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A novel method for the reconstruction of inhomogeneous permittivity profiles of spherical dielectric objects illuminated by higher order TEmn and TMmn spherical modes is presented. The overall technique is based on the derivation of Riccati-similar nonlinear differential equations in a spherical coordinate system for both TE and TM illuminations as a part of the direct problem formulation. These differential equations are then inverted using a quasi-linear approach to obtain a closed-form expression of the radially varying permittivity profile of spherical objects in terms of a spherical Fourier-Bessel transform of the measured spectral domain reflection coefficient data. To validate the proposed method, several examples with different mode illuminations and with different noise levels are considered for reconstructions. A good agreement between the actual and the reconstructed permittivity profiles even under high noisy conditions shows that our method is not much sensitive to the presence of noise in the reflection coefficient data.