A mission to the focus of the solar gravitational lens could produce images with unprecedented angular resolution and sensitivity. In the context of trying to resolve the time variable thermal signature of continents on other Earth-like exoplanets, we develop an approach to improve the image reconstruction performance by using azimuthal variations in the Einstein Ring's intensity. In the first post-Newtonian approximation to General Relativity, an arbitrary disk intensity distribution in the source plane is mapped to a narrow annulus around the Einstein Ring, with each azimuthal element corresponding to a sector in the disk. A matrix-based linear measurement model at various fixed signal-to-noise ratios demonstrates that this extra information is useful in improving the reconstruction when the image is sparsely sampled, which could improve integration times and temporal errors. Various issues and future outlooks are discussed.
