Efficient and high-fidelity polarization demosaicking is critical for industrial applications of the division of focal plane (DoFP) polarization imaging systems. However, existing methods have an unsatisfactory balance of speed, accuracy, and complexity. This study introduces a novel polarization demosaicking algorithm that interpolates within a three-stage basic demosaicking framework to obtain DoFP images. Our method incorporates a DoFP low-cost edge-aware technique (DLE) to guide the interpolation process. Furthermore, the inter-channel correlation is used to calibrate the initial estimate in the polarization difference domain. The proposed algorithm is available in both a lightweight and a full version, tailored to different application requirements. Experiments on simulated and real DoFP images demonstrate that our two methods have the highest interpolation accuracy and speed, respectively, and significantly enhance the visuals. Both versions efficiently process a 1024*1024 image on an AMD Ryzen 5600X CPU in 0.1402s and 0.2693s, respectively. Additionally, since our methods only involve computational processes within a 5*5 window, the potential for parallel acceleration on GPUs or FPGAs is highly feasible.