A method to calibrate angular positioning errors using a laser tracker and a plane mirror

Published

March 20, 2025

Author(s)

Balasubramanian Muralikrishnan, Katharine Shilling, Vincent Lee, Olga Ridzel, Glenn Holland, John Villarrubia

Abstract

We describe a method to calibrate angular positioning errors of a rotation stage using a laser tracker (LT), a plane mirror mounted on the stage, and stationary registration nests placed around the stage. Our technique involves determining the direction of the normal vector to the plane of the mirror at each angular step by performing two LT measurements – one directly to a stationary spherically mounted retroreflector (SMR), and another to the same SMR by bouncing the laser off a mirror mounted on the rotation stage. Because the angular range that can be measured from a single LT position is limited by the angle of incidence on the mirror, multiple LT stations are necessary to cover the full 360°, hence the need for stationary registration nests to tie the LT data into a common coordinate frame. We compare this technique against a direct approach involving a rigid bar with two SMRs mounted on the rotation stage so that we can measure the direction of the line joining the SMRs at each angular position using the LT and therefore the angle between positions. Through experiments, we demonstrate that our mirror-based approach provides errors on the order of ± 0.5 arcseconds, smaller than the ± 1.5 arcseconds for the direct approach, when compared against a reference instrument with accuracy less than 0.3 arcseconds. Through simulations, we estimate the uncertainty in our mirror-based angle measurements to be 0.4 arcseconds (k = 2). Placing the LT close to and the SMR away from the rotation stage results in lower uncertainty for our mirror-based angle measurements.

Citation

Sensors

Volume

25

Pub Type

Journals

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Keywords

angular positioning error, laser tracker, rotation stage

Citation

Muralikrishnan, B. , Shilling, K. , Lee, V. , Ridzel, O. , Holland, G. and Villarrubia, J. (2025), A method to calibrate angular positioning errors using a laser tracker and a plane mirror, Sensors, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=959152 (Accessed October 22, 2025)