Coverage is a prominent indicator for measuring the quality of service in directional sensor networks. From the perspective of energy and deployment costs, full coverage may be expensive or unrealistic, partial coverage can operate more energy-efficient by scheduling working status of sensors. In certain practical application scenarios, irregular obstacles like trees, mountains, buildings, and vehicles, which have adverse influence on QoC, often exist in the field of interest (FoI). Meanwhile, due to sensors may fall near the border of the FoI, it also has effect on the coverage contribution. In this paper, we assume that sensors are randomly deployed in a square FoI with irregular shape obstacles existence, and introduce the concept of occlusion coverage of partial targets. Afterwards, we take the border effects into account and derive the critical sensor density for achieving an expected coverage ratio with a high probability. Finally, we conduct a series of simulation experiments to verify the accuracy between simulation results and numerical results, and take analysis of mean absolute error between them. The results show that our method has good performance on estimating critical sensor density.INDEX TERMS directional sensor networks, target coverage, critical sensor density, irregular obstacles, border effects