## 1 Introduction  
In recent years, soft actuators are widely used to implement surgical tasks due to its large-scale deformation and compliant adaptation to meet the complex elastic structures of the human organs and tissues [1; 2; 3]. The soft actuators can deform to absorb the energy generated by a variety of stimulation, including electrical charges, hydraulic actuating, pneumatic actuating and chemical reactions, etc. In particular, considering the advantages of easy fabrication, low material cost and lightweight, etc., the pneumatic actuating soft actuators are promising for surgical applications [4], and the use of soft manipulators in surgical operations could overcome the limitations of the current rigid surgical system. Consequently, compared with some traditional rigid and hard continuum surgical manipulators, the soft biological materials could considerably reduce the harm, which is caused by the robotic manipulators, and the soft surgical manipulators are inherently compliant and intrinsically safe in the interaction with humans. While current researchers have emphasized the promising potential of soft manipulators in surgical applications, the lack of complicate shape measurement and monitoring for soft actuator are greatly limiting their practical application. In order to reliably and widely use these actuators in soft surgical manipulator, mastering the relationship between shape measurement and position control of the actuator is indispensable. Considering the flexible bodies of the soft manipulator, some conventional rigid sensors, like encoders and strain gauges [5; 6] have problems of complex cable networks, electromagnetic and noise signal interference, etc., and the rigid sensor will damage human tissue when the manipulator interacts with the human organs surround it [7; 8; 9]. The visual-based sensing systems are also inapplicable due to the narrow spaces and various obstacles in human body. At present, the embedded flexible sensing devices and methods that can be applied to the shape measurement and position control of soft surgical actuators are desired. Different from above-mentioned sensors, the optical fiber sensors have advantages of small size, light weight, fast response, small transmission loss, not be affected with electromagnetic interference and easy to be buried into the interior of the material [10; 11]. More importantly, the optical fiber sensor is harmless when in contact with human tissues and organs [12; 13; 14; 15], and the optical fiber sensor can be embedded into the flexible body of the soft manipulator to realize its morphological sensing. Consequently, these distinctive characteristics of the optical fiber sensor make it more advantageous, and the prospects for soft surgical robotics and biomedical applications; and several types of research of optical fiber sensors have been investigated in recent years. In [12], the fiber sensors were embedded into a piece of garment, and the motion performance of the patient was evaluated by the angle of joint, which is monitored by the embedded fiber sensors; this sensing garment is comfortable for patients and has good response to the flexion motion of the elbow. As proposed in [13], the bending state of a manipulator was measured by an optical fiber sensing system and the mechanism of this sensing system based on a laser power modulation. Although this sensing system has good accuracy in measuring bending angles, bending radius and orientation of the flexible segment, its 3D shape reconstruction and visualization monitoring are not realized. In addition, this sensing system adopts three optical fibers to interpolate the bending radius and the elongation of the manipulator, and this undoubtedly increases the complexity of the theoretical models of the manipulator.