The problems of the scattering off the perfect conductor sphere and the dielectric sphere have the exact solutions. But there are no exact solutions for the scattering off a multi-layered dielectric sphere with a metallic cap like the Lunberg lens reflectors which is used as a strong omni-directional reflector found in many microwave applications. Haruo Sakurai applied the modal expansion technique and point-matching method (PMM) to study the scattering of the Lunberg lens reflectors. The problem is eventually formulated as 2MN by 2MN simultaneous matrix equation with M regions each having 2N unknowns due to two set of coupled polarization vectors. Strictly speaking, the formulae of the mode matching method for the problem of the scattering of the dielectric sphere are not exact. Furthermore, the size of the simultaneous matrix equation is also unnecessarily too larger. In this thesis, we employ an integral equation formulation in the Frequency-domain together with the modified impedance transformation technique for the spherically layers to study the scattering of the Lunberg lens reflectors. We show that the formulae of the integral equation are exact and using an equivalent matrix equation, that the entire problem can be reduced to a N by N matrix equation where N is the number of terms of the expansion of the unknown field in the opening. To verify our formulation we compute the total field of the plane wave incident upon the multi-layered micro lenses and compared the results with those from the geometric optics. We get good agreement for the regions that both theories apply. Small discrepancy is also observed and is consistent with the theoretical prediction.