Fabrication imperfections must be considered during the configuration of programmable photonic integrated circuits (PPICs). Therefore, characterization of imperfections is crucial but challenging, especially for PPICs based on recirculating waveguide meshes. In this Letter, we propose a characterization method based on an optimization method assisted by a step-by-step parameter space reduction technique, capable of greatly broadening the range of characterized parameters compared to existing methods. Our method ensures precise characterization, enabling the modeling of defective meshes with an error of 0.35 dB. Furthermore, the method was tested under various scenarios to evaluate its stability and robustness. Finally, we applied our method to implement six different types of finite/infinite impulse response (FIR/IIR) filters to demonstrate its effective application in off-chip configuration.