Nucl ear I nst rument s and Methods in Physi cs Resear ch A 342 ( 1994) 600- 608 Nort h-Hol l and Coded aper t ur e i magi ng usi ng i mperf ect det ect or syst ems K . Byar d, D . Rams den Depart ment of Physi cs, The Uni ver si t y of Sout hampt on, Sout hampt on S09 5NH, UK ( Recei ved 6 Sept ember 1993) NUCLEAR I NSTRUMENTS & METHODS IN PHYSI CS RESEARCH Sect i on A The i magi ng pr oper t i es of a gamma- r ay t el escope whi ch empl oys a coded aper t ur e in conj unct i on with a modul ar det ect i on pl ane has been i nvest i gat ed . Gaps in t he det ect i on pl ane, whi ch ar i se as a consequence of t he desi gn of t he posi t i on sensi t i ve det ect or used, pr oduce ar t i f ac t s in t he deconvol ved i mages whi ch r educe t he si gnal to noi se r at i o f or t he det ect i on of poi nt sour ces . The appl i cat i on of an i t er at i ve i mage pr ocessi ng al gor i t hm is shown t o r est or e t he i mage qual i t y to t hat expect ed f r om an i deal det ect or . The ef f i ci ency of i mage pr ocessi ng has enabl ed its subsequent appl i cat i on to a gener al coded aper t ur e syst em in or der to gai n a si gni f i cant i mprovement in t he f i el d of vi ew wi t hout compr om i si ng t he angul ar r esol ut i on . 1 . I nt r oduct i on Si nce its concept i on by Mert z and Young t hi r t y year s ago [ 1] coded aper t ur e i magi ng has become of gr eat i mport ance as t he maj or i mage f ormat i on t ech- ni que in har d X- r ay and gamma-ray ast ronomy . Thi s i magi ng t echni que mak es use of a mas k havi ng a car e- f ul l y chosen pat t er n of opaque and t r anspar ent r egi ons whi ch cast s a shadow of t he gamma- r ay sky ont o a posi t i on sensi t i ve det ect i on pl ane . Var i ous conf i gur a- t i ons have been used wi t h di f f er ent t ypes of posi t i on sensi t i ve phot on det ect or s . Among t hese ar e t he Anger camer a used in bot h t he SI GMA [ 2] and GRI P [ 3] exper i ment s, mul t i wi re gas pr opor t i onal count er s as used by t he Bi rm i ngham Uni ver si t y XRT [ 4] , and mul t i -l ayer ar r ays of smal l sci nt i l l at i on cr yst al s, as en- vi saged f or t he I NTEGRAL i nst rument [ 5] . In many cases, t he desi gn of a gamma- r ay t el escope syst em has been const r ai ned by t he choi ce of t he mas k pat t er n whi ch has been sel ect ed so as to pr ovi de t he best possi bl e i mage qual i t y consi st ent with t he ex- pect ed posi t i on r esol ut i on of t he det ect or and t he r equi r ed f i el d of vi ew ( FOV) . Work by Feni mor e [ 6] , and by Got t esman and Feni mor e [ 7] has shown t hat t he uni f or m ly r edundant ar r ays ( URA) and modi f i ed URAs ( MURA) pr ovi de t he best ar t i f act f r ee i mages when one has t he pr obl em of i magi ng t he gamma- r ay sky wher e weak poi nt sour ces ar e expect ed to be f ound in t he pr esence of a hi gh l evel of backgr ound . Ot her pat t er ns may , however , be pr ef er r ed f or di f f er ent ap- pl i cat i ons [ 8- 11] . The URA and MURA pat t er ns ar e i deal l y sui t ed to a near l y squar e det ect i on pl ane, but 0168- 9002/ 94/ $07 . 00 © 1994 - El sevi er Sci ence B .V . Al l r i ght s r eser ved SSDI 0168- 9002( 93) E1241- 0 t hi s has l ed to an i nef f i ci ent use of t he det ect i on pl ane when t hey have been coupl ed to det ect or s whi ch have a di f f er ent nat ur al shape si nce it has been nor mal pr act i ce to sampl e t he shadowgr am compl et el y . For exampl e, t he SI GMA t el escope whi ch used a cl assi c Anger camer a havi ng a ci r cul ar cr yst al det ect or whi ch pr ovi ded a usef ul ci r cul ar ar ea of about 1250 cm 2 was onl y abl e to mak e use of a squar e r egi on havi ng an ar ea of onl y 800 cm 2 because of t he const r ai nt to f ul l y sampl e t he squar e shadow of t he mas k . Si nce t he desi gn f or t hat i nst rument was f r ozen, var i ous ot her opt i ons have become avai l abl e t hat coul d have bot h i mproved t he sensi t i vi t y and enl ar ged t he FOV of t hat t el escope . Hexagonal URA pat t er ns [ 12] woul d have pr ovi ded a bet t er mat ch to t he ci r cul ar act i ve ar ea of t he det ect i on pl ane and so woul d have i ncr eased t he FOV. A si m i l ar FOV i mprovement woul d have been possi bl e if t he t essel at i on aper t ur es [ 13] had been avai l abl e . A t echni que r ef er r ed t o as par t i al cycl e aver agi ng [ 14] coul d al t er nat i vel y have been used to i mprove t he sensi t i vi t y achi eved with t hi s i nst rument . Thi s paper expl or es t he i mage qual i t y and t he sensi t i v- ity t hat woul d be achi eved usi ng a t el escope desi gn in whi ch t her e is a m i smat ch bet ween t he ar ea of t he shadowgr am cast by t he mas k and t he usef ul ar ea of t he posi t i on sensi t i ve det ect or . It al so seeks to f i nd how f ar t he i mage def ect s may be m i ni m i sed by t he use of appr opr i at e i magi ng pr ocessi ng t echni ques . The mot i vat i on f or t hi s st udy was pr ovi ded, in par t , by a r ecent eval uat i on of a br oad band posi t i on sensi - tive det ect or based on a Hamamat s u phot omul t i pl i er t ype R- 3292 [ 15] whi ch can pr ovi de a ci r cul ar 80 cm 2