In the active optics (AO) system of large closed-looped survey telescopes, wavefront sensing based on defocused star images is necessary. To realize the effective operation of the AO system, this study investigates the relationship between the boundary area of a defocused image and wavefront sensing accuracy. First, a curvature sensing (CS) algorithm is introduced according to the irradiance transport equation of an electromagnetic wave. Then, by considering astigmatism and coma as examples, the influence of typical boundary conditions on wavefront sensing is theoretically investigated. Subsequently, the influence of different pixel resolutions on the completeness of information is analyzed. Finally, under the limit sampling rate, the wavefront reconstruction error is simulated and analyzed. The experimental results show that the error introduced on the edge of a unit circle is approximately 35% (without iteration).When a defocused star point image is below 100 pixels, its ability to carry information rapidly decreases.When it is close to 100 pixels, the detection error of the coma is 0.08 wavelength, which is approximately 14% lower than that at 400 pixels. Therefore, considering the error convergence effect of closed-loop active optics and ignoring the boundary effect can satisfy the requirement of active optical wavefront sensing in the case of a low time-spatial resolution, that is, at a low sampling rate. However, in the case of measurements with a high time-spatial resolution, the influence of the edge cannot be ignored.