National Calibration Facility for Retroreflective Traffic Control Materials (2005)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

D-1 APPENDIX D SAMPLE MAP REPORT REPORT OF CALIBRATION for the Retroreflectance MAP Service for Coefficient of Retroreflected Luminance Reported to: Company ABC Attn.: John Doe 100 1st Avenue Hometown, MD 10000 (See your Purchase Order No. XYZ, dated December 32, 2000) 1. Purpose of Measurements The purpose of this test is to determine the coefficient of retroreflected luminance for two white bead sheeting retroreflectors and a white prismatic cube-corner retroreflector. Also, the luminous transmittance of seven colored glass filters is determined. The NIST and the participating laboratory have accomplished these determinations. Conclusions for these determinations are presented. 2. Materials The retroreflectors and colored filters contained in the MAP package are described in detail in reference [1]. The serial numbers for the retroreflectors is MAP-R11, MAP-R12, and MAP-R13 and are scribed on the back of the retroreflector. The serial numbers for the colored filters is MAP-F11, MAP-F12, MAP-F13, MAP-F14, MAP-F15, MAP-F16, and MAP-F17. 3. Measurement Methods Measurements made by the NIST are described in reference [2]. Measurements made by the participating laboratory were performed using its normal operating procedures.

D-2 4. Results of Measurement The results of the MAP comparison are shown in Tables 1 and 2 for the retroreflectors and Table 3 for the colored glass filters. Since NIST measured the MAP package before and after the participating laboratory made its measurements, three values are reported for each condition. A. Retroreflectors In addition to the angular parameters α, β1, β2, and ε we define some quantities relevant to data analysis in Tables 4 and 5. (1) The quantity R ∆R100 is the upper bound of the uncertainty in R predicted by the uncertainties of the angular parameters expressed as a percent and estimated from data supplied by the participant. (2) The quantity P P R R 3100 δ× is three times the standard deviation of the mean R obtained from repeated measurements by the participant expressed in percent. (3) The quantity L is the uncertainty in R due to aperture centroid (source and receiver), linearity, and color temperature of the source and photopic response of the receiver expressed in percent. (4) The quantity PLAB is the sum of (1), (2) and (3). It is an upper bound of the uncertainty in R due to the participating laboratory and is expressed in percent. (5) The quantity U is the sum of PLAB, PNIST (the upper bound on the uncertainty due to NIST [1]), and a third component which estimates changes in the retroreflectance of the MAP sample due to possible temperature and pressure changes in its environment. (6) The quantity B is the percent change in the measurements made by NIST before and after the measurements performed by the participating laboratory. (7) The quantity D is the percent difference between the NIST average of before and after measurements and the value obtained by the participating laboratory. B. Colored Filters The bounds on the uncertainties of the luminous transmittance values for the colored glass filters are listed in Table 6. (1) The quantity PY 3 δ× is three times the standard deviation of the mean.

D-3 (2) The quantity C is the difference between the Y values obtained by NIST before and after the participating laboratory. (3) The quantity U is the sum of items (1) and (2) and bounds on the uncertainties due to NIST [1]. (4) The quantity D is the difference between the participant values and the NIST values. 5. Conclusion If D>U; then there is a bias. A. Retroreflectors Since D<U in Tables 1 and 2 for both the bead sheeting retroreflectors and the prismatic retroreflector, we conclude that the estimates given by the participant used to obtain M are valid. Therefore, the quantities M are realistic bounds on the participant’s measurement process. B. Colored Glass Filters Since D>U in Table 4 in some cases, we conclude that there exists a bias in three cases. It is necessary for the participant to decide if these biases are of an acceptable level. In the other cases, we conclude that the bias of the participating laboratory is equal to or less than U. Prepared by: C. Cameron Miller Optical Technology Division Physics Laboratory (301) 975-4713 Approved by: Yoshihiro Ohno For the Director, National Institute of Standards and Technology (301) 975-2321 References: [1] C.Miller, NIST Special Publication XXX “Retroreflectance MAP Service for Coefficient of Retroreflected Luminance” (2005). [2] C. Miller, NIST Special Publication 250-XX “Retroreflection Calibration” (2005).

D-4 Table 1 – Results of the pilot intercomparison with Laboratory XX - Beaded. α [°] β1 [°] NIST R before R Laboratory XX NIST R after High Intensity White 0.200 -4.00 4.0854 4.110 4.0048 0.200 20.00 3.8072 3.817 3.7393 0.200 40.00 2.4309 2.407 2.4065 1.500 -4.00 0.1991 0.203 0.1960 1.500 20.00 0.1914 0.196 0.1904 1.500 40.00 0.1371 0.139 0.1342 Engineering White 0.200 -4.00 1.6180 1.626 1.5572 0.200 20.00 1.2014 1.230 1.1522 0.200 40.00 0.3491 0.362 0.3317 1.500 -4.00 0.1340 0.133 0.1291 1.500 20.00 0.1245 0.125 0.1195 1.500 40.00 0.0776 0.0787 0.0744

D-5 Table 2 – Results of the pilot intercomparison with Laboratory XX - Prismatic (ε = 0°) α [°] β1[°] β2[°] NIST R before R Laboratory XX NIST R after Prismatic Reflector 0.500 0.00 0.00 0.9042 0.915 0.9163 0.500 -10.00 0.00 0.8820 0.873 0.8870 0.500 10.00 0.00 0.8548 0.864 0.8585 0.200 0.00 0.00 5.5970 5.704 5.5657 0.200 -10.00 0.00 4.7419 4.930 4.7694 0.200 10.00 0.00 4.7238 4.786 4.6381 0.500 0.00 -20.00 0.3690 0.421 0.3311 0.500 -10.00 -20.00 0.2949 0.333 0.2825 0.500 10.00 -20.00 0.3080 0.325 0.2813 0.200 0.00 -20.00 2.1500 2.408 1.9783 0.200 -10.00 -20.00 1.9689 2.196 1.8271 0.200 10.00 -20.00 2.0741 2.196 1.8842 0.500 0.00 20.00 0.4284 0.425 0.3766 0.500 -10.00 20.00 0.3114 0.300 0.3044 0.500 10.00 20.00 0.3717 0.362 0.3167 0.200 0.00 20.00 2.8327 2.814 2.4938 0.200 -10.00 20.00 2.0371 1.960 1.9794 0.200 10.00 20.00 2.5243 2.504 2.2998

D-6 Table 3 - Results of the pilot intercomparison with Laboratory XX – Filters Filter NIST Y before Y Laboratory XX NIST Y after MAP-F11 0.01300 0.01338 0.01317 MAP-F11 0.06384 0.06270 0.06419 MAP-F11 0.67456 0.68900 0.67611 MAP-F11 0.79876 0.80600 0.78694 MAP-F11 0.35934 0.36800 0.35723 MAP-F11 0.19549 0.19750 0.19438 MAP-F11 0.00000 0.00001 0.00000 Table 4 – Uncertainty analysis for results with Laboratory XX - Beaded. α [°] β1 [°] ∆R/R [%] 3 x δRP/RP [%] L [%] PLAB [%] U [%] B [%] D [%] High Intensity White 0.200 -4.00 0.86 0.421 2.3 3.581 8.751 0.997 -1.604 0.200 20.00 0.89 0.272 2.3 3.462 8.642 0.900 -1.159 0.200 40.00 1.05 0.432 2.3 3.784 9.004 0.505 0.484 1.500 -4.00 0.95 0.085 2.3 3.335 8.655 0.785 -2.759 1.500 20.00 0.98 0.530 2.3 3.810 9.130 0.262 -2.672 1.500 40.00 0.97 0.124 2.3 3.394 8.534 1.069 -2.470 Engineering White 0.200 -4.00 0.72 0.320 2.2 3.240 8.060 1.915 -2.419 0.200 20.00 0.88 0.422 2.2 3.502 8.422 2.091 -4.521 0.200 40.00 0.90 0.478 2.2 3.578 8.178 2.556 -6.345 1.500 -4.00 0.68 0.130 2.2 3.010 7.750 1.863 -1.102 1.500 20.00 0.74 0.139 2.2 3.079 7.899 2.049 -2.459 1.500 40.00 0.89 1.320 2.2 4.410 9.270 2.106 -3.553

D-7 Table 5 – Uncertainty analysis for results with Laboratory XX - Beaded. α [°] β1 [°] β2 [°] ∆R/R [%] 3 x δRP/RP [%] L [%] PLAB [%] U [%] B [%] D [%] 0.500 0.00 0.00 3.109 1.760 2.6 7.469 14.85 -0.665 -0.522 0.500 -10.00 0.00 2.530 0.461 2.6 5.591 13.02 -0.283 1.300 0.500 10.00 0.00 3.772 0.776 2.6 7.148 15.11 -0.216 -0.858 0.200 0.00 0.00 3.200 0.212 2.6 6.012 13.64 0.281 -2.197 0.200 -10.00 0.00 3.918 0.381 2.6 6.899 15.03 -0.289 -3.666 0.200 10.00 0.00 4.199 0.308 2.6 7.107 15.43 0.916 -2.244 0.500 0.00 -20.00 2.899 1.578 2.6 7.077 22.98 5.413 -20.27 0.500 -10.00 -20.00 4.637 2.683 2.6 9.920 26.62 2.148 -15.35 0.500 10.00 -20.00 3.579 2.594 2.6 8.773 23.07 4.531 -10.30 0.200 0.00 -20.00 5.327 1.049 2.6 8.976 22.88 4.159 -16.66 0.200 -10.00 -20.00 11.24 2.738 2.6 16.58 32.88 3.736 -15.70 0.200 10.00 -20.00 9.527 1.447 2.6 13.57 28.47 4.793 -10.96 0.500 0.00 20.00 2.646 3.505 2.6 8.751 20.19 6.435 -5.590 0.500 -10.00 20.00 3.206 3.626 2.6 9.432 22.03 1.137 2.566 0.500 10.00 20.00 2.982 1.651 2.6 7.233 19.03 7.990 -5.171 0.200 0.00 20.00 2.565 2.452 2.6 7.617 16.94 6.363 -5.660 0.200 -10.00 20.00 6.625 2.322 2.6 11.55 23.65 1.437 2.403 0.200 10.00 20.00 5.065 2.383 2.6 10.05 19.89 4.654 -3.812 Table 6 - Uncertainty analysis for results with Laboratory XX - Filters Filter 3 x δYP C U D D>U MAP-F11 0.0001 0.0001 0.0010 0.0003 No MAP-F11 0.0010 0.0002 0.0022 0.0013 No MAP-F11 0.0035 0.0008 0.0050 0.0137 Yes MAP-F11 0.0035 0.0009 0.0050 0.0082 Yes MAP-F11 0.0052 0.0011 0.0071 0.0097 Yes MAP-F11 0.0048 0.0006 0.0058 0.0026 No MAP-F11 0.0000 0.0000 0.0000 0.0000 No

C. Miller, et. al., Project 05-16 Figure 1 – System for specifying and measuring retroreflectors. Illumination axis Observation axis Datum axis Retroreflector axis First axis Second axis α Third axis β1 β1 β2 β2 ε

C. Miller, et. al., Project 05-16 . Figure 2 – Conceptual drawing of the CHARM facility

C. Miller, et. al., Project 05-16 Figure 3 – Presented is a schematic of the Strip Lamp Projection System Strip lamp Aspheric lens Field aperture Projection lens Source aperture

C. Miller, et. al., Project 05-16 0.9994 0.9996 0.9998 1.0000 1.0002 1.0004 1.0006 0 5 10 15 20 25 30 35 40 45 Burning Time (h) N o r m a l i z e d I n t e n s i t y Figure 4 – Shown is the normalized luminous intensity of the strip lamp source over a 45 h period.

C. Miller, et. al., Project 05-16 2853 2854 2855 2856 2857 2858 0 5 10 15 20 25 30 35 40 45 Burning Time (h) C o r r e l a t e d C o l o r T e m p ( K )

C. Miller, et. al., Project 05-16 Figure 5 – Shown is the correlated color temperature of the strip lamp source over a 45 h period. 2853 2854 2855 2856 2857 2858 0 5 10 15 20 25 30 35 40 45 Burning Time (h) C o r r e l a t e d C o l o r T e m p ( K )

C. Miller, et. al., Project 05-16 Figure 6 – Shown is the sensitivity curves for different materials with respect to CCT. 0.997 0.998 0.999 1.000 1.001 1.002 1.003 2835 2840 2845 2850 2855 2860 2865 2870 2875 CCT [K] N o r m a l i z e d R L White Red Yellow Green Blue

C. Miller, et. al., Project 05-16 White /50 360 460 560 660 760Wavelength (nm) R e t r o r e f l e c t a n c e f a c t o r Figure 7 – Shown is the retroreflectance curves used for the CCT sensitivity calculations. The white signal is divided by 50. Yellow Green Blue Red

C. Miller, et. al., Project 05-16 - 1 5 - 9 - 3 3 9 1 5 -12 -6 0 6 12 Illuminance Horizontal (mm) Vertical (mm) 1.02-1.03 1.01-1.02 1.00-1.01 0.99-1.00 0.98-0.99 0.97-0.98 0.96-0.97 0.95-0.96 0.94-0.95 0.93-0.94 0.92-0.93 0.91-0.92 0.90-0.91 Figure 8 – Shown is the uniformity of the source aperture.

C. Miller, et. al., Project 05-16 Figure 9 – Shown is a demonstration of the aperture synthesis procedure. α0 α1 ε1

C. Miller, et. al., Project 05-16 - 1 5 - 9 - 3 3 9 1 5 -12 -6 0 6 12 Horizontal (mm) Vertical (mm) 1.100-1.200 1.000-1.100 0.900-1.000 0.800-0.900 0.700-0.800 0.600-0.700 0.500-0.600 0.400-0.500 0.300-0.400 0.200-0.300 0.100-0.200 0.000-0.100 Figure 10 – Shown is the model used in calculating the source aperture uniformity dependence for other systems .

C. Miller, et. al., Project 05-16 Prismatic RL = -0.0021111 ∆d2 - 0.0423333 ∆d Beaded RL = -0.002778 ∆d 2 - 0.0260 ∆d -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 -4 -2 0 2 4 Change in Diameter (mm) ∆ R L % Figure 11 – Presented is the RL dependence on the source aperture diameter, where the red squares are the beaded material and the blue diamonds are the prismatic material.

C. Miller, et. al., Project 05-16 - 1 2 5 - 8 5 - 4 5 - 53 5 7 5 1 1 5 -110 -40 30 100 Horizontal (cm) Vertical (cm) 1-1.1 0.9-1 0.8-0.9 0.7-0.8 0.6-0.7 0.5-0.6 Figure 12 – Shown is the uniformity of the projection system at the retroreflector aperture surface.

C. Miller, et. al., Project 05-16 Figure 13 – Shown is a demonstration that the sections of the retroreflective device are illuminated with a different set of angles than the center of the device. α0 α1

C. Miller, et. al., Project 05-16 - 1 5 - 9 - 3 3 9 1 5 -15 -6 3 12 Vertical (cm) Horizontal (cm) 1.000-1.010 0.990-1.000 0.980-0.990 0.970-0.980 0.960-0.970 0.950-0.960 0.940-0.950 0.930-0.940 0.920-0.930 0.910-0.920 0.900-0.910 Figure 14 – Shown is the uniformity of the sphere source projection system at the retroreflector aperture surface.

C. Miller, et. al., Project 05-16 Figure 15 – Shown is a schematic of the goniometer with all the axes labeled. X, X’ Y Z β1’ β2’ ε'

C. Miller, et. al., Project 05-16 Figure 16 – Shown is a picture of the goniometer.

C. Miller, et. al., Project 05-16 Figure 17 - Shown is a schematic of the goniometer communication system. 7 3 3 4 7 3 3 4 8 4 2 0 PXI 1002 UMI-7764 PC MXI- COM 1 Detector Axes Motors COM 2 30 m encoder SX-6 SX-6 SX-6 Goniometer Translation Axes MotorsGoniometer Rotation Axes Motors Environment Dial indicators Future expansion 3 to 30 meters UMI-7764

C. Miller, et. al., Project 05-16 Figure 18 – Shown is the rotation axis of the goniometer.

C. Miller, et. al., Project 05-16 Figure 19 – Shown is the ball tool mounted in the goniometer.

C. Miller, et. al., Project 05-16 Figure 20 – Shown is the front of the vacuum mount.

C. Miller, et. al., Project 05-16 Figure 21 – Shown is the alignment tool in position with a sample mounted.

C. Miller, et. al., Project 05-16 Figure 22 – Shown is a section of the rail system.

C. Miller, et. al., Project 05-16 Figure 23 – Shown is the theodolite distance minus the magnetic encoder distance. -5 0 5 10 15 20 0 5000 10000 15000 20000 25000 30000 35000 Illumination distance (mm) O f f s e t ( m m )

C. Miller, et. al., Project 05-16 RL = -0.053227 d + 1.798443 0.9980 0.9985 0.9990 0.9995 1.0000 1.0005 1.0010 1.0015 1.0020 1.0025 14.96 14.97 14.98 14.99 15 15.01 15.02 15.03 15.04 Illumination distance, d (m) N o r m a l i z e d R L Figure 24 – Shown is the change in RL dependent on the illumination distance.

C. Miller, et. al., Project 05-16 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 0 5 10 15 20 25 30 35 Illumination Distance (m) V e r t i c a l D e v i a t i o n ( m m ) Figure 25 – Shown is the vertical deviation of the sample holder compared to the illumination axis.

C. Miller, et. al., Project 05-16 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 5 10 15 20 25 30 35 Illumination Distance (m) H o r i z o n t a l D e v i a t i o n ( m m ) Figure 26 – Shown is the horizontal deviation of the samples holder compared to the illumination axis.

C. Miller, et. al., Project 05-16 Figure 27 – Presented is a schematic of the photometric detection system. Observer Aperture Collection Lens Diffuser V(λ) filter Detector

C. Miller, et. al., Project 05-16 Figure 28 – Presented is a schematic of the observation angle positioner. Observer Aperture Source Aperture x cy 2 m stage Detector 20 cm stage Rotary stage α

C. Miller, et. al., Project 05-16 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020 400 450 500 550 600 650 700 750 Wavelength (nm) A b s o l u t e R e s p o n s i v i t y ( A / W ) Figure 29 – Shown is the spectral responsivity of the photometric detection system (solid) versus the CIE V(λ) function (dotted). The dashed line at the top shows the difference between the two curves multiplied by 10.

C. Miller, et. al., Project 05-16 RL = -9.0987 x 10-6 d + 0.9998 0.98 0.99 1.00 1.01 1.02 -2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 2 m stage displacement, d (µm) N o r m a l i z e d R L Figure 30 – Shown is the change in RL dependent on the 2 m axis positioning.

C. Miller, et. al., Project 05-16 RL = -1.956 x 10-7 r2 - 9.179 x 10-6 r + 0.9996 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 -600 -400 -200 0 200 400 600 Rotary stage displacement, r (mdeg) N o r m a l i z e d R L Figure 31 – Shown is the change in RL dependent on the rotary stage positioning.

C. Miller, et. al., Project 05-16 RL = -2.2732 x 10-8 d + 1.0001 0.9994 0.9996 0.9998 1.0000 1.0002 1.0004 1.0006 1.0008 -25000 -15000 -5000 5000 15000 25000 20 cm stage displacement, d (µm) N o r m a l i z e d R L Figure 32 – Shown is the change in RL dependent on the 20 cm axis positioning.

C. Miller, et. al., Project 05-16 -23 -13 -3 7 17 - 2 3 - 1 7 - 1 2 - 6 - 1 5 1 0 1 62 0 0 0.2 0.4 0.6 0.8 1 1.2 Vertical (mm) Horizontal (mm) Figure 33 – Presented is the response uniformity of the photometric detection system.

C. Miller, et. al., Project 05-16 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 380 430 480 530 580 630 680 730 780 Wavelength (nm) R e f l e c t a n c e F a c t o r Cyan - CHARM Cyan - STARR Red - CHARM Red - STARR Figure 34 – Sample CHARM and STARR spectra for BCRA tiles.

C. Miller, et. al., Project 05-16 380 430 480 530 580 630 680 730 780 Wavelength (nm) Clear Yellow Mix Figure 35 – Shown is three spectra using the corrected diode array system.

C. Miller, et. al., Project 05-16 Figure 36 – Aperture holders with large and small apertures

C. Miller, et. al., Project 05-16 Figure 37 – Alignment of rotation angle image of sample through theodolite sample theodolite detector aperture at αmax source table detector aperture at αmin ε

C. Miller, et. al., Project 05-16 RL = -2.6361α + 1.7962 0.90 0.95 1.00 1.05 1.10 1.15 0.25 0.27 0.29 0.31 0.33 Observation Angle, α (°) N o r m a l i z e d R L Figure 38 – Shown is the change in RL dependent on the observation angle for a white encapsulated lens signage material.

C. Miller, et. al., Project 05-16 RL = 0.0016 β 1 + 1.0081 0.986 0.988 0.990 0.992 0.994 0.996 0.998 1.000 1.002 1.004 1.006 1.008 -14.0 -12.0 -10.0 -8.0 -6.0 -4.0 -2.0 0.0 Entrance Angle Component, β 1 (°) N o r m a l i z e d R L Figure 39 – Shown is the change in RL dependent on the first entrance angle component for a white encapsulated lens signage material.

C. Miller, et. al., Project 05-16 RL = -4.7841 x 10-5 β 22 + 1.9139 x 10-4 β 2 + 1.00036 0.9980 0.9985 0.9990 0.9995 1.0000 1.0005 1.0010 1.0015 1.0020 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 Entrance Angle Component, β 2 (°) N o r m a l i z e d R L Figure 40 – Shown is the change in RL dependent on the second entrance angle component for a white encapsulated lens signage material.

C. Miller, et. al., Project 05-16 0.9995 0.9996 0.9997 0.9998 0.9999 1.0000 1.0001 1.0002 1.0003 1.0004 1.0005 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 Rotation Angle, ε (°) N o r m a l i z e d R L Figure 41 – Shown is the change in RL dependent on the rotation angle for a white encapsulated lens signage material.

C. Miller, et. al., Project 05-16 Figure 42 – Shown is the set of retroreflective samples used in the MAP service originally.

C. Miller, et. al., Project 05-16 Figure 43 – Shown is the filter set used in the original MAP service.

C. Miller, et. al., Project 05-16 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 -40 -30 -20 -10 0 10 20 30 40 Entrance Angle Component, β 1 [deg] S t d . U n c e r t a i n t y [ d e g ] Figure B-1 – Orientation Angle Uncertainty Dependence

Table 1 - Light Spot Diameter (cm) at Sample Position with 5 mm Field Aperture Sample Distance (m) Lens Focal Length (m) 5 10 15 20 25 30 0.100 24 52.5 77 102 130 154 0.172 13 27 41 55 68 82 0.350 7 15 22 29 37 44 0.600 3.5 7 11 15 19 23 0.750 3.3 6.6 10 13 17 20 Table 2 - Summary of Source Requirements and Characterization Characteristic Requirement Realization short-term stability – 0.030 % (k=2) (monitoring) Stability < 1 % long-term stability – 0.056 % (k=2) (current uncertainty) Spectral Distribution S(λ) of Illuminant A CCT = 2856 K ± 20 K CCT = 2856 K ± 10 K (k=2) Uniformity of source aperture not discussed within 3 % of mean Illuminance uniformity at specimen within 5 % of mean within 1.8 % of mean Aperture size, 6’ at 15 m < 0.1’ 5.96’ at 15 m C. Miller, et. al., Project 05-16

VI CR VL = Table 3 – Uncertainty budget for measuring the lamp current at any time within the year No Quantity Symbol Value Standard Unit Type of Degree of Sensivity Unit Uncertainty Uncertainty evaluation freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Voltage Drop V 1.67000 0.000004 V A 30 10.00000 Ω-1 0.0000400 2 Shunt Resistance R 0.10000 0.00000125 Ω B (cert) ∞ 167.00000 A/Ω 0.0002088 3 DMM Cal Factor Cv 1.00000 0.0000626 B (R) ∞ 16.70000 A 0.0010456 Lamp Current LI 16.70000 0.0021 (k=2) A ∞ 0.00107 V L V L II = ∂ ∂ R L R L II − = ∂ ∂ V I V I C L C L = ∂ ∂ C. Miller, et. al., Project 05-16

Table 4 – Uncertainty budget for measuring the lamp current over the course of a day No Quantity Symbol Value Standard Unit Type of Degree of Sensivity Unit Uncertainty Uncertainty evaluation freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Voltage Drop V 1.67000 0.000004 V A 30 10.00000 Ω-1 0.0000400 2 Shunt Resistance R 0.10000 0.00000125 Ω B (cert) ∞ 167.00000 A/Ω 0.0002088 3 DMM Cal Factor Cv 1.00000 0.0000376 B (R) ∞ 16.70000 A 0.0006272 Lamp Current LI 16.70000 0.0013 (k=2) A ∞ 0.00066 Table 5 - Sensitivity Coefficient with respect to CCT Material Color CCT Expanded Uncertainty (k=2) Sensitivity Coefficient (cd/m2/lx/K) Relative Expanded Uncertainty (k=2) White 10 K -0.0000114 0.011% Red 10 K -0.0001384 0.138% Yellow 10 K -0.0000571 0.057% Green 10 K 0.0000551 0.055% Blue 10 K 0.0001222 0.122% C. Miller, et. al., Project 05-16

Table 6 - Summary of goniometer motion requirements Axis of Motion Range of Motion Minimum Step Size Positioning Accuracy Distance 10 m, 15 m, 30 m N/A + 0.05 % Entrance Angle, β1 ± 90 º 0.02 º <0.1 º Entrance Angle, β2 ± 90 º 0.02 º <0.1 º Rotation Angle, ε ± 180 º 0.04 º <0.2 º Table 7 - Summary of realized goniometer motions and capabilities Axis of Motion Range of Motion Minimum Step Size Positioning Accuracy X (rail – illumination axis) 3 – 33 m < 100 µm < + 0.25 mm X' (parallel to rail) ± 46 cm < 100 µm < + 0.25 mm Y (perpendicular to rail) ± 30.5 cm ± 10 µm < + 0.050 mm Z (vertical) ± 30.5 cm ± 10 µm < + 0.050 mm NIST Entrance Angle, β1’ ± 95 º 0.0002 º <0.001 º NIST Entrance Angle, β2’ ± 95 º 0.0002 º <0.001 º Rotation Angle, ε ± 185 º 0.0002 º <0.001 º C. Miller, et. al., Project 05-16

TRDSAVRDI ++−= Table 8 – Uncertainty budget for setting the absolute position of the magnetic encoder No Quantity Symbol Value Standard Unit Type of Degree of Sensivity Unit Uncertainty Uncertainty evaluation freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Source aperture SA 0.0000 0.0254 mm B ∞ -1.0000 -0.0254 2 Vernier distance VR 3000.0000 0.0100 mm B (cert) ∞ 1.0000 0.0100 3 Dial indicator D 0.0000 0.0115 mm B (R) ∞ 1.0000 0.0115 4 Tape reproducibitily TR 0.0000 0.1732 mm B (R) ∞ 1.0000 0.1732 Illumination dis. DI0 3000.00 0.35 (k=2) mm ∞ 0.1757 C. Miller, et. al., Project 05-16

TRDCCTMDI +++= Table 9 – Uncertainty budget for the illumination distance of a sample No Quantity Symbol Value Standard Unit Type of Degree of Sensivity Unit Uncertainty Uncertainty evaluation freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Tape measurement TM 3000.0000 0.1757 mm B ∞ 1.0000 0.1757 2 Calibration curve CC 0.0000 2.5000 mm B ∞ 1.0000 2.5000 3 Dial indicator D 0.0000 0.0115 mm B (R) ∞ 1.0000 0.0115 4 Tape Reprod. TR 0.0000 0.1732 mm B (R) ∞ 1.0000 0.1732 Illumination dis. DI 3000.00 5.02 (k=2) mm ∞ 2.5122 C. Miller, et. al., Project 05-16

Table 10 – Summarizes the capabilities of the three detector stages Stage gear ratio motor:stage stage distance / motor rev encoder step size min. step (1 motor step) motor steps / encoder step Uncertainty (k=2) Rotation 180:1 2.00° 0.002° 0.00008° 25 0.008° 20 cm 1:1 5000 µm 1 µm 0.2 µm 5 14 µm 2 m 1:1 5000 µm 1 µm 0.2 µm 5 14 µm Table 11 – The chromaticity differences (STARR-CHARM) Tile Color ∆x ∆y White -0.0013 -0.0017 Black -0.0021 -0.0027 Cyan 0.0030 0.0021 Yellow 0.0013 -0.0007 Red -0.0040 0.0003 C. Miller, et. al., Project 05-16

Table 12 - Uncertainty budget for setting the alignment tool No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Plate parallelism C 0.0000 0.003252 deg B (R) ∞ 1.00000 0.003252 2 Source alignment L 0.0000 0.001910 deg B ∞ 1.00000 0.001910 3 Goniometer unc. G 0.0000 0.001000 deg B ∞ 1.00000 0.001000 4 Micrometer unc. M 0.0000 0.006301 deg B (R) ∞ 1.00000 0.006301 Alignment Tool unc. Α 0.0000 0.0148 (k=2) deg ∞ 0.00741 Table 13 - Uncertainty budget for setting arbitrary NIST entrance angle components No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Alignment Tool unc. Α 0.0000 0.007411 deg B (R) ∞ 1.00000 0.007411 2 Mounting sample S 0.0000 0.006301 deg B (R) ∞ 1.00000 0.006301 3 Change in angle ∆β 30.0000 0.001000 deg B ∞ 1.00000 0.001000 NIST entrance angle β#’ 30.0000 0.0196 (k=2) deg ∞ 0.00978 C. Miller, et. al., Project 05-16

Table 14 - Uncertainty budget for calculating CIE entrance angle component, β1 No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 NIST angle 1 β1’ 30.000 0.00978 deg B ∞ 1.06588 0.010424 2 NIST angle 2 β2’ 30.000 0.00978 deg B ∞ -0.26647 -0.002606 CIE entrance angle β1 33.690 0.021 (k=2) deg ∞ 0.01074 1 ' 2 ' 1 2 ' 2 ' 1 2 ' 1 1 cos sin coscos − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ += ∂ ∂ β ββββ β ' 1 2' 2 2 ' 2 ' 1 ' 2 1 tancos sintan ββ ββ β β − = ∂ ∂ C. Miller, et. al., Project 05-16

Table 15 - Uncertainty budget for calculating CIE entrance angle component, β2 No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 NIST angle 1 β1’ 30.000 0.00978 deg B ∞ 0.27735 0.002712 2 NIST angle 2 β2’ 30.000 0.00978 deg B ∞ -0.83205 -0.008137 CIE entrance angle β2 -25.659 0.017 (k=2) deg ∞ 0.008577 ' 2 2' 1 2 ' 2 ' 1 ' 1 2 sincos1 sinsin ββ ββ β β − = ∂ ∂ ' 2 2' 1 2 ' 2 ' 1 ' 2 2 sincos1 coscos ββ ββ β β − − = ∂ ∂ C. Miller, et. al., Project 05-16

Table 16 - Uncertainty budget for setting the aperture separation, c No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Little Stage Movement y 0.018286 0.000029 m B ∞ -0.017453 -0.000001 2 Long Stage Movement x 1.047620 0.000029 m B ∞ 0.999848 0.000029 3 Pointing Rotation r 0.034807 0.000140 rad B ∞ -0.018283 m/rad - 0.000003 Aperture Separation c 1.047141 0.000058 (k=2) m ∞ 0.000029 c rxy y c )2cos( −− = ∂ ∂ π c ryx x c )2cos( −− = ∂ ∂ π c rxy r c )2sin( −− = ∂ ∂ π C. Miller, et. al., Project 05-16

Table 17 - Uncertainty budget for observation distance, d No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Little Stage Movement y 0.018286 0.000029 m B ∞ -1.00000 -0.000071 2 Long Stage Movement x 1.04762 0.000029 m B ∞ 0.00000 0.000000 3 Pointing Rotation r 0.034807 0.000140 rad B ∞ 1.04570 m/rad 0.000146 4 Illumination Distance s 30.00000 0.002512 m B ∞ 1.00061 0.002514 Observation Distance d 30.0000 0.0050 (k=2) m ∞ 0.002519 1−= ∂ ∂ y d )(cos )(cos)sin( 222 2 rxs rx r x d − −= ∂ ∂ )(cos )sin()cos()cos( 222 2 rxs rrx rx r d − += ∂ ∂ )(cos222 rxs s s d − = ∂ ∂ C. Miller, et. al., Project 05-16

Table 18 - Uncertainty budget for arbitrary setting of the observation angle, α No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Illumination Distance s 30.00000 0.002512 m B ∞ -0.04714 deg/m -0.000118 2 Observation Distance d 30.00000 0.002519 m B ∞ -0.04711 deg/m -0.000119 3 Aperture Separation c 1.04714 0.000029 m B ∞ 2.70095 deg/m 0.000078 Observation angle α 2.00000 0.00037 (k=2) m ∞ 0.00019 ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ − −− = ∂ ∂ sd csdds csd s 2 12 222 2 222α ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ − −− = ∂ ∂ sd csd sd cds d 2 12 222 2 222α ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −+ − = ∂ ∂ sd csd sd c c 2 1 222 α C. Miller, et. al., Project 05-16

Table 19 - Uncertainty budget for coefficient of luminous intensity, RI No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Specimen signal mT 1.0000 0.00030 lx A 20 0.2250 m2/lx 0.000068 2 Dark signal mD 0.0001 0.00030 lx A 20 -0.2250 m2/lx -0.000068 3 Illuminance signal mS 1000.000 0.30000 lx A 20 -0.000225 cd/m2/lx2 -0.000068 4 Observation distance d 15.0000 0.00252 m B ∞ 0.0300 cd/m/lx2 0.000076 Coef. of Luminous Int. RI 0.2250 0.00028 (k=2) cd/m2/lx large 0.00014 ST I m d m R 2 = ∂ ∂ SD I m d m R 2− = ∂ ∂ S I S I m R m R − = ∂ ∂ d R d R II 2 = ∂ ∂ C. Miller, et. al., Project 05-16

Table 20 – Summary of the additional uncertainty components for white beaded material Uncertainty Component White Beaded Rel. Std. Unc. Source luminance 0.028 CCT uncertainty 0.069 Source aperture uniformity 0.001 Source aperture size 0.004 Illuminance measurement 0.106 Illuminance uniformity and sample 0.100 Illumination distance 0.015 Amplifier Linearity 0.020 Illuminance unit 0.000 Luminance unit 0.000 Detector uniformity 0.003 Spectral mismatch factor 0.050 Observation distance 0.020 Entrance angle correction, β1 0.002 Entrance angle correction, β2 0.000 Observation angle correction 0.049 Rotation angle correction 0.002 Rotation stage correction 0.008 Long stage correction 0.023 Short stage correction 0.000 Long-term drift of NIST detector 0.025 Stray light 0.050 Sample temperature issues 0.150 Repeatability 0.125 Relative Combined Uncertainty 0.27 Relative Expanded Uncertainty (k=2) 0.55 C. Miller, et. al., Project 05-16

Table 21 – Summary of the additional uncertainty components for red prismatic material Uncertainty Component Red Prismatic Rel. Std. Unc. Source luminance 0.028 CCT uncertainty 0.069 Source aperture uniformity 0.001 Source aperture size 0.007 Illuminance measurement 0.106 Illuminance uniformity and sample 0.100 Illumination distance 0.015 Amplifier Linearity 0.020 Illuminance unit 0.000 Luminance unit 0.000 Detector uniformity 0.003 Spectral mismatch factor 0.150 Observation distance 0.020 Entrance angle correction, β1 0.003 Entrance angle correction, β2 0.000 Observation angle correction 0.074 Rotation angle correction 1.320 Rotation stage correction 0.012 Long stage correction 0.034 Short stage correction 0.000 Long-term drift of NIST detector 0.025 Stray light 0.050 Sample temperature issues 0.200 Repeatability 0.125 Relative Combined Uncertainty 1.4 Relative Expanded Uncertainty (k=2) 2.7 C. Miller, et. al., Project 05-16

Table 22 – Summary of the additional uncertainty components for yellow pavement marking material Uncertainty Component Yellow Pavement Rel. Std. Unc. Source luminance 0.028 CCT uncertainty 0.069 Source aperture uniformity 0.001 Source aperture size 0.007 Illuminance measurement 0.030 Illuminance uniformity and sample 0.250 Illumination distance 0.015 Amplifier Linearity 0.020 Illuminance unit 0.000 Luminance unit 0.000 Detector uniformity 0.003 Spectral mismatch factor 0.100 Observation distance 0.020 Entrance angle correction, β1 0.002 Entrance angle correction, β2 0.000 Observation angle correction 0.049 Rotation angle correction 0.000 Rotation stage correction 0.012 Long stage correction 0.034 Short stage correction 0.000 Long-term drift of NIST detector 0.025 Stray light 0.350 Sample temperature issues 0.150 Repeatability 0.175 Relative Combined Uncertainty 0.51 Relative Expanded Uncertainty (k=2) 1.02 C. Miller, et. al., Project 05-16

Table 23 - Uncertainty budget for measurement of area, A No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Sample length l 0.20000 0.0005 m B ∞ 1.0000 0.0005 2 Sample height h 0.20000 0.0005 m B ∞ 1.0000 0.0005 Sample area A 0.04000 0.0014 (k=2) m2 ∞ 0.0007 C. Miller, et. al., Project 05-16

Table B-1 - Uncertainty budget for orientation angle, ωs No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 CIE entrance angle β1 33.690 0.0107 deg B ∞ 1.5371 0.0165 2 CIE entrance angle β2 -25.660 0.0086 deg B ∞ 0.9509 0.0081 3 Rotation angle ε 0.000 0.1800 deg B ∞ 1.0000 0.1800 Orientation angle ωs -33.006 0.362 (k=2) deg ∞ 0.1809 2 21 1 2 2 1 )sin(cos sin sin βββ β β ω + − = ∂ ∂ s ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = ∂ ∂ 1 2 2 1 2 2 tan sin tan cos β ββ β β ωs 1= ∂ ∂ ε ωs C. Miller, et. al., Project 05-16

Table B-2 - Uncertainty budget for presentation angle, γ No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 CIE entrance angle β1 33.690 0.0107 deg B ∞ 0.7423 0.0079 2 CIE entrance angle β2 -25.660 0.0086 deg B ∞ -3.0306 -0.0261 Presentation angle γ -40.895 0.054 (k=2) deg ∞ 0.0272 2 2 1 2 12 1 tansin costan ββ ββ β γ + − = ∂ ∂ 2 2 1 2 2 2 1 2 sinsincos sin βββ β β γ + = ∂ ∂ C. Miller, et. al., Project 05-16

Table B-3 - Uncertainty budget for observation-elevation angle, a No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 CIE entrance angle β1 88.760 0.00858 deg B ∞ -1.0000 0.00858 2 CIE entrance angle β2 0.000 0.00858 deg B ∞ 0.0000 0.00000 3 Observation angle α 1.050 0.00019 deg B ∞ 0.9992 0.00020 Observation-Elevation a 2.290 0.017 (k=2) deg ∞ 0.0086 ( ) ( ) 2212 21 1 coscos1 cossin βαβ βαβ β −− −− = ∂ ∂a ( ) ( ) 2212 21 2 coscos1 sincos βαβ βαβ β −− −− = ∂ ∂a ( ) ( ) 2212 21 coscos1 cossin βαβ βαβ α −− − = ∂ ∂a C. Miller, et. al., Project 05-16

Table B-4 - Uncertainty budget for RM First azimuthal angle, b No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 CIE entrance angle β1 88.760 0.00858 deg B ∞ 1.2380 0.0106 2 CIE entrance angle β2 0.000 0.00858 deg B ∞ 0.0000 0.0000 3 Observation angle α 1.050 0.00019 deg B ∞ -1.5898 -0.0003 4 Observation-Elevation a 2.290 0.00860 deg B ∞ -0.8348 -0.0072 RM First Azimuthal b 181.179 0.025 (k=2) deg ∞ 0.0128 ( ) ( ) ( )[ ] ( ) ( )[ ] ( )22122 2 11112 2 3 2 2 1 2 11112 2 211 2 2 1 2 2 2 1 2 1 coscos1cos sinsincoscossin1cos coscos1 sinsincoscossincossincos coscos1 sinsin2sin )sgn( ββ αββαβββ ββ αββαββββββ ββ αβαβ ββ − −+− − ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − −+− − − −− −= ∂ ∂ a a b ( ) ( ) ( )[ ] ( ) ( )[ ] ( )22122 2 11112 2 3 2 2 1 2 11112 2 221 2 2 1 2 112 2 2 2 coscos1cos sinsincoscossin1cos coscos1 sinsincoscossincossincos coscos1 coscossin )sgn( ββ αββαβββ ββ αββαββββββ ββ αβββ ββ − −+− − ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − −+− − − − −= ∂ ∂ a a b ( ) ( ) ( ) ( )[ ] ( )22122 2 11112 2 2 2 1 2 11112 2 2 coscos1cos sinsincoscossin1 coscos1cos cossinsincossin )sgn( ββ αββαβββ ββ αββαβββ β − −+− − ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − −−− −= a a ( ) ( ) ( ) ( )[ ] ( )22122 2 11112 2 2 2 1 22 11112 2 2 coscos1cos sinsincoscossin1 coscos1sincos sinsincoscossin )sgn( ββ αββαβββ ββ αββαβββ β − −+− − ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ − −+− −= ∂ ∂ a aa a b C. Miller, et. al., Project 05-16

Table B-5 - Uncertainty budget for Illumination Elevation angle, e No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 CIE entrance angle β1 88.760 0.0086 deg B ∞ -1.0000 -0.0086 2 CIE entrance angle β2 0.000 0.0086 deg B ∞ 0.0000 0.0000 Illumination Elevation ε 1.240 0.017 (k=2) deg ∞ 0.0086 2 2 1 2 21 1 coscos1 cossin ββ ββ β − − = ∂ ∂e 2 2 1 2 12 2 coscos1 cossin ββ ββ β − − = ∂ ∂e C. Miller, et. al., Project 05-16

Table B-6 - Uncertainty budget for RM Second Azimuthal angle, d No Quantity Symbol Value Standard Unit Type of Deg. of Sensitivity Unit Uncertainty Uncertainty eval. freedom Coefficient Contribution Xi xi u(xi) νi ci ui(y) 1 Orientation angle ωs 0.000 0.1800 deg B ∞ 1.0000 0.1800 2 RM First Azimuthal b 0.000 0.0128 deg B ∞ 1.0000 0.0128 Illumination Elevation d 180.000 0.361 (k=2) deg ∞ 0.1805 1= ∂ ∂ s d ω 1= ∂ ∂ b d C. Miller, et. al., Project 05-16