TABLE OF CONTENTS The intersecting canonical body approximation (ICBA), for the cases 
, n = 2,3, was developed in the following series of papers: [384], [381], [382], [380], [460], [461], [386], [462], [463], [389], and [327].
The ICBA assumes that the amplitudes in the partial wave representation of the scattered field are nearly those of a canonical body, for example, a circular cylinder in the 2D problem. This is true locally for each observation angle, the canonical body having the same local radius at this angle as that of the real body. The reconstruction of the shape of the body, represented at a given angle by its local radius, then proceeds by minimizing the discrepancy between the measured or simulated data and the estimation thereof. This is done at each observation angle. In one of its forms, the procedure enables the reconstruction of the local radius of the body for a given polar angle by solving a single nonlinear equation [381], [382], [380], [460], [384], [386], [389]. Another variant consists of finding this local radius by minimizing the L 2 cost functional of the aforementioned discrepancy.
The remainder of this section is concerned with the use of the ICBA for solving boundary identification problems of a 2D body located in free space, and the following will be shown: (i) that the reconstruction of the boundary of the body is not unique for both (synthetic) simulated and (real) experimental data, and (ii) that it is possible...
