Preliminaries of Six-Degree-of-Freedom Ultra Resolution Metrology with Laser Beams and Convex Mirrors

In recent years, high resolution metrology up to nano-scale has attracted substantial attention due to the increasing need of ultra precision measurement systems for MEMS and NEMS calibration. In this paper, an analytical and numerical investigation for the proposed design of a 6-degree-of-freedom (6-dof) universal ultra precision metrology system using relatively simple and inexpensive but highly sensitive set up is presented. This system utilizes a convex mirror and two flat mirrors, one angled and one vertical, as targets to reflect the laser beams onto photo detectors. These targets, placed on the object of interest for metrology applications, change the direction of the reflected beam when there is any movement in the object, which is detected by the photo detectors. The use of convex and angled mirrors enhances the sensitivity of the system greatly. Geometric relationships are established among all the optical components to predict the final intersection points of the laser beams reflected from the targets with the photo detector planes. These relationships are used to establish a Jacobian partial derivative matrix, which is further used to estimate the target pose when the photo detector outputs are given. Numerical simulation of the measurement process is performed using MATLABreg. Assuming the approximate distance from laser beams origin to targets and the targets to photo detectors as 50 mm and photo detector resolution as 0.1 mum, translations and rotations less than 50 nm and 2 arc sec, respectively, can be measured accurately