Comprehensive calibration of omnidirectional mirror and catadioptric optical system dedicated to high-speed video registration of lightning

• Calibration of omnidirectional mirror dedicated for lightning location purposes. • Mirror with settable reflection angle range and projection characteristics. • Estimation of complex 2D image deformations originated by the mirror surface. • Mirror image deformation distinguished from optical recorder distortion. • Universal design process applicable to all types of omnidirectional mirrors. The paper presents calibration setup and method dedicated to almost all types of omnidirectional mirrors such as hyperbolic and elliptic as well as including those with analytically or even numerically defined curvature. At its initial stage the calibration procedure use a pinhole and fisheye camera calibration algorithms to estimate and remove optical distortions introduced to catadioptric system by the image recorder and lens. The next stage allows to calculate the projection characteristics of the mirror and complex matrix of image deformation which can be further used for a low-cost image correction. Calibration procedure was verified using mirror prototypes manufactured with application of CNC milling machines and Physical Vapor Deposition technique. Three mirrors with 15°, 30° and 45° top view angles were tested. Projection characteristics were evaluated for a set of wide range cloud-to-ground lightning video registrations. Proposed method can be implemented to improve quality of omnidirectional observation and photogrammetry.