Real-time medical imaging guidance for robotic surgeries is made possible by the excellent imaging quality of MRI. MRI-compatible robotic joint actuators are essential for these systems. Among various MRI-compatible actuation methods, pneumatic motors are considered optimal due to their sterility, safety, reliability, and ability to generate bidirectional continuous rotations like BLDC motors. Accurate encoders are vital for real-time measurement and precise control of pneumatic motors. This paper proposes a modularly-designed MRI-compatible bidirectional rotary encoder using optical fibers, presenting design methodology and experimental evaluation. Compared with a commercial encoder, the proposed encoder exhibits a maximum error of 0.01 rad for position measurement mode and 0.1 rad/s for speed measurement mode. This modularly-designed MRI-compatible rotary encoder significantly improves accuracy compared to state-of-the-art competitors and is suitable for rotary actuators in MRI or similar harsh environments.