Regularized Quasi-Newton method for inverse scattering problems

Direct reconstruction of complex refractive index distribution from boundary measurement of intensity and normal derivative of intensity

We present an optical tomographic reconstruction method to recover the complex refractive index distribution from boundary measurements based on intensity, which are the logarithm of intensity and normal derivative of intensity. The method, which is iterative, repeatedly implements the forward propagation equation for light amplitude, the Helmholtz equation, and computes appropriate sensitivity matrices for these measurements. The sensitivity matrices are computed by solving the forward propagation equation for light and its adjoint. The results of numerical experiments show that the data types ln(I) and partial differential I/ partial differential n reconstructed, respectively, the imaginary and the real part of the object refractive index distribution. Moreover, the imaginary part of the refractive index reconstructed from partial differential I/ partial differential n and the real part from ln(I) failed to show the object's inhomogeneity. The value of the propagation constant, k, used in our simulations was 50, and this value resulted in smoothing of the reconstructed inhomogeneities. Thus we have shown that it is possible to reconstruct the complex refractive index distribution directly from the measured intensity without having to first find the light amplitude, as is done in most of the currently available reconstruction algorithms of diffraction tomography.