National Calibration Facility for Retroreflective Traffic Control Materials (2005)

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CHAPTER 6 OVERALL UNCERTAINTY BUDGET The final uncertainty budget summarizes all of the details presented in Chapters 2 – 5. CIE 54.2 defines three coefficients that are analyzed in this chapter. The coefficient of luminous intensity is calculated using the following equation, ( ) S 2 DT I m dmm R ⋅− = (15) where mT is the photometer reading of the specimen, mD is the photometer reading of a non- retroreflecting specimen, d is the observation distance, and mS is the photometer reading of the light source perpendicular to the source at the illumination distance. The uncertainty budget for the equation 15 is shown in Table 19. However, Table 19 does not include a correction factor that is composed of all the topics discussed in Chapters 2 – 5. Table 20 is a summary of all these components for an actual white encapsulated lens piece of signage material. Items 12 through 15 depend on the uncertainty of the four CIE goniometer system angles and the material under test. For each sample to be calibrated these dependency curves have to be determined. Figures 38, 39, 40, and 41 show the dependency curves for the sample piece of signage material. Including the additional uncertainty components, the best measurement capability for the CHARM facility is 0.55 % (k=2) The sample piece of signage material represents an almost ideal sample. Table 21 summarizes the components for a red microprismatic piece of signage material. The uncertainty in the spectral mismatch correction factor increases and the uncertainty due to the rotational angle dependence can become dominant. Depending on the rotational angle chosen the uncertainty can be from 0.09 % to 1.32 %. Therefore the overall relative expanded uncertainty for the best measurement capabilities for microprismatic material is from 0.70 % to 2.7 % (k=2). Table 22 summarizes the components for a yellow beaded sample of pavement marking material. The pavement marking material samples are typically very non-uniform, increasing that component of uncertainty. Pavement marking material also has a significant component of uncertainty due to the dark signal measurement. Since the signal level is small, the scattered light from the front edge of the pavement marking material and off of the equipment causes a standard uncertainty contribution of 0.35 %. The overall expanded uncertainty for the best measurement capability of pavement marking material is1.02 % (k=2). 45

Equation 15 describes a ratio method for the determination of the coefficient of luminous intensity. Another method is the direct luminous intensity method where the illuminance is measured with a photometer calibrated for illuminance responsivity and the luminance is measured with a calibrated luminance meter. The relative expanded uncertainty for the illuminance responsivity is 0.40 % and for the luminance responsivity is 0.50 %. These additional uncertainty components among others bring the total relative expanded uncertainty for a direct luminous intensity calibration of ideal material to 1.0 % (k=2). The coefficient of retroreflection is calculated using the following equation, ( ) S 2 DT A mA dmm R ⋅ ⋅− = (16) and the coefficient of retroreflected luminance is calculated using the equation, ( ) ( ) 21S 2 DT L coscos ββα −⋅⋅ ⋅− = mA dmm R (17) where A is the area of the sample. Currently, the procedure written in many standards requires that physical measurement of the sample area. Without preparing a special sample that has a well-defined mask, the area will be difficult to measure with a small uncertainty. Table 23 shows an example uncertainty budget for the measurement of the area of a 20 cm x 20 cm sample with an uncertainty of 0.5 mm on the length and width. The area measurement becomes the primary uncertainty component, 1.77 %, which makes the overall relative expanded uncertainty 3.6 % (k=2) for an ideal material. NIST staff is working on writing measurement procedures that do not require the physical measurement of the sample area. Simply the sample area crosses out; therefore, the measurement is not dependent on the sample area. 46