National Calibration Facility for Retroreflective Traffic Control Materials (2005)

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CHAPTER 5 ABSOLUTE ALIGNMENT The most critical aspect of the NIST Reference Retroreflectometer is the alignment of the three components: the source optical system, the goniometer and the detection system. The following sections describe the methods for aligning the components and the effect on the four angles used for defining the retroreflective geometry. The expected uncertainty from these alignment procedures is calculated. SETTING THE ILLUMINATION AXIS The first axis that must be defined is the illumination axis. The illumination axis is defined as the axis from the retroreflector point of reference pointing to the source point of reference. The points of reference are defined as the center of the goniometer and the source aperture. Unique to the NIST retroreflectometer is the capability to move the goniometer along a rail system, varying the source to sample distance from 3 to 32 m. The left rail (when looking at the sample face) is the reference rail and determines the horizontal position of the goniometer center. As discussed in Chapter 3, the goniometer center is preserved within ± 1 mm upon translation along the 30 m rail system. Our goal is therefore to set the illumination axis collinear with the goniometer center path. A variable diameter iris is placed on the goniometer sample holder and centered on the goniometer center. The goniometer is positioned at the minimum source-sample distance, and the source light is centered on the iris by adjusting the vertical table height and the horizontal position of the source rail. The goniometer is then moved to the maximum distance and the adjustment process repeated. This process is repeated iteratively until no further adjustments to the source position are required. ABSOLUTE NIST ENTRANCE ANGLE COMPONENTS ALIGNMENT The absolute alignment of the NIST entrance angle components, β1’ and β2’, relies on the light source that defines the illumination axis described previously. A 30.48 cm square precision flat (± 0.0173 mm, uncertainty in parallelism) aluminum plate with a small hole is mounted against the hard stops on the goniometer sample holder, using tooling pins to locate the center of the hole at the center of the goniometer. A front surface mirror is pressed against the flat back of 39

the aluminum plate. Thus the mirror is plane parallel with the goniometer sample-mounting surface. The reflected source beam can be centered on the source aperture within 1 mm by adjusting the pitch and yaw of the goniometer in fine increments. The alignment tool is then mounted and the micrometers are set to zero. The uncertainty for the NIST entrance angle components is reduced to the items used to calibrate not procedural transfers or measured quantities. The following equation, MGLCA +++= (6) is used to model the absolute calibration of the alignment tool, where C is the uncertainty comparing the front surface of the mirror to the front surface of the precision flat aluminum plate, L is the angular contribution of the source alignment procedure, G is the angular contribution due to the goniometer, and M is the uncertainty of the micrometer readings. The standard uncertainty of the micrometers is 0.0115 mm across a typical sample distance of 210 mm, which works out to be a standard uncertainty of 0.0063º. Table 12 shows the uncertainty budget for setting the alignment tool. The uncertainty of setting arbitrary NIST entrance angle components is composed of the alignment tool uncertainty, A, the uncertainty of mounting a sample, S, and the resolution of the goniometer, ∆β, as shown in the following model and Table 13, β∆β ++= SA'# . (7) Therefore, for any arbitrary NIST entrance angle components the absolute uncertainty will be ± 0.020° (k=2). To convert the NIST entrance angle components to the CIE goniometer system entrance angle components the following equations are used, ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ' 2 ' 1 1 cos tan arctan β ββ , and (8) ( )'2'12 sincosarcsin βββ = (9) when –90º < β1’ < 90º and –90º < β2’< 90º. The uncertainty for this conversion is presented in Table 14 and Table 15. The uncertainty varies for the chosen angles but is on the order of ± 0.020° (k=2) for angles that are not at the extreme of the goniometer motion. To set the absolute entrance angle for pavement marking samples, a precision 90° (± 0.00278°) reflective alignment cube is mounted against the sample hard stops. The reflected source beam is positioned on the source aperture as described above to set the absolute entrance 40

angle to 90°. The uncertainty of the alignment cube is 0.001604° and the type of evaluation is B(R), which stands for a Type B evaluation derived from a rectangular distribution. The specification on the alignment cube is 0.00278°, which is a tolerance following a rectangular distribution. To approximate a rectangular distribution as a normal distribution, the tolerance is divided by the square root of three, as shown in the GUM. The other difference between setting signage versus pavement marking material is the distance between the micrometers on the alignment tool. The standard uncertainty of the micrometers is 0.0115 mm across a typical sample distance of 145 mm for β2’ and 600 mm for β1’, which works out to be a standard uncertainty of 0.0091º and 0.0022º, respectively. By substituting these uncertainty values into the tables, the expanded uncertainties for the CIE goniometer parameters are determined to be 0.0069° (k=2) for β1 and 0.0006° (k=2) for β2. ABSOLUTE OBSERVATION ANGLE ALIGNMENT The next parameter to set is the position of the observer aperture. Ideally, if the observer aperture could be positioned in the same physical space as the source aperture, the encoders for the observation angle positioner could be read and the observation angle equal to zero (α = 0) would be determined. Since this is not physically possible, the observer aperture must be positioned in a known location and measured to determine its exact location. Figure 36 shows a drawing of the source and observer aperture holders. We presently use either 26 mm or 43 mm diameter apertures. A variety of apertures sizes can be constructed to match the customers’ requests. The important aspects of the aperture designs are the reference pins at the top of the holders, which are machined to position the outside edge of the pin at the center of the aperture (to within 0.025 mm) and in the aperture plane (shown in the top view of Figure 36). The first stage to be set absolutely is the rotation stage. A collimated laser is positioned at the goniometer center, or reflected from the center of the β alignment mirror. The laser originates along the illumination axis, at the sample point of reference. The laser or reflected beam is aimed at the detector by a defined movement of the goniometer yaw axis. The detector mounting plate is fitted with a 4 mm pinhole in place of the detector aperture. An aluminum cylinder, having the same diameter as the photopic detector package and equipped with a quadrature detector at its axis, is mounted in place of the photopic detector. A computer code positions the rotation stage such that the output of the quadrant detector is balanced. The 41

rotation stage is thus aligned with the observation axis to within a standard uncertainty of ± 0.008°. To calibrate the small stage, the observer aperture is positioned 1 cm behind the source aperture. To approximately zero the long stage a simple photodiode is positioned toward the goniometer viewing the aperture source such that only half the photodiode is illuminated. The edge of the source aperture is imaged on the photodiode. The long stage is moved across the source aperture until the signal on the photodiode becomes constant. At the apex of the curve the observer aperture is directly behind the source aperture. A micrometer measures the distance between the aperture faces. With this measurement, the small stage is absolutely calibrated for position to the uncertainty of its encoder (± 0.014 mm) and the uncertainty of the reference pins (± 0.014 mm) for an expanded uncertainty of ± 0.050 mm (k=2). Another issue is that since the observer aperture is not positioned at the center of the rotation stage, the rotational movement causes a change in the position not just the viewing angle. To decouple this movement the position of the rotation center must be determined. To determine the center of rotation, the observer aperture is moved roughly to the center. A computer read micrometer is positioned against the reference pin. The 20 cm stage is moved until the micrometer reading does not change when the rotation stage is moved. By knowing the distance the reference pin is away from the center of rotation, the position change due just to rotation can be calculated. To calibrate the long stage, the long stage moves the observer aperture 5 cm away from the source aperture and the small stage positions the observer aperture reference pin at the center of rotation. A micrometer measures the distance between the reference pins. With this measurement the long stage is absolutely calibrated for position to an expanded uncertainty of ± 0.050 mm (k=2). The illumination distance is measured by a magnetic tape that is mounted to the goniometer and the rail system. The observation distance is initially set by the magnetic tape and the absolute position of the small stage. The observation distance is then calculated by the movement of the small, long, and rotation stages. By knowing the illumination distance, the observation distance and the aperture separation, the absolute observation angle can be calculated by the law of cosines. The aperture separation is calculated using the equation, )2cos(2 22 rxyxyc −−+= π , (10) 42

and Table 16 shows a typical uncertainty budget. The observation distance is calculated using the equation, )(cos)sin( 222 rxsyrxd −+−= , (11) and Table 17 shows a typical uncertainty budget. This equation comes from solving the law of cosines, )2cos()(2)( 222 rydxxyds −+−++= π (12) for the observation distance, d. In this case, the observation distance cannot be solved using a right triangle because the 90° angle formed by the illumination axis and the long stage has uncertainty that is not accounted for in an equation using d = x/sin(r) - y. The arbitrary setting of the observation angle is calculated using the equation, ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ = − sd cds 2 cos 222 1α , (13) and Table 18 shows a typical uncertainty budget. The observation angle is set to an expanded uncertainty of ± 0.00037° (k=2). ABSOLUTE ROTATION ANGLE ALIGNMENT The procedure reported here for setting the absolute rotation angle (ε) differs significantly from that described in the Phase I report. We acquired a theodolite, which allows the use of a method that is significantly easier, less prone to operator error, and still retains an acceptable uncertainty. The rotation angle is the angle of the datum axis relative to the observation half-plane. We use the earth’s gravitation field as our point of reference to set the observation half plane and also to measure the datum axis thus determining the absolute rotation angle. The procedure follows: First a theodolite is positioned approximately 15 m from the detector stage and set level versus gravity to ± 0.00055º. The vertical position of the source aperture is determined. The detector aperture at the minimum observation angle is set equal to the source aperture in the vertical plane. The detector is moved to the maximum observation angle and the vertical position determined. The source table legs are adjusted to minimize the vertical difference. A limiting uncertainty of ± 0.48 mm in setting the detector aperture is the alignment of the theodolite crosshair on the detector aperture target. This represents an angular uncertainty in the 43

observation half-plane of 0.014°. Leveling of the table did not significantly affect the position of the illumination axis because at αmin the detector aperture is directly over the fixed legs of the table, and only a 1 mm adjustment in the legs under the aperture near αmax was required. This part of the procedure is only required once, unless the source table is moved. The second step in this alignment procedure is to measure the sample datum axis rotation relative to the gravitational point of reference. The theodolite is now conveniently mounted near the operator station. It is again set level versus gravity to ± 0.00055°. The sample is mounted on the goniometer and the ε axis is simply rotated to line up the datum axis with the optical crosshairs in the theodolite. A schematic of this procedure is shown in Figure 37. This optical alignment can be performed to a standard uncertainty level of 0.18°. The dominating component of the 0.18° is the width of the sample. A wider sample can be set with a smaller uncertainty. The expanded combined uncertainty for setting the rotation angle is ± 0.36° (k=2). Since the NIST goniometer is not the same as a CIE goniometer, a correction is required for the rotation angle. The correction is calculated using the equation, ( )'2'11 sintantan ββε∆ −= . (14) The uncertainty due to this correction is significantly smaller than the uncertainty of ε. 44