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smail , ivison & blain ( 1997 , hereafter sib ) recently detected a new population of distant galaxies in a deep survey of gravitational lensing clusters in the submillimetre waveband using scuba on the jcmt ( holland et al .
subsequent deeper integration in these fields , and observations of another five cluster fields confirm the results ( smail et al .
1998 ; blain et al . 1998 ) .
the identification of the brightest 850-@xmath2 m source with a dust - shrouded starburst / active galactic nucleus at redshift @xmath3 ( ivison et al .
1998 ) and the non - correspondence of the detected sources with cluster galaxies support these claims . prior to these observations the surface density of faint galaxies in this waveband was uncertain by up to three orders of magnitude ( blain & longair 1993 , 1996 , hereafter bl96 ) , but it is now known to an accuracy of about 50 per cent .
the estimation of the magnitude of confusion noise ( scheuer 1957 ) due to the submillimetre - wave continuum radiation of discrete extragalactic sources has previously required extensive extrapolation from the results of observations of low - redshift galaxies ( longair & sunyaev 1969 ; franceschini et  al .
1989 ; helou & beichman 1990 ; fischer & lange 1993 ; toffolatti et  al . 1995
; gawiser & smoot 1997 ) , and so the uncertainties in the estimates obtained were large as compared with those in the radio and far - infrared wavebands .
our new direct observations allow more reliable estimates to be made .
first , we briefly discuss our observations at 850@xmath2 m .
we introduce a simple parametric model of galaxy evolution , which is similar in form to the _ iras_-based models discussed by bl96 , but fitted to the counts derived by sib , to predict the properties of confusing sources at other millimetre / submillimetre wavelengths .
these models include _ only _ the contribution from dusty extragalactic objects . at the longest and shortest wavelengths in this waveband a significant contribution to confusion
is expected due to other sources of radiation  discrete extragalactic non - thermal radio emission and galactic dust emission respectively .
secondly , we present our estimates of confusion noise as a function of both the angular scale and wavelength of observations . finally , we discuss the relevance of confusion for observations of both distant galaxies and the cmbr using existing and planned millimetre / submillimetre - wave telescopes : the jcmt / scuba ; the airborne stratospheric observatory for infrared astronomy ( sofia : becklin 1997 ) ; the large millimeter telescope ( lmt / gtm ) , a ground - based 50-m single - antenna telescope ( schloerb 1997 ) that will incorporate the bolocam bolometer array receiver ( mauskopf & bock 1997 ) ; large ground - based millimetre / submillimetre - wave interferometer arrays ( mias : brown 1996 ; downes 1996 ) ; the esa _ far - infrared and submillimetre telescope _ ( _ first _ : pilbratt 1997 ) and _ planck surveyor _ ( bersanelli et al . 1996 ) space missions , and balloon - borne instruments , for example boomerang ( lange et al . 1995 ) .
parameters of these instruments and telescopes are listed in table1 .
an advanced - technology 10-m ground - based telescope is also planned for the south pole ( stark et al .
1998 ) .
0.75 mm    ' '' ''    1.2 mm    .instrumental parameters for instruments and telescopes shown in fig.2 , and a large mia .
references can be found in section1 .
it is proposed to attach a prototype of the bolocam instrument destined for the lmt to the 10.4-m caltech submillimeter observatory ( cso ) . unless otherwise stated the sensitivities quoted refer to a 1@xmath0 detection in a 1-h integration including overheads .
[ cols= " < , < , < , < " , ]     1.2 mm    ' '' ''    1.2 mm     p1.1 cm p1.1 cm p1.5 cm p1.3 cm p1.3 cm 2.00 & 150 & 106 & @xmath4 & @xmath5 + 1.38 & 217 & 51 & @xmath6 & @xmath7 + 0.85 & 353 & 19 & @xmath8 & @xmath9 + 0.55 & 545 & 19 & @xmath10 & @xmath11 + 0.35 & 857 & 19 & @xmath12 & @xmath13 +    ' '' ''
1 .   we have estimated the source confusion noise expected in millimetre / submillimetre - wave observations , based on direct observations of distant galaxies at a wavelength of 850@xmath2 m ( sib ) .
although comparable in magnitude to previous estimates of the confusion noise , our predictions are much less dependent on either extrapolations or model - dependent factors . 2 .
reliable limits to the maximum depth of galaxy surveys that can be carried out using either ground - based or space - borne telescopes are imposed by these estimates . for example , a 1@xmath0 sensitivity limit of about 0.4mjy is predicted for the jcmt / scuba at 850@xmath2 m .
this limit could be reached in a fully - sampled map after about 300h of integration in a single field , and so is unlikely to present a problem to planned surveys .
future airborne and space - borne submillimetre - wave telescopes are expected to be confusion limited much more quickly , and so extremely deep millimetre / submillimetre - wave galaxy surveys will require the subarcsecond resolving power of large ground - based interferometer arrays . 3 .
our estimates will be useful for planning and operating future millimetre / submillimetre - wave telescopes .
a _ first _
survey should cover a large area of sky and not involve integrations longer than a few hours in any single - pointed field .
confusion noise arising from distant dusty galaxies will dominate instrumental noise in the planned all - sky survey using the _ planck surveyor _ hfi instrument at frequencies greater than 350ghz .
confusion noise will be more severe in the fields of clusters , reducing the efficiency of _ planck surveyor _ for the detection of the sunyaev 
zeldovich effect .
we thank sarah church , andy harris , mike jones , anthony lasenby , malcolm longair , richard saunders and roberto terlevich for useful discussions , and an anonymous referee for his / her helpful comments .
the collaboration conducting the observations underlying this work now includes jean - paul kneib .
rji and irs are supported by pparc advanced fellowships .
holland w.s . ,
, lightfoot j.f . , jenness t. , robson e.i . , cunningham c.r .
, laidlaw k. , 1998 , in phillips t.g .
ed . , advanced technology mmw , radio and terahertz telescopes .
spie vol . 3357 , spie , bellingham , in press                                stark a.a . , carlstrom j.e . , israel f.p
, menten k.m . ,
peterson  j.b . , phillips t.g . , sironi g. , walker w.w . , 1998 , in phillips t.g .
ed . , advanced technology mmw , radio and terahertz telescopes .
3357 , spie , bellingham , in press ( astro - ph/9802326 )
the first observations to detect a population of distant galaxies directly in the submillimetre waveband have recently been made using the new submillimetre common - user bolometer array ( scuba ) on the james clerk maxwell telescope ( jcmt ) . 
 the results indicate that a large number of distant galaxies are radiating strongly in this waveband . here 
 we discuss their significance for source confusion in future millimetre / submillimetre - wave observations of both distant galaxies and cosmic microwave background radiation ( cmbr ) anisotropies . 
 earlier estimates of such confusion involved significant extrapolation of the results of observations of galaxies at low redshifts ; our new estimates do not , as they are derived from direct observations of distant galaxies in the submillimetre waveband . 
 the results have important consequences for the design and operation of existing and proposed millimetre / submillimetre - wave telescopes : the _ planck surveyor _ survey will be confusion - limited at frequencies greater than 350ghz , even in the absence of galactic dust emission ; a 1@xmath0 confusion noise limit of about 0.44mjybeam@xmath1 is expected for the jcmt / scuba at a wavelength of 850@xmath2 m ; and the subarcsecond resolution of large millimetre / submillimetre - wave interferometer arrays will be required in order to execute very deep galaxy surveys .    
 galaxies : evolution  galaxies : formation  cosmic microwave background  cosmology : observations  diffuse radiation  
 radio continuum : galaxies