How Accurate Can a Laser Tracker Be?

Published: Wednesday, May 16, 2018 - 11:00

Laser trackers are widely used for metrology and precision surveys. Depending on the approach, range, and instrument itself, the measurement accuracy can vary from millimeter to micron. Several applications of laser trackers used in the National Synchrotron Light Source II (NSLS-II) project will be explained in this article to show examples of using laser trackers to achieve very high accuracy.

Introduction

The NSLS-II at Brookhaven National Laboratory is one of the newest and most advanced synchrotron facilities in the world. With state-of-the-art design and a 3 GeV, 500 milliamp electron storage ring, it will enable the study of material properties and functions with nanoscale resolution and exquisite sensitivity by providing world-leading capabilities for X-ray imaging and high-resolution energy analysis. It currently is running at 300 mA with 19 operational beam lines. There are nine more beam lines to be accomplished during fiscal year 2018.¹

Figure 1: The layout of the NSLS-II storage ring, experimental hall, and survey monuments (blue crosses represent survey monuments)

For construction and maintenance purposes, a very high alignment accuracy is required. For example, the global deviation of the components with the circumference of 792 m ring should be smaller than ±3 mm, as shown in table 1. Figure 1 shows the dimension of the NSLS-II. Although the diameter is only about one-third of the circumference, there is no direct visibility diametrically. Penetrations are reserved for the primary control network survey, which requires the floor monuments to be projected on top of the roof.² A laser tracker is employed to establish precise installation data with preferably less than 1 mm accuracy. A survey control network is made of monuments (shown as crosses in figure 1).

Another key requirement is that the relative alignment deviation of two adjacent girders, which are about 3 m long and several meters apart, should be greater than ±0.1 mm. Considering that there are several contributing factors, such as alignment datum error, instrument error when tying into data, and residuals of alignment, the requirement is very tight.

However, the most stringent requirement is the relative alignment of multiple magnets on a common girder, which should not exceed ±0.03 mm.³ With the help of the laser tracker for initial setup, a high-precision, vibrating wire measurement technique is adopted to achieve the requirement  and maintain the profile of an assembly.⁴

Table 1: Alignment tolerances

To realize the above alignment goals for the NSLS-II project, along with other instruments, a laser tracker is widely used. Generally, about 25 micron accuracy can be achieved by a laser tracker for short distances, but the accuracy will decrease as the distance increases. However, to fulfill the requirement of the project, the laser tracker must measure a large distance (~800 m). For short distances, a ~10 microns measurement accuracy is needed. Both scenarios are extremes for a laser tracker application. Through careful design and implementation, a high accuracy has been achieved for various situations. This article will illustrate several examples.

Evaluate error by standard error ellipse

When it comes to the term of measurement error, there are several terms that can be confusing, such as “precision,” “accuracy,” “repeatability,” “uncertainty,” “standard deviation,” and “root mean square” (RMS). For surveying and mapping, the concept of error ellipse, as illustrated in figure 2, is widely used.⁵ X and Y axes show the defining frame, and the U and V axes represent the direction of the largest and smallest deviation, respectively. Comparing with standard deviation rectangle, the weakest direction of a point can be easily seen. Commercial survey adjustment software, such as Star*Net, provide error ellipse information.⁶ During the design and analysis stages of the NSLS-II project, STAR*NET software is employed, and some of the results will be detailed in the following section. Based on the experience, evaluating error by standard error ellipse is reliable.

Figure 2: Standard error ellipse

Measures to improve the performance of a laser tracker

It's a common sense that laser tracker can get 3D coordinates with respect to the instrument frame by measuring two angles and one distance. To understand the accuracy, the resolutions of the angular decoders and distance measurement sensor must set the limitation of a laser tracker. Besides, the calibration of the instrument, as well as the ambient conditions and training of an operator, are all contributing factors to the performance.⁷

To improve the performance of a laser tracker, all impacting factors should be controlled. For example, the laser trackers used in NSLS-II are periodically calibrated. For high-precision applications, a controlled environment is always ensured. Then, and most important, a trained team is employed to operate the laser trackers. With those conditions maintained, thorough analysis and planning can been done for all the tasks to be performed. R&Ds are performed for some of the critical tasks before the formal survey is started.

For various applications, one key technique we use is to measure a component with multiple setups. By measuring the same components, along with enough common targets, at different instrument locations, the measurement accuracy can be significantly improved. Figure 3 demonstrates the measurement setup of laser trackers in an environmentally controlled room.

Figure 3: 12 tracker setups to measure girder and magnet fiducials. Click here for larger image.

When multiple setups are not feasible, multiple shots are enforced instead for high-precision applications. By measuring the fiducials of a component for a couple of rounds, the measurement accuracy can be improved.

High precision has been achieved in very large-scale and small-scale dimensions along with a measurement accuracy varying from millimeters to several microns.

Establish a high-accuracy installation control network in ~800 m dimension, both globally and locally

Figure 4: Long-distance survey by a AT401 laser tracker (dash line is about 238 m and only partially successful). Click here for larger image.

In regards to the global and local alignment tolerance, the goal is to establish a control network with ~±1 mm global accuracy and ~±0.05 mm local accuracy.

There are two tiers of the control network: primary and secondary. The purpose of the primary control network is to establish the connection with construction data and provide a high-level orientation to the secondary control network. Besides ensuring high global accuracy, the secondary control network provides the necessary density of precise reference points to ensure the local tolerance can be achieved. For the primary control network, the direct long-distance shooting of the laser tracker is tested. For the secondary control network, the short-distance performance and the accumulation of short distance to a large-scale dimension are demonstrated.

Direct long-distance performance of the laser tracker

The measurement method for the primary control network has evolved. Figure 4 shows the observations as represented by the solid lines and result obtained by AT401 during the fourth round of the survey. The monuments of the points that begin with “S” are the ones that are located on the floor of the storage ring tunnel. To ensure visibility, they are projected on the roof of the tunnel via the penetrations reserved in the roof to ensure the line of sight vertically. Large penetrations are reserved in the building to ensure the line of sight horizontally.

The AT401 laser tracker is mounted on the top of the central monument and shoots all other monuments with multiple times. The distance from the instrument to the target is about 125 m. Although the network has an apparent weakness in shape, the semi-major axis of all the error ellipses of all the monuments is smaller than 0.5 mm (1σ). The deviation between primary and secondary monuments is less than ±1 mm.

A test was performed during the fifth round of the survey using the AT401 laser tracker to measure longer distances, for example, from S1 to S3, S2 to S4, etc., as represented by the black dash line in figure 4. The distance from instrument to target is about 238 m. However, although some measurements have been taken successfully, others failed.

Short and indirect long-distance performance
Figure 5 shows the monument, instrument, and observations of NSLS-II’s secondary control network in one cell out of 30. The monuments are permanently attached to the wall or buried in the cement of floor. For the whole tunnel enclosure, more than 1,000 monuments are used to get better geometry and precision.

Figure 5: The monument, instrument, and observations of NSLS-II’s control network in one cell out of 30. Click here for larger image.

The control network was originally designed to be measured by a laser tracker and digital level, which compensate for one another’s shortcomings and achieves a desirable performance, both horizontally and vertically. However, the AT401 laser tracker is used for most of the survey rounds. According to its specifications, the AT401 has an angular precision of 0.5 in. and a distance precision of ±5 micron. This is a significant improvement, angle-wise, compared with previous laser tracker models. What’s more, the internal level has the capability of 0.5” precision which is comparable with a precision level. It can be deemed as a combination of total station, laser tracker and digital level, which is a preferable scenario for control network survey.²

As can be seen in figure 5, the instrument is set up densely among the monuments, with more than 150 stations. The accuracy is improved by redundant measurements. Spatial Analyzer’s Unified Spatial Metrology Network (USMN) is used to get the optimal coordinates of all the monuments and instruments.³ In order to maintain the level of information of the AT401 laser tracker, their rotation in a horizontal plane is forced to remain stationary during the computing process. According to the computation result, some of the bad measurements are eliminated. STAR*NET is used to simulate the process, and it shows that the goals of ~±1 mm global accuracy and ~±0.05 mm local accuracy are achievable with the design.

With real measurement data and an assumed accuracy of 1.0 arc-second’s accuracy for the horizontal and vertical angles, and 7.6 µm + 2.5 µm/m for distance, the global and local accuracy (1σ) computed by STAR*NET is shown in table 2. The top part shows that the average absolute error is better than ±1 mm, and the bottom part shows that the relative error is better than ±0.05 mm.

Table 2: Statistics of STAR*NET

The control network has been measured eight times so far to record the dynamics of the tunnel and maintain precise alignment data.

Achieve better than 30 m accuracy for assembling several magnets on a common girder magnetically

The tolerance of ±0.03 mm regarding magnets on a common girder is tough to realize. In order to address the stringent magnet-alignment requirement, a vibrating wire technique is used. The magnetic measurement and alignment is conducted in an environmentally controlled room (ER). After alignment, the girders must be transported to the tunnel and repositioned relative to the tunnel control network. The girder has six or eight supports, depending on its location, which induces the girder profile to change by as much as ±50 microns or higher. Therefore, the girder profile must be established before leaving the ER and be reproduced after arriving at the tunnel. The NSLS-II survey team calls this process “girder profiling.”⁸

Error estimate
The error sources between magnets in one girder, as well as their magnitudes and originations, are listed below:
• Vibrating wire system error, < ±10 microns. The error magnitude is estimated based on numerous tests.
• Magnetic alignment residual error, ±6 microns. The error magnitude is a statistic of 46 girders aligned.⁹
• Girder profile establishment error in ER, ±9 microns. The error magnitude’s result is simulated according to conservative laser tracker performance.

Figure 6 shows the repeatability of eight girder fiducials for one girder during the repeatability test, which follows the setup as shown in figure 3.

Figure 6: The relative deviation of girder fiducials between two rounds of observations

• Girder profile remeasurement error in tunnel, ±9 microns. The error magnitude’s result is simulated according to the laser tracker’s specification. Figure 7 shows the instrument setup and simulation result of a girder-profile reproduction in the tunnel. Two laser trackers work together. After initial adjustment, all the monuments and girder fiducials are shot four times in each instrument position to improve accuracy. The priorior slope distance, horizontal and vertical angle accuracy are given as 20 microns, 0.5 arcsecond, and 0.5 arcsecond, respectively. The posterior vertical standard deviation of the girder fiducials is less than ±9 microns for each.
• The sphericity and optical centering error of the spherically mounted reflector (SMR) is about ±6 microns.
• Girder-profile reproduction residual error in tunnel, ±10 micron. When the adjustment result is acceptable, a six-tracker setup is conducted to record the final position of the girder and magnet fiducials. Figure 8 shows the residuals of all the girder profiles. It is calculated by averaging every girder fiducial, each of which are symmetrically located relative to the girder’s center line.

With all the errors accumulated, according to the law of error propagation, the final magnet-alignment error is about ±20 microns. As explained above, although the alignment tolerance is ±30 microns, several steps, which require better than 10 microns, must be precisely enforced to fulfil the requirement. Considering the time spent and people involved, it’s the most complicated alignment work of the NSLS-II project.

Figure 7: Layout of two trackers’ setup and observation scheme. Click here for larger image.

Figure 8: The profile residuals for all girders. Click here for larger image.

Achieve several-micron accuracy with mirror-surface survey

Mirror surface is usually precisely manufactured with nanometer planar accuracy. The paper, “NSLS-II Girder Profiling Activities,” discussed the approach to realize a noncontact survey.⁸ However, it’s agreed that the edges of the mirrors can be touched by the SMR; therefore, a direct-mirror survey is widely used because it is more straightforward and simple.

Figure 9: Measure a mirror surface directly. Click here for larger image.

Figure 9 shows the error of the fitted plane by measuring the mirror surface directly with a 0.5-in. SMR. As a result of the high precision of its manufacture, it can be treated as having zero errors for the purpose of comparing it with the measurement of a laser tracker. As illustrated in the graph, only small portions of the horizontal and vertical angular decoder are used, and therefore the most significant contributing factor is the interferometer of the laser tracker. Because the interferometer is highly accurate, the planarity of the fitted plane looks very good (±3.6 microns).

Move large device in certain direction with a couple of micron accuracy
It’s a common practice to adjust a component with respect to certain data, for example, the precise survey control network mentioned above for accelerator alignment. However, due to the data error and instrument error, there is usually more than 50 microns residual, even with a carefully designed procedure.

For the NSLS-II project, following the four steps described below results in a better-than 10 microns residual:
1. First, measure the location of the component with multiple (i.e., more than three) setups to get an accurate, as-built location of the component and adjacent survey reference points.
2. Second, set up the instrument and fit it to the reference points by using the as-built reference coordinates generated above.
3. Third, adjust the component to the desired amount with respect to the as-built location of the component.
4. Fourth, perform multiple setups of the laser trackers to get the new, as-built location after adjustment.

The first step is very important because it will generate an accurate reference file that includes both the data and the location of the component generated by using the multiple-setup strategy. Thus, the uncertainties of data and the location of the component will be largely eliminated. Likewise, the fourth step will produce an accurate new location of the components so that the reported number is more accurate.

IVU moving up 100 microns
During the running of the machine, the NSLS-II physicist believed that one of the in-vacuum undulators (IVU) needed to be moved upward by 100 microns. The steps described above were followed, and fewer than 10 microns of residuals were obtained, as indicated in figure 10.¹⁰

Figure 10: Diagram of an in-vacuum undulator to be lifted by 0.100 mm. Click here for larger image.

Comparison with vibrating wire measurement system
As a simulation to test the laser tracker’s alignment precision, during the vibrating wire measurement, one magnet for the last production girder (C19G4) was intentionally left with an offset of (0.066, 0.125) mm. Then laser trackers were used to align this quad into the best-fit magnetic center line. After multiple alignment steps, the laser tracker-based alignment reported a final offset of (0.0023, 0.0094) mm. Compared with the offset of (–0.001, 0.012) mm from the vibrating wire observation, the deviation between the two systems is only (–0.003, 0.003) mm in this case.

Summary

Laser trackers are widely used in the NSLS-II project. For large-scale dimensions such as the storage ring with a circumference of ~800 m, the accuracy of globally ±1 mm and locally ±0.05 mm can be achieved by use of the AT401 laser tracker. For an assembly of components or small components, by careful design, an accuracy of several to 10 microns is achievable.

However, the good performance is independent of a well-maintained instrument, stable environment, good procedures, and most important of all, a skilled survey and alignment team. Otherwise, uncontrolled performance and even blunders could happen.

Acknowledgement
The authors would like to thank all the colleagues who contributed in the alignment work of NSLS-II project.

References
1. https://www.bnl.gov/ps/nsls2/about-NSLS-II.php, June 7, 2017.
2. Yu, C., et al., “The storage ring control network of NSLS-II,” International Workshop on Accelerator Alignment 2014 Proceedings.
3. “NSLS-II Preliminary Design Report,” June 7, 2017, http://www.bnl.gov/nsls2/project/PDR/.
4. Jain, A., et al., “Vibrating wire R&D for alignment of multipole magnets in NSLS-II,” http://www.slac.stanford.edu/econf/C0802113/papers/P019.pdf.
5. Wolf, Paul R. and Charles D. Ghilani, Adjustment computations: Statistics and least squares in surveying and GIS, Third edition (Wiley Interscience, 1996).
6. Starplus Software, STAR*NET Manual, v. 6, August 2002.
7. Yu, C., et al., “The accuracy enhancement measures for laser tracker,” Science of Surveying and Mapping [J] 2007 (3), pp. 54–56 (in Chinese).
8. Yu, C., et al., “NSLS-II Girder Profiling Activities,” International Workshop on Accelerator Alignment, 2012 Proceedings.
9. Jain, A., “Measurement Status and Girder Alignment,” NSLS-II project internal report, June 2012.
10. Yu, C., et al., Noncontact measurement of mirrors with a laser tracker. The Journal of the CMSC [J]. Vol. 11, No. 2, pp. 13–17.
11. Yu, C., et al., “16 ID 100-Micron Lift Survey Report,” NSLS-II project internal report, May 2017.

About The Author

C. Yu, F. Karl, M. Ilardo, M. Ke, S. Sharma