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In recc nt yca rs a c on s id e ra bl e a mount of th eo re ti c a l, expe rim e nt a l, a nd co m p ut a tiona l work in th e d e ve lopm e nt and appli ca t ion of tec hniqu es for acc ura te m eas ure m e n t of mi c rowav e a nt e nn as ha s bee n s u c cess full y co mpl e te d a t the Na tion a l Burea u of S tanda rd s (a nd wo rk is co ntinu in~). Thi s pa pe r prese nt s and ex te nd s th e ba sic plan e-wave s('a tt e rin~-rn a tri x form ali sm a nd prese nts ne w ge nera li ze d or a djoint rec iproc it y re la ti o ns fo r a nt e nn as. Th e PW S M formali s m is e min e ntl y s uit ab le fo r th e fo rmula ti on a nd sol u ti o n of prob le m s in vo lvin g int e rac ti on s a t a rbit ra r y di s ta nces a nd for th e express io n o f co nve nt io na l asymp toti c quantiti es , s u c h as gain , e ffec ti ve a rea, a nd po la ri za ti o n. It h as in parti c u la r e n ab le d de riva ti on of t wo ne w tec hni qu es th a t pe rmit acc ura te, " probe -co rre c te d " a nt e nn a meas ure - Ill e nt s a t g rea tl y red uc e d d is ta nces: ( I ) by deco n vo lut ion o f tra ns ve rse s ca nnin g d a ta, tak e n with d "" ell! (w here ell! = a'/2,,-) a nd (2) by ex tra po la ti o n of receive d s ig n al o bsc r ved as a fun c tion of di s ta nc e d ,with d -rI". Th e s e tcc hniq ues bas ica ll y d e te rmin e th e sca la r produc t, C, of two vec tors ch a ra c t e ri s ti c respec ti ve ly of th e tra ns mittin g a nd th e rece ivin g a nt e nn as. For mul as fo r utili za ti o n o f Coda t a, ta kin g full ac cuu nt of po la ri za ti on c harac te ri sti cs and not req uirin g rec ipruca l ant e nn as, a rc ~ive n for (a) one -un know n-ant e nn a. (b ) ge n e ra lize d t wo ·id e nti ca l-ant e nn a. and (c) ge n c r a li zed three-antenna Ill eas ureme nt tec hniqu e s .K ey wo rd s: A nt enn a-a nt e nn a int erac ti on s: ant e nn a me as ure m ent s: a nt enn a th eu r y: sca tt e rin g-matrix th eo ry of a nt e nn a s .