Sara Allin
email: s.m.allin@lse.ac.uk

Cristina Masseria

Elias Mossialos

Equity in health care use among older people in the United Kingdom: an analysis of panel data

Keywords: equity, health care, elderly

This paper uses panel data to investigate the extent of income-related inequity in the likelihood of visiting a GP, specialist, dentist and hospital among individuals aged 65 and over in the United Kingdom. The probability of accessing health care is predicted with separate random effects probit panel models using data from the British Household Panel Survey for the period 1998-2006. We use well-established methods based on the concept of the concentration curve to compare the cumulative distribution of health care utilisation with the cumulative distribution of the population ranked by income. The results find evidence of inequity in specialist and dental care, but only slight inequity for GP care and not significant inequity in hospital admissions. Levels of inequity are highest for specialist and dental care, even when users of the private sector are excluded from analyses. The mobility index is also used to compare short-and lung-run estimates of inequities and show that upwardly income mobile individuals contribute to inequity in the long run.

I. INTRODUCTION

Health systems with universal health care coverage aspire to align the distribution of health services according to need. Policy documents in the United Kingdom (UK) consistently endorse such equity goals in health care (Department of Health, 2000[START_REF] Wooldridge | Econometric analysis of cross section and panel data Cambridge[END_REF], 2006a;[START_REF] Oliver | The English National Health Service: 1979-2005[END_REF]. This paper draws on panel data from the UK to measure equity in the use of health care services in the older population during the period 1998-2006, a period that has been characterized by increased policy interest in equity goals in the NHS alongside a significant increase in spending on health care.

International comparisons of equity in utilisation of health services in the general population reveal that the UK is relatively equitable (van Doorslaer, Masseria, & the OECD Health Equity Research Group Members, 2004). However recent reviews of the literature and empirical studies find little or no evidence of inequity in general practitioner (GP) and inpatient service use, whereas low income individuals appear to make less use of secondary and dental care than would be predicted based on need [START_REF] Dixon | Is the British National Health Service equitable? The evidence on socio-economic differences in utilisation[END_REF][START_REF] Goddard | Equity of access to health care services: theory and evidence from UK[END_REF][START_REF] Morris | Inequity and inequality in the use of health care in England: an empirical investigation[END_REF]. Contradictory results have been obtained: one study that used 2001 British Household Panel Survey (BHPS) did not find significant inequity in GP or specialist visit probability [START_REF] Van Doorslaer | Explaining income-related inequalities in doctor utilisation in Europe[END_REF], while another study based on the 1996 European Community Household Panel (ECHP) found a modest but significant pro-rich inequity in the probability of contacting both a GP and specialist (van Doorslaer, Masseria, & the OECD Health Equity Research Group Members, 2004).

Inpatient care has generally shown to be equitable [START_REF] Masseria | Income related inequality in the probability of a hospital admission in Europe[END_REF], although as noted by [START_REF] Dixon | Is the British National Health Service equitable? The evidence on socio-economic differences in utilisation[END_REF], by measuring inpatient care at an aggregated level, inequity in the treatment of specific diseases and in elective procedures may be masked [START_REF] Dixon | Trends in hip and knee joint replacement: socioeconomic inequalities and projections of need[END_REF][START_REF] Morris | Inequalities in coronary revascularisation during the 1990s: evidence from the British regional heart study[END_REF][START_REF] Neal | Sociodemographic factors and delays in the diagnosis of six cancers: analysis of data from the "National Survey of NHS Patients: Cancer[END_REF]. Though inconclusive, the international F o r P e e r R e v i e w 3 population-level studies point to a fairly equitable distribution of health service use by income in the general population relative to other industrialized countries, although service-specific studies reveal inequity in certain preventive and specialized services.

In the context of a universal health system that provides the majority of services free at the point of delivery, inequitable utilisation could be due to individuals' knowledge of available services and their need for services, characteristics of the doctor-patient relationship, and the existence of barriers to access that disproportionately affect the lower socioeconomic groups [START_REF] Dixon | Is the British National Health Service equitable? The evidence on socio-economic differences in utilisation[END_REF]. In other words, higher socioeconomic groups have a louder 'voice' allowing them better to navigate the health system than those with less socioeconomic advantage; they may be better able to acknowledge their needs, identify the services available, and make demands on their GPs such as for specialist referrals [START_REF] Dixon | Is the British National Health Service equitable? The evidence on socio-economic differences in utilisation[END_REF]. The presence of a parallel private sector may also give rise to inequitable utilisation whereby individuals with private insurance coverage, who are drawn from the higher socioeconomic groups [START_REF] King | The determinants of private medical insurance prevalence in England[END_REF], are afforded easier access in particular in the form of lower waiting times for specialty and surgical interventions. Analyses of the 2001 Commonwealth Fund International Health Policy Survey found that those with private coverage had significantly reduced odds of reporting to wait 6 months or more for elective surgery [START_REF] Schoen | Inequities in access to medical care in five countries: findings from the 2001 Commonwealth Fund International Health Policy Survey[END_REF].

To date there has been relatively scant attention paid to investigating equity among the older population; the highest consumers of health services who face potentially greater difficulties in accessing care. Of the total number of inpatient procedures and interventions 4 group, however, that comprised around 16% of the population in that year (Department of Health, 2006b). Barriers to access in the general population are likely to be more pronounced among older people. Limitations in mobility, insufficient social support, and reduced access to health and health care information sources such as the internet probably increase with age. A recent review of the literature of inequalities in the use of services among older people in England found evidence of inequitable utilisation, in particular for specialized services, which the authors attributed to differences in individuals' knowledge of services, expectations of the benefits of treatments, likelihood of delaying seeking treatment, confidence interacting with health care professionals, and transportation-related barriers to access [START_REF] Fernandez | Inequalities in the Use of Services Among Older People in England. A Rapid Review of the Literature for Age Concern[END_REF].

The present study contributes to the literature on inequity in older people in the UK by measuring income-related inequity after controlling for differences in need in the use of GP, outpatient, inpatient and dental check-ups with longitudinal data from the period 1998 to 2006. Panel analyses have the advantage of allowing us to control for unobserved time-invariant individual heterogeneity. A further advantage of panel data to model demand for health care is that it allows us to control for the past year's utilisation and to measure trends over time. By using the mobility index is also possible to analyse differences in inequity due to changes in income ranking over time. If access to health care is systematically associated with income over time, long-run income-related health inequality will differ from measurements made over a short time span. Inequity will tend to increase in the long run if higher health care users are upwardly income mobile or lower health care users are downwardly income mobile, and vice versa. The dependent variables of health care utilisation were measured by four separate questions asking the respondent whether he or she had visited a GP/family doctor, outpatient specialist, hospital as an inpatient, and dentist for a check-up in the past year.

Utilisation of GP, specialist, inpatient and dental care are considered separately, and are measured as dichotomous (yes/no) variables to indicate the likelihood of a contact. Over the nine-year period, 85.6% of the sample had visited a GP at least once in the past year, 42.3% visited a specialist at least once in the past year, 16.5% had been treated in hospital as an inpatient in the past year, and 44.5% visited a dentist for a check-up at least once in the past year. GPs act as gatekeepers to specialist and hospital services in the UK (except F o r P e e r R e v i e w 6 in the case of emergencies); therefore, the extent of GP use in the past year is included as an independent variable in the models of GP, specialist and hospital services.

The survey further distinguishes between public (NHS) and private specialist, inpatient and dental services; public utilisation is measured by excluding individuals who reported that their service use was fully or partly private. A description of all variables in the models for the period 1998-2006 is presented in Table 1.

Insert Table 1 here

Measures of need are examined separately and approximated from several health and demographic indicators. Self-assessed health (SAH) derives from the combination of two questions: "Please think back over the last 12 months about how your health has been.

Compared to people of your own age, would you say that your health has on the whole been: excellent, good, fair, poor, or very poor?" and "In general would you say your health is: excellent, very good, fair, or poor". Four categories were created following the methods of (Hernández-Quevedo, Jones, & Rice, 2005): excellent; very good or good; fair; and poor or very poor. One-year lagged self-assessed health in four categories was not found to significantly affect utilisation and therefore was not included in the final models. More specific need indicators were also included.

The BHPS includes different types of health problems, such as problems with sight, hearing, skin conditions/allergy, chest/breathing, heart/blood pressure, stomach or digestion, diabetes, anxiety or depression, alcohol or drugs, epilepsy, migraine, cancer, stroke, and other problems; these are included as dummy variables. Finally, age groups, gender, and whether the individual reports any limitations in daily activities due to health problems are included. An assumption that underlies this research is that individuals with health conditions and poorer self-assessed health have a greater need for health care, an assumption that is likely to hold in the majority of cases. However it is important to acknowledge the possibility that some health conditions may not need physician services 7 [START_REF] Culyer | Equity and equality in health and health care[END_REF][START_REF] Goddard | Equity of access to health care services: theory and evidence from UK[END_REF]; instead, they may require allied health services or social services, for example, which may lead to an overestimate of inequity. Sensitivity analyses that included age and gender interaction terms did not affect the results and therefore were not included in the final estimations. Also, when we included health conditions as a dummy variable that takes a 1 if the individual reports any conditions and 0 if he or she reports no conditions the estimates of inequity remained unchanged, and in the final analyses we included the health conditions separately.

This comprehensive set of needs indicators is included in order to be consistent with the literature and to overcome the limitations and potential biases associated with crude self-assessed health [START_REF] Lindeboom | Cut-point shift and index shift in selfreported health[END_REF][START_REF] O'donnell | Equity and distribution of UK National Health Service resources[END_REF][START_REF] Van Doorslaer | Does inequality in self-assessed health predict inequality in survival by income? Evidence from Swedish data[END_REF]. Community-level health indicators such as mortality rates are not included as these have been shown to be unrelated to individuallevel health care utilisation [START_REF] Morris | Inequity and inequality in the use of health care in England: an empirical investigation[END_REF]. In the case of dental check-ups, only age is considered to be 'need-related' in the absence of oral health indicators.

The standard set of indicators of socioeconomic status that have been shown to affect the use of health care services are included the models. One such measure is housing tenure (whether the household owns their home, rents privately, or rents socially).

Particularly among individuals who are retired, home ownership represents an important indicator of socioeconomic status [START_REF] Costa-Font | Housing assets and the socio-economic determinants of health and disability in old age[END_REF][START_REF] Crystal | The economic well-being of the elderly[END_REF]. Since studies have shown that different levels of knowledge of available services and communication skills with health professionals may drive socioeconomic inequalities, it is important to measure the effect of education on utilisation. Highest educational qualification is grouped into three categories: no qualifications, non-advanced qualifications, or advanced qualifications. Socio-demographic information on marital status (not married, widowed, or married) and smoking status (current smoker or not) is also included [START_REF] Grundy | Health inequalities in the older population: the role of personal capital, social resources and socio-economic circumstances[END_REF]. We also consider whether the individual is covered by private medical insurance (PMI) (which can be either through self or spouse), which reduces the cost of private health services. Such coverage would be expected to increase utilisation overall, as shown with specialist services [START_REF] Jones | The impact of having supplemental private health insurance on the use of specialists[END_REF], but not necessarily the use of NHS services when these are considered separately.

Region of residence (in 19 regions) is included in order to control for regional differences in supply across the UK [START_REF] Gravelle | Inequality in the geographical distribution of general practitioners in England and Wales 1974-1995[END_REF][START_REF] Hann | The maldistribution of general practitioners in England and Wales: 1974-2003[END_REF][START_REF] Moles | Inequalities in availability of National Health Service general dental practitioners in England and Wales[END_REF][START_REF] Propper | Impact of patients' socioeconomic status on the distance travelled for hospital admission in the English National Health Service[END_REF]. GP visits in the previous survey year is also included as an explanatory variable in the models (except dental care), since previous utilisation is predictive of current utilisation [START_REF] Propper | The demand for private health care in the UK[END_REF], and GPs serve as the gatekeepers to specialist and inpatient care. Lagged utilisation of specialist or dental services is not included to limit possible specification bias arising from a correlation between income and past use. Time dummies are included in the models in order to capture any changes in utilisation over time. 2Income, the variable used to rank the sample, is measured as net household income in the last year. Income is derived from disaggregated income sources including labour and non-labour income, transfer income, investment income, benefit income and pension income. It is equivalized for household composition using the OECD equivalization scale and is adjusted by an annual 'before housing costs' price index to express incomes in January 2008 prices [START_REF] Levy | Documentation for Derived Current and Annual Net Household Income Variables, BHPS waves 1-16, UK Data Archive Study[END_REF]. Labour income contributes only 6% to total household income, and the majority of the sample (85%) has no labour income. Income from benefits and pension makes up the large part of household income, on average contributing 65% and 24%, respectively. Income is unequally distributed across this older population, with a Gini index of income inequality of 0.28 (which is slightly less unequal than in the general population, 0.30). Income levels are relatively low. The median with income at the 10 th percentile at £6200, and the 90 th income percentile is £20,517.

Measures socioeconomic and health status are unlikely to be completely independent: higher education is associated with higher income, and both are associated with better health. However the literature is consistent in accepting the possible collinearity of independent variables for the sake of preventing bias from omitted variables [START_REF] Gravelle | Economic studies of equity in the consumption of health care[END_REF]. It is also possible that there is reverse causality between income and utilisation, whereby under-utilisation of services leads to worse health outcomes and, consequently, lower income. However there is considerable agreement in the literature on the direction of causality from income to health as opposed to from health to income. Those studies that have attempted to correct for potential endogeneity of income found either that the effect of income on health does not change, or it increases, when instrumental variable approaches are taken [START_REF] Ettner | New evidence on the relationship between income and health[END_REF]Lindhal, 2005;[START_REF] Lecluyse | The relationship between income and health: using information on separation allowances to single out causality from correlation[END_REF] or that by using inheritance as an instrument for short-term changes in wealth, the effect of such changes in wealth on health becomes nonsignificant [START_REF] Meer | Exploring the health-wealth nexus[END_REF].

III. ANALYTIC STRATEGY

Equity can be understood as the extent to which health care utilisation is affected by factors unrelated to the need for health care, such as income and other socioeconomic indicators [START_REF] Gravelle | Economic studies of equity in the consumption of health care[END_REF]. In this study, we estimate income-related inequity in health care utilisation based on the concept of concentration curves, which compare the cumulative distribution of health care utilisation with the cumulative distribution of the population ranked by income [START_REF] Kakwani | Socioeconomic inequality in health: measurement, computation and statistical inference[END_REF][START_REF] O'donnell | Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and their Implementation[END_REF][START_REF] Wagstaff | Equity in health care finance and delivery[END_REF]. First, we calculate the concentration index (CI) for unadjusted utilisation. (2)

y it * = X ' it β + Z' it δ + α i + ε it
X and Z are the vectors of need and non-need variables, and the error term is represented by two components, α i and ε it . The former is the individual effect that is treated as random while the latter is the idiosyncratic disturbance. than those with lower income, and negative if those with higher income are less likely to use health services than the lower income individuals. In all models the dependent variable is binary, therefore the minimum and maximum possible values of the CI range between µ-1 and 1-µ, where µ is the variable mean (O'Donnell, van Doorslaer, [START_REF] O'donnell | Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and their Implementation[END_REF]. The 'convenient regression' of CI and HI on the income rank is used to calculate the standard errors of the indices, and we use a between effects OLS. We also calculate HI separately for each of the nine years to compare it to the overall level of HI that is estimated with the above panel methods to observe any changes over time and to calculate a mobility index.

By using multiple waves of the BHPS (an unbalanced panel) it is possible to account for individual-specific unobservable effects in the error term [START_REF] Wooldridge | Econometric analysis of cross section and panel data Cambridge[END_REF].

The advantage of the random effects model over a fixed effects model is that it permits the inclusion of covariates with limited (or no) time-variation; such an approach is consistent with the literature [START_REF] Propper | The demand for private health care in the UK[END_REF][START_REF] Van Ourti | Measuring horizontal inequity in Belgian health care using a Gaussian random effects two part count data model[END_REF]. The random effect model provides efficient estimates of the coefficients and also gives information on the extent of variability in health care use due to individual effect, under the assumptions that both error terms are normally distributed and independent of the independent variables.

A longitudinal perspective enables us to assess whether inequalities have reduced or increased with time and to identify the role of changes in income rank on utilisation. By measuring inequalities in the short-term (using cross-sectional data) and long-term (aggregated over a series of periods), a mobility index (MI) can be created [START_REF] Jones | Measurement and explanation of socioeconomic inequality in health with longitudinal data[END_REF]). This index is equal to one minus the ratio of the long-term inequity index and the weighted sum of all the short-term inequity indices. Weights (w t ) are equal to the ratio between the short-run and the long-run average utilisation of health care.

∑

, where (4)

w t = y t T s y T .
If the long-term index is equal to the weighted sum of the short-term inequity indices, MI equals zero. In this situation income ranking remains constant over time. Whenever there is perfect mobility in both access to health care and income over time, then the long-run HI equals zero and therefore the MI equals 1. If MI is negative (positive) the long-term inequity is larger (smaller) than the short-term estimate of inequity. These differences between the short-and lung-run estimates of HI emerge if there is income mobility that is systematically associated with differences in the utilisation of health care. When downwardly (upwardly) income mobile individuals have a lower (higher) income rank in the long-run than in the short-run, this increases income-related inequality.

One methodological challenge associated with panel data is attrition, or the rate of drop-outs between years. Studies using BHPS data have demonstrated that there are systematic patterns of attrition by socioeconomic characteristics and health status, although they argue that this does not bias the panel data estimates [START_REF] Contoyannis | The dynamics of health in the British Household Panel Survey[END_REF][START_REF] Jones | Health related attrition in the BHPS and ECHP: using inverse probability weighted estimators in nonlinear models[END_REF].

IV. RESULTS

The results of the random effects probit models for the likelihood of accessing each health service during the period 1998 to 2006 are reported in Women are significantly more likely to visit a GP and dentist, and less likely to be admitted as an inpatient.

Among the non-needs factors, higher income individuals are more likely to visit a specialist and dentist, but there is no significant association with GP or inpatient care.

Holding PMI is significantly associated with the likelihood of GP, specialist or dentist visit but not hospital admission. Home ownership and higher educational qualifications are significantly associated with outpatient and, to a greater extent, dental services. As expected, previous contact with health care, as measured by one-year lagged GP visits, increases the likelihood of current use. The time dummies reveal time trends in specialist care, with an increasing likelihood of a visit over the nine-year period, and an increase in the likelihood of a dental check-up only in the past three years.

Insert Table 2 here

The role of individual effects varies to some extent across the four utilisation categories, and explains between 20% (hospital inpatient) and 80% (dental check-up) of the variation in utilisation. This suggests that the importance of using a panel data approach is greatest for the model of dental care.

The estimates of inequity strengthen the results that we obtain with the probability models; Figure 1 shows the estimates of income-related inequity across the different sectors. The needs-adjusted indices of HI are positive and significantly different from zero for GP, specialist and dental care. Over the nine-year period there is little change in the estimates of inequity in GP and inpatient care, although there appears to be a slight decline in inequity in the likelihood of a specialist and dentist visit during this period (Table 3).

The mobility index shows a clear role of income ranking on estimates of inequity. For all services but GP, the long run inequity index is higher than the average of the short-run indices. This implies that there are systematic differences in utilisation among individuals who are downwardly and upwardly income mobile. For specialist and hospital care, and

Insert Table 3 here

To test whether the observed inequity by income is due to a greater likelihood of health care use in the private sector among higher income groups, we exclude individuals who reported to have accessed inpatient, specialist, or dental services from the private sector and re-estimate HI. Inequity in inpatient care remains insignificant but is closer to zero. However, significant inequity remains in specialist and dental care despite notable reductions in magnitude (Figure 1).

Consistent with previous international comparisons of equity in health service use that included the UK, we tested the effect of considering only age, gender, self-assessed health and activity limitations as needs indicators. The estimates of inequity were only modestly affected by excluding the health conditions from the models of utilisation. For specialist care the index of inequity increased slightly (to 0.59), which suggests that income may capture some of the effect of the omitted needs variables.

V. CONCLUSIONS

Using panel data methods to estimate equity in health care use among older people in the UK, this study finds evidence of inequity in specialist and dental care, but little or no inequity in GP and hospital inpatient care. Inequitable specialist and dental care is partly explained by the use of private services among higher income groups, but inequity among NHS service users remains significant. The panel analyses reveals that indicators of health care need are most significantly associated with utilisation, non-need indicators are also significant, consistent with previous studies of the general and older populations [START_REF] Dixon | Is the British National Health Service equitable? The evidence on socio-economic differences in utilisation[END_REF][START_REF] Fernandez | Inequalities in the Use of Services Among Older People in England. A Rapid Review of the Literature for Age Concern[END_REF][START_REF] Morris | Inequity and inequality in the use of health care in England: an empirical investigation[END_REF]. Moreover, by comparing short run indices with long-run Primary care is relatively equitable, as demonstrated by the index of inequity that is very close to zero, alongside no significant marginal effect of income on the probability of a visit. This is consistent with previous studies of the general population that have found a modest negative association between income and GP visits [START_REF] Morris | Inequity and inequality in the use of health care in England: an empirical investigation[END_REF] and a zero index of inequity by income (van Doorslaer, Masseria, & the OECD Health Equity Research Group Members, 2004).

As with primary care, we do not find any evidence of inequity in the likelihood of an inpatient admission, consistent with previous studies of the general population [START_REF] Masseria | Income related inequality in the probability of a hospital admission in Europe[END_REF]van Doorslaer, Masseria, & the OECD Health Equity Research Group Members, 2004). When individuals who used only private inpatient care are excluded from the analysis (5% of those who reported at least one inpatient stay), the effect of PMI becomes negative, and needs-adjusted income-related inequity nears zero. This finding suggests that the existence of an extensive private sector may drive inequitable utilisation even if at present inequity is not significant.

Disaggregating elective versus emergency care, and day versus inpatient care would be beneficial in future research, since specific studies, e.g. of hernia repair, point to an inequitable distribution [START_REF] Seymour | Age, deprivation and rates of inguinal hernia surgery in men. Is there inequity of access to healthcare?[END_REF]. Although they estimated a similar index of inequity, [START_REF] Morris | Inequity and inequality in the use of health care in England: an empirical investigation[END_REF] found a significant effect of income on the likelihood of admission to hospital, unlike in our analyses of older people.

The likelihood of visiting a specialist is more concentrated among the richer older people than the poor, even when we consider only the NHS users. This is consistent with the positive income effect on specialist use (and index of income-related inequity) that was found in the late 1990s among the general English population [START_REF] Morris | Inequity and inequality in the use of health care in England: an empirical investigation[END_REF][START_REF] Morris | Inequity and inequality in the use of health care in England: an empirical investigation[END_REF]. The finding that those with higher education are more likely to visit a specialist is also consistent with previous studies, such as among arthritis sufferers [START_REF] Propper | Access to health care resources in the UK: the case of care for arthritis[END_REF].

This education effect also supports the theory that communication with providers and health literacy facilitates access to services. Also a survey of 1400 UK residents from 2001 found that individuals with below-average incomes were significantly more likely to answer yes to the question of whether it was extremely or very difficult to see a specialist when needed, an effect that remained even after adjusting for health, age, education, residence and immigrant/minority status [START_REF] Schoen | Inequities in access to medical care in five countries: findings from the 2001 Commonwealth Fund International Health Policy Survey[END_REF]. There is no clear trend in inequity over the nine-year period, since estimates fluctuate quite largely across the years. However, it seems that overall a slight decline in specialist (and dental care) inequity took place over the time frame of the study, suggesting that the extensive health reforms of this period may have been effective in better aligning the distribution of specialist services with need among the older population.

The greatest inequity was found in dental check-ups, both among all users and only those who visited NHS dentists. Compared to the over-50 population in other European countries and the United States, the level of inequity in dental care that we find would place it second highest among 12 countries (second to the US) [START_REF] Allin | Measuring Socioeconomic Differences in Use of Health Care Services by Wealth Versus by Income[END_REF]. The income effect on dental use shown here and in the general population (van Doorslaer, Masseria, & the OECD Health Equity Research Group Members, 2004) is unlikely to be an effect of being rich versus poor but an income gradient across the population since a previous study found that cost-related difficulties in accessing care were reported about equally across the above-and below-average income groups [START_REF] Schoen | Inequities in access to medical care in five countries: findings from the 2001 Commonwealth Fund International Health Policy Survey[END_REF]. Hefty user fees in the NHS likely deter lower income individuals from seeking dental care. Despite many older individuals having special dental needs, such as treatment for tooth decay and gum disease, 82% of the over-60 age group receive no financial assistance for the significant co-payments for NHS services:

80% of treatment costs [START_REF] Robinson | The Economics of Dental Care London: Office of Health Economics[END_REF]. Past years have seen an 17 increase in the proportion of older individuals retaining their original teeth [START_REF] Batchelor | Changes in self-reported attendance of British adults for dental check-ups between 1991 and 2000[END_REF]; the proportion of over 65s who are edentulous has fallen from 79% in 1978to 46% in 1998(Office for National Statistics, 1998). Because education is also associated with dental check-ups, inequity may be driven by both cost and information barriers; the information hypothesis is consistent with a previous study of over-60s in England that found that higher education and social class, but not income, affected utilisation [START_REF] Mcgrath | Factors influencing older people's self reported use of dental services in the UK[END_REF]. Another possible explanation for high levels of inequity in dental care is that private dentists may avoid treating particularly old, frail or unhealthy patients because the fee is perceived to be too low relative to costs of treating these patients [START_REF] Holm-Pedersen | Dental care for aging populations in Denmark, Sweden, Norway, United Kingdom, and Germany[END_REF]. Therefore a public subsidy, in particular for older people, may play some role in mitigating the financial barrier to dental care in light of the well established impact of insurance on demand for dental care and the negative price elasticity of demand [START_REF] Sintonen | Economics of dental services[END_REF].

In conclusion, we find that wealthier older people, and those with increasing income over time, are significantly more likely to see a doctor, have an outpatient visit and a dental check-up than those with lower income. The highest level of inequity was found in the sector that is the most privatized in terms of funding and delivery -dental care, which suggests that increasing private sector capacity or co-payments in other sectors would have the effect of increasing existing levels of inequity. By using panel data these analyses yield more robust findings than conventional cross-sectional approaches; further work could address the dynamic nature of income and health in the older ages and the impact of inequitable utilisation on inequalities in health. Note: Morris et al calculated an index of income-related inequity of -0.022 for GP, 0.048 for specialist, and 0.012 for hospital inpatient (the index represents the sum total of non-need contributions to inequality by income) for the period 1998-2000 using the nationally representative Health Survey for England [START_REF] Morris | Inequity and inequality in the use of health care in England: an empirical investigation[END_REF].

F

  that were delivered in the year 2006-2007 in public (National Health Service; NHS) hospitals, 44% were for individuals aged 60 and over (who made up 21% of the population in mid-2006) (Office for National Statistics, 2008; The NHS Information Centre, 2008). Moreover, in 2003-04 people aged 65 and over accounted for approximately 43% of total expenditure on hospital and community health services, a

  This study was conducted using data from the BHPS, a longitudinal cohort survey of adult members of a nationally representative sample of UK households 1 . Initial household selection was made using a two-stage clustered probability design and systematic sampling. The survey collects data from all adult members of the household.Those in the initial sample are followed until they refuse to participate, die, or are lost to follow-up; each year approximately 0.5% of the sample died. The present study included all individuals aged 65 or over in the period 1997 to 2006, as 1997 was the first year Northern Ireland was included. We include one-year lagged variables in the models, therefore the final sample covers the years 1998 to 2006, with observations in 1997 used to create the lagged variables for 1998. Proxy respondents due to inability to respond themselves (about 4% of the sample) were excluded from the analysis, as well as observations with any missing information on the variables of interest (a further 2% of the sample). The resulting sample is an unbalanced panel of 4104 individuals yielding 19,538 observations.

  among the 65 years and older population group is £10,618,

σ

  is the variance of the income rank (R) in the population (calculated separately by survey year), y is the utilisation variable of interest, and m y is the weighted mean of utilisation. Unadjusted CI equals zero if all individuals have an equal probability of seeking health care, regardless of income.Second, utilisation is regressed on a set of needs and non-needs variables.Estimates of each health care use (GP, specialist, hospital or dental care) are obtained by using a random effects probit model where the dependent variable y i equals 1 if the individual used health care or zero otherwise.

  Third, we hold the non-needs variables constant (at the sample means) to predict needs-adjusted utilisation for each individual, and then standardize utilisation to the sample mean. This standardization calculates the level of utilisation that is expected on the basis of the average utilisation in the sample for individuals with the same level of need. Needs-standardized utilisation then replaces actual utilisation in equation (1) to calculate the CI of needs-standardized inequality, which is interpreted as horizontal inequity (HI). HI would equal zero if after controlling for differences in need, the probability of health care use is independent of income. The estimate of HI is positive if need higher income individuals are more likely to use health care

  extent also for dental care, upwardly income mobile individuals contribute to inequity; patterns of utilisation are not only pro-rich, but individuals with faster growing incomes have a greater likelihood of accessing these services.

  it appears that upwardly mobile individuals are more likely to access specialist and hospital care, and, to a less extent, dental care. These findings are consistent with analyses of other European countries (Bago d'Uva et al 2008).

  Figure 1. Indices of inequity in the likelihood of a GP, specialist, inpatient and dental contact, with 95% confidence intervals

Table 2 .

 2 Indicators of health care need are the most significant determinants of health service use in all areas (except dental

	health service increases with most health conditions and with worse self-assessed health.
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	13

care where only age was considered needs-related). Older individuals are more likely to be admitted to hospital, and less likely to visit a dentist. The likelihood of contact in any

Table 1 . Description of independent variables and descriptive statistics (1998-2006)

 1

	o r
	P
	e
	e r
	R
	e
	v i e
	w

Table 2 . Random effects probit models: determinants of health service use

 2

				Specialis
		GP		t		Hospital		Dentist
	Indicators of health
	care need	ME	SE	ME	SE	ME	SE	ME	SE
	Age 70-74	-0.009	0.040	-0.002	0.033	0.034	0.039	-0.289**	0.052
	Age 75-79	0.016	0.045	0.002	0.039	0.121**	0.042	-0.574**	0.068
	Age 80-84	0.031	0.054	0.004	0.046	0.213**	0.048	-0.931**	0.086
	Age 85+	0.071	0.066	-0.012	0.057	0.342**	0.057	-1.253**	0.112
	Female	0.081**	0.036	-0.036	0.034	-0.110** 0.033	0.320**	0.080
	Self-assessed health
	good	0.279**	0.040	0.239**	0.042	0.193**	0.055
	fair	0.521**	0.051	0.610**	0.046	0.617**	0.058
	poor	0.649**	0.072	1.005**	0.055	1.204**	0.064
	Health limitations	-0.025	0.034	0.070**	0.024	0.104**	0.027
	Health problems
	limbs	0.136**	0.032	0.101**	0.027	-0.008	0.030
	sight	-0.011	0.048	0.258**	0.036	0.051	0.037
	hearing	0.056	0.038	0.084**	0.031	0.004	0.032
	skin	0.080	0.057	0.145**	0.041	-0.009	0.043
	chest	0.174**	0.046	0.127**	0.034	0.070**	0.034
	heart	0.398**	0.033	0.158**	0.026	0.094**	0.029
	stomach	0.184**	0.055	0.297**	0.037	0.178**	0.037
	diabetes	0.283**	0.067	0.310**	0.048	-0.008	0.047
	anxiety	0.113	0.069	-0.013	0.046	-0.075	0.047
	alcohol	-0.265	0.299	0.185	0.245	0.529**	0.231
	epilepsy	0.183	0.241	0.409**	0.181	0.351**	0.168
	migraine	0.129	0.083	-0.066	0.058	-0.123	0.063
	other problems	0.281**	0.070	0.246**	0.046	0.238**	0.048
	Socioeconomic, socio-demographic and lagged utilisation variables
	Income (logarithm)	-0.018	0.033	0.084**	0.028	0.048	0.030	0.278**	0.045
	Marital status
	not married	-0.123	0.052	-0.058	0.048	0.034	0.048	-0.088	0.103
	widow	-0.094** 0.040	-0.070	0.036	0.093**	0.036	-0.232**	0.073
	Smoker	-0.180** 0.046	-0.235** 0.043	-0.160** 0.044	-0.675**	0.084
	Housing tenure
	home owner	0.075	0.042	0.141	0.038	-0.034	0.037	0.615**	0.082
	rents privately	0.130	0.081	0.094	0.070	-0.010	0.071	0.087	0.127
	Private insurance	0.178**	0.064	0.142	0.056	0.069	0.060	0.470**	0.103
	Educational qualifications
	non-advanced	0.067	0.041	0.185	0.038	0.081**	0.037	0.900**	0.092
	advanced	0.151**	0.050	0.220	0.046	0.104**	0.046	1.548**	0.112
	GP visits in past year	0.415**	0.016	0.165**	0.011	0.132**	0.012
	Time dummies
	1999	-0.056	0.066	0.108**	0.052	0.069	0.060	0.003	0.071
	2000	0.025	0.062	0.122**	0.048	-0.055	0.056	-0.056	0.068
	2001	-0.024	0.061	0.182**	0.049	-0.041	0.056	0.079	0.068
	2002	-0.012	0.062	0.128**	0.050	-0.093	0.057	0.091	0.070
	2003	-0.020	0.063	0.214**	0.050	-0.070	0.057	0.035	0.072
	2004	-0.026	0.065	0.158**	0.050	-0.033	0.057	0.188**	0.074
	2005	0.005	0.063	0.139**	0.051	-0.059	0.058	0.281**	0.075
	2006	0.002	0.064	0.244**	0.051	-0.081	0.058	0.249**	0.077
	Constant	-0.346	0.320	-2.518	0.271	-2.702	0.293	-3.091	0.444
	Rho	0.196		0.313		0.202		0.799

Note: **indicates statistical significance at p<0.05; * at p<0.10. ME is marginal effect, SE is standard error. Also included are 19 regional dummies.

F o r P e e r R e v i e w

23

Table 3 . Horizontal inequity (HI) in the likelihood of GP, outpatient, inpatient and dentist use, 1998-2006 cross-sections and panel estimates

 3

	GP	Specialist		Hospital		Dentist
	HI	95%CI	HI	95%CI	HI	95%CI	HI	95%CI
	1998	0.007 (-0.004, 0.019)	0.071 (0.035, 0.106)	0.035 (-0.022, 0.092)	0.171 (0.138, 0.203)
	1999	0.002 (-0.010, 0.014)	0.018 (-0.017, 0.052)	0.018 (-0.043, 0.079)	0.132 (0.099, 0.166)
	2000	0.015 (0.006, 0.024)	0.067 (0.040, 0.094)	0.041 (-0.008, 0.090)	0.163 (0.135, 0.191)
	2001	0.009 (0.000, 0.018)	0.043 (0.018, 0.069)	0.013 (-0.037, 0.063)	0.125 (0.099, 0.152)
	2002	0.012 (0.004, 0.021)	0.056 (0.027, 0.082)	0.002 (-0.049, 0.053)	0.126 (0.101-0.152)
	2003	0.015 (0.007, 0.024)	0.052 (0.027, 0.076)	0.032 (-0.017, 0.082)	0.131 (0.106, 0.156)
	2004	0.006 (-0.004, 0.015)	0.025 (-0.001, 0.051)	0.026 (-0.025, 0.077)	0.122 (0.099, 0.146)
	2005	0.010 (0.001, 0.019)	0.043 (0.017, 0.069)	-0.024 (-0.076, 0.028)	0.111 (0.088, 0.134)
	2006	0.004 (-0.005, 0.013)	0.028 (0.005, 0.051)	0.022 (-0.028, 0.072)	0.095 (0.072, 0.117)
	1998-2006	0.007 (0.002, 0.013)	0.055 (0.040, 0.069)	0.025 (-0.003, 0.054)	0.130 (0.112, 0.148)

The data and tabulations used in this publication were made available through the ESRC Data Archive. The ESRC Research Centre originally collected the data on Microsocial Change at the University of Essex (now incorporated within the Institute for Social and Economic Research). Neither the original collectors of the data nor the Archive bear any responsibility for the analyses or interpretations presented here.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Ethnicity has been shown to impact utilisation(Morris et al., 2005), but such information was not included in this study due to the limited information on non-white ethnic groups: in the first wave of the survey, 93% declared white ethnicity, 4% did not respond, and the remainder chose one of six options.


S Gossler
email: stefan.gossler@aei.mpg.de

A Bertolini

M Born

Y Chen

K Dahl

D Gering

C Gräf

G Heinzel

S Hild

F Kawazoe

S Goßler

O Kranz

G Kühn

H Lück

K Mossavi

R Schnabel

K Somiya

K A Strain

J R Taylor

A Wanner

T Westphal

B Willke

K Danzmann

The AEI 10 m prototype interferometer

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

Introduction

In the AEI 10 m Prototype Interferometer facility we shall test and develop advanced techniques that have the potential to be used for future upgrades to GEO-HF [START_REF] Lück | The transition to GEO HF submitted to JPCS[END_REF]. Among these are the digital control and data system, and high-power laser systems. A second goal is to provide training for scientists who will install these techniques in GEO-HF and operate that gravitational-wave observatory.

However, the 10 m Prototype facility will also host experiments in their own rights. We have designed the main instrument, a Michelson interferometer, such that it will be capable of reaching a sensitivity effectively limited by quantum noise in the measurement band. Photon shot noise and quantum back-action noise at the interferometer mirrors will be the dominant noise sources in a band around 100 Hz. This sensitivity is referred to as the standard quantum-limit (SQL). Reaching or even surpassing the SQL for an interferometric measurement is a long-standing goal in precision metrology [START_REF] Caves | Quantum-Mechanical Radiation-Pressure Fluctuations in an Interferometer[END_REF][START_REF] Jaeckel | Quantum Limits in Interferometric Measurements[END_REF]4]. With the setup described in this article we will tackle this challenge with macroscopic test masses of 100 g each. Once the SQL is reached, various techniques, such as squeezedlight input, can be leveraged towards achieving sub-SQL sensitivity.

Vacuum system

The vacuum system for the AEI 10 m Prototype consists of three tanks with a diameter of 3 m and a height of 3.4 m, separated by 11.65 m. The tanks are connected by 1.5 m diameter beam tubes. There are no gate valves to shut off certain sections of the vacuum system. Overall, the vacuum system encloses about 100 m 3 . It is designed such that it fits neatly into the existing lab facilities (see Fig. 1). For the roughing a screw pump with a pump rate of 170 l/s at atmospheric pressure is attached to one of the tubes. Two magnetically levitated turbo-molecular pumps with a pumping speed of 2000 l/s each, backed by a single Scroll pump, evacuate the system to 10 -6 hPa within 12 hours. After about one week of pumping a pressure of 10 -7 hPa is reached. The residual gas pressure is dominated by water vapour as the system was not baked. However, longer pumping will further reduce the pressure.

All flanges up to 600 mm diameter are sealed with copper gaskets. Flanges bigger than that, i.e. 1000 mm at the doors of the tanks, 1500 mm at the tube sections, and 3000 mm at the lids of the tanks, are sealed with two Viton O-rings each. The gap in between these two O-rings is pumped by another Scroll pump. This scheme of differential pumping allows us to reach a low residual gas pressure while keeping the cost for the vacuum system at a tolerable level.

The two Scroll pumps, for backing and differential pumping, are installed in a separate pump room. The Scroll pumps are set up on a double-stack vibration isolator made of two granite plates (ca. 200 kg each) and two layers of Sorbothane hemispheres. The pumps themselves are also isolated by another layer of Sorbothane dampers.

The vacuum system is fully installed and operational since May 2009.

Isolation tables

The isolation tables are the mechanical interface between the vacuum system and the suspension systems supporting the main and ancillary optics of the interferometer. As the experimental hall is located in downtown Hannover, surrounded by roads and tramways, anthropogenic noise is the main source of seismic disturbances measured in the lab. Vertical and horizontal displacements up to 300 nm (RMS value) above 1 Hz have been measured on the hall floor during daytime. The optics suspensions have their resonances in the 1 Hz to 10 Hz band and therefore, it is important to reduce the amplitude of the motion of the optical tables at those frequencies to avoid overloading the optics control systems causing noise injection and limiting the sensitivity of the experiments.

The optical tables consist of a welded stainless-steel honeycomb structure of dimensions 1750 × 1750 × 400 mm. Each table is supported by a Seismic Attenuation System (SAS). The SAS is a six degrees of freedom vibration isolator, providing the necessary shielding from the ground microseismic noise which is the main environmental source of disturbance in the frequency range from 0.1 Hz to 100 Hz. The SAS is a completely custom made device capable of providing vibration isolation factors not achievable in a single stage, to our knowledge, by any other existing commercial or laboratory developed system. Its design is derived from a prototype device (HAM-SAS: Horizontal Access Module Seismic Attenuation System) built by Caltech in 2006 in the framework of the R&D for the gravitational wave detector AdvLIGO [START_REF] Stochino | The Seismic Attenuation System (SAS) for the Advanced LIGO gravitational wave interferometric detectors[END_REF]. Attenuation factors larger than 70 dB at 10 Hz are expected in both the vertical and horizontal direction.

The seismic attenuation of the SAS is obtained passively by using mechanical oscillators to attenuate vibrations, as second-order low-pass filters, above their natural frequency. Each table sits on three vertical vibration isolators (named filters) which provide mechanical compliance along the vertical, pitch and roll degrees of freedom. The tables operate with very low natural frequencies, 0.05 Hz in the horizontal and 0.1 Hz in the vertical direction, respectively, allowing large vibration suppression ratios to be achieved. The isolation goal is 60 dB at 3 Hz in both directions.

Each filter consists of a tunable spring made of a crown of curved cantilever blades which are compressed against each other: the constrained radial stress creates an antispring effect (geometric anti-spring) that leads to a very low effective stiffness in the vertical direction at the nominal load [START_REF] Bertolini | Seismic noise filters, vertical resonance frequency reduction with geometric anti-springs: a feasibility study[END_REF]. Natural frequencies down to 0.2 Hz can be obtained by mechanical adjustment of the compression rate; even longer natural periods can be achieved by applying positive feedback (electronic anti-spring). The inertia of the blades limits the minimum vibration transmissibility to -60 dB, which can be improved to -80 dB by using the built-in compensators (so-called magic wands).

The three filters are mounted on a rigid plate supported by three inverted pendulum (IP) legs: very low natural frequencies (around 0.05 Hz) are achieved for the horizontal (X,Y) translational modes and for the yaw mode. This is done by suitably sizing the IP bottom flexures to compensate for the load gravitational torque which drives the system towards instability [START_REF] Takamori | Inverted pendulum as low-frequency preisolation for advanced gravitational wave detectors[END_REF]. The short flexure hinges at the top of the IP allow the filter plate to wobble in the horizontal plane preventing its pitch/roll movement. The inertia of the legs would limit the IP minimum vibration transmissibility to -70 dB. However, by tuning the built-in counterweights up to -90 dB can be achieved.

The amplification of the seismic noise at the SAS resonances would make the motion of the tables uncomfortably large at low frequencies. Hence, the attenuators are instrumented with a range of sensors (linear variable differential transformers and horizontal accelerometers) and voice-coil actuators to perform electronic modal damping. The SAS control is based on rather elementary feedback filters and is limited to a few Hertz bandwidth. The natural completion to the local SAS action is the global inter-table distance and attitude stabilisation using the signals from the Suspension Platform Interferometer (SPI).

The isolation tables are scheduled for installation in spring 2010.

Suspension Platform Interferometer

Even though the optical tables are highly isolated and separated by merely 12 m, there will be some residual differential motion between them. This relative motion will be sensed by the Suspension Platform Interferometer. The obtained signals can then be used to apply the according feedback to the tables via voice-coil actuators.

The SPI consists of a set of three heterodyne Mach-Zehnder interferometers. One of them is used as a reference interferometer, the other two measure the differential motion between the optical tables. The equal arm length reference interferometer is set up on the central isolation table. It is used to substract all laser noise that came in on the way between the laser and the optical setup inside the vacuum system. The two measurement interferometers have each a short arm (ca. 10 cm) and a long arm (ca. 22 m). This large mismatch in arm length leads to strong coupling of laser frequency noise. As the measurement frequency is very low, a molecular iodine reference was chosen to stabilise the laser frequency to, thus allowing operation of the SPI at the required level.

The optical signals are obtained with a set of quadrant photodiodes which are read out by a LISA Pathfinder-style phasemeter. The phasemeter itself is based on FPGAs (field programmable gate arrays) to allow fast processing of the signals. The data from the phasemeter are sent via an enhanced parallel port to the phasemeter interface (PMI).

The PMI provides a microcontroller-based ethernet interface, designed to connect the SPI to our digital control system (CDS) with the required low latencies.

All relevant optical components of the SPI are bonded onto low-expansion glass plates to avoid thermal drifts. The design goal for the SPI is to reduce the differential motion between the tables to less than 100 pm/ √ Hz and 10 nrad/ √ Hz at 10 mHz. These goals are set by experiments to be conducted for the LISA space-borne gravitationalwave detector and geodesy missions within the QUEST cluster of excellence.

For the full details and current status of the SPI setup please refer to [START_REF] Dahl | Towards a Suspension Platform Interferometer for the AEI 10 m Prototype[END_REF].

Suspensions

The ambitious goals of the AEI 10 m Prototype Interferometer impose strict limits on the noisy motions of the measurement optics. As in all current (and planned) full-scale interferometric detectors, the optics will be suspended as the final stages of (multiple cascaded) pendulums, where the natural frequency-filtering effect is used to isolate the optics from seismic motions at frequencies above the pendulum resonances.

There will be three classes of suspensions required for the first set of experiments: those forming the frequency-reference cavity, the main interferometer optics, and ancillary optic suspensions.

Frequency-reference cavity optics

The first optical setup to be implemented in the prototype will be a suspended frequencyreference cavity, used to suppress laser frequency noise. This will consist of a threemirror, high-finesse triangular-ring cavity. The mass of the optics was chosen to be 850 g; balancing the reduction of radiation pressure induced noise with the desire to have a compact suspension. The suspension system will comprise three stages of similar mass. The final silica optic will be suspended from an intermediate aluminium mass by thin stainless steel wires: 55 µm diameter wire will be used to both lower the stage's vertical resonance frequency to 20 Hz and raise the first violin mode to 400 Hz, keeping these features out of the measurement band of the main interferometer.

The intermediate stage is connected to the uppermost stage via stainless steel wires attached to cantilever springs (made of maraging steel) mounted on the upper stage. These springs help to lower the overall vertical resonance frequencies, thus reducing additional noise contributions from vertical-to-horizontal noise coupling. The upper stage is then used to provide local eddy-current damping of pendulum resonances, as well as providing a platform for the application of alignment and drift control signals through adapted Bosem-style magnet and coil assemblies. Finally, the uppermost stage is joined to a suspension cage structure by two additional cantilever blades.

Interferometer optics

To reach SQL limited sensitivity, high laser power and low mirror masses are required. A mirror mass of 100 g should allow this goal to be reached while still allowing a practicalthough challenging -suspension design to be realised. In order to sufficiently isolate the optics, a triple-stage suspension (with two stages of vertical isolation) will be needed.

The final stage will comprise a monolithic all-silica structure with the optics suspended from four 20 µm fused silica filaments to reduce suspension thermal noise.

Ancillary optics

Other optics are required to steer and point the laser beam into and out of the main interferometer and the vacuum system. Due to the excellent isolation provided by the isolated optical tables and the SPI system, such ancillary optics can be isolated with relatively simple single-stage suspensions systems, with no additional vertical isolation.

Laser system

We will use a 35 W solid-state laser as the light source for the AEI 10 m Prototype Interferometer [START_REF] Frede | Fundamental mode, single-frequency laser amplifier for gravitational wave detectors[END_REF]. In this laser system the light of a commercially available 2 W Nd:YAG seed laser passes through four Nd:YVO4 crystals in an amplifier configuration. Each of these crystals is pumped by a 400 µm diameter fibre-coupled laser diode with a nominal power of 45 W and a numerical aperture of 0.22. To increase the lifetime of the diodes the pump power is set to 33 W during nominal operation. The 3 × 3 mm cross section laser crystals consist of a 2 mm undoped and a 8 mm long doped Nd:YVO4 region (0.3 at.%). The undoped region was bonded to the crystal to reduce thermal stress at the surface where the pump beam enters. The laser crystals are wrapped in thin indium foil and mounted inside a water-cooled copper block. The 2 W NPRO (Non-Planar Ring Oscillator) beam is amplified to a power level of 35 W when passed through the four laser heads. The wavelength matching between the Nd:YAG and the Nd:YVO4 system is done by temperature tuning of the NPRO. The relative power noise (RPN) of the 35 W front end is identical to that of the NPRO at Fourier frequencies below 50 Hz and exceeds it by a factor of up to 5 for frequencies in the audio band. The spatial beam quality of the NPRO (97 % TEM 00 mode content) is only slightly degraded by the amplification process; 95 % of the power of the 35 W front end was measured to be in the TEM 00 mode. Passing the beam through a photonic-crystal fibre and a subsequent rigid-spacer pre-modecleaner cavity of moderate finesse (F ≈ 500) will further improve the spatial profile and reduce the beam pointing fluctuations.

Frequency stabilisation

The frequency fluctuations of the 35 W laser are at the same level as those of the 2 W NPRO seed. Owing to the fact that we will use mirrors of only 100 g for the main interferometer, radiation-pressure noise will prevent us from using the interferometer itself to provide a frequency reference. Hence, we will use a dedicated suspended optical resonator for the laser frequency stabilisation. This frequency-reference cavity consists of three mirrors that form a triangular-ring resonator of about 24.6 m round-trip length. Two mirrors will be placed on the central optical table while the mirror at the small angle of the triangle will be set up on the south table.

The sum of all displacement-noise equivalent fluctuations in this system needs to be suppressed to 10 -17 to 10 -19 m/ √ Hz from 20 Hz to 1 kHz. This level is 10 times smaller than the strict requirement, allowing us a sufficient safety margin. The total noise of the reference cavity will be dominated by seismic motion, thermal noise, and shot noise in the low, middle, and high frequency region, respectively. As described above, a triple-cascaded pendulum suspension system was chosen to isolate the mirrors from seismic motion. The relevant suspension design parameters (e.g. wire thickness and length) as well as substrate material, are chosen to minimise thermal noise. Optical design parameters (e.g. laser power inside the cavity, overall reflectivity of the cavity) as well as the mirror mass (850 g) are tuned to optimise shot noise performance and radiation pressure noise. A small amount of light (130 mW) from the 35 W laser will be picked off and injected into the reference cavity. As the cavity finesse is high (F = 7300) the circulating power is large enough to optimise the shot noise limited signal-to-noise ratio, but small enough that the radiation pressure noise from classical intensity noise will not be limiting.

For the control of the cavity length and thus, of the laser frequency the Pound-Drever-Hall scheme is applied. Angular motions will be revealed via differential wavefront sensing. At frequencies well above the pendulum resonances, the length of the free reference cavity is used as a frequency reference. Below these frequencies the cavity length is locked to a molecular iodine reference. As such, the laser frequency will be stabilised to the length of the reference cavity at all relevant Fourier frequencies.

Control and Data System

To collect and digitise data from the many sensors and to control the interferometer we use the control and data system (CDS) software developed by LIGO. The CDS is used for both collecting science data and data from ancillary systems such as environmental monitoring devices. In the initial configuration the AEI 10 m Prototype Interferometer requires about 500 channels forming multiple-input multiple-output control loops. Digital-to-analog conversion (DAC) and analog-to-digital conversion (ADC) is performed using 16 bit fully differential PC-expansion cards with either PCI-X or PCIe bus connection and a maximum sampling frequency of 256 kS/s per channel. However, the standard sampling frequency is 64 kS/s. For the most sensitive channels we use 18 bit cards in order not to be limited by noise from the DAC/ADC. The frontend machines are standard Opteron or Xeon based servers.

As control and data acquisition has to be performed in real-time, special care has to be taken to choose low-latency hardware. As standard gigabit ethernet possibly imposes high latencies we use fibre-based Myrinet connections for low-latency communication. The CDS software is based on a real-time enabled Linux operating system. Operator control screens and channel access are realised with the Experimental Physics and Industrial Control System (EPICS).

The software architecture on our CDS system, namely the real-time code generator, allows us to use Matlab/Simulink or C-code to design a circuit, which is then used to build a real-time kernel module. This module is then loaded onto a real-time enabled frontend computer and can be controlled via the EPICS control channels and screens.

Optical layout and design sensitivity

The main instrument in the AEI 10 m Prototype Interferometer facility is a 10 m Michelson interferometer with Fabry-Perot cavities in the arms (Fig. 2). The arm cavity finesse will be about F ≃ 675. However, there will be no recycling techniques such as signal-or power-recycling in the first round of experiments.

A speciality of our design is the use of Khalili cavities as compound end mirrors to minimise coating thermal noise [START_REF] Khalili | Reducing the mirrors coating noise in laser gravitational-wave antennae by means of double mirrors[END_REF]. The end test mass in each arm consists of a Fabry-Perot cavity locked to anti-resonance for the carrier light. The input end test mass (IETM) will carry only two coating doublets (51 % power reflectivity) while the end end test mass (EETM) will have a coating stack made of 15 doublets to form a highly reflecting mirror. As a result, the IETM itself introduces only moderate coating thermal noise. The higher level of coating thermal noise originates from the EETM, but this is reduced by the transmissivity of the IETM. In this way, the overall coating thermal noise from the compound end mirror can be reduced by a factor of about 3 when compared to a conventional single mirror of the same reflectivity. Thus, the contribution from the input test mass dominates the mirror coating thermal noise. The Khalili cavities will be locked independently of the main interferometer via the injection of an offset phase-locked sub-carrier beam from the rear side.

The design sensitivity of the main interferometer is given in Fig. 3. The sensitivity is shaped such that a gap between the sum of the quantum noise and the sum of all classical noise contributions opens up at around 100 Hz to 200 Hz. Around this sweet spot of sensitivity a factor of about 3.3 separates the two curves. This gap will later allow us to achieve a sensitivity beyond the SQL. Such a sensitivity can be reached when injecting squeezed states of light at the appropriate orientation of the squeezing ellipse, or when applying the scheme of back-action evasion read out [START_REF] Kimble | Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics[END_REF].

Conclusion

We have presented the design and current status of the AEI 10 m Prototype Interferometer. It aims to achieve sub-SQL sensitivity by use of advanced techniques, such as Khalili cavities as compound end mirrors, an advanced passive and active isolation system, monolithic mirror suspensions, a well stabilised high-power laser system, and the injection of squeezed light or application of back-action evasion techniques.

Acknowledgments

This work was supported by the QUEST cluster of excellence of the Leibniz Universität Hannover.

Figure 1 .

 1 Figure 1. The vacuum system is set up in the downstairs area of the AEI prototype hall. The upstairs area is used for assembly of mechanical components before installation as well as for other optical experiments.

Figure 2 .

 2 Figure 2. The basic optical layout for the first round of experiments in the AEI 10 m Prototype facility. Shown are the frequency reference cavity and the main interferometer along with the most relevant design parameters. Note, that only 5 W input power will be used for the first experiments.

Figure 3 .

 3 Figure3. The design sensitivity of the AEI 10 m Prototype Interferometer. The black straight line is the SQL, the red solid curve is the sum of quantum noise, the blue solid line is the sum of all classical noise sources. The dashed area in between the sum of classical and quantum noise is the QND regime that we hope to be able to explore by applying e.g. the back-action evasion technique (red dashed curve).


M P Edgar
email: m.edgar@physics.gla.ac.uk

B W Barr

J Nelson

M V Plissi

K A Strain

O Burmeister

M Britzger

K Danzmann

R Schnabel

T Clausnitzer

F Brückner

E-B Kley

A Tünnermann

Diffraction gratings have been considered as input couplers for Fabry-Perot cavities in future gravitational wave detectors. We experimentally demonstrate the use of a triple-suspended, diffractively-coupled cavity and examine conventional Pound-Drever-Hall length sensing and control techniques to maintain the required operating condition.

Utilizing the diffractively-coupled Fabry-Perot cavity we investigate the effects associated with translational grating motion, and observe a unique 1/f slope in the magnitude of the frequency response when monitoring the forward-reflected error signal.

Experimental demonstration of a suspended, diffractively-coupled Fabry-Perot cavity

Introduction

Current laser interferometric gravitational wave detectors (LIGO [1], GEO600 [2], VIRGO [3], and TAMA [4]) operate with partially transmissive components such as beam splitters and cavity input couplers. To enhance detector sensitivity several techniques are implemented, such as power recycling, signal recycling and optical cavities. The power incident on some of the optical components within these Michelsonbased topologies is of the order 1 kW at a wavelength of 1064 nm. Proposed designs for the next generation of gravitational wave detectors require even higher circulating light power to meet ambitious sensitivity targets, however this has troublesome implications. The optical components are typically manufactured with a fused silica substrate and a dielectric coating. A constant small fraction of incident light is always absorbed in the optical substrates of partially transmissive optics, and causes localized heating which leads to thermal lensing due to a change of refractive index with temperature [5]. The strongest thermal lenses that will limit the detector sensitivity will occur inside the beam splitter and cavity input coupler's hence investigations into new technologies and interferometer topologies are currently underway to help overcome these concerns.

Diffractive reflection gratings offer a novel approach for splitting and recombining light fields without transmission through optical substrates and is a technology currently being tested for the third generation of detectors like the Einstein Telescope [6]. These devices may also provide the solution for reducing the thermal noise contributions in optical components and suspensions if cryogenic techniques are adopted in the future ‡. For instance, it has been shown that the thermal expansion coefficient of silicon, which is opaque at 1064 nm, can reach zero at low temperatures, suggesting that the thermoelastic noise contribution should also become negligible [7]. There has also been considerable progress towards manufacturing monolithic diffraction gratings, known as waveguide gratings, which could potentially improve thermal noise limits associated with coating materials [8]. However, a theoretical analysis of gratings used as input couplers has revealed additional characteristics to be expected in the detected control signals. In particular, translational motion of the diffractive coupler relative to the laser beam could introduce additional phase and alignment noise when compared to an equivalent traditional cavity configuration [9]. It is therefore important to understand how to model diffractive couplers and validate such simulations by experiment, which henceforth forms the basis of this manuscript.

Upgrading the Glasgow 10 m prototype

A number of theoretical and table-top experiments have examined the input-output amplitude and phase relations for a three-port diffractively coupled Fabry-Perot cavity [10,11]. The Glasgow 10 m prototype interferometer was commissioned as a diffractively-coupled optical cavity, as illustrated in figure 1, for investigating such devices in a suspended environment. The cavity optics in this system were suspended as triple pendulums with two stages of cantilever-mounted spring blades for enhanced vertical isolation and freedom of motion. The diffraction grating under investigation was manufactured by etching a binary structure into a fused silica substrate then coating with multiple alternating layers of tantala (Ta 2 O 5 ) and silica (SiO 2 ), to give an ultra low-loss low-efficiency three-port grating with a period d = 1450 nm [12]. The grating was mounted in a second order Littrow configuration, and illuminated at an angle of 47.2 degrees with 181 mW of s-polarized light at 1064 nm wavelength, from a Nd:YAG laser (Model Mephisto 2000NE from Innolight). The configuration chosen provides weak coupling into and out of the cavity, ensuring that the resulting system is directly comparable with a conventional Fabry-Perot cavity.

Control and length sensing signal extraction

Conventionally, to maintain a gravitational wave detector at the operating point, monochromatic laser light, known as the carrier light, is held resonant inside the optical cavities of the interferometer by suitable feedback control. Modulation sidebands are added to the carrier light before entering the system, as prescribed in the Pound-Drever-Hall (PDH) technique [13], and the light exiting the cavity is subsequently detected on tuned photodetectors located at the output ports. The detected light is demodulated with a local oscillator, at the modulation frequency, to obtain information regarding the interaction of the frequency components. The bi-polar error signal obtained indicates the relative length between the cavity mirrors and can then be used to control the cavity length through suitable electronic feedback. From figure 1 it can be seen that our system has three detection ports, and to enable signal extraction from each output required the carrier light to be twice modulated. As with the traditional PDH technique the modulation frequency for the forward-and back-reflected ports can be arbitrarily chosen and for convenience 10 MHz was used in our system. However, to monitor the cavity length with the transmitted port required the use of sidebands just off-resonance at 15.24 MHz, close to the free spectral range (FSR) of our cavity of 15.27 MHz.

Modeling a diffractively-coupled Fabry-Perot cavity

The study of interferometer topologies is reasonably straightforward when dealing with the simple relationships among linear light fields and numerical techniques are routinely used to compute the signals obtained at various photodetectors in response to changes in the relative positions of the optics. This is necessary for the development of length sensing and control schemes required to keep the interferometers at the desired operating point and to read out the signals, including the gravitational wave signal. A traditional two-port Fabry-Perot cavity couples one input field to two output fields and can be modeled using the amplitude reflection/transmission efficiencies of the mirrors. However, by replacing the input coupler with a three-port diffractive reflection grating, each input field couples to three output fields. Implementing the configuration used in this investigation, determines a second order Littrow incident beam (θ i = arcsin(λ/d)) coupling to the orders 0, 1, 2 and a normal incident beam coupling to the orders -1, 0, +1. This type of coupling leads to more complex phase relations compared to a conventional two-port cavity, which can be represented by a scattering matrix:

S 3p =     η 2 e iφ 2 η 1 e iφ 1 η 0 e iφ 0 η 1 e iφ 1 ρ 0 e iφ 0 η 1 e iφ 1 η 0 e iφ 0 η 1 e iφ 1 η 2 e iφ 2     , (1)
where η 0,1,2 and φ 0,1,2 are the amplitude diffraction efficiencies and phase changes on diffraction for zeroth, first and second orders respectively, and ρ 0 is the amplitude reflectivity at normal incidence. For each output port of the cavity, the field amplitudes have already been investigated [10] and can be described by:

c 1 = η 2 e iφ 2 + η 2 1 e 2i(φ 1 +φ) d, (2)
c 2t = iτ 1 η 1 e i(φ 1 +φ) d, (3)
c 3 = η 0 + η 2 1 e 2i(φ 1 +φ) d, (4)
where the resonance factor is defined by d = [1 -ρ 0 ρ 1 e 2iφ ] -1 , φ represents the phase acquired after one round-trip of the cavity, and ρ 1 and τ 1 are the amplitude reflectivity/transmittivity efficiencies of the end mirror. From the specifications of our grating, as presented in table 1, and the reflection/transmission efficiencies (ρ 1 /τ 1 ) of the end mirror, all the cavity properties can be determined numerically. Furthermore, based on the field equations 2,3 and 4 a numerical simulation of the diffractive cavity could be built, using the MATLAB software package. This simulation allowed us to compare experimental findings for the amplitude and power of output light fields, with modeled predictions.

Experimental results

The FSR of our cavity is 15.27 MHz and by monitoring the DC signal from the transmitted port, the corresponding full width half maximum (FWHM) was determined to be 13.80 ± 0.64 kHz. The finesse of our cavity was measured to be 1107 ± 51, and from the simulation an expected finesse of the diffractive cavity was calculated to be 1177 ± 27, showing good agreement. From the grating parameters used in our model we were also

L G = 1 -(ρ 2 0 + 2η 2 1
), which was determined to be 0.199%, closely matching a measured value of 0.177 ± 0.025% carried out at AEI in Hannover. Furthermore, based on the specifications of the end mirror and the measured DC light power detected at the transmitted output port we were able to calculate the circulating power in the cavity to be around 15 W.

One way to establish whether the sensing signals predicted by the model agree with experiment is to sweep the length of the cavity by at least one round-trip wavelength (one FSR in frequency terms). Then the demodulated signal from each port can be compared to the prediction. The slope of this signal at the operating point gives the response for that output port, otherwise known as the effective optical gain. In this experiment, instead of sweeping the cavity length the laser frequency was swept. This has the advantage that it does not risk causing alignment changes of the cavity that could cause higher order cavity modes to become excited thus producing extra features in the result.

The radio-frequency (RF) signal from each detection port can be demodulated in two orthogonal phases, we call these 'in-phase' and 'quadrature-phase' respectively. The demodulation phase in the 'quadrature-phase' case was adjusted to minimize the detected signal, while the 'in-phase' signal was obtained by adding a 90 degree phase shift in the demodulation process. The demodulated signals obtained in the experiment are shown in figure 2 and are seen to be in good qualitative agreement with modeled predictions. The discrepancies between the experiment and modeled length sensing signals can be attributed to the finite rate of sweep in the experiment. The model is 'quasi-static' and therefore does not predict the slight asymmetry in the patterns seen in the experiment as stored light leaks out after a small delay. There is a practical limit to how slow a sweep can be made due to uncontrolled 1 Hz motion of the pendulums, since longitudinal, lateral and angular motion of the mirrors cause small misalignments. These effects are almost unavoidable with suspended optics.

It is essential to calibrate the demodulated signals detected at each port with the modeled signals to investigate the level of quantitative agreement. This required comparison between the relative size of the in-phase slopes to that of the transmitted port. The ratios of the signal responses are presented in table 2 and indicate good agreement.

Analysis of figure 2 indicates that only the transmitted signal will be symmetrical around the center of resonance. This is because light has been diffracted into the cavity only once, and therefore all frequency components receive the same phase shift before resonating. From previous investigations with table-top cavities [11], the extent of the asymmetry was seen to be determined by the values of the η 0 and η 2 diffraction efficiencies. With our numerical simulation accurately validated by experiment, we were also able to probe the effects of asymmetry on the demodulated output signals by altering the grating parameters. An interesting result of this analysis is that, through careful choice of demodulation phase, we can extract signals from each of the reflected ports which sum together to reconstruct a traditional PDH locking signal (see figure 3). This has been compared to other measurements carried out with different apparatus that show the same effect, made at AEI [START_REF] Britzger | Personal Communication[END_REF]. The diffractive optic used in our investigation had a second order diffraction efficiency close to the minimum possible, hence the forward reflected signal had a shape that closely resembled the PDH signal. It was possible to lock the cavity using the signal from this port, although not quite at the center of resonance, therefore the cavity was instead locked to the transmitted error signal (which does exhibit symmetrical behaviour around the center of resonance). Locking to this port also makes it possible to investigate the dynamic behaviour and additional effects associated with suspended diffractively coupled optical systems.

Investigations of grating interferometers have shown additional phase and alignment noise, when compared to traditional mirror topologies [9]. Using electromagnetic actuators positioned at the back and side of the test mass holding the diffractive optic it was possible to inject motion both along the cavity axis (longitudinal) and perpendicular (translational). By observing the forward-reflected signal we were able to demonstrate the effects associated with translational grating motion. Injecting longitudinal motion on the test mass produces a 1/f 2 shape in the magnitude of the frequency response of the demodulated signal. This effect is seen in both mirror coupled and diffractively coupled cavities. However, translational motion of the grating produces a 1/f shape which is not observed in a mirror coupled cavity and can therefore be attributed to the properties of the grating. A full theoretical analysis has been undertaken by our colleagues at Birmingham University and has now been published [START_REF] Hallam | [END_REF]. This new feature is due to side induced phase sidebands, introduced on the light entering the cavity, that propagate through the cavity and then interact with additional side induced phase sidebands exiting the cavity. Many of the frequency components on the exiting light cancel, however, the remainder can be detected on a photodetector and demodulated to give this unique behaviour. A full analysis of this work has been carried out and is in the process of publication.

Conclusion

In conclusion, we have constructed a suspended diffractively-coupled Fabry-Perot cavity within the Glasgow 10 m prototype interferometer and developed a numerical model for the system. From the simulation we were able to investigate the use of conventional techniques for length sensing and control signal extraction from a diffractively coupled Fabry-Perot cavity. Our experimental results provided qualitative and quantitative verification of the theoretical framework supporting grating interferometers. It was possible to adapt our numerical model to show the extent of asymmetry in both reflected demodulated signals and furthermore reconstruct a symmetrical PDH signal with these signals, irrespective of their shape. Additionally, we have revealed the unique behaviour associated with translational grating motion and verified the 1/f shape in the frequency response with theoretical predictions. Further work on the dynamic effects associated with gratings will be published in a later paper.

Figure 1 .

 1 Figure 1. (Color online) Topology of the Glasgow 10 m prototype (left) showing the traditional and diffractive interferometer arms and simplified schematic (right) of the three-port grating, used in second order Littrow configuration, as the input coupler for a diffractive cavity. Tuned photodiodes (PD's) are positioned at all 3 output ports to detect the DC power and RF component for derivation of the control signals.

Figure 2 .

 2 Figure 2. (Color online) Normalized RF power for each output port; forward-reflected (top), transmitted (middle), and back-reflected (bottom). The measured data and modeled predictions of the length sensing signals are presented on the left and right hand side respectively. The solid (black) trace indicates in-phase measurements, and the dashed (red) trace indicates quadrature-phase. The absolute scaling between modeled forward-reflected, transmitted, and back-reflected ports is 163:1:2.

Figure 3 .

 3 Figure 3. (Color online) Modeled demodulated signals; back-reflected (red) and forward-reflected (blue) indicated by dashed traces, and the combined back-reflected + forward-reflected (black) indicated by a solid trace. The grating parameters used here are for an ideal (lossless) grating with ρ 0 = 0.99663, η 1 = 0.0407, and η 0 = η 2 = 0.7065.

Table 1 .

 1 Parameter values of the grating, provided by AEI in Hannover where it was first tested.

	Parameter Value[%]
	ρ 2 0	99.663
	η 2 0	99.840
	η 2 1	0.069
	η 2 2	0.016
	able to calculate the expected grating loss using the identity

Table 2 .

 2 The measured and modeled signal response for each port show the correct scaling relative to transmitted port.

	Parameter	Measured Value[dB] Modeled Value[dB]
	back-reflected/transmitted	-26.93	-22.51
	transmitted/transmitted	0	0
	forward-reflected/transmitted 43.07	44.74

‡ Note, care must be taken to ensure the coating thickness minimizes substrate heating due to evanescent fields.

Acknowledgements

The authors would like to thank Szabi and Zsuzsa Marka and all other organizers of the Amaldi8 conference in New York. This work was supported by the University of Glasgow and the Science and Technology Facilities Council. The authors would also like to thank the Sonderforschungsbereich TR7 of the Deutsche Forschungsgemeinschaft for financial support.