On the Bojarski-Lewis inverse scattering method

We assume that the backscattered electromagnetic far-field of a perfectly conducting scatterer is known for all aspects and for frequencies greater in magnitude than some positive number
m
. Then using standard integral equation techniques, we show how numerical instability enters into the Bojarski-Lewis inverse scattering method. Since the assumed knowledge of the backscattered field is even more complete than can be expected with radar, these results show that for radar applications the Bojarski-Lewis method is numerically unstable. Moreover we show, as expected, that the degree of instability depends directly upon
m
. The more low frequency information we haves (i.e, the smaller
m
is), the more stable the method is. In the concluding remarks is noted a recent constrained Bojarski-Lewis method that overcomes much of the instability of the original unconstrained method studied here.