A simplified and versatile calibration method for multi-camera optical systems in 3D particle imaging

This article describes a stereoscopic multi-camera calibration method that does not require any optical model. It is based on a measure of the light propagation within the measurement volume only instead of modeling its entire path up to the sensors. The calibration uses simple plane by plane transformations which allow us to directly link pixel coordinates to light rays. The appeal of the proposed method relies on the combination of its simplicity of implementation (it is particularly easy to apply in any sophisticated optical imaging setup), its versatility (it can easily handle index-of-refraction gradients, as well as complex optical arrangements), and its accuracy {we show that the proposed method gives better accuracy than commonly used techniques, based on Tsai's simple pinhole camera model [R. Tsai, J. Rob. Autom. 3, 323 (1987)], while its numerical implementation remains extremely simple}. Based on ideas that have been available in the fluid mechanics community, this method is a compact turn-key algorithm that can be implemented with open-source routines.