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Spotlight on Optics


  • April 2013

Optics InfoBase > Spotlight on Optics > Precision absolute positional measurement of laser beams

Precision absolute positional measurement of laser beams

Published in Applied Optics, Vol. 52 Issue 12, pp.2527-2530 (2013)
by Ewan D. Fitzsimons, Johanna Bogenstahl, James Hough, Christian J. Killow, Michael Perreur-Lloyd, David I. Robertson, and Henry Ward

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Spotlight summary: Displacement interferometry systems require precise knowledge about the beam alignment relative to the motion axis of the object/stage to be measured. This is not only a challenge for space instrumentation as Fitzsimons et al. have presented, but also for calibrating the linear axes of machine tools, coordinate measuring machines, and semiconductor positioning equipment. In terms of scale, refractive index uncertainty is widely considered the largest error contributor to displacement interferometry systems in air, with fractional error limits on the order of 1 part in 108. After refractive index, however, the beam alignment relative to the motion axis (or cosine error) is often the next largest error contributor. The displacement error due to cosine error approximately scales with the sum of the squares of the deviation from normal for the aligned beam to the target mirror (alpha) and the cosine error (beta). When both alpha and beta are at the 20 μrad levels that Fitzsimons et al. have achieved, the error scales fractionally at 4 parts in 1010. This error is higher than one would normally expect from laser frequency instability and other typical sources.

The method presented in this work also addresses the common problem of crosstalk in aligning displacement interferometry systems. Traditionally, two different sensors (and setups) have been used to measure lateral (straightness) and angular (cosine) errors separately. Approaching the errors separately can lead to significant crosstalk that may adversely affect one or both measurements. For example, as an optical beam passes through a planar surface, the output beam is laterally shifted due to refraction as a function of plate thickness, refractive index, and the rotation angle. If the intention of passing the optical beam is to measure lateral errors, and angular errors are not simultaneously addressed, then a slight angular error can appear as a lateral error. Fitzsimons et al. address this by simultaneously measuring both angular and lateral errors. This is especially useful because their ideal alignment target is the centers of both quadrant detectors. For a fixed artifact, there is only one solution where that alignment is achieved, minimizing the chance for crosstalk between angular and lateral errors. Even errors due to wavefront distortion in their beamsplitter and folding mirrors are essentially unique to that particular artifact, meaning that if this artifact is used for multiple optical beams, then all beams would be aligned with the same artifact errors, making those errors effectively common mode between optical beams to within the accuracy of the artifact.

The authors have presented an alignment artifact that enables simultaneous calibration of lateral and angular alignment errors in beam pointing with a high fidelity, reducing their contribution to overall target positioning uncertainty, which is critical for many applications.

--Jonathan D. Ellis

Technical Division: Optical Design and Instrumentation
ToC Category: Instrumentation, Measurement, and Metrology
OCIS Codes: (120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology
(220.1140) Optical design and fabrication : Alignment
(220.4610) Optical design and fabrication : Optical fabrication
(120.6085) Instrumentation, measurement, and metrology : Space instrumentation

Posted on April 15, 2013

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