We propose a calibration methodology for a novel type of inward-looking spherical light field acquisition device comprised of a moving CMOS camera with two angular degrees of freedom around an object. We designed a calibration cube covered with ChArUco markers to resolve viewpoint ambiguity. Our calibration model includes 20 unknowns describing the spherical parameters and the camera's geometrical and internal properties. These parameters are jointly optimized to reduce the reprojection error of the calibration cube's markers from multiple viewpoints, resulting in a model that can predict the pose of the camera from any other viewpoint. We successfully tested this calibrated model with a photogrammetry experiment followed by view synthesis of novel views using the resulting depth maps. Results show that the reconstructed image is highly accurate when compared to a real-life capturing of the same view.