The THz frequency spectrum opens a lot of applications in the imaging at sub-mm level. The increase of the operating frequency band for SAR imaging systems to the THz range has proportionally affected the amount of raw data to be stored and used for accurate image reconstruction. As a consequence, improvements in the existing SAR imaging algorithms to reduce the amount of data needed to achieve the appropriate quality of imaging is desired. This paper introduces the phase control procedure as an extension to the existing sinc interpolator for backprojecting complex-valued FMCW SAR data into a defined image plane. The proposed extension controls the phase of interpolated complex-valued SAR data parameters so that it includes appropriate information about the range distance between the SAR system and the given point of space. The extended algorithm is incorporated into the global backprojection algorithm and examined on the measurement data acquired via the 2pSENSE FMCW SAR system. The efficiency of the extended algorithm is evaluated through the comparison with the conventional nearest neighbor and sinc interpolation algorithms. © 2022 Warsaw University of Technology.