Daniel S. Sawyer

ASME B89.4.19 Performance Evaluation Tests and Geometric Misalignments in Laser Trackers.

Small and unintended offsets, tilts, and eccentricity of the mechanical and optical components in laser trackers introduce systematic errors in the measured spherical coordinates (angles and range readings) and possibly in the calculated lengths of reference artifacts. It is desirable that the tests described in the ASME B89.4.19 Standard [1] be sensitive to these geometric misalignments so that any resulting systematic errors are identified during performance evaluation. In this paper, we present some analysis, using error models and numerical simulation, of the sensitivity of the length measurement system tests and two-face system tests in the B89.4.19 Standard to misalignments in laser trackers. We highlight key attributes of the testing strategy adopted in the Standard and propose new length measurement system tests that demonstrate improved sensitivity to some misalignments. Experimental results with a tracker that is not properly error corrected for the effects of the misalignments validate claims regarding the proposed new length tests.

Measuring Scale Errors in a Laser Tracker's Horizontal Angle Encoder Through Simple Length Measurement and Two-Face System Tests.

We describe a method to estimate the scale errors in the horizontal angle encoder of a laser tracker in this paper. The method does not require expensive instrumentation such as a rotary stage or even a calibrated artifact. An uncalibrated but stable length is realized between two targets mounted on stands that are at tracker height. The tracker measures the distance between these two targets from different azimuthal positions (say, in intervals of 20° over 360°). Each target is measured in both front face and back face. Low order harmonic scale errors can be estimated from this data and may then be used to correct the encoder’s error map to improve the tracker’s angle measurement accuracy. We have demonstrated this for the second order harmonic in this paper. It is important to compensate for even order harmonics as their influence cannot be removed by averaging front face and back face measurements whereas odd orders can be removed by averaging. We tested six trackers from three different manufacturers. Two of those trackers are newer models introduced at the time of writing of this paper. For older trackers from two manufacturers, the length errors in a 7.75 m horizontal length placed 7 m away from a tracker were of the order of ± 65 μm before correcting the error map. They reduced to less than ± 25 μm after correcting the error map for second order scale errors. Newer trackers from the same manufacturers did not show this error. An older tracker from a third manufacturer also did not show this error.

A novel artifact for testing large coordinate measuring machines

We present a high-accuracy artifact useful for the evaluation of large CMMs. This artifact can be physically probed by the CMM in contrast to conventional techniques that use such purely optical methods as laser interferometers. The system can be used over large distances; for example, over 4 meters, with an uncertainty of less than one part per million. The artifact is relatively inexpensive, robust for use in reasonable industrial environments, and significantly reduces testing time over traditional step gauge measurements.

Assessing ranging errors as a function of azimuth in laser trackers and tracers

Tilt and radial error motion of a laser tracker head as it spins about the two rotation axes result in small but measurable ranging and angle errors. The laser tracer, on the other hand, measures range with respect to the center of a high quality stationary sphere. It is therefore not expected to be influenced by the radial error motions of the carriage that carries the optics and the source, but the form error of the reference sphere and possibly the eccentricity in its placement with respect to the circular path traced by the carriage will be contributors to the ranging errors. In this paper, we describe experiments to assess the magnitude of these ranging errors as a function of the azimuth angle in different laser trackers and a laser tracer.

Development of tools for measuring the performance of computer assisted orthopaedic hip surgery systems

In the late seventies a sensor was invented, which could track the movement of athlete body parts. In the early eighties an improved version of this sensor was introduced, by a group of NIST researchers, for the calibration and the performance testing of industrial robots. In the late eighties people experimented with the use of these sensors for human brain operations and in the early nineties these sensors were introduced to orthopaedic operations and the field of Computer Assisted Orthopaedic Surgery (CAOS) was born. Although significant progress has been made in the design and use of these sensors for medical applications, there are still sources of accuracy errors that must be addressed. This paper describes our work on the development of tools for the calibration and performance testing of CAOS systems, which can be used inside operating rooms.

Performance evaluation of laser trackers

The American Society for Mechanical Engineers (ASME) recently released the ASME B89.4.19 Standard [1] on performance evaluation of spherical coordinate instruments such as laser trackers. At the National Institute of Standards and Technology (NIST), we can perform the complete set of tests described in the Standard, and have done so for a variety of laser trackers. We outline the tests described in the Standard, discuss our capabilities at the large-scale coordinate metrology group, and present results from B89.4.19 tests conducted on a few trackers. We also outline an analysis approach that may be used to evaluate the sensitivity of any measurement, including the tests described in the B89.4.19 Standard, to different geometric misalignments in trackers. We discuss how this approach may be useful in determining optimal placement of reference lengths to be most sensitive to different geometric misalignments.

Evaluation of a laser scanner for large volume coordinate metrology: a comparison of results before and after factory calibration

Large volume laser scanners are increasingly being used for a variety of dimensional metrology applications. Methods to evaluate the performance of these scanners are still under development and there are currently no documentary standards available. This paper describes the results of extensive ranging and volumetric performance tests conducted on a large volume laser scanner. The results demonstrated small but clear systematic errors that are explained in the context of a geometric error model for the instrument. The instrument was subsequently returned to the manufacturer for factory calibration. The ranging and volumetric tests were performed again and the results are compared against those obtained prior to the factory calibration.

A Low-Cost Fiducial Reference Phantom for Computed Tomography

To detect the growth in lesions, it is necessary to ensure that the apparent changes in size are above the noise floor of the system. By introducing a fiducial reference, it may be possible to detect smaller changes in lesion size more reliably. We suspend three precision spheres with a precision structure built from pieces from a popular children’s building toy. We measure the distances between the centroids of the structures three ways; namely, with a high-precision mechanical method, micro computerized tomography, and medical computerized tomography. The three methods are in agreement, and also agree with the design values for the structure. It is also possible to pick a threshold so that the three spheres have their nominal volumes in the medical computerized tomography images. The use of volumetric measures allows the determination of lengths to much less than the voxel size using materials which have x-ray properties within the range of the human body. A suitable structure may be built with a very small parts cost.

Methods and Considerations to Determine Sphere Center from Terrestrial Laser Scanner Point Cloud Data

The Dimensional Metrology Group (DMG) at the National Institute of Standards and Technology (NIST) is performing research to support the development of documentary standards within ASTM E57 committee. This committee is addressing the point-to-point performance evaluation of a subclass of 3D imaging systems called Terrestrial Laser Scanners (TLSs) which are laser-based and use spherical coordinate system. This paper discusses the usage of sphere targets for this effort and methods to minimize the errors due to the determination of their centers. The key contributions of this paper include the methods to segment sphere data from TLS point cloud and the study of some of the factors that influence the determination of sphere centers.

A Model for Geometry-Dependent Errors in Length Artifacts

We present a detailed model of dimensional changes in long length artifacts, such as step gauges and ball bars, due to bending under gravity. The comprehensive model is based on evaluation of the gauge points relative to the neutral bending surface. It yields the errors observed when the gauge points are located off the neutral bending surface of a bar or rod but also reveals the significant error associated with out-of-straightness of a bar or rod even if the gauge points are located in the neutral bending surface. For example, one experimental result shows a length change of greater than 1.5 µm on a 1 m ball bar with an out-of-straightness of 0.4 mm. This and other results are in agreement with the model presented in this paper.