For industrial control systems (ICS), many existing defense solutions focus on detecting attacks only when they make the system behave anomalously. Instead, in this work, we study how to detect attackers who are still in their hiding phase. Specifically, we consider an off-path false-data-injection attacker who makes the original sensor's readings unavailable and then impersonates that sensor by sending out legitimate-looking fake readings, so that she can stay hidden in the system for a prolonged period of time (e.g., to gain more information or to launch the actual devastating attack on a specific time). To expose such hidden attackers, our approach relies on continuous injection of ``micro distortion'' to the original sensor's readings, either through digital or physical means. We keep the distortions strictly within a small magnitude (e.g., $0.5\%$ of the possible operating value range) to ensure that it does not affect the normal functioning of the ICS. Micro-distortions are generated based on secret key(s) shared only between the targeted sensor and the defender. For digitally-inserted micro-distortions, we propose and discuss the pros and cons of a two-layer least-significant-bit-based detection algorithm. Alternatively, when the micro-distortions are added physically, a main design challenge is to ensure the introduced micro-distortions do not get overwhelmed by the fluctuation of actual readings and can still provide accurate detection capability. Towards that, we propose a simple yet effective Filtered-$Δ$-Mean-Difference algorithm that can expose the hidden attackers in a highly accurate and fast manner. We demonstrate the effectiveness and versatility of our defense by using real-world sensor reading traces from different industrial control (including smart grid) systems.