Abstract: Assessment of the radiaton characteristics of certain types of radome-covered antennas poses the problem of transmission of amplitude tapered-aperture fields through a generally-curved dielectric taper. Modeling the amplitude taper by a Gaussian, the incident illumination can be generated by a source at a complex coordinate location. The radome problem is then addressed by tracing complex ray fields from the complex source point through the complex extension of the radome contiguration to the real location of the observer. The complex ray tracing takes into account multiple reflection inside the radome, and the multiple internal reflected complex ray can be combined into a "collective ray" which is weighted with a corrected transmission coefficient. The formulars developed in this study are applicable to generally-curved radomes, though parabolic shell radomes are chosen as the mathematical models for numerical computations.