Statistical distribution of the amplitude and phase of a multiply scattered field

Abstract

Th e probability di s t ribu Lion of t he a m p li tude and pha se o f the s um o f a large num ber of random two-di m ens i ona l vecto rs is derived under t he fo ll ow i ng gen e ral cond i t io ns : B oth t he amp li tud es a nd th e pha ses of the component vector s a re random , t he di sL ribu tion s b eing a rbitrary wit hin th e va li di t. \7 of t he Central Lim it Th e or e m ; in part i cular , the d is- t r ib u t i on s of t he individual v eetor s need not be ident ical , the ampl i tude and pha se of each c o mp o ne nt v ec tor n eed not be ind ep e nd e n t a nd the di tr ibu tio n s Ileed not b e s ymmel ri cal. T he di s Lr i bution s form e rly d e riv ed b y R a yle igh , nic e, H oy t , a nd Heckmanll ar e s hown lo be special ca ses of thi s di s Lribu t ion .