Propagation of angular errors in two-axis rotation systems

Abstract

Two-Axis Rotation Systems, or "goniometers," are used in diverse applications including telescope pointing, automotive headlamp testing, and display testing. There are three basic configurations in which a goniometer can be built depending on the orientation and order of the stages. Each configuration has a governing set of equations which convert motion between the system "native" coordinates to other base systems, such as direction cosines, optical field angles, or spherical-polar coordinates. In their simplest form, these equations neglect errors present in real systems. In this paper, a statistical treatment of error source propagation is developed which uses only tolerance data, such as can be obtained from the system mechanical drawings prior to fabrication. It is shown that certain error sources are fully correctable, partially correctable, or uncorrectable, depending upon the goniometer configuration and zeroing technique. The system error budget can be described by a root-sum-of-squares technique with weighting factors describing the sensitivity of each error source. This paper tabulates weighting factors at 67% (k=1) and 95% (k=2) confidence for various levels of maximum travel for each goniometer configuration. As a practical example, this paper works through an error budget used for the procurement of a system at Sandia National Laboratories.

A new spectrogoniophotometer to measure leaf spectral and directional optical properties

“…Instruments suited to such measurements exist (Buratti et al, 1988;White et al, 1998) and could be used to initiate new studies to confirm this result. Other improvements in the design of the SGP are likely to decrease the uncertainties, for instance the use of a reference panel similar to the leaf in thickness and scattering features or the investigation of angular error propagation in rotation systems, which basically depend on the apparatus configuration (Torrington, 2003).…”