As the foundation of virtual content generation, cameras are crucial for augmented reality (AR) applications, yet their integration with transparent displays has remained a challenge. Prior efforts to develop see-through cameras have struggled to achieve high resolution and seamless integration with AR displays. In this work, we present LightguideCam, a compact and flexible see-through camera based on an AR lightguide. To address the overlapping artifacts in measurement, we present a compressive sensing algorithm based on an equivalent imaging model that minimizes computational consumption and calibration complexity. We validate our design using a commercial AR lightguide and demonstrate a field of view of 23.1° and an angular resolution of 0.1° in the prototype. Our LightguideCam has great potential as a plug-and-play extensional imaging component in AR head-mounted displays, with promising applications for eye-gaze tracking, eye-position perspective photography, and improved human-computer interaction devices, such as full-screen mobile phones.