A novel method of optical diffraction tomography (ODT) to image weakly scattering, electrically large, two-dimensional (2D) objects using the far-zone scattered field data is presented. The proposed technique is based on the expansion of the target object function in terms of Fourier-Bessel basis functions and an alternative approximation for the total electric field within the support of the investigated scatterer. Analytical (Mie) plane-wave scattering by a layered, circularly symmetric, lossy cylinder, and finite-difference time-domain simulations involving plane-wave scattering by a more general, lossless phantom are utilized to compare the performance of the proposed method with that of the standard ODT techniques, which are based on the Born approximation and the Fourier diffraction theorem. Quantitative and qualitative superiority of the presented method is demonstrated. The proposed 2D technique can be readily extended to more realistic three-dimensional cases. With proper (cylindrical-spherical) receiver configuration, the proposed method can be used without being confined to far-zone observations.