The Spherical Geometry Algorithm (SGA) demonstrates superior capability in achieving efficient and precise spaceborne SAR image formation processing, even under challenging imaging conditions including non-linear radar trajectories and spherical Earth surface geometry. Nevertheless, the original SGA is specifically developed for spotlight SAR data processing and can't directly applied to processing spaceborne SAR data in other modes. In this paper, we first analyze the limitations of the SGA algorithm when applied to stripmap or TOPS mode SAR processing, and then propose an improved SGA algorithm which can process both stripmap and TOPS SAR data. Compared with the original algorithm, the new algorithm has two main differences. Firstly, in order to avoid undersampling during azimuth resampling in both modes, an instantaneous Doppler centroid removal process was added before azimuth interpolation processing by exploiting the endomorphism property of resampling operation. Secondly, the spectral analysis method used for the final step of azimuth compression in the original SGA has been replaced with a new matched filtering processing, which can avoid image aliasing in azimuth direction and improve computational efficiency. Measured real data processing results are presented to demonstrate the validity of the proposed algorithms.