In a recent article, the authors developed a new optical interferometric telescope architecture based on compressive sensing theory (CS-CPCIT)(Liu et al., MNRAS, 478, 2065, 2018). A new optical interferometric telescope, also known as the Segmented Planar Imaging Detector for Electro-optical Reconnaissance (SPIDER)(Duncan et al., AMOS Conf., 27, 2015), provides a significant reduction in the weight, size and power consumption compared with traditional optical interferometry. The new CS-CPCIT system has a more concise structure and a better spatial frequency sampling capability compared to those of SPIDER. In this paper, we propose an update to CS-CPCIT, which changes the relationship between the number of spatial frequencies sampled and the number of lenslets from linear to quadratic while maintaining a concise structure. Other attractive properties of the update to CS-CPCIT include a high sampling efficiency and a greatly improved maximum number of spatial frequencies that can be sampled. © 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement.