You are an expert at summarizing long articles. Proceed to summarize the following text: 
cepheid variables have been used to determine galactic distances for many decades ( e.g. @xcite , @xcite and references therein ) . the relationship between their period of pulsation and luminosity has been considered to be well defined at several times during its lifetime . however , the effect of the cepheid s chemical composition on the period - luminosity ( pl ) relation has never been adequately determined , leaving the relation open to systematic uncertainties that have not been fully investigated . proper calibration of this relation is essential not just to explain how metallicity affects the pulsations of cepheids , but to tie down the zero point of the extra - galactic distance scale and thus properly measure the hubble constant . metallicity and differential absorption will both change stellar colours @xcite . theoretical models ( e.g. ) show that the metal content of a cepheid will affect the derived distance modulus . if a star of an unknown metallicity is at an undetermined distance then it is difficult to untangle these two effects on the stars colours . ideally the pl relation would remove this problem as the distance to the star could be found without calculating the colour of the cepheid . the problem arises as the calibration of the pl relation does not take this effect into account . the distances that were used to calibrate the zero point of the relation were determined without considering how the reddening of the cepheids was affected by the combination of these two mechanisms , meaning that a systematic offset may have been introduced into the relation . there has been some investigation into the effect that metallicity has on the pl relation , beginning with @xcite . and used the cepheids detected in the eros gravitational lensing survey to show that discrepant values of @xmath7 could be reconciled by applying a metallicity correction to cepheid distance moduli . @xcite used the hubble space telescope to observe cepheids in m  101 , a nearby spiral galaxy with active star formation regions but low dust extinction properties . choosing a galaxy with low extinction means that there would be less reddening from dust ; any reddening of the colour of the cepheids could be explained as a metallicity effect . this study found that @xmath8 mag dex@xmath9 ( see also freedman et al . , 2001 ) . however , their conclusions were based on small numbers of cepheids , combined with the pl relations from @xcite . it is far from ideal to use such a small sample to quantify an effect that could mean that the entire extra - galactic distance scale is subject to a systematic offset . using a similar method but with a larger sample of cepheids , @xcite found @xmath10 mag dex@xmath9 . using a large sample of nearly 700 cepheids in 17 galaxies , @xcite had found a result compatible with these other works . most works use a sample of cepheids covering a range in metallicity and enforce consistency between distance moduli ; this is what @xcite and @xcite did for instance . an alternative approach used e.g. by @xcite is to assume that the distances to several galaxies are known a priori , from the tip of the red giant branch in their case , and find the correction needed to bring cepheid distances to these galaxies in agreement with that other standard candle . there are two possible solutions to the problem of the metallicity - extinction degeneracy . the method followed by @xcite is one possibility , the elimination of extinction from the equation . theoretically this method should work , but in practice it is not so simple . @xcite chose a galaxy with low extinction , not zero extinction . this implies that the extinction is not entirely eliminated , leaving the degeneracy that we are trying to overcome . however , this degeneracy could be removed by using the reddening - free wesenheit magnitude @xmath1 pl relation to calculate the distance . by eliminating extinction in this way , any discrepancies in the apparent distance modulus could be explained by the metallicity effect . the work presented here is based on a multi - epoch survey of m33 conducted with the wiyn 3.5 m telescope . m33 is a well studied galaxy , with observations of cepheids performed by hubble as early as 1926 @xcite . as it is nearby , many studies have determined the distance of m33 using different and independent methods , such as eclipsing binaries @xcite , the tip of the red giant branch ( trgb ) , masers @xcite and cepheids themselves @xcite . although some of these methods may not provide the same accuracy that a cepheid distance does , they allow us to have an independent starting point for our analysis of the pl relation of m33 . one of the reasons that m33 was chosen for this study is that it is well studied . its inclination angle is 53@xmath11 , and so any effect on distance modulus ( @xmath12 ) from the orientation will be extremely small . the effect on @xmath12 due to the orientation of the galaxy was found to be very small ( less than 0.01 mag ) . the metallicity gradient across the galaxy is well defined , so the chemical composition of the cepheids is relatively easy to determine just from their position in the galaxy . these properties inherent to m33 make it the ideal target for a study of this nature . the paper is organised as follows . section  [ observations ] describes our observations . section  [ data - reduction ] describes the reduction process , including the development of the photometry pipeline and the final calibration and astrometry . section  [ results ] contains the final catalogues and assesses the accuracy of the photometry , with the final pl relations and distances in section  [ pl - relation ] . finally , we examine the effect of metallicity on our results and derive a value for the metallicity correction parameter @xmath13 . the data set consists of 25 epochs of @xmath14 images of four fields of m33 obtained between 1998 and 2001 on the 3.5 m wiyn telescope . the first 20 epochs used the wiyn s2 kb imager , a single thinned tek / stis 2048x2048 ccd with 21 @xmath12 m pixels . for the final 5 epochs the new mini - mosaic ( mimo ) camera was used . the mini - mosaic consists of two thinned site 2048x4096 ccds with 15 @xmath12 m pixels . a single exposure covered @xmath15 arcmin for the imager , and @xmath16 arcmin for the mini - mosaic , with pixel scales of 0.195 and 0.141 arcsec pixel@xmath9 respectively . four fields were observed for the survey , two in the centre of m33 , and two in the outer , southern part of the galaxy . the locations of the fields are shown in figure  [ fields - figure ] . the j2000.0 coordinates of the fields are shown in table  [ field - table ] . all the fields were observed in the @xmath17 , @xmath18 and @xmath19 filters with both cameras . the position of the fields were chosen such that the metal - rich population at the centre of the galaxy could be compared with the more metal - poor population in the outer region . cepheids tend to be concentrated in the spiral arms , so the outer fields were located in the southern part of the galaxy to coincide with the clearest arm . the positions of the fields and the addition of the mini - mosaic camera meant that some objects were observed in either both inner or both outer fields , giving up to 38 observations for objects in the overlap regions . .j2000.0 coordinates of the four fields . m33 - 1 and m33 - 2 are situated in the centre of the galaxy . m33 - 3 and m33 - 4 are in the southern spiral arm . deprojected angular and linear distances of each field to the centre of the galaxy are given , assuming m33 is at a distance of 840 kpc , has an inclination angle of @xmath20 and the major axis has a position angle of @xmath21 . [ cols="<,^,^,^,^",options="header " , ]     [ different - pls ]    to quantify the effect of metallicity we use @xmath13 , as defined in equation  [ gamma ] . we can substitute @xmath22 for @xmath23 mag , using the full sample distance moduli , and @xmath24 . this leads to a metallicity correction of @xmath25 mag dex@xmath9 . this is compatible with recent measurements , such as that of @xcite . our final distance measurement for m33 is calculated by assuming an lmc metallicity of @xmath26 @xcite . using @xmath25 we find that the metallicity corrected distance modulus to m33 is @xmath6 , consistent with recent trgb distance measurements . the individual distance moduli derived for each cepheid are shown in figure  [ distances ] . the uncertainty on our result is significant . by using a larger cepheid sample the contribution from the distance moduli could be reduced . also , the sample only covers the two extremes of the metallicity gradient . we will investigate the effect further using the data from @xcite . their sample contains over 2000 cepheids spread over the entire galaxy , and hence the entire [ o / h ] range . this will allow us to fully investigate the effect over a wide range of [ o / h ] , rather than just fitting a straight line to two points , and the use of so many cepheids will bring the random uncertainty down considerably . we note that the largest contribution to the error budget is the uncertainty on the metallicity gradient of m33 . this could be reduced using a large sample of cepheids . recent work by @xcite has shown that the two periods of double mode cepheids can be used to calculate their metallicity . by using a large sample of these stars across the whole galaxy , in combination with observations of fundamental mode cepheids covering the same area it would be possible to calculate @xmath13 with a much higher degree of accuracy . we have produced a photometric catalogue in @xmath17,@xmath18 and @xmath19 for over 200,000 objects in two regions of m33 , identifying 167 fundamental mode cepheids . using the reddening free wesenheit lmc pl relations we have established distances to the two regions as @xmath27 mag and @xmath28 mag . the difference in these two distance moduli is believed to come from the effect of metallicity on the zero - point of the pl relation , and hence its effect on cepheid distances . we have quantified this effect by the parameter @xmath29}$ ] and find a value of @xmath25 mag dex@xmath9 , consistent with other recent estimates . for the range of metallicities discussed here it is appropriate to include @xmath13 in the pl relation . this leads to the numerical pl shown in equation  [ altered - num - pl ] , assuming an lmc distance modulus of 18.4 mag . the metallicity of the region in question is denoted by @xmath30_{mes}$ ] . @xmath31_{lmc } - \log[o / h]_{mes } ) \end{split } \label{altered - num - pl}\ ] ]    the analysis presented here assumes that _ only _ the zero - point of the pl relation changes with metallicity ; the slope does not significantly change between the mw and lmc metallicities . we have repeated the analysis using the mw slope of the @xmath1 pl relation from f07 and we found the same value for @xmath13 . this is an important result as it means that we can find reddening- and metallicity - corrected cepheid distances for any population from two colour ( @xmath18 and @xmath19 ) photometry without the time consuming task of calculating internal @xmath32 values for other galaxies . as noted above , the final result and particularly the error are significantly affected by the value of metallicity one uses for each region . we have used the recent results from . @xcite found a much shallower gradient however . using their values of metallicity in our two fields , we find @xmath33 mag dex@xmath9 , incompatible with other determinations of this parameter such a large value of @xmath13 would have dramatic effects on the distance scale . in particular , it would change the distance to the lmc by so much that the cepheid distances would become incompatible with all other measurements . the difference in distance moduli between the two fields is an argument in favour of a rather large metallicity gradient in m33 . however , the metallicity gradient of m33 is still subject to strong debate and , to quote @xcite , `` ... the expectation of homogeneous azimuthal metallicity in patchy star - forming spiral galaxies seems naive ... '' . our extension of the work of @xcite based on double - mode cepheids in m33 will shed light on this discrepancy by measuring the metallicity and its gradient using many more positions . hopefully this paper serves as an example of the need for better determinations of the metallicities of _ all _ galaxies where cepheids have been observed . it is also important to note the correlation between this work and the hubble key project @xcite ; although the m33 cepheids have shorter periods than the average in the hst project , the value of @xmath13 that we find is consistent with their work . we will further investigate the effect of metallicity by applying the methodology described above to the catalogues from @xcite . with the large number of cepheids we will be able to sample the whole [ o / h ] range of the galaxy and the whole @xmath34 parameter space , finally calibrating the effect that has plagued the cepheid pl relation and distance scale for many decades . we would like to profusely thank j .- beaulieu and j .- b . marquette for the m33 fundamental mode cepheid catalogues which have proved to be invaluable to this work . we are indebted to p.  stetson and k.  stanek for their assistance with creating and testing the photometry pipelines . we thank the referee , p. fouqu , for his swift and thorough report that significantly improved the content and presentation of this paper . vs is supported by an stfc studentship . alibert y. , baraffe i. , hauschildt p. allard f. , 1999 , a&a , 334 , 551 beaulieu j .- p . et al . , 1997 , a&a , 318 , l47 beaulieu j .- p . , buchler j.  r. , marquette j .- b , hartman j.  d. , schwarzenberg - czerny a. , 2006 , apj , 653 , l101 bell r. a. , rodgers a. w. , 1969 , mnras , 142 , 161 brooks r.  s. , wilson c.  d. , harris w.  e. , 2004 , aj , 128 , 237 bonanos a.  z. , et al . , 2006 , apj , 652 , 313 bono g. , caputo f. , fiorentino g. , marconi m. , musella i. , 2008 , apj , 684 , 102 brunthaler a. , reid m.  j. , falcke h. , greenhill l.  j. , henkel c. , 2005 , science , 307 , 1440 caputo f. , marconi m. , musella i. , santolamazza p. , 2000 , a&a , 359 , 1059 cardelli j.  a. , clayton g.  c. , mathis j.  s. , 1989 , apj , 345 , 245 crockett n.  r. , garnett d.  r. , massey p. , jacoby g. , 2006 , apj , 637 , 741 galleti s. , bellazzini m. , ferraro f.  r. , 2004 , a&a , 423 , 925 ferrarese l. , silbermann n.  a. , mould j.  r. , stetson p.  b. , saha a. , freedman w.  l. , kennicutt , r.  c. , jr . , 2000 , pasp , 112 177 fernie j.  d. , 1969 , pasp , 81 , 707 fouqu p. et al . , 2007 , a&a , 476 , 73 freedman w.  f. , madore b.  f. , 1990 , apj , 365 , 186 freedman w.  f. , wilson c.  d , madore b.  f. , 1991 , apj , 372 , 455 freedman w.  l. et al . , 2001 , apj , 553 , 47 hartman j.  d. , bersier d. , stanek k.  z , beaulieu j .- p . , kaluzny j. , marquette j .- b . , stetson p.  b. , schwarzenberg - czerny a. , 2006 , mnras , 371 , 1405 hubble e.  p. , 1926 , apj , 63 , 236 kennicutt r.  c. , jr . , et al . , 1998 , apj , 498 , 181 kim m. , kim e. , lee m.  g. , sarajedini a. , geisler d. , 2002 , aj , 123 , 244 kochanek c.  s. , 1997 , apj , 491 , 13 kudritzki r.  p. , urbaneja , m.  a. , bresolin f. , przybilla n. , gieren w. , pietrzyski g. , 2008 , apj , 681 269 landolt a.  u. , 1992 , aj , 104 , 340 mcconnachie a.  w. , irwin m.  j. , ferguson a.  m.  n. , ibata r.  a. , lewis g.  f. , tanvir n. , 2004 , mnras , 350 , 243 macri l.  m. , stanek k.  z , bersier d. , greenhill l.  j. , reid m.  j , 2006 , apj , 652 , 1133 magrini l. , vlchez j.  m. , mampaso a. , corradi r.  l.  m. , leisy p. , 2007 , a&a , 470 , 865 massey p. , olsen k.  a.  g. , hodge p.  w. , strong s.  b. , jacoby g.  h. , schlingman w. , smith r.  c. , 2006 , aj , 131 , 2478 monet d.  g. et al . , 2003 , aj , 125 , 984 ngeow c. , kanbur s.  m. , neilson h.  r. , nanthakumar a. , buonaccorsi j. , 2009 , apj , 693 , 691 pena m. , peimbert m. , torres - peimbert s. , ruiz m.  t. , maza j. , 1995 , apj , 441 , 343 pietrzynski g. , gieren w. , fouqu p. , pont f. , 2002 , aj , 123 , 789 sakai s. , ferrarese l. , kennicutt jr . , r.  c. , saha , a. , 2004 , apj , 608 , 42 sasselov d.  d. et al . , 1997 , a&a , 324 , 471 simon n.  r , lee a.  s. , 1981 , apj , 248 , 291 stetson p.  b. , 1987 , pasp , 99 , 191 stetson p.  b. , 1990 , pasp , 102 , 932 stetson p.  b. , 1994 , pasp , 106 , 250 stetson p.  b. , 2005 , pasp , 117 , 563 szabados l. , 2003 , in gaia spectroscopy : science and technology , ed . u. munari , asp conf . , 298 , 237 udalski a. , soszynski i. , szymanski m. , kubiak m. , pietrzynski g. , wozniak p. , zebrun k. , 1999 , acta astron . , 49 , 223
we present the results from a multi - epoch survey of two regions of m33 using the 3.5 m wiyn telescope . 
 the inner field is located close to the centre of the galaxy , with the outer region situated about @xmath0 kpc away in the southern spiral arm , allowing us to sample a large metallicity range . 
 we have data for 167 fundamental mode cepheids in the two regions . the reddening - free wesenheit magnitude @xmath1 period - luminosity relations were used to establish the distance modulus of each region , with @xmath2 and @xmath3 . 
 the apparent discrepancy between these two results can be explained by the significant metallicity gradient of the galaxy . 
 we determine a value for the metallicity parameter of the period 
 luminosity relation @xmath4 = @xmath5 , consistent with previous measurements . 
 this leads to a metallicity corrected distance modulus to m33 of @xmath6 mag . 
 catalogues 
 cepheids  galaxies : individual : m33  galaxies : distances and redshifts