AN ANALYTICAL DEVELOPMENT OF A UNIVERSAL DISPLACEMENT MEASUREMENT SYSTEM FOR ULTRA-PRECISION METROLOGY

Abstract

In recent years, precise metrology up to nanoscale has attracted substantial attention due to an increasing need for ultra-precision measurement systems for micro electro mechanical systems (MEMS) and nano electro mechanical systems (NEMS) calibration. In this paper, an analytical and numerical investigation for the proposed design of a 6-degree-of-freedom (6-dof) universal measurement system, using a 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 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 greatly enhances the sensitivity of the system. 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 MATLAB®. Assuming the approximate distance from laser beam origin to target and the target to photo detector as 50 mm, and photo detector resolution as 0.1 µm, translations and rotations less than 50 nm and 2 arc sec, respectively, can be measured accurately. The highest amount of sensitivity in translation is obtained along the Z-axis with minimum a measurement of 3.4 nm; the highest amount of sensitivity in rotation is along the pitch-axis with a minimum measurement of 0.145 arc sec. The corresponding low sensitivity axes are X-axis and yaw-axis, with minimum measurements of 35 nm and 2 arc sec, respectively. The sensitivity and the resolution of the system can be increased many times further by increasing the curvature of the convex mirror or by increasing the distance between the target and the detectors. The analytical and simulation results of this work yield a scientific and engineering guideline for the development of meso, micro, as well as nanoscale metrology systems.