Near-Field Imaging of Interior Cavities (Communications in Computational Physics, 2020)
A novel method is developed for solving the inverse problem of reconstructingthe shape of an interior cavity. The boundary of the cavity is assumed to be a smalland smooth perturbation of a circle. The incident field is generated by a point sourceinside the cavity. The scattering data is taken on a circle centered at the source. Themethod requires only a single incident wave at one frequency. Using a transformedfield expansion, the original boundary value problem is reduced to a successive sequenceof two-point boundary value problems and is solved in a closed form. Bydropping higher order terms in the power series expansion, the inverse problem is linearizedand an explicit relation is established between the Fourier coefficients of thecavity surface function and the total field. A nonlinear correction algorithm is devisedto improve the accuracy of the reconstruction. Numerical results are presented to showthe effectiveness of the method and its ability to obtain subwavelength resolution.