The effect of lens distortion in angle measurement based on four-quadrant detector

•A model of the distorted spot energy distribution related to lens parameters and incident angle is proposed.•According to the model, the error rule caused by the distortion to the angle measuring system based on 4-QD is deduced.•An experimental system is designed to quantitatively measure the relationship between lens distortion coefficient and angle measurement error.•Some methods to reduce the effect of distortion in angle measuring system with large FOV are discussed.