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1、10.3TranslationalSymmetry247suppere˙upper()swgtPsmax,s=úúddee˙˙Lss()(),sWe˙,,s(10.34)slower0whereeee˙upper()sL∫min[]˙src()mins,,()s,,s˙trg()Wmins()s,,s(10.35)sslower∫max[]srcmin,,,strgmin,(10.36)ssupper∫min[]srcmax,,,strgmax,(10.37)andssrc,min,ssrc,max,strg,min,andstrg,maxaretheminimum
2、andmaximumskewnessvaluesforthephasespacesofthesourceandthetarget.Nowthatwehavederivedtheupperlimitonthetransferred?ux,weareinapositiontowritedownformulasfortheupperlimitsonef?ciencyandconcen-tration.Wede?netheef?ciencyhforinhomogeneoussourcesandtargetsastheactualweighted?uxtransferredt
3、othetargetdividedbytheweighted?uxthatwouldbeachievedifallofthesourceradiationweretobetransferredtotheregionofthetarget’sphasespaceforwhichtheweightfunctionhasitsmaximumvalue:wgtPh∫,(10.38)WPmaxsrctot,whereWmaxisthemaximumtargetweightvalueandPsrc,totisthetotal?uxemittedbythesource.Simil
4、arly,theconcentrationCisde?nedastheactualweighted?uxtransferredtothetargetdividedbytheweightedtarget?uxlevelthatwouldbeachievedifallofthetarget’sphasespaceweretobe?lledwithradiationhavingradianceequaltothemaximumradiancelevelofthesource:wgtPC∫,(10.39)wgtLmaxetrgtot,wgtwhereLmaxisthemax
5、imumradiancevalueofthesourceandetrg,totisthetotalweightedtargetétenduestrgmax,eupper()seewgt=ddsW˙˙(e,.s)(10.40)trgtot,úússtrgmin,0Theupperlimitsonef?ciencyandconcentrationareobtainedbysubstitutionofwgtwgtPmax,sforPinEqs.(10.38)and(10.39):wgtPmaxs,hmaxs,∫(10.41)WPmaxsrctot,andwgtPmaxs,
6、Cmaxs∫.(10.42),wgtLmaxtrgtote,10.3TRANSLATIONALSYMMETRYJustastherotationalskewinvariantisconservedforeachraypropagatedthroughanaxisymmetricopticalsystem,ananalogousquantity—knownasthe248Chapter10ConsequencesofSymmetrytranslationalskewinvariant—isconservedforeachraypropagatedthroughatra
7、nslationallysymmetricopticalsystem.Whenthetranslationalskewnessdis-tributionofasourceisdifferentfromthatofthetarget,translationallysymmet-ricnonimagingsystemsaresubjecttoperformancelimitationsanalogoustothosediscussedinthelastsectionforaxisymmetricopticalsystems.(Bortz,Shatz,andWinst
