Introduction
When building complex systems for optics, semiconductor manufacturing, or advanced metrology, positional accuracy is paramount. While Zaber linear stages deliver exceptional performance right off the production line, achieving micron-level accuracy requires carefully controlled calibration.
This article explains Zaber's process of achieving that accuracy and how you can maintain it with your own equipment. Specifically, we will break down:
- The Mechanics of Precision: A look at the sources of mechanical error (such as drive screw deviations, encoder anomalies, and Abbé errors) and how Zaber's calibration process reduces or eliminates them.
- Best Practices for an Optimized System: How external environmental factors like mounting plate flatness, fastening torque, and minute temperature shifts can impact accuracy, and how to avoid common pitfalls.
- Metrology and Verification: A transparent overview of the stringent, nanometer-accurate measurement system Zaber uses to verify performance, ensuring our stages operate exactly as specified in real-world conditions.
Linear Stage Calibration
Calibration is the process of measuring the position error of a stage and using the error values to create a correction table or correction factor, then verifying the performance with the correction applied. This correction can be saved in the stage’s memory, allowing the stage to compensate for these errors, providing a much higher level of performance. This article will delve into the typical sources of error in a stage, demonstrate the significant performance improvements calibration can provide, and describe the precise measurement system Zaber uses for these calibrations.
What the correction looks like:
- A correction table of up to 64 points, equally spaced over the travel of the stage.
- For direct drive stages with analog encoders, a secondary correction is also performed for short scale interpolation error (known as Subdivisional Error).
Figure 1. A typical correction profile demonstrating position error over travel distance before and after calibration.
Sources of Error in Linear Stages
Many components in a stage contribute to the stage’s overall accuracy, but the sections below will describe the most significant error sources, and how Zaber’s calibration process corrects those errors.
Drive Screw Error
Figure 2. The drive screw is often the largest source of error in open-loop screw driven stages.
Note - Zaber is currently trialing calibration of some open-loop screw driven stages. All closed-loop stages get calibrated.
Open-loop screw driven stages position the carriage by assuming a certain distance traveled per revolution of the drive screw, and rotate the screw accordingly. For these stages, the drive screw is often the largest source of error. Direct drive stages avoid this error entirely.
Error Sources
There are two errors typically associated with drive screws:
- Screw pitch error - Due to the pitch of the screw being slightly too long or too short.
- Once-per-revolution error - Due to a bow in the screw or eccentricity in the screw mounting points.
Typical Error Profile
- Screw pitch error - A linear trending error over the length of the stage. This is often the largest source of error for a stage without a linear encoder.
- Once-per-revolution error - A sinusoidal error that is synchronous with screw rotation.
Figure 3. Typical uncalibrated error profile for a drive screw, showing both linear and sinusoidal errors.
Improvement
- Screw pitch error - This can be almost completely removed.
- Once-per-revolution error - Since this error can repeat over a very short period, a finely spaced calibration table or an additional correction would be required to eliminate it.
Figure 4. Position error of a drive screw stage after calibration, with screw pitch error mostly eliminated.
Encoder Error
Figure 5. Linear encoders provide direct position feedback for immediate accuracy boosts.
Stages with linear encoders rely on position feedback from the encoder to position the carriage. Linear encoders provide an immediate accuracy boost when added to screw driven stages, and their remaining error is easier to correct with calibration. The main source of error prior to calibration is the accuracy of the encoder scale and optical read head.
Error Sources
Encoder errors can be broken down into two components:
- Scale Pitch Error - The encoder scale pitch is the spacing between the lines on the scale (typically 20 μm for Zaber stages).
- Subdivisional Error - A cyclic error that occurs due to imperfections in the analog signals generated by the encoder read head. Ideally, as the read head passes across the lines on the scale it produces two perfect sinusoidal curves, phase shifted by 90 degrees. To achieve a resolution finer than the encoder pitch, the controller uses these signals to interpolate between the lines. Error in these signals creates error in the interpolation.
Typical Error Profile
- Scale Pitch Error - Deviation from the nominal spacing tends to be fairly consistent across the length of the scale, thus, creating a linear trending error.
- Subdivisional Error - This error is generally a small consistent sinusoidal error, with a very short period. Typically much less than 1 μm.
Figure 6. Typical uncalibrated error profile for a linear encoder showing scale pitch deviation.
Improvement
- Scale Pitch Error - Almost completely removed.
- Subdivisional Error - Generally, less than 0.1 μm of error remains. Some of the small ripples visible are from subdivisional error.
Figure 7. After calibration, scale pitch error is largely removed, leaving only minor subdivisional error ripples.
Pitch/Yaw Abbé Error
Figure 8. Pitch and Yaw Abbé errors introduce translational positioning errors.
Abbé error is a translational error that occurs due to rotation of the carriage. See our Application Note for a detailed description of the impact of abbe errors on motions systems.
Error Sources
Pitch and yaw abbé errors are due to a lack of flatness or straightness in the bearing rails, and/or forces imparted from bearing drag, the drive screw, or an external source. External forces can create significant abbé error, especially for low stiffness stages. For an unloaded stage, the biggest contributors tend to be:
- Pitch Abbé Error - Stages tend to conform to a lack of flatness in the mounting surface. Even when mounted to the relatively flat surface of an optical breadboard, pitch abbé error could be significant.
- Yaw Abbé Error - Lack of stiffness due to inadequate/uneven bearing preload can create yaw abbé error.
Typical Error Profile
Abbé error can take a variety of shapes. It can be anything from a sharp spike to a linear trend, and it scales with distance from the point of rotation.
- Pitch abbé error - If the stage isn’t well supported on a flat surface, this will match the shape of the supporting surface.
- Yaw abbé error - For a two axis stage, this can vary for one axis, depending on the position of the other axis.
Figure 9. Position error varies significantly at different heights (stagetop vs 50 mm above) due to pitch Abbé error.
Improvement
Most abbé error can be corrected by calibration. However, it can only be corrected at one distance from the center of rotation.
- Pitch abbé error - At Zaber, pitch abbé error is corrected at 20 mm or 50 mm above the stagetop, depending on the stage size.
- Yaw abbé error - For 2-axis stages, yaw abbé error is corrected for one axis when the other axis is at its center of travel.
Figure 10. Pitch Abbé error can be successfully corrected via calibration for a specific height above the stagetop.
External Error Sources
Regardless of how accurate a stage is on its own, the following conditions need to be controlled for the stage to perform at its best.
Mounting Plate Flatness and Mounting Torque
Figure 11. An insufficiently flat mounting surface can induce Abbé errors.
Think of a mounting plate like the foundation of a house. If the foundation isn’t flat, it’s hard to make the rest of the house square. The mounting plate for a stage is just as important. Zaber stages are calibrated on a very flat surface, but any lack of flatness in their eventual mounting location will create abbé error in the stage once it is bolted down.
A stage may not be pulled completely flat to the mounting surface if too few fasteners are used or if mounting torque is insufficient. Using all mounting holes (or every second set for longer stages) and torquing to at least 1 Nm for M3 fasteners or 2 Nm for M6 is a good place to start.
Thermal
Figure 12. Thermal stability is critical to stage accuracy.
Thermal stability is critical; even a 1°C temperature change can introduce tens of microns of error in a stage. As a rule of thumb, expect 10-20 μm of expansion/contraction for every °C temperature change per meter of stage length. Zaber stages are calibrated at 20 ± 1 °C, and maintaining operation within this range will ensure optimal performance.
External Loads or Vibration
Figure 13. External loads can introduce unintended positional errors.
A varying load being applied to the carriage will introduce positional errors. Choosing a suitably stiff stage for the application, and isolating the stage from external vibrations will help to maximise positional accuracy.
Zaber’s Measurement System
The measurement system at Zaber consists of a multi axis interferometer, mounted on a motorized alignment system. Using an interferometer provides nanometer accurate measurements, and the automatic alignment system provides consistent alignment, with minimal alignment error.
The device to be calibrated is mounted on an AA-grade granite surface plate, which is the industry standard for a metrology reference surface. This plate is supported by a pneumatic damping table to minimize the effect of external vibrations.
Figure 14. Zaber’s measurement setup utilizes a multi-axis interferometer and a vibration-isolated granite surface plate.
The Calibration Process
While each step in the calibration process presents opportunities for measurement error, Zaber has, over the years, refined its procedures through automation and stringent control over environmental conditions, ensuring reliable and consistent measurements.
Mounting
Stages are mounted with screws in most/all of their mounting points, and an automatic torque driver is used to provide consistent mounting torque. This ensures that the stage will be pulled flat to the mounting surface.
Automated Alignment
Zaber uses a fully automated alignment system to help minimize alignment error, and to allow automated calibration of up to three stages without any operator intervention. This system ensures an efficient and repeatable alignment process free of human error. To make this possible, we built this system ourselves using standard Zaber components. You can read the full story of how we engineered it here.
Figure 15. The automated alignment system minimizes human error during the calibration setup process.
Acclimatization
A thermal acclimatization is performed before calibration, and regular measurements are automatically taken during the acclimatization process to verify that the stage has reached a stable temperature before the calibration begins.
Figure 16. Linear error stabilizes over time during the thermal acclimatization process before calibration begins.
Analog Encoder Calibration
For direct drive stages with analog encoders, the first step of calibration involves adjusting the encoder gain and DC offset. This removes a short scale repeating error, which results in improved accuracy for small moves, as well as improved velocity stability at low speeds.
Figure 17. Adjusting the encoder gain and DC offset reduces short-scale repeating errors.
Measuring Error to Build the Calibration Table
An initial measurement of the stage’s position error is performed, and a correction table with up to 64 points is then created based on those errors. For positions between the points, the correction will be interpolated.
Verification
After applying the correction table, a 128 point measurement of position error is performed to verify that any remaining error is below the accuracy specification of the stage. Using a higher number of points for verification ensures we capture interpolation errors between the correction points. For linear encoder stages, a calibration report that details the remaining error is provided with the stage.
Figure 18. The final verification step generates a calibration report detailing the remaining position error across the stage's travel.
Measurement System Accuracy
The overall accuracy of calibration is defined by the performance of the complete measurement system. The table below details the expected error contributions from Zaber's system.
| Source | Expected Error Magnitude | Notes |
|---|---|---|
| Interferometer positional accuracy | Typically < 50 nm. Worst case 170 nm for 1m stage, with 200 mm uncorrected deadpath and 0.1 °C variation. |
SP 5000 TR measurement uncertainty = 150 nm / m. Temperature error for uncorrected deadpath = 1 µm/°C/m * 0.1 °C * 0.5 m. Interferometer accuracy traceable to German national standards institute (PTB). |
| Interferometer alignment | < 4 nm | 0.005 deg alignment tolerance. Worst case would be with 1 m stage. |
| Abbé error due to surface plate | Typically < 0.1 μm of pitch abbé for most stages with 20 mm measurement height. In the worst case, 0.8 μm for a 1 m long stage, with 50 mm measurement height. |
The surface plate has a smooth curve of ~2 arc seconds of pitch over its length. |
| Abbé error due to mounting | < 0.1 μm of pitch abbe error for stages with 20 mm measurement height. < 0.2 μm for 50 mm measurement height. |
Even if all mounting screws are used, the order in which they are fastened, the exact torque achieved, and the stage temperature before fastening, can all have a minor impact on the resulting flatness of the stage. |
| Stabilization after motion | 50 nm | A compromise between waiting for complete stabilization after a move and achieving adequate measurement error. |
| Typical Total Measurement Uncertainty | ±300 nm | |
| Worst Case Total Uncertainty | ±1.2 μm | For a 1 m stage. |