothenburg approved the study.

Clinical characteristics

Smoking history was coded as current versus never or former smoker (smoking cessation at least one year before inclusion in the study) and hypertension was defined by pharmacological treatment for hypertension prior to the event.

Genotyping

Because the causative functional variant(s) in the region 9p21 has not yet been identified, a region of 44kbp, between position 22071397 and 22115503, on 9p21 was tagged using HapMap CEU data (Rel 23a) and HaploView 4.1 (r 2 =0.8 and minor allele frequency (MAF) 0.1), resulting in 6 tag SNPs, rs10965227, rs1547705, rs7857345, rs1333045, rs1333040, and rs10757278. The analysed region includes SNPs that in previous studies have been shown to associate to IA (figure 1). [START_REF] Bilguvar | Susceptibility loci for intracranial aneurysm in european and japanese populations[END_REF][START_REF] Helgadottir | The same sequence variant on 9p21 associates with myocardial infarction, abdominal aortic aneurysm and intracranial aneurysm[END_REF] The SNP rs1537378, recently found to be associated to the ischemic stroke subtype large vessel disease (LVD), was also included. [START_REF] Gschwendtner | Sequence variants on chromosome 9p21.3 confer risk for atherosclerotic stroke[END_REF] Genotyping was performed by TaqMan Assays. Primers and probes were obtained from Applied Biosystems (C_31288976_10, C_1754687_20, C_29146326_10, C_8766826_10, (C_8766795_10), C_11841860_10, and C_83169_10). Amplifications were carried out on a 384 Well GeneAmp ® PCR System 9700 (Applied Biosystems) and fluorescence was analysed on an ABI PRISM ® 7900HT Sequence Detector System (Applied Biosystems). Genotyping was performed blinded to case-control status. The assay for rs1333040 (C_8766795_10) failed and could not be replaced. The five SNPs that were successfully genotyped tag 90% of the genotyped SNPs in HapMap, in the region of interest.

Statistics

Allele frequencies were derived from genotype data, and deviations from the Hardy Weinberg equilibrium (HWE) were tested. Associations between single SNPs and case control status were investigated using univariate and multivariate binary logistic regression using an additive model. The multivariate model included hypertension and smoking status as covariates. The interaction between genotype and smoking/gender was also tested in a binary logistic regression. Haplotype frequencies and associations between haplotypes and case controls status were estimated using THESIAS. [START_REF] Tregouet | A new java interface implementation of THESIAS: Testing haplotype effects in association studies[END_REF] This method uses a stochastic EM algorithm for likelihood maximisation. The individual likelihood for each haplotype was used to estimate odds ratios (ORs) for each haplotype by comparison to a reference haplotype represented by the most frequent haplotype. Data was analysed using SPSS 16.0 (SPSS Inc, USA), and statistical analyses were performed in a two tailed fashion. P<0.05 was considered significant. The studied SNPs have MAFs between 0.14 and 0.50 (median 0.30) according to HapMap (CEU population), and it was estimated that the study has 80% power to detect an OR of 1.45 at the 5% level for SNPs with a MAF of 0.3 for the risk allele. No correction for multiple testing was conducted since most SNPs are in high LD and a Bonferroni correction would be too conservative.

Missing values

Information on smoking status was missing in six cases due to intervening death, and information on hypertension was missing in one case. Genotyping success rates were between 98 and 100%.

RESULTS

Clinical characteristics for this sample have been published. [START_REF] Ladenvall | Association between factor XIII single nucleotide polymorphisms and aneurysmal subarachnoid hemorrhage[END_REF] In short, the mean age of patients and controls was 55 (range 20-81) years and 74% were females. As expected, smokers were more frequent in cases compared to controls (54% versus 20%). Furthermore, 23% of patients and 19% of controls had antihypertensive treatment. Genotype frequencies are presented in table 1. In controls all genotype frequencies were consistent with HWE.

Two SNPs showed a significant association with aSAH in univariate logistic regression analysis (table 2). The uncommon allele (G) of SNP rs10757278 was associated with an increased risk of aSAH. This association remained significant after adjustment for hypertension and smoking (table 2). For comparative purpose with earlier data, ORs for both heterozygote and heterozygote subjects were calculated. The univariate ORs for aSAH were 1.25 (95% CI 0.80-1.95) and 1.95 (1.18-3.22) for heterozygote subjects and for subjects homozygote for the rs10757278 G allele, respectively. The corresponding multivariate ORs were 1.38 (95% CI 0.85-2.24) and 2.01 (1.16-3.49), respectively. Approximately 24% of the patients and controls were homozygous for the rs10757278 G allele, which is in line with previous studies on individuals of European descent. [START_REF] Helgadottir | The same sequence variant on 9p21 associates with myocardial infarction, abdominal aortic aneurysm and intracranial aneurysm[END_REF] The uncommon allele (A) of rs1333045 was associated with a decreased risk of aSAH (table 2). However, this association did not remain significant after adjustment for hypertension and smoking (table 2). In the logistic regression analysis an additive model was used. Because the causative variant is unknown, the genetic effect remains to be determined. In addition, we therefore compared genotype frequencies in cases and controls by the chi-square test. For the lead SNP, rs10757278, there was also a significant difference with regard to genotype frequencies between cases and controls (table 1). Haplotype analysis, including SNP rs10965227, rs1547705, rs7857345, rs1333045, and rs10757278, did not add any further information compared to single SNP analyses (data not shown).

Because rs10757278 was the lead SNP in the overall analysis, we focused on this variant in subsequent subanalyses. In a sex specific subanalysis no significant sex specific difference was detected. Multivariate ORs of aSAH for rs10757278 were 1.49 (95% CI 1.07-2.07, p=0.02) and 1.27 (95% CI 0.74-2.16, p=0.39) for women and men, respectively.

Smoking is considered to be the most important modifiable risk factor for aSAH, [START_REF] Feigin | Risk factors for subarachnoid hemorrhage: An updated systematic review of epidemiological studies[END_REF] and evidence of an interaction between current smoking and familial aggregation of IA/SAH has been reported. [START_REF] Woo | Smoking and family history and risk of aneurysmal subarachnoid hemorrhage[END_REF] In our sample, 371 participants (79 patients and 292 controls) were nonsmokers and 172 (98 patients and 74 controls) were smokers. An association between aSAH and rs10757278 was found in non-smokers, but not in smokers (univariate OR 1.47, 95% CI 1.03-2.10, p=0.03 and OR 1.37, 95% CI 0.89-2.11, p=0.15 respectively). However, there was no significant interaction between genotype and smoking status, i.e. there was no significant difference in the effect of rs10757278 between non-smokers and smokers.

Genotype frequencies for the additional SNP, rs1537378, are presented in table 1. In controls the genotype distribution was in HWE. No significant association with aSAH was detected (table 2). This SNP was not included in the haplotype analysis, since it is located in another linkage disequilibrium (LD) block compared to the other SNPs in this study.

DISCUSSION

This case-control study with participants from Sweden provides evidence for an association between genetic variations on chromosome 9p21 and ruptured IA, thus confirming earlier data on an association between genetic variants on this genetic region and IA. [START_REF] Bilguvar | Susceptibility loci for intracranial aneurysm in european and japanese populations[END_REF][START_REF] Helgadottir | The same sequence variant on 9p21 associates with myocardial infarction, abdominal aortic aneurysm and intracranial aneurysm[END_REF] In addition, this association was shown to be independent of hypertension as well as smoking.

The 9p21 candidate region investigated in this study is 44kbp. In addition to the SNPs showing association to IA in previous studies, this region also harbours SNPs that have shown to associate with CAD in several GWAS. [START_REF] Helgadottir | Genome-wide association study of 14,000 cases of seven common diseases and 3,000 shared controls[END_REF][12][START_REF] Samani | Genomewide association analysis of coronary artery disease[END_REF][START_REF] Mcpherson | A common allele on chromosome 9 associated with coronary heart disease[END_REF][START_REF] Broadbent | Susceptibility to coronary artery disease and diabetes is encoded by distinct, tightly linked SNPs in the ANRIL locus on chromosome 9p[END_REF] We found the rs10757278 G allele to be significantly associated with an increased risk of aSAH. The effect of the G allele was additive with univariate ORs of 1.25 and 1.95 for heterozygote and homozygote subjects, respectively. This finding is in line with results from a recent study on three different populations from northern Europe with different vascular phenotypes, including IA and abdominal aortic aneurysms (AAA). [START_REF] Helgadottir | The same sequence variant on 9p21 associates with myocardial infarction, abdominal aortic aneurysm and intracranial aneurysm[END_REF] With regard to the phenotype IA, patient inclusion in the mentioned study was based on the diagnosis of IA, but approximately 87% of the patients had suffered from aSAH. The ORs for IA in all three populations combined were 1.38 (95% CI 1.18-1.63) and 1.72 (1.39-2.13) for subjects who were heterozygote and homozygote for the G allele, respectively. A similar effect of the G allele was observed with regard to the risk of AAA. [START_REF] Helgadottir | The same sequence variant on 9p21 associates with myocardial infarction, abdominal aortic aneurysm and intracranial aneurysm[END_REF] Peripheral artery disease and stroke (large artery atherosclerotic or cardiogenic stroke) also showed significant association with rs10757278 in this study, but with lower ORs. [START_REF] Helgadottir | The same sequence variant on 9p21 associates with myocardial infarction, abdominal aortic aneurysm and intracranial aneurysm[END_REF] There is one additional study showing association between 9p21 and IA. [START_REF] Bilguvar | Susceptibility loci for intracranial aneurysm in european and japanese populations[END_REF] The Caucasian populations in this study were from Finland and the Netherlands and in the two cohorts approximately 81% of the patients had suffered from aSAH. Associations to IA were observed for three SNPs on 9p21, rs1333040, rs10116277, and rs2383207, with ORs of 1.58-1.66 for homozygote subjects. As the lead SNP in the present study, rs10757278, is in LD with rs1333040, rs10116277, and rs2383207 (r 2 =0.57, 0.89, and 0.86, respectively) our results are in agreement with the study conducted by Bilguvar et al. [START_REF] Bilguvar | Susceptibility loci for intracranial aneurysm in european and japanese populations[END_REF] As there is one study showing association between variants on 9p21 and arterial stiffness, and there is data indicating that arterial stiffness is involved in the development of hypertension, [START_REF] Liao | Arterial stiffness and the development of hypertension. The ARIC study[END_REF][START_REF] Dernellis | Aortic stiffness is an independent predictor of progression to hypertension in nonhypertensive subjects[END_REF] it may be important to adjust for hypertension when assessing the association between 9p21 and ruptured IA. We found the association between aSAH and the SNP rs10757278 to be independent of hypertension and also of smoking. This is in line with some studies on other vascular phenotypes that report independent association between 9p21 and IS, [START_REF] Gschwendtner | Sequence variants on chromosome 9p21.3 confer risk for atherosclerotic stroke[END_REF][START_REF] Smith | Common genetic variants on chromosome 9p21 confers risk of ischemic stroke: A large-scale genetic association study[END_REF] the IS subtype LVD, [START_REF] Gschwendtner | Sequence variants on chromosome 9p21.3 confer risk for atherosclerotic stroke[END_REF][START_REF] Olsson | Genetic variation on chromosome 9p21 shows association with the ischaemic stroke subtype large-vessel disease in a Swedish sample aged ≤70[END_REF] CAD, [START_REF] Mcpherson | A common allele on chromosome 9 associated with coronary heart disease[END_REF] and myocardial infarction (MI). [START_REF] Samani | Genomewide association analysis of coronary artery disease[END_REF][START_REF] Mcpherson | A common allele on chromosome 9 associated with coronary heart disease[END_REF] There are however, conflicting data from two studies that observed associations between genetic variations on 9p21 and IS or MI, that did not remain significant after adjustment for vascular risk factors. [START_REF] Matarin | Whole genome analyses suggest ischemic stroke and heart disease share an association with polymorphisms on chromosome 9p21[END_REF][START_REF] Zee | Two common gene variants on chromosome 9 and risk of atherothrombosis[END_REF] However, the latter studies had smaller sample sizes.

Interestingly, there is evidence of an interaction between familial aggregation of IA/SAH and current smoking. [START_REF] Woo | Smoking and family history and risk of aneurysmal subarachnoid hemorrhage[END_REF] However, we did not find any significant interaction between rs10757278 and smoking. Similar findings could be seen for CAD. [START_REF] Broadbent | Susceptibility to coronary artery disease and diabetes is encoded by distinct, tightly linked SNPs in the ANRIL locus on chromosome 9p[END_REF] Thus, the interaction between family history and smoking is likely to be mediated by other genes. In fact, preliminary data from a GWAS on Caucasian families from the United States, show a multiplicative interaction between smoking and SNPs in the phosphodiesterase 1A (PDE1A) and type IX collagen (COL9A1) genes for IA susceptibility. [START_REF] Broderick | The interaction of genes and smoking in the familial intracranial aneurysm (FIA) study: A genome-wide association study (GWAS)[END_REF] We also investigated rs1537378, which is located outside the previously analysed LD block on 9p21, because this SNP was recently reported to show association with the ischemic stroke subtype LVD. [START_REF] Gschwendtner | Sequence variants on chromosome 9p21.3 confer risk for atherosclerotic stroke[END_REF] In contrast to LVD, we did not detect an association to aSAH.

The 9p21 locus harbouring rs10757278 does not contain any protein coding genes, but a large non-coding RNA (ncRNA) ANRIL. As for most ncRNAs, there is limited knowledge about the function of ANRIL, but expression of ANRIL has been detected in a wide range of cell types and tissues, including AAAs, [START_REF] Broadbent | Susceptibility to coronary artery disease and diabetes is encoded by distinct, tightly linked SNPs in the ANRIL locus on chromosome 9p[END_REF] and ANRIL was suggested as the prime 9p21 candidate gene for CAD. [START_REF] Broadbent | Susceptibility to coronary artery disease and diabetes is encoded by distinct, tightly linked SNPs in the ANRIL locus on chromosome 9p[END_REF] Furthermore, studies indicate that genetic variations on 9p21 influence the expression of ANRIL. [31][32][START_REF] Liu | INK4/ARFtranscript expression is associated with chromosome 9p21 variants linked to atherosclerosis[END_REF] Potentially interesting genes adjacent to the investigated region are CDKN2A and CDKN2B. CDKN2A encodes two proteins, p14 (ARF) and p16 (INK4a). CDKN2B encodes p15 (INK4b). These are all tumour suppressor proteins involved in proliferation, aging, and senescence.[34] It has also been proposed that p16 can modulate the production of inflammatory molecules such as matrix metalloproteinase 3 (MMP-3) and monocyte chemoattractant protein 1 (MCP-1). [START_REF] Nonomura | Direct modulation of rheumatoid inflammatory mediator expression in retinoblastoma protein-dependent andindependent pathways by cyclin-dependent kinase 4/6[END_REF] Additionally, expression of ANRIL is positively correlated with the expression of p14, and possibly also with that of p16 and p15, in both physiologic and pathologic conditions suggesting a coordinated transcriptional regulation of theses genes. [START_REF] Pasmant | Characterization of a germ-line deletion, including the entire INK4/ARF locus, in a melanoma-neural system tumor family: Identification of ANRIL, an antisense noncoding RNA whose expression coclusters with ARF[END_REF] Further work is needed to determine if the association between 9p21 and aSAH is mediated through ANRIL and/or any of the mentioned genes. Moreover, it can not be excluded that the SNPs of interest could be situated in a distant enhancer effecting genes further away.

This study has some limitations worth noting. Although patients were recruited consecutively, there is of course a recruitment bias due to early fatality as well as due to the fact that patients with initial signs of an unfavourable prognosis often are treated outside the NICU. The inclusion criteria being aSAH also introduced some bias because some patients with poor prognosis do not undergo angiography. The control group was recruited by random sampling from the general population in the same geographical areas as the patients, which makes the possibility of selection bias in this group less likely. In the present study, we controlled for the risk factors hypertension and smoking. However, we did not control for alcohol intake, because it is difficult to obtain reliable data on this variable. The main advantages of our study are the relatively homogeneous and large patient group with confirmed ruptured aneurysms, a population based control group, and a well characterised sample with regards to the risk factors hypertension and smoking.

In conclusion, this study shows a significant association between genetic variation on chromosome 9p21 and aSAH with rs10757278 as the lead SNP. This association was independent of hypertension and smoking.

Figure 1

 1 Figure 1 Graphic representation of the LD structure in the region 9p21 between position

Table 2

 2 Association between SNPs on 9p21 and aSAH

		Uncommon	Univariate	Multivariate*
	SNP	allele	OR (95% CI)	OR (95% CI)
	rs10965227	G	0.85 (0.62-1.17), p=0.32	0.83 (0.58-1.19), p=0.31
	rs1547705	C	1.37 (0.93-2.01), p=0.11	1.39 (0.91-2.11), p=0.12
	rs7857345	A	0.77 (0.58-1.01), p=0.06	0.80 (0.59-1.07), p=0.14
	rs1333045	A	0.76 (0.59-0.98), p=0.04	0.78 (0.59-1.02), p=0.07
	rs10757278	G	1.40 (1.09-1.80), p=0.01	1.42 (1.08-1.87), p=0.01
	rs1537378	A	0.78 (0.60-1.02), p=0.07	0.8 (0.60-1.07), p=0.14
	aSAH, aneurysmal subarachnoid haemorrhage
	OR, odds ratio
	CI, confidence interval
	ORs were calculated using an additive model

*Multivariate analysis adjusted for hypertension and smoking status

Acknowledgements

The authors wish to thank Ingrid Eriksson, Ingrid Eiving, Ingrid Pettersson, and Catherine Ritzén for excellent technical support. We also thank the Genomics Core Facility, at the Sahlgrenska Academy at the University of Gothenburg.

Funding

This study was supported by the Swedish Research Council (K2008 65X-14605-06-3), grants from the Swedish state under the LUA/ALF agreement (ALFGBG-11206), the Swedish Heart Lung Foundation (20070404), the Swedish Stroke Association, the Rune and Ulla Amlövs Foundation for Neurological Research, the John and Brit Wennerström Foundation for Neurological Research, and the Yngve Land Foundation for Neurological Research. The founding sources did not influence the study design, the collection, analysis, and interpretation of data, or drafting and writing of the manuscript.

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Competing Interest:

None declared.


Baptiste Laborie
email: baptistelaborie@mnhn.fr

Françoise Viénot

Sabine Langlois

Methodology for constructing a colour-difference acceptability scale

Keywords: Acceptability, colour-difference, category scaling, plasma display panel

Observers were invited to report their degree of satisfaction on a 6-point semantic scale with respect to the conformity of a test colour with a white reference colour, simultaneously presented on a PDP display. Eight test patches were chosen along each of +a*, -a*, +b*, -b* axes of the CIELAB chromaticity plane, at Y=80 +/-2 cd.m -². Experimental conditions reliably represented the automotive environment (patch size, angular distance between patches) and observers could move their head and eyes freely.

 and logistic regression) and the medians method. We describe in detail a case where all methods yield substantial but slightly different results. The solution proposed by the regression method which works with incomplete matrix and yields results directly on a colorimetric scale is probably the most useful in this industrial context. Finally we summarize the implementation of the logistic regression method over four hues and for one experimental condition.

Introduction

Purpose

Car manufacturers are increasingly incorporating displays inside their vehicles. Due to the increasing amount of displayed information and to the large variety of technologies, one of the main issues raised by these new interfaces is the conformity of the screens with a target and specifically in terms of displayed colours. Colorimetry proposes different solutions in terms of colour difference perceptibility and colourdifference acceptability [START_REF] Witt | CIE colour difference metrics[END_REF]. Colour-difference perceptibility deals with the ability of an observer to detect a difference between two colour samples. The smallest perceptible difference is known as a just-noticeable difference (JND). In a psychophysics experiment where a series of colour tests are to be compared with a colour reference, a colour-difference threshold can be derived from the statistical count of non-perceived and perceived colour differences. However, practically, in an industrial process, repeatability and reproducibility of a colour target may be difficult to achieve at a reasonable cost. Moreover, when asked to provide a visual judgment, an observer may interpret the acceptable colour-difference, depending upon the intended or anticipated end use of the product [START_REF] Judd | Color in business, science, and industry[END_REF]. Thus colour-difference acceptability results from a compromise between the process outcome and the customer expectations [START_REF] Berns | Billmeyer and Saltzman's Principles of color technology[END_REF]. An additional complexity is that the user environment may vary in terms of stimulus configuration, background and luminous adaptation. To characterize displays in the real automotive context, information is needed on colour comparison experiments when the background is not uniform, when the stimuli are positioned at a distance, when the observer can freely explore the visual field.

Background

When a producer must deliver a product of the desired colour with its variation controlled to an extent appropriate for the product's use and the customer's expectations, he may start with the colour-difference equations recommended by the CIE for specifying industrial colour-differences. The CIE ΔE 94 and CIEDE2000 equations are based on CIELAB colour difference specifications and can be used to derive-colour difference tolerances by introducing factors to correct for the parametric effects of various conditions of use [START_REF] Cie | Industrial Colour-Difference Evaluation[END_REF][START_REF] Cie | Improvement to Industrial Colour-Difference Evaluation[END_REF]. Meanwhile, rigorous reference conditions define material and viewing environment characteristics to which the colour-difference model applies. Unfortunately, several viewing conditions imposed by, such as uniform background, sample pairs with direct edge contact and foveal viewing, may considerably deviate from the reference viewing conditions in practical situations. Since the CIECAM02 colour appearance model has been developed to predict corresponding colours in asymmetric conditions, allowing for surround and background effects, a few attempts have been made to propose modified versions of CIECAM02 to fit small colour difference (SCD) and large colour difference (LCD) data sets. The LCD group includes six data sets having CIELAB colour difference values ranging from 9 to 14 with an average of 10. Thus a unique polar structure consisting of lightness, colourfulness and hue angle could be used to develop uniform colour spaces in which equal distances approximately represent equal colour differences [START_REF] Luo | Uniform colour spaces based on CIECAM02 colour appearance model[END_REF].Whereas a large colour-difference is easily perceived, it seems difficult for an observer to identify the colour attribute responsible for a colour difference. Only 72.4% successful identification was obtained for an average value of 15.8 CIELAB units [START_REF] Melgosa | Are we able to distinguish color attributes?[END_REF].

Usually, every manufacturing company defines experimentally its own colour tolerance. Thus, several observers are invited to judge whether the colour difference between a sample and standard is acceptable for a given set of viewing conditions or with respect to the end-use of the product. Pairs of samples are sorted between "pass" and "fail". Cumulative percentages for each class are plotted versus the instrumental colour difference calculated using a colour-difference equation. A decision is made that minimizes the number of instrumental wrong decisions [START_REF] Berns | Billmeyer and Saltzman's Principles of color technology[END_REF]. The procedure is very efficient economically. Nonetheless, it needs to be repeated every time the quality of the manufacturing process changes.

The hypothesis that colour discriminability and colour appearance are controlled by a common set of mechanism has been tested through experimental determination of JNDs and asymmetric matching. The proposed model presumes that the JND proportion has equal changes in the neural response along a single stimulus dimension and therefore reflect the local slope of an appearance response function. Thus discrimination data can be used to infer the appearance response function and eventually using a parametric description of this function [START_REF] Grand | Optique physiologique, tome II: lumière et couleurs[END_REF][START_REF] Hillis | Do common mechanisms of adaptation mediate color discrimination and appearance? Uniform backgrounds[END_REF]. Whichever generality the model has, it satisfies only the limited set of stimulus conditions chosen in the experiment.

An additional difficulty arises when two patches that are being compared are well apart, because peripheral colour vision is inevitably implicated. Colour discrimination in the periphery of the visual field has been examined through various psychophysical approaches. Asymmetric colour matches between a foveal three primary colour mixture and an extrafoveal monochromatic test showed a progressive reduction in size and shape of the chromaticity diagram with increasing distance from the fovea up to 50° [START_REF] Moreland | Peripheral colour vision[END_REF]. Discrimination that depends only upon S-cones was improved by introducing a small gap between the two fields to be compared [START_REF] Boynton | The gap effect: chromatic and achromatic visual discrimination as affected by field separation[END_REF]. Evaluation of the effect of sample proximity upon threshold colour differences and upon sensitivity to small but clearly perceived colour differences indicated that field separation affects chromatic discrimination while no measurable loss of supra-threshold chromatic discrimination was recorded when the test field and the comparison field were separated by as much as 4.1° of visual angle. Nevertheless, large observer variability was encountered. [START_REF] Sharpe | Proximity factor in color-difference evaluations[END_REF]. Measured by a method of two-alternative spatial forced choice along either the L/(L +M) or the S/(L +M) axis of colour space, chromatic discrimination was found optimal when there was a small spatial interval between the boundaries of the stimuli; thereafter thresholds rose moderately with increasing angular separation, up to 10°. The two stimuli were presented shortly (100 ms) and at 5° eccentricity with a fixation point [START_REF] Danilova | The comparison of spatially separated colours[END_REF]2006).Provided that the stimulus size is optimal (8°), colour stimuli along the (S-(L+M)) or the (L-M) chromatic direction could be reliably detected, identified and discriminated at eccentricities up to 50°. Although, the decline in reddish-greenish L-M sensitivity was greater than for bluish-yellowish (S-(L+M)) sensitivity, the decrease in sensitivity with peripheral presentation could be compensated by increasing the size of the stimulus [START_REF] Hansen | Color perception in the intermediate periphery of the visual field[END_REF].Visual experiments were conducted to investigate parametric effects of sample separation and sample size in assessing colour difference. The observer was asked to grade the colour difference between two samples with respect to the differences between a series of samples from a grey scale and a "standard" grey sample. It was found that if both grey scale pair and test pair have a 3-in gap (3-in is also the size of a sample), the colour difference perceived is slightly smaller (8%) than if both pairs are in hairline separation. It is clear that, in this condition, the effect of sample separation is reduced out by the same separation of the grey scale pair [START_REF] Xin | Investigation of parametric effects using medium colour-difference pairs[END_REF].

Proposal

Finally, the user satisfaction is the main concern for manufacturers. What is the acceptable colour-difference for most observers? We acknowledge that the measurement of colour difference threshold is not of any help when dealing with suprathreshold colour differences. We have to design an experiment to measure the acceptability of colour differences. Due to the specific use of colour in displays, the measurement should be made in similar conditions to the automotive context. Furthermore, because of the ongoing change in technology, a unique decision point might not be exploited in the future, so a category scale is preferred.

To answer the question "What is the acceptable colour-difference for most observers?", we propose to ask a number of observers what would be their degree of satisfaction in terms of colour conformity if they were offered to compare the colour of two displays mounted on the dashboard of the vehicle. Colours should be presented to the observer as far as possible in real life conditions where the observer explores the stimulus at will. We propose to construct an acceptability scale by linking the CIELAB colour-difference specification and the degree of satisfaction of the observers in terms of conformity of two colours. Category scaling differs from threshold measurement in the sense that it deals with the subjective assessment of a perceived attribute which reflects the quality of a product rather than with the ability of the individual to discriminate between JND values of the attribute [START_REF] Krantz | Visual scaling[END_REF][START_REF] Engeldrum | Psychometric Scaling: A Toolkit for Imaging Systems Development[END_REF]. In this study, we propose a category scale where category labels are adjectives easily understood by the observer. The underlying framework of a category scaling procedure is given by Torgerson as the Law of Categorical Judgment (Torgerson, 1958, chapter 10). -"A psychological continuum of the attribute of interest is postulated". Any given stimulus elicits a response in the psychological continuum of the subject. Nevertheless, the value of the response is not always the same and all values associated with this stimulus are normally distributed in the psychological continuum. -Another assumption is that the psychological continuum of the subject can be divided into a number of ordered categories. Additionally a given category boundary is not always located at a particular point on the continuum.

It is defined by a mean location and dispersion. A complete form of the law of categorical judgment is usually too complex to bring a solution. For this reason, Torgerson has proposed a classification and simplifications of the problem. In this study, we have investigated the degree of satisfaction of observers in relation with the difference between two white patches using category scaling. The range of colour differences exceeds the traditional limits of colorimetric differences. We have chosen experimental conditions that reliably represent the automotive environment (patch size, angular distance between patches). Finally, we could compare the results from several scaling methods.

Methods

Display calibration

Colour patches were presented on a large Plasma Display Panel (PDP) (Pioneer KRP-500M, 50", 1920 x 1080 pixels).

-Gamma setting. Automatic controls were disconnected. "Brightness" and "Contrast" were fixed to avoid saturation. The final gamma equalled 2.2.

-RGB setting:

The maximum luminance of each primary was adjusted to obtain sRGB white (x=0.3127, y=0.3290). Contrary to what could be achieved in computer-controlled CRT displays [START_REF] Cie | The Relationship between Digital and Colorimetric Data for Computer-Controlled CRT Displays[END_REF][START_REF] Iec | sRGB default RGB colour space[END_REF], neither the standard matrix, nor the interchannel matrix could provide a workable display calibration. The strategy adopted to circumvent this problem has been to build look-up-tables (LUT) around every target colour. Moreover, the displayed image is continuously changed by the built-in energy saving mode to reduce its energy consumption. In particular, the light smoothly shuts down when no event occurs in the image. To avoid any instability of the luminance, we have refreshed at regular time intervals some part of the image that lied out of a region of interest.

Psychophysical experiment

Experimental conditions

This study was part of a research program on colour-difference acceptability in an automotive context. The experiment took place in the laboratory where the surrounding conditions were created to simulate the automotive interior. The observer was seated at a distance of 1 meter from a 50" PDP display. This geometrical configuration reproduces at best the geometry of a seated driver facing the steering wheel of the vehicle and seeing in his viewing field the dashboard with all displays.

As a whole, it was possible to display colour patches at eccentricity as far as 40

degrees. The advantage of the PDP technology is its lambertian emissivity which ensures the validity of display calibration at any viewing angle. The observer could move his head and eyes freely. The background could be grey, black or the photograph of an automotive interior. Additionally, a video projector illuminated a part of the wall surface at the top of the display, at the same luminance as the background, in order to extend the field of view as through the windscreen. The photography (Figure 1) illustrates these experimental conditions.

A pair of square patches was displayed on the PDP display at a photopic luminance level, one being the reference colour, the other being the test colour.

-In this experiment, the reference colour was white (D65) at luminance Y=80 cd.m -².

-In this experiment, the background and the illuminated part of the wall were grey (Y=73 cd.m -²).

-The size of the two patches was 1 degree for simulating telltales or 5 degrees for simulating typical dashboard displays.

-An angular distance between the two patches was chosen so as to simulate the real automotive configuration. The angular distance between the two patches was either10 arc min. between borders as a margin can never be avoided between two real displays, or one stimulus size between borders for simulating two non-contiguous real displays, or 30 degrees between centers that is approximately the distance between the straight ahead direction and a control display such as the global positioning system (GPS) panel, or 40 degrees between centers that is approximately the distance between the straight ahead direction and the most eccentric real advanced driving assistance system (ADAS ) display.

-The time of presentation was controlled at 500 ms, 600 ms, 1,3 s, or 1.8 s, i.e.

500 ms plus at least two saccade durations between a pair of remembered positions [START_REF] Hallett | Eye Movements. In: Handbook of Perception and Human Performance[END_REF], in order to allow the observer to look to and from between the two patches according to the angular distance between them.

-2. between "Very Unsatisfied" and "Unsatisfied" responses. It resulted that, in the main experiment, each experimental condition (size, angular distance, hue axis) was associated with a specific eight stimulus range that covers at best the psychometric scale of all observers (Table 1 gives an example).

Choice of the test colours

Procedure

Each participant received instructions prior to the experiment. He was explained that he would have to rate his degree of satisfaction with respect to a difference of colour between two square patches. Instructions indicated that the square patches were representative of two displays on two telltales. They required the participant to evaluate the difference of colour between the two colour patches as he would deliver a judgment about the conformity of the colour of two displays in an automotive context.

Instructions (in French) were read to the observer prior the experiment: "Imagine that you have acquired a vehicle having two screens. The manufacturer wanted these screens to both the same white background in order to satisfy you. … After having observed an image, we ask you to note your degree of satisfaction as for the respect of the intentions of the manufacturer."

The observer was invited to report his (her) degree of satisfaction on a 6-point semantic scale with respect to the similarity of the test colour with the reference colour. Category labels were "Very Unsatisfied", "Unsatisfied", "Lightly Unsatisfied", "Lightly Satisfied", "Satisfied", "Very Satisfied". The reason for choosing an even number psychometric scale instead of the common odd number practice arose from the car manufacturer requirement of a final decision on dissatisfaction / satisfaction. At the beginning of the experiment a training session was implemented for the observer to get used to the stimuli and the task. Then, three experimental cycles were conducted in a session, with a choice of three backgrounds.

Only the results obtained on a grey uniform background have been used to construct the colour-difference acceptability scale presented here. Within each cycle, several runs were prepared, each corresponding to a [size, angular distance] pattern. The sequence of eight runs formed a digram-balanced design [START_REF] Keppel | Design and analysis. A researcher's handbook[END_REF] to counterbalance both immediate sequential effects and the pairing of experimental conditions (size and angular distance) between subjects experiments. Within each run, the 32 (4 hues * 8 test colours) pairs of colour patches were randomized, among which four repetitions of the identity pair. We wrote our experiments in Matlab, using the Psychophysics Toolbox extensions [START_REF] Brainard | The Psychophysics Toolbox[END_REF][START_REF] Pelli | The VideoToolbox software for visual psychophysics: Transforming numbers into movies[END_REF]."

Participants

Thirty-two subjects (eight women aged 20-29, eight women aged 30-40, eight men aged 20-29, eight men aged 30-40) participated in the experiment. All participants had normal colour vision, tested with the Ishihara's and D15 tests for colour deficiency.

All observers participated in all experiments.

Scaling methods

Scaling methods require every observer to rate each sample on a category scale, that is to place each sample in a category. Data are entered in a frequency matrix giving the number of individuals who placed a stimulus into a category. The frequency matrix has as many rows as the number of stimuli and as many columns as the number of categories (Table 1).The scaling methods that are described in the literature can be divided in two classes, depending whether one considers that the stimuli responses or the categories have fixed position on the psychological continuum of the observers.

Regression methods ( 1986) [START_REF] Bonnet | [END_REF] has introduced a method to establish a category scale under the assumption of fixed positions of the stimuli responses on the subjective continuum of the observer. The cumulative proportion matrix (Table 2) is calculated from the frequency responses matrix and transformed into a matrix of z-values from the standard normal deviate distribution. Then for each category in turn, we calculate the psychometric function that relates the z-values to the stimulus values (in physical units). The transformation in z-value linearizes the psychometric function. Using a linear regression model, we determine the equation of the function which has the form: z j = aS j + b, where S j is the value of the stimulus i (in physical units) and z j is the z-value associated with the stimulus for the relevant category. We solve the equation for z j = 0 and obtain the category boundary, directly expressed in physical units (Table 3).

An akin method is to fit a sigmoid to all values of cumulative proportions (Figure 2), for each category. Then, both parameters of the sigmoid are determined using a logistic regression. The equation of the sigmoid allows us to calculate the limit of each category for 0.5 cumulative frequency, expressed in physical units (Table 3).

The fitting quality can be evaluated by calculating the p-value of each parameter. The fitting is satisfactory if the p-value is smaller than 0.05.

Medians method

The medians method [START_REF] Bonnet | [END_REF]1986, page 148;Torgerson, 1958, page 72) is based on the assumption of fixed position of the categories on the subjective continuum of the observers. The category boundaries in physical units are given by the median value between categories. Practically, for each stimulus we calculate the cumulative frequency from the frequency responses matrix and allocate to each stimulus the scalar median value of the cumulative frequency. Then, plotting the scalar median value versus the stimulus physical value, we can determine by linear interpolation the physical value of the category boundaries. Note that taking the median value rather than the mean value reduces the impact of outliers.

Category scaling after Torgerson and DMT

Within Torgerson's framework [START_REF] Torgerson | Theory and methods of scaling[END_REF], our experimental situation complies with the model of "Class II" which involves replications over individuals, each stimulus being judged once by each subject. The simplification corresponds to "Condition B" where it is assumed that the category boundaries are fixed throughout the experiment. The full category scaling consists of determining the scale values, their dispersion and the category boundaries. From the frequency matrix, a cumulative frequency matrix is obtained with a number of columns equal to the number of category boundaries, which yields a cumulative proportion matrix and is transformed in z-units. At the end, the procedure yields the sample scale values, their dispersion and the category boundaries on the same scale. Due to the matter we were dealing with, the frequency data matrix is likely to be incomplete. A solution has been proposed by Dieterich, Messick and Tucker that [START_REF] Engeldrum | Psychometric Scaling: A Toolkit for Imaging Systems Development[END_REF] has named the DMT method and has implemented in MathCad. The method gives the sample scale values and category boundaries on a z-scale. It also uses a weighting function that equals zero when the z-value is unity or zero values, and which is related to the variance of the proportion otherwise. As a minimum, there should be non-zero frequencies in at least three categories to yield a workable solution. We wrote the program in MatLab to implement the solution. We added a step to transform the zvalues into colorimetric specifications.

Results

Whereas results depend upon the experimental condition, we focus on methodology.

To facilitate the comparison of results obtained with different category scaling methods, we first propose an example related to colour differences along one hue axis, for one given experimental condition. Secondly, we summarize the results provided by the most direct scaling method over four hue axes and for the same experimental condition.

Example for the comparison of scaling methods

The example deals with the judgements of 32 observers. Indeed, not all methods would yield a complete solution when a small number of observers' results are entered. The case presented here refers to 1 degree patches, 30 degrees apart, on grey background and according to a variation along the +a* axis.

Original data are reported in Table 1. The first step consisting in the production of cumulative response functions is common to all methods (Table 2).

Table 3 presents the results obtained using the Bonnet's, logistic regression, medians and Torgerson-DMT methods and shows the estimated parameters provided by each method as well as the CIELAB values of the category boundaries.

 Bonnet's method

A linear regression is performed on z-values obtained from the cumulative proportion matrix. For every boundary, the slope a and intercept b stemming from the linear regression and the coefficient of determination of each of them is given. The values of all category boundaries are obtained except the "Very Satisfied / Satisfied" category boundary. Although the value is provided, it is negative (equal to-1.53) and has no physical reality.

 Logistic regression

A sigmoid is fitted on each column of the cumulative proportion matrix. The coefficients b1 and b2 are presented with the p-values (for each sigmoid). We notice that p-values always exceed 0.05. The category boundary "Very Satisfied / Satisfied" is negative (equal to -1.18) and has no physical reality. For this boundary, the pvalues are larger than 0.51.

 Medians

The category boundaries are obtained except for the "Very Satisfied / Satisfied" boundary which cannot be calculated. Indeed we note that the rating of the identical colour pair is lower than the median rating that would have been attributed to this boundary.

 Torgerson-DMT

Torgerson-DMT method provides the values of all the boundaries as well as the position of the samples and their dispersion. Results are expressed in z-values (Table 4 and Figure 3). However, it is not possible to connect directly those values with the physical continuum. To establish the connection, an additional step (not included in the original Torgerson's method) is necessary. Here, we have fitted a line to the distribution of z-values vs. CIELAB specification of samples and we have used this linear model to allocate CIELAB specification to the category boundaries.

 Comparison of the scaling methods

The comparison of the scaling methods shows that:

-No method has allowed us to obtain the category boundary "Satisfied / Very Satisfied".

-The results returned by the four methods are only slightly different (Figure 4).

Results from Bonnet's and logistic regression methods superimpose as expected since they only differ with respect to the fitting method.

-In the following section, as long as the difference of results for a given category boundary is small enough with respect to the car manufacturer expectation, we will present results from the logistic regression since the method directly exploits the observers' judgments.

Complete study of one experimental case over four hue axes

The results presented here (Table 5) refer to 1 degree patches, 30 degrees apart, on grey background. We report on the category boundaries obtained along the -a*, +a*, -b*, +b* axes. For every category boundary, the colour tolerance is higher on the b* axis than on the a* axis, about twice as much higher. Such information is valuable for the car manufacturer. We observe that the category boundary "Satisfied / Very Satisfied" is never achieved along any axis. Computation has also shown that the pvalues of the coefficients b1 and b2 specifying the "Satisfied / Very Satisfied" sigmoid are very high (0.40 to 0.83) and much higher than for the other category boundaries.

Discussion

Colour tolerance, Categorical scales and ecological validity

As stressed in the introduction, the measurement on colour difference threshold may not be of any help when dealing with suprathreshold colour differences, as it is often the case in industry. In the experimental case presented in the results section, which correspond to 1° patches 30° apart, the limit of satisfaction / unsatisfaction is a few CIELAB units, from 2.06 to 6.08 , what is higher than the colour difference threshold but would not be considered as a "large colour difference" after Luo et al. [START_REF] Luo | Uniform colour spaces based on CIECAM02 colour appearance model[END_REF]. Remarkably, the extent of the full category scales is large. This might be in relation with the fact that it seems difficult for an observer to identify the colour attribute responsible for a colour difference, as reported by [START_REF] Melgosa | Are we able to distinguish color attributes?[END_REF].

Above all, the full category scale is about twice as large for the -b* +b* axis (4.92 and 6.08) than for the -a* +a* axis (2.06 and 2.85). Thus neither the CIELAB metrics nor a metrics allowing for weighting independently the chroma and hue differences would render this asymmetry. Let us propose an explanation. It is possible that the subject's judgement is based on appearance. It is also possible that he is influenced by his everyday experience of the white colour mainly dominated by daylight. In such case, the larger tolerance judgement along the -b* +b* would simply reflect the anisotropic distribution of natural light. The missing value for the lower category deserves attention. The difficulty in determining the limit "Very satisfied" / "Satisfied" comes from the low number of responses "Very satisfied", even for the identity patch. It should be emphasized that the experiment that we conducted is not a threshold experiment but an acceptability experiment. It is possible that the judgement of the observer rely on some interpretation.

We insist on the necessity to recruit a sufficient number of observers. When a large number of subjects is examined, and provided that the problem reduces to finding the boundary between "satisfied" and "unsatisfied" judgements, it is expected that all methods yield practically congruent information as all of them rest on the midpoint of the cumulative probability function where the data are robust and the function is usually close to linear. Precisely, the medians method merely retains data bracketing the midpoint, Bonnet's method excludes extreme data, and the logistic regression and DMT method reduce the weights of the extreme data of the full probability distribution. Although the DMT method is recognized as being the most elegant, it possesses drawbacks in practical situations such as the one that we have studied. In our example, all configurations have fortunately fulfilled the necessary completeness condition. Nevertheless, over the wide range of stimuli that were of interest to us, i.e.

covering the full judgement scale from "Very Satisfied" to "Very Unsatisfied", extreme stimuli of the scale are likely to incompletely fill the full categories. For instance, if among all stimuli representative of the variety of items issued from different manufacturing processes, some are under the quality requirement of the client, missing categories could frequently occur. Then the completeness condition might not be fulfilled. In the industrial context, the regression solutions are probably the most useful. They deal with sub-matrices of the frequency responses where the problem reduces to a threshold problem. Thus, when the exact values of the stimulus are known, the methods provide a straightforward positioning of the boundary.

Scaling large colour differences

The maximum likelihood difference scaling (MLDS) method was introduced for estimating suprathreshold differences between stimuli and assigning them numbers that accurately predict an observer's judgments [START_REF] Maloney | Maximum likelihood difference scaling[END_REF][START_REF] Charrier | Maximum likelihood difference scaling of image quality in compression-degraded images[END_REF]. The series of stimuli that elicit a perceptual judgement should be distributed across a range of one-dimensional perceptual variables. For instance, the method was successfully applied to colour patches that fall on a greenish-reddish line in the colour space that is along the a* direction. The results tell us whether the observer sees marked or slight change between adjacent stimuli. Such a piece of information would be valuable to a car manufacturer. However in the MLDS model, the authors have set the outmost stimulus scale values to 0 and 1, which prevents the user to compare scales in various directions of the colour space and to interpret the scale values in terms of a semantic scale. Indeed, what guarantees the elegance and the robustness of the MLDS method is, no semantic interpretation is given to the scale built by the observer. The results of the difference scaling do not tell us anything about the feeling of the observers whereas the industrial needs to relate human perception to a quantitative scale. We may add that the double pair arrangement required by the MLDS design would not be workable when the colour pair is made of well apart colour patches. Nevertheless, a comparison between MLDS approach and Torgerson-DMT or Bonnet's or logistic regression categorical scaling approach could be of the highest interest.

Conclusion and perspective

Finally, the colour-difference acceptability scales that we have constructed using the logistic regression method directly reflect the perception of the participants. They could not have been derived from a simple colour-difference threshold experiment.

Designing the experiment with no repetition has shortened the experimental session so that several observers could participate which, is of primary importance in an industrial and commercial context. In the future, we could compare homogeneous groups of observers selected among the participants. We could also extend the experiment to other colours centres and other backgrounds which would offer the possibility to investigate appearance and the role of cognitive processes in colour context.

Tables with captions

  Eight test colours were chosen along the four hue axes +a*, -a*, +b*, -b* of the CIELAB chromaticity plane, in the interval [0, ΔC*max], at Y=80 +/-2 cd.m -². A colour pair is made of a white patch and a test colour patch. This makes 32 colour pairs for every size and angular distance experimental condition. Thus the null colour difference was included four times. Prior to the main experiment, three observers having experience with psychophysical experiments participated in the selection along each axis of the colour patch with maximum ΔC*. They were given the same instructions as in the main experiment (see next paragraph) but an adaptative procedure allowed us to bracket the range of the stimulus around the boundary

Figures captions Figure 1 :

 captions1 Figures captions

Figure 2 :

 2 Figure 2: Logistic regression results. Every sigmoid corresponds to a category boundary. Categories are indicated between curves.

Figure 3 :

 3 Figure 3: Torgerson-DMT. Results are expressed in z-units. CIELAB ΔC* magnitude values associated with the test samples are fixed and marked next to the symbols. Interpolation allows to calculate the ΔC* magnitude values associated with the category boundaries as given in Table4.

Figure 4 :

 4 Figure 4: Category boundaries resulting from the Bonnet's, logistic regression, median and Torgerson-DMT methods. The case presented here is: patches of 1 degree, separated from 30 degrees, on grey background and according to a variation along the axis +a*.

Table 1 .

 1 Frequency responses matrix. Experimental condition: size 1 degree, angular distance 30 degrees, colour difference along CIELAB +a* axis.

	Category label

Table 2 .

 2 Cumulative proportion matrix. Experimental condition: size 1 degree, angular distance 30 degrees, colour difference along CIELAB +a* axis.

	Category label

Table 3 .

 3 Results obtained thanks to the Bonnet's, logistic regression, median and Torgerson-DMT methods. The case presented here is: patches of 1 degree, separated from 30 degrees, on grey background and according to a variation along the axis +a*.

	CATEGORY BOUNDARIES

Table 4 .

 4 Results obtained usingTorgerson-DMT method (in z-values). The case presented here is: patches of 1 degree, separated from 30 degrees, on grey background and according to a variation on the axis +a*.

	Sample	z-values	Dispersions
	S1	1.00	0.35
	S2	0.99	0.46
	S3	0.28	0.66
	S4	-0.19	0.85
	S5	-0.53	0.73
	S6	-0.96	0.81
	S7	-1.71	0.84
	S8	-1.87	0.94
	Category	z-values
	boundaries
	VU / U	-1.64
	U / LU	-0.42
	LU / LS	0.45
	LS / S	0.82
	S / VS	1.29

Table 5 .

 5 Results obtained thanks to the logistic regression. The cases presented here is: patches of 1 degree, separated from 30 degrees, on grey background and according to a variation on the axis -a*, +a*, -b* and +b*. Results are expressed in terms of CIELAB colour differences.

	CATEGORY BOUNDARIES

Acknowledgements

We thank Xavier Chalandon (Renault) for encouraging this work, Jean Le Rohellec (CRCC), David Blumenthal (Renault) and Antoine Saint-Marcoux (Renault) for help in statistics, Kristyn Falkenstern for suggestions and observers for their availability.

All experiments were performed with Psychtoolbox-3 (http://psychtoolbox.org).


J.-M Flaud

F Kwabia Tchana

W J Lafferty

C A Nixon

High resolution analysis of the ν 26 and 2ν 9ν 9 bands of propane: Modeling of Titan's infrared spectrum at 13.4 µ µ µ µm

Keywords: High resolution IR, Propane, Molecular parameters

High resolution analysis of the ν26 and 2ν9 -ν9 bands of propane: Modeling of Titan's infrared spectrum at 13.4 µm

The 13.4 µm absorption region of propane is of very high interest since this is the spectral region that led to the first detection of this molecule in the atmosphere of the giant planets [START_REF] Tokunaga | The detection of C 3 H 8 (Propane) on Jupiter , 1983[END_REF][START_REF] Greathouse | The first detection of propane on Saturn[END_REF] and Titan [START_REF] Maguire | Propane and Methyl Acetylene in Titan's atmosphere[END_REF]. Note as well that the 748 cm -1 band has been exclusively and extensively used to derive the abundance and/or concentration profiles of propane in the Titan atmosphere (see for example refs. [START_REF] Kim | The abundance of methane-d 1 in the atmosphere of Titan, derived from 8 to 14 µm thermal emission[END_REF][START_REF] Coustenis | Titan's atmosphere from Voyager Infrared Observations. IV Latitude Variations of Temperature and Composition[END_REF][START_REF] Roe | Propane on Titan[END_REF]). In fact, it is only recently that other spectral regions have been used for this purpose [START_REF] Nixon | Titan's prolific Propane: The Cassini CIRS perspective[END_REF]. The propane absorption at 13.4 µm is mostly due to the ν 26 band [START_REF] Shimanouchi | Tables of molecular vibrational frequencies[END_REF]. It has been studied at high resolution using a tunable diode laser spectrometer and analyzed assuming that the 26 1 vibrational state was isolated [START_REF] Gassler | Tunable diode laser spectra and assignment of the 748 cm -1 band of propane[END_REF]. In this case such an assumption was valid given the J and K a range of the observed transitions.

In this paper, we present an extensive analysis of the 13.4 µm absorption region of propane combined with an analysis of the 27.4 µm region. It was necessary to work simultaneously in these two spectral regions since the 26 1 ro-vibrational levels interact strongly with the 9 2 ro-vibrational level though an intense A-type Coriolis resonance. While the 26 1 rotational levels were observed in the 13.4 µm spectral domain, the 9 2 rotational levels were derived from assigning the 2ν 9ν 9 hot band in the 27.4 µm spectral region. The 2ν 9 band is quite weak and cannot be observed at 13.4 µm except where the 9 2 levels resonate with 26 1 levels.

Propane is an asymmetric top with C 2v symmetry. Its structure and symmetry properties are given in Fig. 1 of ref. [START_REF] Flaud | First high resolution analysis of the absorption spectrum of propane in the 6.7 µm to 7.5 µm spectral region[END_REF].

II. Experimental details

The high-resolution absorption spectrum of propane was recorded using the Bruker IFS 125HR Fourier transform spectrometer 1 (an upgraded version of the IFS 120HR) at LISA in Créteil.

The spectrometer was equipped with a Globar source, a Ge/KBr beamsplitter and a MCT photovoltaic detector cooled by liquid nitrogen. The Fourier transform spectrometer (FTS) was 1 Certain commercial equipment instruments or materials are identified in this paper to adequately specify the experimental procedure. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology nor does it imply that the materials or equipment identified are necessarily the best available for the purpose. (which corresponds to a resolution of 0.002 cm -1 , as defined by Bruker) and was not numerically apodized.

The White-type multipass absorption cell, made of pyrex glass and equipped with CsBr windows, was connected to the FTS with a dedicated optical interface (six mirrors) inside the sample chamber of the FTS. Its base length is 0.80 m, and, for the experiment described here, an optical path of 19.2 m was used. The sample of propane was obtained from Sigma Aldrich. The chemical purity of propane was specified to 99.97% and was used without further purification. The absorption cell was evacuated and filled with 273.6 (7) Pa (2.052 (5) Torr) of pure propane. Sample pressure in the cell was measured using calibrated MKS Baratron gauge (accuracy of 0.25%) with a full scale reading of 10 Torr. The White-type long path cell was at a room temperature of 22 °C.

The spectrum was calibrated with residual CO 2 and H 2 O lines observed in the spectrum between 600 and 1400 cm -1 , with their wavenumbers taken respectively from HITRAN04 [START_REF] Rothman | The HITRAN 2008 molecular spectroscopic database[END_REF] and Toth [START_REF] Toth | ν 2 band of H 2 16 O: line strengths and transition frequencies[END_REF]. The spectral calibration is accurate to within 0.0003 cm -1 (RMS).

Fig. 1 gives an overview of the propane spectrum showing the high signal-to-noise ratio which was obtained. The distinctive shape of the C-type ν 26 band with its narrow Q-branch is easily recognizable.

III. Analysis and results

The assignment process was started using the upper state constants of [START_REF] Gassler | Tunable diode laser spectra and assignment of the 748 cm -1 band of propane[END_REF] and considering 26 1 as an isolated vibrational state. It was possible to assign transitions with low and medium J and K a quantum numbers rather easily. However, as soon as K a values around 15 and 16 were reached, it appeared that the predicted positions obtained using a single Watson-type Hamiltonian were incorrect; the predictions clearly became worse with increasing K a values. Looking for possible interacting states, one option was to consider an A-type Coriolis interaction between the rotational levels of the 26 1 and 9 2 vibrational states. The corresponding Hamiltonian matrix is given in Table 1.

As preliminary band centers and rotational and centrifugal distortion constants for the 9 2 state, we extrapolated the values previously obtained for the 9 1 state [START_REF] Kwabia Tchana | The first high-resolution analysis of the low-lying ν 9 band of propane[END_REF]. In this way, high K a transitions of ν 26 could better predicted and confidently assigned. As a result, good predictions could be made for the together with the ν 26 transitions were fitted using the two state model (Table 1). Note that these 2ν 9 transitions could be observed only because they borrow their intensity from the strong resonating ν 26 lines. In fact, 2ν 9 is very weak and no other transitions belonging to this band could be observed at 13.4 µm. We then decided to look for the 2ν 9 -ν 9 hot band located at about 370 cm -1 . At room temperature this band has an intensity of about 33% of the corresponding cold band, ν 9 . Assigning this hot band proved to be not too difficult given the previous assignments at 13.4 µm and the quality of the model. We worked simultaneously in both regions until it was not possible to assign any additional new lines.

Table 2 gives the number of levels and the range of quantum numbers, J and K a which were observed for both states. These levels were fit using the two state Hamiltonian model given in Table 1. The fit is quite nice as can be seen from the statistical analysis of Table 2 and the standard deviation of 0.41 x 10 -3 cm -1 . The corresponding spectroscopic constants are given in Table 3. Using these spectroscopic constants, we have generated a line list of positions and intensities for the ν 26 and 2ν 9 bands at 13.4 µm and for the 2ν 9 -ν 9 hot band at 27.4 µm. Fig. 1 presents a simulation of the entire 13.4 µm region showing the good agreement between the observed and calculated spectra.

Note the appearance of hot bands around 749.5 and 750.9 cm -1 which are not included in the simulation. Fig. 2 shows a portion of the ν 26 spectrum where high K a r R transitions are clearly visible.

One high K a r R transition of 2ν 9 is seen in the spectrum. We note that these 2ν 9 transitions can be seen only because high K a levels of 9 2 resonate with high K a levels of 26 1 through a strong A-type Coriolis resonance. Finally, in Fig. 3 the p Q 9 -branch of the hot band 2ν 9 -ν 9 is clearly visible. In all cases the agreement between simulation and observation is quite good showing the quality of the simulations.

IV. Application to Titan

Recently, Titan's mid-infrared spectrum was searched for the presence of multiple propane bands [START_REF] Nixon | Titan's prolific Propane: The Cassini CIRS perspective[END_REF], using data recorded by the Cassini Composite Infrared Spectrometer [START_REF] Flasar | Exploring the Saturn system in the thermal infrared: the Composite Infrared Spectrometer[END_REF]. This research demonstrated that at least five further bands are now clearly detected, in addition to the ν 26 band traditionally used to measure propane in outer planet atmospheres, and providing the opportunity to make multiple independent estimates of the abundance of the gas. [START_REF] Jacquinet-Husson | the 2003 Edition of the GEISA/IASI spectroscopic database[END_REF] used to model the ν 26 was not fitting all the propane emission, especially a suspected hot band on the short wavelength side of the main band.

We have therefore sought to check whether the new parameters for the ν 26 and other bands at 13.4 µm improve the fitting of the Titan spectrum in this region, using the same dataset and model as [START_REF] Nixon | Titan's prolific Propane: The Cassini CIRS perspective[END_REF]. Fig. 4 shows the comparison between the Titan spectrum (0.5 cm -1 apodized resolution) and three models (see [START_REF] Nixon | Titan's prolific Propane: The Cassini CIRS perspective[END_REF] for details), including a no-propane model for reference. It is immediately apparent that the new propane list 2 provides a significantly improved fit to the spectrum (χ 2 /n reduces from 6.9 to 2.4) especially in the hot band emission centered near 749.75 cm -1 . Moreover, the inferred abundance in VMR of propane at 2 mbar increases by a factor of ~1.6 to (6.6±0.7) × 10 -7 , reducing the discrepancy with the ν 18 band from -1.5 × 10 -7 , to +0.9 × 10 -7 -an agreement finally to within the predicted measurement error.

V. Conclusion

A complete and simultaneous analysis of high-resolution Fourier transform spectra recorded in the 748 and 370 cm -1 regions has permitted the assignment of a large number of transitions of the ν 26 and 2ν 9 bands of propane at 13 µm and of the accompanying hot band 2ν 9ν 9 at 27.4 µm. A set of accurate spectroscopic constants was obtained for both upper states using a two state Hamiltonian model taking explicitly into account the strong A-type Coriolis interaction linking the rotational levels of the 26 1 and 9 2 vibrational states. Application of the new line list to the modeling of a low-latitude Titan spectrum significantly improves the fitting between model and data relative to the publicly available GEISA data, and should provide a substantial increase in accuracy for researchers using the ν 26 band to measure propane's abundance in planetary atmospheres.

Acknowledgments 2 The linelist can be obtained from the authors.. cold band [START_REF] Rothman | The HITRAN 2008 molecular spectroscopic database[END_REF]. All the 2ν 9ν 9 lines are well modeled. Table 1: Hamiltonian matrix used to calculate the {26 1 , 9 2 } interacting states of propane.

( ) [ ] ( ) ( ) 2 xy v v 2 1 2 v v 2 1 2 z v v 2 1 v v W J C B J C B J C B A E H - + + + + - + = ( ) { } 2 2 xy v J 2 xy 2 z v K 2 2 v J 2 2 z v JK 4 z v K J 2δ J , J δ ∆ J ∆ J ∆ J J J - - - - - ( ) ( ) 3 2 v J 2 2 2 z v JK 2 4 z v KJ 6 z v K H J H J H J H J J J + + + + { } { } ( ) 2 2 2 y x v J 2 2 xy 2 z v KJ 2 xy 4 z v K J 2h J , J h J , J h J J + + + ( ) ( ) ( ) 4 2 v J 3 2 2 z v JJK 2 2 4 z v KJ 2 6 z v KKJ 8 z v K L J L J L J L J L J J J J + + + + + { } { } { }( ) ( ) 3 2 2 y x v J
+ + + + J J v-off-diagonal operators: C A = A 1 h J z + A 2 h {i J y , J x }+ A 3 h J z J 2 + A 4 h {{i J y , J x }, J z 2 }
with {A , B} = AB + BA, J ± = J x i J y and J xy 2 = J x 2 -J y 2

Absorbance

Obs.

Calc.

High K a lines of the  26 band of propane

  6.7 Pa (0.05 Torr) pressure (to minimize residual H 2 O and CO 2 absorption in the spectra), and a 1.3 mm entrance aperture diameter was used. The spectrum was the result of the coaddition of 600 interferograms collected with a Maximum Optical Path Difference (MOPD) of 450 cm

  with K a values ranging from 18 to 23. These transitions could be observed and

Formatted:FormattedFig. 1 .

 1 Fig. 1. Overview of the ν 26 band of propane. The distinctive shape of this typical C-type band is clearly visible.

Fig. 2 .

 2 Fig. 2. High K a lines of the ν 26 band of propane. The 2ν 9 line is visible only because it borrows its intensity from ν 26 through a strong A-type Coriolis resonance.

Fig. 3 .

 3 Fig. 3. The p Q 9 -branch of the 2ν 9ν 9 hot band of propane. The lines marked with a * belong to the ν 9

Fig. 4 .

 4 Fig. 4. Upper panel: Titan spectral average, 30°S-30°N latitude, 100-150 km detector centers (black line) compared to three models: (i) no propane, C 2 H 2 , C 2 H 6 and HCN only (blue); (ii) GEISA 2003 propane atlas (green); (iii) propane atlas from this work (red). Lower panel: the data-model residual.Note that the GEISA 2003 atlas lacks the hot band emission at 749.75 cm -1 that is fitted in the new model.

9 -

 9 branch of the 2 9 -  hot band of propane

  Using a newly-available line list for several bands near 7 µm [10], Nixon et al. made the first measurement of propane's abundance 18 band at 7.3 µm, applied to Titan low-latitude limb data, comparing it to a simultaneous measurement using the ν 26 band. The resulting abundances(Volume mixing ratio (VMR)): (5.7±0.8) × 10 -7 and (4.2±0.5) × 10 -7 respectively did not quite overlap at 1-σ level of error, and in addition it was clear that the GEISA 2003 spectral data

	Molecular Physics
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Table 2 :

 2 Range of quantum numbers observed for experimental energy levels of the vibrational states 26 1 and 9 2 of propane.

Table 3 :

 3 Vibrational band centers, rotational and Coriolis interaction constants (in cm -1 ) for the {26 1 , 9 2 } interacting states of propane.

	Page 11 of 18	Molecular Physics

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  Overview of the  26 band of propane

	Page 13 of 18 Page 15 of 18				Molecular Physics Molecular Physics Molecular Physics	Molecular Physics
				Table 3
			0 0	Table 2	26 1	9 2
		E v	Vibrational State		26 1 748.530882(80) 9 2	740.29213(10)
	Absorbance	A B C ∆ K x 10 6 ∆ JK x 10 7 ∆ J x 10 7 δ K x 10 7 δ J x 10 8 H K x 10 10 H KJ x 10 11 H JK x 10 13 H J x 10 13 h K x 10 12 h KJ x 10 12 h J x 10 13 L K x 10 15 L KKJ x 10 16 L J x 10 19	F o r P e e r R e v i e w Number of levels 1062 741 J max 58 46 K max 31 26 0.0000≤δ<0.0003 78.5% 70.6% 0.0003≤δ<0.0006 13.3% 18.1% 0.0006≤δ<0.0012 6.4% 7.3% 0.0004≤δ<0.0035 1.8% 4.0% Std, Deviation (10 -3 cm -1 ) 0.41 δ = |E Obs. -E Calc | in cm -1 F o r P e e r R e A h 3 0.98996(2000) x 10 -6 A h 4 -0.20140(9000) x 10 -6 w A h 2 0.4739(1700) x 10 -5 e i A h 1 0.4458926(1400) x 10 -1 v 0.9742562313 a 0.97455697 (170) 0.99582808(210) 0.2817271865 0.280898922(500) 0.281336087(650) 0.2488055608 0.248098043(410) 0.247503322(560) 5.324721011 5.356984 (5000) 6.799600(8900) -8.998168326 -8.85088(2500) -8.49929(2100) 2.402258565 2.389984(2300) 2.346993(3200) 1.035202827 1.1900(1500) 6.6482(3000) 4.659136555 4.69748(1300) 4.67524(2000) 1.147493844 1.20062(4600) 2.20292(9100) -4.071816910 -4.6480(3700) b 5.193592962 b b 2.755239426 b b -2.568443533 b b 1.377953277 b b 1.197995448 b b -2.625149429 b b 4.703253742 b b -7.104915228 b b <9 2 | 26 1 > F o r P e e r R e v i e w 2  20 20d -19 19d F o r P e e r R e v i e w -45 11d -42 12d O n l y -39 13d O n l y -23 19d Obs. Calc. -23 18d 24 19d 24 20d 40 14d 43 13d 27 18d -26 17d 30 17d 33 16d 36 15d -29 16d 46 12d -32 15d -35 14d
			700	787.5	720	O n l y 740 760 787.6 O n y l Wavenumber (cm 787.7 -1 ) Wavenumber (cm -1 )	780	800 787.8	820
				13
					14

URL: http://mc.manuscriptcentral.com/tandf/tmph a Ground state values from ref. [14]. b Fixed at ground state values. c Uncertainties are 1σ. Page 14 of 18 URL: http://mc.manuscriptcentral.com/tandf/tmph URL: http://mc.manuscriptcentral.com/tandf/tmph