Fused-like angles: replacement for roll-pitch-yaw angles for a six-degree-of-freedom grating interferometer

Representation of orientation is important in a six-degree-of-freedom grating interferometer but only a few studies have focused on this topic. Roll-pitch-yaw angles, widely used in aviation, navigation, and robotics, are now being brought to the field of multi-degree-of-freedom interferometric measurement. However, the roll-pitch-yaw angles are not the exact definitions the metrologists expected in interferometry, because they require a certain sequential order of rotations and may cause errors in describing complicated rotations. The errors increase as the tip and tilt angles of the grating increase. Therefore, a replacement based on fused angles in robotics is proposed and named “fused-like angles.” The fused-like angles are error-free, so they are more in line with the definitions in grating interferometry and more suitable for six-degree-of-freedom measurements. Fused-like angles have already been used in research on the kinematic model and decoupling algorithm of the six-degree-of-freedom grating interferometer.