Fig. 1. The square boundary array, where the red circles represent the spatial position of the transmitting antenna and the green circles represent the spatial position of the receiving antenna, blue stars show the positions of the equivalent phase center

Fig. 2. Sparse array equivalent phase center schematic

Fig. 3. The main steps of the proposed algorithm

Fig. 4. （a） The original image generated by the FFT algorithm （b） The auto- focus image generated by the SLIM algorithm （iteration number = 2） （c） The auto-focus image generated by the modified SLIM algorithm （Th_dB = -15dB and no iteration）

Fig. 5. The simulation model of THZ letter.

Fig. 6. （a） The original image generated by the FFT algorithm （b） The auto-focus image generated by the SLIM algorithm （iteration number = 2） （c） The auto-focus image generated by the modified SLIM algorithm （Th_dB = -20dB and no iteration）

Fig. 7. （a） The original image generated by the FFT algorithm （b） The auto-focus image generated by the SLIM algorithm （iteration number = 2） （c） The auto-focus image generated by the modified SLIM algorithm （Th_dB = -20dB and iteration number = 2）

Fig. 8. Images under different iteration numbers of the SLIM algorithm. （a） 1 （b） 2 （c） 3 （d） 4

Fig. 9. Images under different iteration numbers of the modified SLIM algorithm （Th_dB = -20 dB）. （a） 1 （b） 2 （c） 3 （d） 4

Fig. 10. The Contrast criteria of different iterations.