Mathematical model of coordinate transformations for 3D Depth-of-field collection system

Calculating the Cartesian coordinate is the first step of image reconstruct based on primitive information from laser scanner. A novel 3D Depth-of-field information collection system in this article is consisted of tow 2D laser scanners and a servo-actuates rotating mirror assembly. The system has a much higher detecting precision than others which drive 2D laser scanner to rotate to get the 3^rd dimension using motor. On the other hand the relationship between the 3D Cartesian coordination and the primitive information collected by the system is much more complicated than others because of the mirror assembly. Therefore traditional mathematical model which change polar coordinate to Cartesian coordinates can not be used to our system. In the article we build the solid geometry model of the laser beam between laser scanner and the detected object based on optical theory. Then a mathematical model for the transformations from primitive information to Cartesian coordinate is built according to the geometry model. The mathematical model has been tested in simulation on PC.