# Linear Positioning Accuracy

A variety of techniques are available to incrementally position a user payload along a linear axis. Leadscrews and ball screws are by far the most common, although linear motors are also used. Linear positioning accuracy is simply the degree to which commanded moves match internationally defined units of length.

It is important to realize that use of a leadscrew with a specified cumulative lead error, periodic error, and repeatability does not ensure that the positioning table will provide that level of accuracy. Among the factors which conjoin to degrade overall performance are thermal expansion, due both to ambient temperature changes and nut-friction induced heating, and Abbé error. Both of the latter effects produce different error values, depending on the location on the user payload. In the case of leadscrew thermal expansion, the position of the nut relative to the stage duplex bearing is important, while for Abbé error, it is the distance from the leadscrew centerline to the customer payload.

## Geometry and Multi-Axis Errors

As mentioned above, angular errors in the stage ways degrade linear positioning accuracy through Abbé error. X-Y Tables have an additional parameter that impacts accuracy to a substantial degree: orthogonality, or the degree of squareness between the two axes. This parameter is held to less than 50 arc-seconds on our commercial grade tables, and less than 20 arc-seconds for precision models. For the latter case, a 300 mm travel corresponds to 30 microns of error due to orthogonality alone. We can, upon request, prepare tables which are square to within 10 arc-seconds; note, however, that trying to get the level of orthogonality lower than the value for yaw has limited meaning. Custom systems (typically air bearing designs) can hold orthogonality errors to below 2 arc-seconds. Another error source in systems with two or more axes is opposite axis error, which results when one axis has a straightness error. It is the job of the leadscrew or encoder on the other axis to provide accuracy in this direction, but since they are on two separate axes, this error is not corrected. Cosine error, or inclination of the leadscrew or encoder to the ways, is usually slight, but grows in importance with short travel, interferometer based stages. All of the above geometry errors are amenable to cancellation through mapping.