The use of 3D measurement in endoscopic images offers practicality in cancer diagnosis, computer-assisted interventions, and making annotations for machine learning training data. An effective approach is the implementation of an active stereo system, using a micro-sized pattern projector and an endoscope camera, which has been intensively developed. One open problem for such a system is the necessity of strict and complex calibration of the projector-camera system to precisely recover the shapes. Moreover, since the head of an endoscope should have enough elasticity to avoid harming target objects, the positions of the pattern projector cannot be tightly fixed to the head, resulting in limited accuracy. A straightforward approach to the problem is applying auto-calibration. However, it requires special markers in the pattern or a highly accurate initial position for stable calibration, which is impractical for real operation. In the paper, we propose a novel auto-calibration method based on differential rendering techniques, which are recently proposed and drawing wide attention. To apply the method to an endoscopic system, where a diffractive optical element (DOE) is used, we propose a technique to simultaneously estimate the focal length of the DOE as well as the extrinsic parameters between a projector and a camera. We also propose a multi-frame optimization algorithm to jointly optimize the intrinsic and extrinsic parameters, relative pose between frames, and the entire shape.Clinical relevance- One-shot endoscopic measurement of depth information is a practical solution for cancer diagnosis, computer-assisted interventions, and making annotations for machine learning training data.