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Most modern applications of precision positioning stages are related to the ... Measuring and characterizing stage performance: Indicators, laser interferometers ...

Graduate Technical Article Review:

"Accuracy in Positioning Systems"

by Kevin McCarthy New England Affiliated Technologies

( cy.pdf)

Date: 11/6/2007

Reviewed by: Jason Ruhl

Email: [email protected] Phone: 520-461-5894

Prepared for: For Dr. Jim Burge

OPTI 521

Executive Summary:

The paper "Accuracy in Positioning Systems" by Kevin McCarthy of New England Affiliated Technologies (Danaher Motion) ( cy.pdf) is reviewed below because it contains general and useful information with regard to identifying, specifying and measuring errors and deviations associated with precision linear stages and positioning systems.

Most modern applications of precision positioning stages are related to the semiconductor industry and to precision instrumentation systems that require extremely high levels of positional accuracy on the order of fractions of microns.

Mr. McCarthy discusses the follow topics: 1. History and motivation for precision motion applications 2. Stage Error: Accuracy, Resolution, and Repeatability, linear errors (vertical and horizontal run-out), and angular errors (Pitch, Roll and Yaw, Abbe error, Cosine error) 3. Methods of decreasing error such as improving leadscrews, including rotary encoder on drive, adding linear encoders to stage ways, including grating interferometers, and use mapping techniques. 4. Measuring and characterizing stage performance: Indicators, laser interferometers


In this paper, the author describes how there is currently a lack of understanding among manufacturers and designers about how to characterize stage performance. Manufacturers often over-state stage performance by simply calculating the ideal performance based on the specifications of the system parts. This idealized estimate of performance is rarely met in practice. Additionally, the author complains that many designers and manufacturers interchange the terms "Accuracy", "Precision", "Repeatability", and "Resolution" inappropriately, thus causing confusion and incorrect stage specs.


Today, performance of single axis linear positioning systems is generally characterized by three parameters; way accuracy, resolution, and repeatability.

Stage accuracy is a measure of how closely a system can achieve a commanded position. Factors affecting accuracy include: • Accuracy of the way, or stage frame. This is determined by the accuracy of the bearing mounting surfaces and the bearings themselves, for example. • Accuracy along the ways. This is determined by factors affecting incremental motion such as deviation of leadscrew from perfect, feedback devices, nut and screw interaction, bearings, etc.

The ways alone can have accuracy errors in all the degrees of freedom. Linear sources of error include: • Flatness, or vertical run-out • Straightness, or horizontal run-out Consider ways that are perfectly straight relative to themselves. If they are mis-oriented relative to the reference (or mounting) surfaces, run-out will occur, as shown in Figure 1. [pic] Figure 1: Vertical Run-out Error example (Source: McCarthy)

Angular sources of error in the ways include: • Roll • Pitch • Yaw Figure 2 shows how pitch error can occur. [pic] Figure 2: Pitch Error example (Source: McCarthy)


Resolution is defined as the smallest positional increment that can be achieved. Resolutions on the order of 0.1 micron can be achieved in open- loop high pitch leadscrew systems. System with feedback mechanisms may achieve 0.01 microns, an order of magnitude more resolution.


The author defines repeatability as a measure of the ability of a system to consistently return to the same commanded position. He stresses that this does not depend on accuracy of the commanded position, only on the ability for the system to return to the same position over and over. Repeatability can be specified as bi-directional or uni-directional, with the repeatability from two directions or only one being considered. Good repeatability will result in low scatter of data points for repeat attempts to move to any commanded position. Generally, factors such as changing temperatures, expanding materials, wear, and wind-up/backlash in the drive components will be responsible for repeatability errors.

Leadscrew Systems

Most linear positioning systems of low to medium accuracy will employ leadscrews as the primary rotary to linear drive elements. These typically use either recirculating ball bearings or friction nuts. Leadscrew accuracy will affect overall system accuracy, while nut design will control repeatability. Screws can be formed or ground. Formed screws are lower in cost but less accurate with 25 to 75 micron over 250 mm of travel. Ground screws are very expensive but can achieve accuracies on the order of 8 to 20 micron over 250 mm of travel.

Some issues concerning leadscrews include the fact that leadscrews are usually constrained by thrust bearings that can result in a few microns of thrust error. Also, in friction nuts, friction imposed thermal gradients cause expansion and results in positional errors. Additionally, compliance in the nut material will allow deflections under load and cause errors.

Feedback – Encoders

Rotary encoders can be mounted to the shaft of the drive, usually a stepper motor. Unfortunately, the only advantage this offers is to reduce errors inherent in the motor drive. It also guarantees that errors due to missing steps from the motor do not occur. Linear encoders are placed along the travel of the stage nearest the payload so that it measures as closely as possible the actual position of the payload. Linear encoders can have various types of electrical outputs with the most common being digital quadrature. However, analog, or sinusoidal encoders can achieve higher resolutions, since they can be subdivided infinitely, so are limited only by the electronic processing equipment resolution. Some drawbacks of linear encoders include: 1. Errors due to thermal expansion of the encoder strip, which can be offset by matching the CTE with the CTE of the ways that it is mounted on. 2. Offset errors between the encoder and the payload. This can be reduced by placing the encoder strip as close to the payload as possible. 3. Linear encoders cannot provide feedback for systems with more than one axis, since they only measure in one axis.

Grating Interferometers exploit the fact that as gratings in encoders become increasingly small, diffraction effects become dominant. These can achieve 0.5 micron resolution. This type of encoder uses specialized optics to measure phase relations in light from the grating.

Grating Interferometers are very costly to incorporate into a system. Additionally, they cannot detect multi-axis errors such as orthogonality, and they are subject to high Abbe errors. Figure 3 shows a schematic of a grating interferometer. [pic] Figure 3. Grating Interferometer (source McCarthy)

Abbe, Cosine, and Angular Errors

McCarthy describes various angular errors. Abbe error is the result of angular errors in the ways combined with the offset error between the position-determining device such as leadscrew and the linear encoder. The angular error causes the encoder reading to be biased due to the angular offset. Figure 4 shows this schematically.

Figure 4: Example of how Abbe Error can occur. (Source: McCarthy) Abbe error is difficult to measure, and relies on accurate measurements of angular errors in the ways. Angular errors in the ways can be measured using a laser interferometer set up with dual paths. Sources of angular error in the system include: 1. Curvature of the ways. 2. Entry and exit of balls in recirculating bearings. 3. Variations in bearing pre-loads along the way. 4. Insufficient preload or too much backlash in the ways. 5. Torsional compliance in the ways due to external forces or overhang moments due to load travel. Cosine Errors result from angular misalignments between orientation of the reference way and the position determining device (leadscrew, encoder, etc.). Typically, cosine errors can be held negligible because alignment of ways with encoders, for example, is easily achieved to high accuracy.

Mapping Techniques

The author proposes mapping as a valuable way to reduce systematic errors. These include any errors that remain constant over time, such as Abbe error, Deviations from orthogonal in multi-axis systems, leadscrew periodic errors, backlash, and cosine errors. Mapping is achieved by characterizing the stage motion using a known calibration standard such as a laser interferometer or low-e glass grid plates, and mapping all points such that a relation between the commanded position and the achieved position can be correlated and used to adjust inputs to achieve desired output position. Mapping is especially effective when there are a few normally commanded positions. Commanded points can be interpolated from the mapping, and high accuracy can be achieved. Mapping is limited by thermal expansion variations in the system, and requires a lot of mapped points per rotation of the screw to ensure cyclic errors are also accounted for. This requires a lot of data storage and look-up. Mapping also is difficult for production of stages, since each stage must be individually characterized and its mapping stored with it. Any physical change to the stage would also require remapping.

Laser Interferometers

Laser interferometer are the best means of characterizing a stage because they have high resolution, non-contact sensing, and accuracies up to 0.02 ppm. There are two types of laser interferometers: Fringe counting and two- frequency systems. Fringe counting interferometers are similar to the Michaelson interferometer. The two-frequency system interferometer uses two similar frequencies. One of the frequencies, when reflected from the moving target, experiences a Doppler shift. This system is considered much higher performing than the fringe counting type. However, it is more costly.

Interferometers set up to measure stage performance can be configured in many ways. Generally, a retro-reflector is placed on the moving target. Various resolutions can be achieved by the arrangement of the reflectors and beam path. One typical configuration is shown in Figure 5. [pic] Figure 5. Simple laser interferometer setup (Source: McCarthy)

Some sources of error in making measurements with laser interferometers include: • Speed of light variation due to air temperature, pressure, etc (variation of refractive index of the air) • Reflector and interferometer alignment • Thermal expansion of positioning table, stage, laser mounts, etc • Cosine error • Differential flexure of positioning table top through out travel

Multi-Axis Systems and System Design

McCarthy points out in this paper that one of the main factors characterizing the performance of multi axis systems is the orthogonality of the axes. This is the measure of by how much independent axes depart from true 90-degree angles. 20 arc seconds will result in up to 25 microns of position error over 250mm of travel.

McCarthy discusses basic stage design. He distinguishes the types of rolling elements used in tables as recirculating or non-recirculating. One source of error that occurs in recirculating types is small angular deviations caused in the ways as the balls enter and exit the race. Another source of error inherent in stage designs is pitch deviation due to overhang. As the stage moves to any extreme limit of travel, the payload and top stage shuttle is overhanging the bottom of the stage, and a moment occurs. Te author also discusses air bearings. These are very precise,but require great effort to implement and operate. He also discusses choices in linear actuators, such as piezo-electric actuators, stepper motors, leadscrew, and nuts. Linear stepping motors are described as having low damping and poor stiffness.


The author concludes that low and moderate precision stage specifications usually only include a few (and often misunderstood) parameters. But he suggests that stages with more detailed specifications would benefit vendors and designer significantly.


McCarthy, Kevin. Accuracy in Positioning Systems. New England Affiliated Technologies, Reprinted from the Motion Control Conference Proceedings, March 19 – 21, 1991. ( cy.pdf)