National Calibration Facility for Retroreflective Traffic Control Materials (2005)

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CHAPTER 3 GONIOMETER CHARACTERISTICS The heart of the new Center for High Accuracy Retroreflection Measurements is a high- precision, six-axis goniometer designed and built by Dynamic Structures and Materials, LLC (DSM) shown schematically in Figure 15 and pictured in Figure 16. The axes shown in Figure 15 are all indicated for movement in the positive direction, and the source and detector lie in the horizontal plane (parallel to the Y axis). The goniometer is attached to a carriage on a precision rail assembly, which allows the illumination distance to be varied from 3 m to 33 m. The X’, Y, Z, β1’, β2’, ε’axes are all under closed-loop control, while the X axis is positioned manually. The ε’axis rotation stage is attached to a short manual translation stage on the Z axis stage to allow adjustment for sample thickness. Samples are attached to a plate with a vacuum mount system on the ε’axis rotation stage. Rotation of the β1’ frame allows both signs (diameters up to 1 m) and pavement markings to be accommodated on the goniometer, as well as the detector. The goniometer is rated to hold 25 kg and remain in tolerance. The specifications for wide range of motion, high angular resolution, and accuracy resulted from the desire to use the equipment as a research instrument as well as a calibration device. The goniometer system requirements determined from the documentary standards are listed in Table 6 and the final specifications are presented in Table 7. The NIST goniometer is not a CIE goniometer as described in CIE Publication 54.2 “Retroreflection: Definition and Measurement.” The CIE goniometer is defined as having the first or fixed axis perpendicular to the plane containing the observation axis and the illumination axis. The NIST goniometer was chosen to have the first axis parallel to the observation half- plane because of stability. The observation half-plane in the NIST retroreflectometer is horizontal to the floor instead of vertical. The axis labels for the NIST goniometer are β1’, β2’, and ε’. The transformation equations to set the NIST goniometer based on CIE goniometer coordinates are, ( )12'1 sincosarcsin βββ = (2) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = 1 2' 2 cos tan arctan β ββ (3) 21

( )21' sintanarctan ββεε −= (4) GENERAL CONSTRUCTION REQUIREMENTS All frames and brackets were made of aluminum to keep the weight to a minimum. Square aluminum frames were pinned and bolted together with aluminum epoxy. The cross- section dimensions and other bracing were designed to provide frame stiffness that is consistent with the resolution and accuracy specified for each axis. Steel was used for keyed shaft connections and steel thread inserts were used on aluminum parts where frequent disassembly and re-assembly is expected such as the vacuum mount. Exposed surfaces were painted flat black. Surfaces that could not be painted were covered with black aluminum sheeting that was glued to the surface. All cables and vacuum lines were cleanly routed and bundled with appropriate strain relief for the full range of motion. GONIOMETER COMMUNICATIONS A remote PC controls the motion of the system's axes through custom software written under National Instruments' LabWindows. MXI-3 technology, a PCI master/slave system, is used to couple the remote PC via a fiber optic data link running the length of the range to a National Instruments PXI-1002 chassis incorporated into the goniometer's structure. The fiber optic along with a power cable and future cabling are bundled in a cable holder. The cable holder rolls with the goniometer as it moves along the rails. The PXI chassis also houses two NI PXI-7334 stepper motor motion cards and a NI PXI-8420/4 card to provide an interface for RS- 232 communication with the system's environmental monitor (temperature and relative humidity) and 3 depth gauges used in the alignment tool. Communication with the 30 m encoder is achieved through a SSI/RS232 interface connected to a COM port on the remote PC. DSM also incorporated an enclosure in the system's structure to protect the stepper motor drives and two NI UMI-7764 Universal Motion Interfaces. The UMI boxes provide connections for step and direction signals from the motion controllers to the stepper motor drives as well as connections for the majority of the position encoders. Emergency-stop switches installed on the goniometer frame in easy reach of any bystander are routed to relays that disable power to the system's motors. A schematic of the communication system is shown in Figure 17. 22

THREE AXES OF ROTATION The goniometer consists of a yaw frame sized to rotate just within an external pitch frame. The internal yaw frame is the β1’ axis and is designed so that the frame, bearing mounts, and counterweights do not obscure the frontal view of the specimen through its entire ± 95° of rotation (with the β2’ axis near zero). The β2’ axis, the external pitch frame, is mounted in a U- frame, which forms the base that sits on the rail system. Attached to the vertical translation axis on the yaw frame is a rotation angle axis, ε’, having ± 185° of rotation shown in Figure 18. Its axis is perpendicular to and intersects with the β1’ and β2’ axes when the Z (vertical) stage is positioned at its zero location. The accuracy of the goniometer's motion control system over such large motion ranges is made possible through the use of high-end motion components and sensors. Five-phase Vexta Nanostep® CFKII 569 stepping motors were chosen to produce precision motion for the three rotational axes of the goniometer. When set at the smallest step angle, the five-phase Vexta stepper motors have 125,000 steps per revolution. DSM coupled the stepper motors to high accuracy harmonic drives with a 160:1 gear reduction that yielded a potential resolution of greater than 20 million steps per revolution. DSM selected HD Systems harmonic drive gear reducers to couple with the stepping motors. The HD Systems CSF-2UH gearheads have virtually zero backlash and come with built in roller bearings to support the output shaft. The HD harmonic drives provided dramatic increases in stepper motor holding torque to control the rotation of the large goniometer support frame with authority. Using rotary encoders to provide position feedback, actual “closed-loop” minimum step size for the three rotational axes was less than 0.0002 degrees. Limit switches were incorporated into the frame to protect each axis against overtravel by disabling signals to the respective axis' motor. The encoders selected for the three rotary axes are from the Mercury 2000 family of high precision encoders from MicroE Systems, Inc. The optical encoders use glass-scales with interpolator electronics that enable up to 4.19 million counts per revolution. MicroE Systems precisely mounted the glass scales to DSM’s custom-designed encoder hubs. The encoders' small read heads were easily incorporated into the goniometer's structural design, and their robust tolerance to misalignment made adjustments during installation fast and simple. To determine if the rotary axes met the contract specifications, the goniometer was positioned at 30 m. A mirror was securely mounted to the vacuum mount. A collimated laser 23

originating near the source aperture was reflected by the mirror to a 20 cm x 25 cm target ruled in millimeters. The position of the laser spot on the target could be measured accurately to < 1 mm vertically and horizontally. Thus, the measurement uncertainty is equal to 0.001° at 60 m; therefore, the β1’ and β2’ movements meet specifications. Initially the epsilon prime axis did not meet specifications. When set up in the pavement marking geometry configuration, rotation of ε’ resulted in a significant (>0.02°) deviation of the reflected laser spot from a vertical line. Simultaneously with the sudden deviation, the encoder lost thousands of counts, such that the rotational positioning accuracy of ε' was also out of specification (>0.02°). The ε’ harmonic drive was disassembled, cleaned and reassembled by DSM. When tested again, the problems were no longer observed, and the ε’ axis could be accurately positioned to within 0.001°, just as β1’ and β2’. An additional aspect of the rotary axes is that when an axis rotates, the center point should not move outside of a sphere of confusion. The contract specification stated “The intersection of β1’, β2’ and ε’ axes shall not move outside of a sphere that has a diameter of 0.5 mm when all three axes are rotated.” A method of locating the depth and height of the β1’, β2’ and ε’ axis intersection yielded a measurement of the sphere of confusion, which was within specifications. The method follows: 1. A straightedge was temporarily clamped to the β2’ frame such that the top of the straightedge was coplanar with the β2’ center of rotation. The distance from the straightedge face to the β2’ pivot points was 73.30 mm. 2. The depth stage was set to position the center of the ball tool 73.30 mm from the straightedge face. Figure 19 shows a picture of the ball tool mounted on the goniometer. 3. The Z-axis height was set by visually aligning the ball center to the top of the straightedge, using a spirit level as a guide. 4. Dial indicators were attached to the alignment tool to measure ball run-out in the vertical (Z direction) and horizontal (X direction) plane. 5. With the β2’ frame near vertical and the β1’ frame near β = 0°, ε’ run-out was measured to be 0.00 mm in the vertical plane and ± 0.06 mm in the horizontal plane. 24

6. The proper position of the depth stage was fine-tuned by iteratively moving the β1’ stage throughout its motion range and adjusting the depth to minimize the displacement of the ball in the vertical plane. The resultant run-out measured ± 0.06 mm (vertical) and ± 0.08 mm (horizontal). 7. Similarly, the optimum Z stage position was found by moving the β2’ frame throughout its range of motion and adjusting Z to give minimal displacement in the horizontal plane. The resultant run-out measured ± 0.06 mm (vertical) and ± 0.17 mm (horizontal). In conclusion, for any one-axis move, the sphere of confusion is an ellipsoid having a height in the Z direction of 0.35 mm and a width in the X direction of 0.12 mm. Both dimensions are less than the 0.5 mm maximum specified. The sphere of confusion specified in the contract with the goniometer designer was the smallest Project 05-16 could afford. The wobble measured in the rotation axis, ε’, causes a deviation in setting the β1’ and β2’ axes. Also, the vacuum mount that is affixed to the collet on the rotation drive is not exactly perpendicular to the illumination axis. Therefore, as the rotation axis turns slight corrections are applied to the β1’ and β2’ axes. The correction curve for these corrections is repeatable for the particular vacuum mount and is addressed in the uncertainty calculations of the absolute alignment chapter. THREE AXES OF TRANSLATION The accuracy of the goniometer's translation systems is made possible through the use of high-end motion components and sensors. Two-phase Vexta CSK 268MAT stepping motors were chosen to produce precision motion for driving the linear axes of motion. The Z-axis is a linear translation stage mounted directly in the β1’ frame for moving the sample up and down. The X’ and Y-axes are linear translation stages incorporated into the goniometer base. The X’- axis moves the goniometer along the illumination axis and the Y-axis moves the goniometer perpendicular to the illumination axis. The Y and Z-axes are operated in closed loop mode with optical encoders to provide positional accuracy of better than 0.05 mm. The X’ stage requirements are less stringent. Open loop control provides positional accuracy of 0.25 mm. Linear movement of Y and Z-axes was validated using a Mitutoyo dial indicator modified to accept various standardized extensions up to 610 mm. In the case of the Z-axis, 25

accurate readings could not be attained by this method. Therefore motion was measured using the Leica 3000 theodolite positioned 3 m from the sample holder face. Results of the validations are summarized in Table 7. SAMPLE HOLDER AND DEPTH POSITIONING A vacuum mount holds the samples in place, as described below. It consists of six 8 cm diameter vacuum cups arranged to hold various shaped signs and road marking material as shown in Figure 20. The vacuum system pulls the specimen against machined rails so that the sample is positively registered to a fixed depth. The vacuum cups are sized to hold about 10 kg. This represents a safety factor of two over the expected maximum sample weight. The vacuum system is designed so that individual or sets of vacuum cups can be selected or deselected quickly by the machine operator. The vacuum source is routed to the sample holder plate as to allow free movement of the full range on all the other axes. A manually adjustable stage connects the sample holder to the β1’ frame. The purpose of the manual axis is to adjust the depth of the sample holder plate so that the surface of the sample is coplanar with the β1’ and β2’ axes to minimize any offset distance, which would cause errors in the measurement. A precision alignment fixture is used to determine when the surface of the sample is properly positioned (Figure 21) using a four step procedure. 1. A front surface mirror is fixed to the back side of a precision jig plate 30 cm x 30 cm x 1 cm in size, having a flatness and parallelism of 25 µm. This assembly is referred to as the β alignment plate. The β alignment plate is placed in the sample position, and the laser beam that defines the illumination axis is reflected back at the source. The β1’ and β2’ axis are adjusted to center the reflected beam within 0.002° of the source aperture. This step determines the β(0°,0°) position of the sample plate. This alignment procedure is elaborated on in the Absolute Alignment chapter. 2. The alignment fixture is mounted to the goniometer base and the front plane of the β alignment plate is measured using three digital dial indicators in a triangular arrangement. 3. The sample plate is retracted by a translation of the depth stage, the β alignment plate is removed, and a new sample is mounted. 26

4. The sample front surface is brought up to the dial indicators. Adjustment of the depth and β1’ and β2’ (if necessary) position the retroreflective surface of the sample coplanar with the β1’ and β2’ axes. The detector system mounts directly onto the vacuum mount using pins and bolts. The detector system is placed at the center of the goniometer for source characterization and calibrations procedures. The X’, Y and Z-axes are programmed to automatically center the detector aperture on the illumination axis. THE RAIL SYSTEM AND DISTANCE DEPENDENCE The rail system supports the horizontal linear axis and the goniometer. It extends from 3 m to 33 m from the source aperture and is operated manually. The system is composed of two 19 mm diameter chrome plated rails 141 cm apart continuously supported by inverted T-shaped aluminum, which is then supported by posts that are anchored into the concrete floor with epoxy. A sample of the rail section is shown in Figure 22. The goniometer and rail system has a magnetic tape encoder with a resolution of 10 µm and an accuracy of 0.3 mm. Once the goniometer is manually put in a position it is locked into place. Additionally, a linear drive is mounted to the clamping blocks to provide ± 46 cm of automated positioning along the illumination axis. Installing the rail system was accomplished over several days. Following the center marks and hole outlines previously laid down, a 2.5 cm diameter hole was drilled to a depth of 4 cm to 5 cm at each of the 100 positions. A 12.7 cm diameter hole was cut through the linoleum using a carbide-tipped hole saw. The linoleum was removed using an air chisel. The chisel was also used to remove adhesive and roughen the concrete surface for better adhesion of the epoxy grout. The left rail, as viewed from the source end, was installed first. The rail was tipped on its side, and 6.4 cm studs were installed fully, and then backed out one full turn to allow for height adjustment. A support consisting of wood blocks and tapered shims was positioned every 60 cm along the rail length. A 10 mm x 10 mm retroreflection target was positioned on a pillow block over the rail center. Using a Leica 1100 total station (a theodolite with electronic distance measuring capabilities) leveled to ± 2 arc seconds, the height of the target at each position was set to 133 mm ± 0.5 mm vs. an arbitrary reference. The longitudinal position of the rail was 27

adjusted a few millimeters to prevent some of the studs from contacting the sides of the holes. In the lowest part of the floor, 7.6 cm or 8.9 cm bolts with or without heads were used in place of the studs, to ensure that the bolts were at least 1.3 cm below the concrete surface. After positioning the rail side-to-side to within 0.5 mm of 0° ± 2 arc seconds and verifying the height, the studs were anchored with Drylock hydraulic cement in five sections of ten holes each. Position of the rail was verified by two independent methods. A Leica 3000 theodolite was positioned directly over the rail near the longitudinal midpoint. Rail height was measured using a vertical stick placed at 5 m intervals. The rail height was verified to be flat within ± 0.5 mm over the 30 m. The deviations were random, not indicating a slope. The bow of the rail was measured to be less than 1 mm from end to end. In the second method the Leica 1100 was positioned over the rail midpoint, and height of the target on the pillow block was measured. A variation of less than ± 1 mm was observed. Based on these measurements we conclude the rail is straight and level within ± 1 mm over the 30 m distance. Following position verification, the support pads were permanently located by pouring a Five Star rapid epoxy with aggregate foundation. The second rail was installed in an identical fashion with the following exceptions: The studs were fully screwed in, as no adjustments were necessary in the case of the first rail. The side-to-side variation was held to within 1 mm (not 0.5 mm) of 0° ± 2 arc seconds and not verified. This is acceptable as the goniometer base floats on the second rail pillow blocks, allowing up to ± 3.2 mm side-to-side movement. The height was again held to 133 mm ± 0.5 mm. Before the goniometer was mounted on the rail system, a magnetic tape was installed on angle aluminum that runs the length of the rail system. The magnetic encoder head is mounted on the goniometer and has a resolution of 10 µm and an accuracy of 0.3 mm. An issue with the magnetic tape is applying the proper tension during the application process. The improper amount of tension introduces a systematic error in the magnetic tape. A correction curve was calculated by comparing the Leica 1100 theodolite to the readings of the magnetic encoder. The data is presented in Figure 23. The magnetic tape was stretched 13 mm over the 35 m length. The uncertainty of the calibration curve is dependent on the standard uncertainty of the theodolite, which is ± 2. 5 mm. 28

The overall uncertainty of the distance is a combination of the calibration curve and the initial absolute calibration of the magnetic encoder, which involves the accuracy or reproducibility of the magnetic encoder, the alignment tool uncertainty, the source aperture reference post uncertainty and the uncertainty of the 3 m vernier owned by NIST. Two researchers operate the vernier by one holding the fixed end at the source aperture reference post and the other sliding the adjustment inline with the front surface of the β alignment plate. The machining tolerance in the source reference post is 0.025 mm, which comes from the machine shop capabilities. The electronic dial indicators on the alignment fixture are referenced to this surface. The uncertainty budget for setting the absolute position of the magnetic encoder is presented in Table 8. The total uncertainty budget for the illumination distance of a sample is summarized in Table 9, and the expanded uncertainty is less than the requirement of 10 mm. The sensitivity coefficient for the illumination distance was determined experimentally and is shown in Figure 24. The sensitivity coefficient does not follow the inverse square law because the projection source is not a point source. The overall relative expanded uncertainty for RL due to the uncertainty in the illumination distance is 0.03 % (k=2). At the same time the theodolite was used to measure the distance, the vertical and horizontal deviation of the sample holder was determined. The vertical deviation of the goniometer system's center over the 30 m rail length is within ± 0.75 mm, and horizontal deviation of the center is within ± 1.0 mm. The data for these measurements are shown in Figures 25 and 26. Calibration curves were derived from this data. The contribution of uncertainty to the overall uncertainty budget for RL is presented in the Absolute Alignment Chapter. The shiny rails caused scattered light depending on the position of the sample. Two baffles were constructed that sit on the rail system. They are positioned at appropriate distances to block scattered light, yet do not interfere with the measurement. The baffles also lift off the rail system. Another significant source of scattered light was the back wall of the facility, especially when the goniometer β1’ frame is rotated to measure pavement marking material. An approximately 3 square meter beam stop was constructed from two glossy black acrylic panels. The panels measure 122 cm x 122 cm each and are attached to movable supports so they can be positioned to completely capture the source beam beyond the end of the rail. The angle of the panels is adjustable to minimize back reflection. With the beam stop in place, the source beam 29

terminus is nearly invisible under even the darkest room conditions. Additionally, black carpeting was installed between the rails to eliminate reflection from the floor tile. The black carpeting has a visible reflectance value of < 1 % (400 nm to 700 nm) measured by a portable spectrometer. 30