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Uncertainty Analysis for Angle Calibrations Using Circle Closure.

W Tyler Estler¹

¹National Institute of Standards and Technology, Gaithersburg, MD 20899-0001.

Journal of Research of the National Institute of Standards and Technology

|December 24, 2016

Summary

This study presents novel angle calibration methods for precise measurements without external references. These techniques reduce uncertainty and improve accuracy for small angle measurements using electronic autocollimators.

Keywords:

angle metrology autocollimators calibration closure dimensional metrology indexing tables measurement uncertainty optical polygons self-calibration

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Area of Science:

Metrology
Optical Engineering
Instrumentation

Background:

Accurate angle calibration is crucial for precision engineering and scientific research.
Traditional methods often rely on external reference artifacts, introducing potential errors.
Reducing measurement uncertainty is a key objective in metrology.

Purpose of the Study:

To develop and analyze two novel full-circle angle calibration methods: simple closure and dual closure.
To derive expressions for combined standard uncertainties in angle calibrations.
To evaluate methods for quantifying small angle measurement uncertainty, considering calibration and environmental factors.

Main Methods:

Analysis of simple closure calibration involving sequential comparison of unknown angular segments.
Analysis of dual closure calibration using simultaneous intercomparison of two divided circles.
Derivation of closed-form expressions for combined standard uncertainties following ISO and NIST guidelines.
Quantitative evaluation of small angle measurement uncertainty using electronic autocollimators.

Main Results:

Demonstrated that circle closure provides auxiliary information for complete calibration without external references.
Showcased that both simple and dual closure methods reduce measurement uncertainty.
Derived expressions for combined standard uncertainties applicable to angle calibration.
Quantified the standard uncertainty of small angle measurements, including calibration and air turbulence effects.

Conclusions:

Full-circle angle calibration using closure methods offers a self-contained and accurate approach.
The derived uncertainty expressions provide a robust framework for metrological analysis.
The study offers improved methods for precise small angle measurements in metrology and engineering.