Annular-illumination quantitative phase imaging based on space-domain Kramers-Kronig relations (AIKK) is a newly developed technique that is object-independent and non-iterative reconstructed inherently. Only capturing four low-resolution images, the AIKK system gains a resolution enhancement of nearly twofold. Under matching constraints between the illumination wave vector and pupil function aperture, we set a spectrum sampling criterion and establish a spectrum effective utilization model to search for the optimal solution of spectrum distribution for the specific annular structure. In view of the square spectrum structure, a diagonal-expanded sampling based AIKK method (DES-AIKK) is presented to get rid of the pixel aliasing problem. It is worth noting that the space-bandwidth-time product (SBP-T) further increases to 439.51 megapixels (1.8× of AIKK). Our work provides the guidelines and insights for designing the most suitable AIKK platform for high-throughput microscopic applications in pathology and real-time dynamic observation.