Exact analytical approach for six-degree-of-freedom measurement using image-orientation-change method

An exact analytical approach is proposed for measuring the six-degree-of-freedom (6-DOF) motion of an object using the image-orientation-change (IOC) method. The proposed measurement system comprises two reflector systems, where each system consists of two reflectors and one position sensing detector (PSD). The IOCs of the object in the two reflector systems are described using merit functions determined from the respective PSD readings before and after motion occurs, respectively. The three rotation variables are then determined analytically from the eigenvectors of the corresponding merit functions. After determining the three rotation variables, the order of the translation equations is downgraded to a linear form. Consequently, the solution for the three translation variables can also be analytically determined. As a result, the motion transformation matrix describing the 6-DOF motion of the object is fully determined. The validity of the proposed approach is demonstrated by means of an illustrative example.