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Robert P. Elliott Jr.

Robert P. Elliott Jr.’s default image

CMSC

Measurement Accuracy of a Mirrored Surface Measured Directly Using a Laser Tracker

Published: Thursday, May 22, 2014 - 00:00

Laser trackers and the software that controls them have revolutionized the way metrology data have been taken. With software and hardware advances have come new and better ways to take measurements. One of these advances in metrology software is the ability to measure the angle normal to a mirrored surface with a laser tracker, something which was done with theodolites in the past.

Mirror measurements can be done two ways with laser trackers: indirectly using two measurements of a spherically mounted retroreflector (SMR), and directly by reflecting the laser normal to the mirrored surface. The indirect measurement was studied in a paper published by the CMSC in 2012 (see “Measurement Accuracy of a Mirrored Surface Using a Laser Tracker,” Robert Elliott, 2012).

This article will study the accuracy of a mirrored surface measured with three brands of laser trackers (Leica, Faro, and API). The results of this study are important to understand the accuracy of this method and how the uncertainty of this type of measurement affects resulting data. The data collected by the laser trackers will be of a fixed cube taken at fixed distances along a line. The cube will be fixed on a stable surface, and SMR nests will be distributed around the cube and measured with the tracker. The laser tracker will be moved down a line normal to the cube. Measurements will be taken at 10-ft intervals along this line. Before measurements are taken, the laser tracker will be transformed to the common coordinate system stored in the stable SMR nests that were installed and measured at the beginning of the measurement process. This process will be repeated for the three brands of laser trackers and the results compared.

Laser tracker mirror measurement method

A mirrored surface can be measured with a laser tracker by direct collimation. The tracker is adjusted so that the laser is reflected off the surface of the mirror that is to be measured and returns to the laser tracker along the same line. Once collimation is established, a point is measured using the laser tracker. From this measured point, Spatial Analyzer software1 calculates the vector normal to the mirror and the position of the mirror plane by using the following menu choices: “Construct\Lines\From Instrument Shot.” This method is explained graphically in figure 1.


Figure 1: Construction of a mirror plane from a laser tracker measurement

Test setup

The direct collimation measurement accuracy study was conducted in a 10K-class clean room on the Sunnyvale, California, on the Lockheed Martin campus. The test was conducted on a seismic mass in the clean room that has a floor loading of 3,156 lbs per sq ft. The cube and the tracker positions from 10 ft to 60 ft were located on this seismic mass. The laser tracker positions from 70 ft to 90 ft were not on the seismic mass but on the clean room floor. During testing the air handlers in the clean room were turned down to 40-percent capacity to reduce error from vibration and air currents.

A granite surface plate at one end of the room was used to support the cube during the test. Tape was applied to the table and cube to act as a release agent. The cube was then bonded to the table with hot­melt glue. The cube was not measured for two months and monitored with two theodolites to quantify stability. The cube was also monitored with two theodolites throughout the duration of the test to ensure its position was stable.

A grid of 34 1.5 in. drift nests was bonded to an area of the floor that was approximately 65 ft x 36 ft. A 3­D theodolite system comprised of three theodolites was used to measure the cube and the drift nests. Two of the theodolites in the 3­D system were autocollimated on the cube, and a point measured in Spatial Analyzer. These measurements tied the cube position to the tracker nests in a common coordinate system. The theodolite network was bundled, and a coordinate frame was created from the cube measurement with the X ­axis running along the cube face that was measured with the laser trackers and Z­ axis pointing up. The cube frame is the working frame that the distance data is reported in. This will yield deviations of the tracker measurements with respect to the theodolite measurements of the mirror cube.

These nests were measured by a Leica 8402 laser tracker from six positions. The United Spatial Metrology Network (USMN)3 feature of Spatial Analyzer was used to optimize the uncertainty of the grid measurements. This grid of nests will be used to transform the laser tracker into a common coordinate system as it is moved from station to station. (See figure 2.)

Uncertainty fields were created for the theodolite measured points, and the entire measurement set (trackers and theodolites) was optimized using the USMN with point groups feature of Spatial Analyzer.


Figure 2:
Test setup layout

A line was created from two SMR nests on the right side of the room. This line is orange in color in figure 2. This line was measured with respect to the cube with a theodolite that was “bucked ­in” on the line, meaning the theodolite was positioned so that it was on the line described by the two points. The azimuth of the cube was transferred from the theodolite that was collimated on the X ­axis face of the cube. Knowledge of this line with respect to the cube, combined with initial elevations of two adjacent faces of the cube, allowed monitoring of the cube in three rotations during testing to ensure it was stable.

Laser tracker positions were marked on this line at 10 ft intervals out to 90 ft from the cube along the X ­axis. The laser tracker was moved to each of these positions to measure the cube and grid of fixed nests. These measurements will yield cube normal angles every 10 ft along the line that can be compared to the theodolite measurement of the cube normal in the same coordinate frame to determine the tracker accuracy at distance.

This test will evaluate the effect of distance on the measurement of a mirrored surface using a collimated laser tracker. Each laser tracker will be used to measure a mirror cube at 10 ft intervals out to 90 ft for a total of nine stations per tracker.

Laser trackers tested

Originally three brands of laser trackers were scheduled to be tested: API, Faro, and Leica. The API Tracker 3 and the API Radian trackers were not capable of taking this measurement. The Leica 401 tracker and the Faro X, Ion, and Vantage trackers were tested. The data reported in this article will not reveal the laser tracker that took it. The trackers will be called Tracker A, Tracker B, Tracker C, and Tracker D.


Figure 3:
Laser trackers that were tested

Measurement plan

Each laser tracker was tested from 10 ft to 90 ft from the cube at 10 ft intervals. At each station the 34 1.5 in. SMR nests on the floor were measured, and the tracker was brought into the metrology network using the USMN feature of Spatial Analyzer. At each station two sets of 10 measurements were taken. First, 10 measurements were taken with the tracker continuously collimated on the mirror. These measurements were called “continuously collimated” in the data reported in this article. Next, 10 measurements were taken by pointing the tracker at a SMR nest in the room then back at the cube. These measurements were taken to study the effect of exercising the azimuth and elevation motors before measuring a cube. These measurements were called “off then on” in the data reported in this article. Each data set was averaged, and these averages were reported in this paper. It should be noted that three of the four trackers were capable of collimating on the mirror cube from 10 ft out to 90 ft and one tracker was only able to measure the cube from 10 ft to 50 ft.

Test results

The data were compiled and analyzed in a common coordinate frame that is based on the cube measurements. The first analysis was to compare the range of the minimum and maximum azimuth and elevation of the 10 measurements taken at each station for both continuously collimated and off-then-on testing. The range data yield the accuracy of the tracker in azimuth and elevation at each station. The data are reported in seconds of arc.


Figure 4 and figure 5
Click for larger image.

The first plot (figure 4) is of the range between the minimum and maximum azimuth data point at each distance station when the laser tracker was continuously collimated on the mirror cube while the 10 measurements were taken. The second plot (figure 5) is also the range in azimuth data, but the laser tracker was pointed at an SMR nest and back to the mirror cube for each of the 10 measurements.


Figure 6 and figure 7
Click for larger image.

Figure 6 is of the range between the minimum and maximum elevation data points at each distance station when the laser tracker was continuously collimated on the mirror cube while the 10 measurements were taken. Figure 7 also shows the range in elevation data, but the laser tracker was pointed at an SMR nest and back to the mirror cube for each of the 10 measurements.

Figures 4 through 7 show that the range between the minimum and maximum data points for both the continually collimated and off-then-on cases is very low for both azimuth and elevation. This shows that the data in each set are repeatable.


Figure 8 Figure 9
Click for larger image.

Figure 8 shows azimuth data from 10 ft to 90 ft of the deviation from the X­ axis of continuously collimated mirror cube measurements. Figure 9 shows these data when the laser tracker was pointed at an SMR nest between measurements. Both plots show averages of 10 measurements at each station. Note that Tracker C showed a spike in deviation at 20 ft for both measurement sets. This spike is the result of a calibration error at that distance from the cube. Also note that Tracker D could not collimate past 50 ft. The data show that the deviation from 0° is relatively small and does not increase with distance.


Figure 10 Figure 11
Click for larger image.

Figure 10 shows azimuth data from 10 ft to 90 ft of the deviation in elevation of continuously collimated mirror cube measurements. Figure 11 shows these data when the laser tracker was pointed at an SMR nest between measurements. Both plots show averages of 10 measurements at each station. Note that Tracker C showed a spike in deviation at 80 ft for both measurement sets. This spike is the result of a calibration error at that distance from the cube. Also note that Tracker D could not collimate past 50 ft. The data show that the deviation from level increases with distance, which was expected. The explanation for this error is that the elevation motors have to compensate for gravity when collimated on the mirror. This compensation and the resulting motor corrections cause an uncertainty in elevation. This uncertainty is magnified at distance. This uncertainty isn’t seen in the azimuth data because the laser tracker rotates about the gravity vector for the azimuth-angle portion of a point measurement, and therefore gravity isn’t a factor in azimuth measurements.

Conclusion

Direct collimation is a viable method for measuring mirrored surfaces. When taking this type of measurement, it is important to be sure that the environment is stable. Isolating facility vibration and air currents is very important. Also it is important that the laser tracker is mounted on a stable stand and secured to avoid movement. Calibration of the laser tracker can have an adverse effect on measurements, so performing field checks and verifications is important to do prior to taking measurements.

The azimuth portion of the measurement has less uncertainty than elevation. This is because the azimuth axis is parallel to gravity. The elevation uncertainty is higher because the tracker is constantly correcting for gravity during this measurement due to the weight of the rotating tracker head. These corrections translate into uncertainty that increases with distance.

Using a laser tracker to measure a mirrored surface completely removes human error that is inherent with theodolite measurements of mirrors. Theodolites depend on an operator’s skill at manually aligning a collimated image with a crosshair through the theodolite’s telescope. The uncertainty of this measurement depends on many factors, including operator experience and skill, fatigue, quality of the theodolite, and intensity of the collimated light. These factors are completely eliminated with use of a laser tracker.

Another advantage of using a laser tracker for this type of measurement is the use of common targets when relating a mirror-normal vector to a part coordinate frame. Typically a master reference cube is aligned to a part or vehicle coordinate frame in aerospace applications. A pair of theodolites is autocollimated on adjacent faces of this mirror to level the part. Next, a theodolite is autocollimated on the mirror to be measured. This theodolite is collimated with one of the two theodolites on the master reference cube, and the azimuth of the master reference cube is transferred to the third theodolite. This requires that the two theodolites are set up so that they have line of sight to the mirrored surface they are measuring and each other. The third theodolite is again autocollimated on the mirror to be measured, and the elevation and azimuth are recorded.


Figure 12:
Theodolite measurement of a mirror with respect to a cube

If a laser tracker is used for this measurement, the part to be measured needs to have stable control points installed on the structure that are mapped to the part coordinate frame. The tracker needs to be set up so that it is capable of autocollimating on the mirror to be measured. Next, the tracker measures the control points to transform into the part coordinate system. Once the tracker is transformed, the mirror vector can be measured using the tracker and reported in the part coordinate frame. The only lines of sight required are to the mirror to be measured and to a sufficient number of SMRs to adequately transform the tracker into the part coordinate system. This method also allows the distinct advantage of taking angular data from collimation and 3D data using a single tracker from one position. This will yield the same data as the theodolite method described in the previous paragraph with one instrument instead of three, and only line of sight is required to the mirror to be measured and the control points on the part structure.


Figure 13:
Laser tracker measurement of a mirror with respect to a part

References
1. Spatial Analyzer is a product of New River Kinematics of Williamsburg, Virginia.
2. The Leica 840 laser tracker is a product of Hexagon Metrology of North Kingstown, Rhode Island.
3. Spatial Analyzer and USMN are products of New River Kinematics of Williamsburg, Virginia.

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About The Author

Robert P. Elliott Jr.’s default image

Robert P. Elliott Jr.

Robert P. Elliott Jr. is a systems integration test engineer at Lockheed Martin.