Surface Color 0 45

1 Page 1 0:45 Surface Color Maria E. Nadal Edward A. Early 1 Robert R. Bousquet 2 NIST Special Publication SP250-71 Open at page → 2 Page 2 NIST Special Publication SP250-71 0:45 Surface Color Maria E. Nadal Edward A. Early 1 Robert R. Bousquet 2 Optical Technology Division Physics Laboratory National Institute of Standards and Technology Gaithersburg, MD 20... Open at page → 3 Page 3 1 AFRL/HEDO, 2650 Loiuse Bauer Drive, Brooks City-Base, TX 78235 2 Genesis Engineering Solution, 9811 Greenbelt Road, Lanham, MD, 20706 Certain commercial entities, equipment, or materials may be identified in this docum... Open at page → 4 Page 4 ABSTRACT This document, SP250-71 (2007), NIST Measurements Services: 0:45 Surface Color, describes the instrumentation, standards, and techniques used to measure the surface color of reflective, non-fluorescent materials... Open at page → 5 Page 5 TABLE OF CONTENTS 1. Introduction ........................................................................................................1 2. Theory ......................................................................... Open at page → 6 Page 6 LIST OF FIGURES 3.1 Typical 0:45 spectral reflectance factor of a Spectralon reference standard ..............................................................................................8 4.1 Schematic of the 0:45 re... Open at page → 7 Page 7 LIST OF TABLES 4.1 Geometrical specifications of 0:45 reflectometer ............................................11 4.2 Sources and wavelength of emission lines used for the wavelength calibration. .......................... Open at page → 8 Page 8 1 1. Introduction The National Institute of Standards and Technology (NIST) have a long history in color and appearance, with many important contributions to our present understanding of color measurements. Interest in c... Open at page → 9 Page 9 2 The 0:45 reflectometer consists of a source section, a sample section and a detection section. The source section consists of a dual lamp housing, a double grating monochromator, and optics that direct the incident bea... Open at page → 10 Page 10 3 and reference standard, respectively. The 0:45 signals from the sample and the reference standard are normalized by the signals from a monitor photodiode to account for drift in the radiant flux from the illuminator. M... Open at page → 11 Page 11 4 The reflectance factor R of the sample, for each scan, wavelength, and polarization, is given by ) ,,(),,(),,( sx x iQiNiR σλσλσλ ⋅= . (2.8) Averaging over polarizations, usually σ = 0° and 90° with respect to the plan... Open at page → 12 Page 12 5 () ()() x WkSxλ λλ= () ()() y WkSyλ λλ= () ()() z WkSzλ λλ= where S( λ) is the relative spectral power of one of the CIE standard illuminants, x(λ), y (λ) and z(λ) are the color matching functions of the CIE colorimetr... Open at page → 13 Page 13 6 The chromaticity coordinates are generally specified by x and y, since the two known coordinates can be used to calculate the third coordinate. The two-dimensional plot of (x, y) is called the CIE 1931 chromaticity dia... Open at page → 14 Page 14 7 The reference standards are calibrated on the Spectral Tri-function Automated Reference Reflectometer (STARR) [14]. The STARR instrument is the national reference instrument for spectral reflectance measurements of spe... Open at page → 15 Page 15 8 is 0.4 %. The components of uncertainly are divided into those arising from random and systematic effects. The random effects, which include signal noise, result in a relative expanded uncertainty of 0.02 %. The system... Open at page → 16 Page 16 9 Double Monochomator Sample Wheel Receiver Monitor Recevier Lamp Housing Figure 4.1 Schematic of the 0:45 reflectometer consisting of a monochromatic illuminator, sample wheel, and receivers. The illuminator provides a... Open at page → 17 Page 17 10 length mirror with a 3 times magnification which produces a 10 mm x 12 mm rectangular illumination area on the sample. A periscope follows the ellipsoidal mirror to steer the beam for alignment and to compensate for t... Open at page → 18 Page 18 11 1.36°, to closely match the geometry of STARR. The detector is underfilled with the image of the illumination area at an exitance of 45° to the sample plane. A schematic of the optical path of the receiver is shown in... Open at page → 19 Page 19 12 nm with no polarizer in the beam path and a 22.5° mirror placed in one of the sample compartments. The stray-light rejection level was determined to be 1 x 10 -3 5 nm away from the set wavelength and 1 x 10 -6 15 nm a... Open at page → 20 Page 20 13 Table 4.2 Sources and wavelength of emission lines used for the wavelength calibration. Source Wavelength [nm] Hg 435.834 Hg 546.074 Ne 692.947 Ar 763.510 Table 4.3 Spectral specifications of 0:45 illuminator Property... Open at page → 21 Page 21 14 validation of the instrument includes measurements of reference, check, and comparison standards. The reference standards are measured on STARR every year for the measurement geometry of 0:45 and the wavelength range... Open at page → 22 Page 22 15 52.90 52.92 52.94 52.96 52.98 53.00 53.02 53.04 53.06 53.08 53.10 024681012 Time Measured L* Figure 4.6 Control chart of the measured L* for the cyan tile. The solid lines represent the tolerance condition. The compar... Open at page → 23 Page 23 16 4.4 Calibration Services The 0:45 measurements are available at cost on submitted samples or as a set of calibrated BCRA Series II color tiles available for purchase. A preliminary discussion with NIST staff is requir... Open at page → 24 Page 24 17 The sources of uncertainty associated with the 0:45 reflectometer were identified from the characterization of the instrument [5]. The components of uncertainties were characterized and analyzed in [19, 20]. The proce... Open at page → 25 Page 25 18 Uncertainties in the signals caused by systematic effects are evaluated by Type B methods and are non-linearity of the signal from the sample relative to the signal from the reference standard, and the effect of stray... Open at page → 26 Page 26 19 saturated color samples. The measured spectral reflectance factor is a convolution of the true reflectance factor and the normalized bandpass function. At each wavelength point, measured reflectance factor R m(λ 0) is... Open at page → 27 Page 27 20 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 350 400 450 500 550 600 650 700 750 Wavelength (nm) Reflectance facto r -0.5% 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% Error (%) in Reflectance Factor BCRA yellow (%)Error Fig. 5.2 An example of the... Open at page → 28 Page 28 21 respectively, and are both evaluated using Type B methods for the uncertainty analysis of the 0:45 reflectometer. 5.2 Uncertainty and Correlation of R( λ) Determining the standard uncertainty u(R( λi)) for each source... Open at page → 29 Page 29 22 () () () ()( )( ) )90,(),0,()90,()0,( 2 1 )90,( 4 1 )0,( 4 1 )( 222 °°⋅°°+ °+°= iiii iiiRRrRuRu RuRuRuλλλλ λλλ (5.14) Assuming the sources of uncertainty are completely correlated between polarizations, so r(R( λi,0°)... Open at page → 30 Page 30 23 where Γ represents any of the color space values, u(R( λi)) is the standard uncertainty of the reflectance factor at wavelength λi, and r (R( λi), R(λj)) is the correlation coefficient between reflectance factors at d... Open at page → 31 Page 31 24 The combined color uncertainty assists with interpreting a color difference. Let ΔE 1 and Δ E 2 be the combined color uncertainties of two different specimens, or a single specimen measured by two different instrument... Open at page → 32 Page 32 25 Table 5.1 Standard, u, and expanded (k = 2), U, uncertainties of the CIELAB values for each source of uncertainty for CIE Illuminant D65 and the CIE 1931 Standard Observer and the indicated color tiles. The standard u... Open at page → 33 Page 33 26 Color Tile Value Standard Uncertainty u c U u1 u2 u3 u4 u5 u6 u7 White L* 95.99 0.010 0.000 0.001 0.075 0.075 0.000 0.000 0.11 0.21 a* -0.41 0.007 0.001 0.004 0.000 0.000 0.000 0.001 0.01 0.02 b* 1.13 0.010 -0.006 0.0... Open at page → 34 Page 34 27 Figure 5.3 Standard uncertainties in L*, a*, and b * caused by the indicated sources of uncertainty for selected samples for CIE Standard Illuminant D65 and the CIE 1964 Standard Observer. The standard uncertainties a... Open at page → 35 Page 35 28 Acknowledgments The success of the measurement service for 0:45 Color measurements was aided by the efforts of Dr. Gerald Fraser and Dr. Yoshihiro Ohno. Open at page → 36 Page 36 29 References 1. D. B. Judd and G. Wyszecki, Color in Business, Science, and Industry (3 rd ed.), John Wiley & Sons, Inc., New York, 1975. 2. D. B. Judd, “Contributions to Color Science”, NBS Special Publication 545, U.... Open at page → 37 Page 37 30 22. E. I. Stearns and R. E. Stearns, “An Example of a Method for Correcting Radiance Data for Bandpass Error,” Color Res. Appl. 13-4, 257-259 (1988). 23. Y. Ohno, “A Flexible Bandpass Correction Method for Spectromete... Open at page → 38 Page 38 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 1 Appendix A REPORT OF CALIBRATION 38091S 0:45 Surface Color for Color Tile Set Submitted by: Any Company, Inc. Attn.... Open at page → 39 Page 39 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 2 photodiode. A sample wheel with twenty positions contains the measured items. At each wavelength and polarization,... Open at page → 40 Page 40 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 3 The tristimulus values X, Y, and Z of each item were calculated for CIE standard illuminant D65 and CIE 1931 standa... Open at page → 41 Page 41 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 4 The uncertainties from signal noise include source stability and detector noise. The uncertainty contributions caus... Open at page → 42 Page 42 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 5 Table 1. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of the... Open at page → 43 Page 43 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 6 Table 2. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of the... Open at page → 44 Page 44 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 7 Table 3. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of the... Open at page → 45 Page 45 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 8 Table 4. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of the... Open at page → 46 Page 46 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 9 Table 5. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of the... Open at page → 47 Page 47 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 10 Table 6. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of th... Open at page → 48 Page 48 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 11 Table 7. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of th... Open at page → 49 Page 49 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 12 Table 8. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of th... Open at page → 50 Page 50 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 13 Table 9. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of th... Open at page → 51 Page 51 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 14 Table 10. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of t... Open at page → 52 Page 52 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 15 Table 11. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of t... Open at page → 53 Page 53 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 16 Table 12. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of t... Open at page → 54 Page 54 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 17 Table 13. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of t... Open at page → 55 Page 55 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 18 Table 14. 0:45 spectral reflectance factor R and expanded uncertainty U (k = 2) as a function of wavelength λ of t... Open at page → 56 Page 56 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 19 Table 15. Tristimulus values Y and chromaticity coordinates x and y, with expanded uncertainties U (k=2) for CIE s... Open at page → 57 Page 57 REPORT OF CALIBRATION 38091S 0:45 Surface Color Color Tile Set Any Company, Inc. Serial No.: NISTCS-XX 20 Table 16. Sources of uncertainty and their standard uncertainty or value for a color tile set, set number NISTCS-X... Open at page → 59 Page 59 2 Appendix B Appeared in Color Research Applications, Vol. 29, June 2004 Uncertainty Analysis for Reflectance Colorimetry E. A. Early and M. E. Nadal Optical Technology Division National Institute of Standards and Techno... Open at page → 60 Page 60 3 I. Introduction Determining the uncertainty in the measured color of a specimen has been a topic of interest for many years. 1-9 It has received additional attention with the publication of the ISO Guide to the Express... Open at page → 61 Page 61 4 )( )( )( )( s s i i i iR S S Rλ λ λ λ ⋅= , (2.1) where λi is the wavelength setting of the instrument, S and Ss are the measured signals from the specimen and standard, respectively, and R and Rs are the reflectance fa... Open at page → 62 Page 62 5 where the correlation coefficient is a pure number between –1 and +1, inclusive. For two input quantities that are uncorrelated, r(xk, xl) = 0, while two quantities that are fully correlated have r(xk, xl) = ±1. In gen... Open at page → 63 Page 63 6 Substitution of Eqs. (3.10) and (3.11) into Eq. (3.3) yields the correlation coefficient r(x k, xl). For this technique to work, the correlation coefficients for the additional variables r(q h, qp) must be known. As an... Open at page → 64 Page 64 7 factor R i, given by Eq. (2.2), uncertainties in S i, Ss,i, Rs,i and λ all contribute to an uncertainty in R i. Uncertainties in the final color values can be calculated using two different approaches. In the first, th... Open at page → 65 Page 65 8 i i i ii i iS R S SR S R ,s 2 ,s ,s ,s − = − = ∂ ∂ . (4.2) Substituting these into Eq. (3.4) and dividing by Ri 2 yields the component of standard uncertainty in Ri due to uncertainty in the signals, ),( )()( 2 )()()(... Open at page → 66 Page 66 9 i i i iR S S R ,s ,s λλ∂ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ = ∂ ∂ (4.9) and Eq. (3.4) becomes )( )( 2 2 ,s 2 2 ,s 2 2 c λ λu S S R R R Ru i i i i i i ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ∂ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ = . (4.10) Any uncertainty in Rs,i due to wavelen... Open at page → 67 Page 67 10 ξξξ∂ ∂ = ∂ ∂ ∂ ∂ = ∂ ∂ i i ii i iiR R RR R RR ,s ,s ,s ,s and (4.13) ξξξ∂ ∂ = ∂ ∂ ∂ ∂ = ∂ ∂ j j jj j jjR R RR R RR ,s ,s ,s ,s . (4.14) Therefore, the correlation coefficient is given by ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ ⋅ ⎟ ⎟ ⎠ ⎞... Open at page → 68 Page 68 11 .)()(),(2)()( 1 11 2 2 1 2 c jiji j m i m ij i i m i i RuRuRRr R X R X Ru R X Xu ⋅⋅⋅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ =∑∑∑ − =+== (4.18) From Eq. (2.3), the sensitivity coefficients are i... Open at page → 69 Page 69 12 .)()(),(2 )()(),(2 )()(),(2 )()()()( 2 2 2 2 2 2 2 ZuYuZYr ZY ZuXuZXr ZX YuXuYXr YX Zu Z Yu Y Xu X u c ⋅⋅⋅⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ Γ∂ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ Γ∂ + ⋅⋅⋅⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ Γ∂ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ Γ∂ + ⋅⋅⋅⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ Γ∂ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ Γ∂... Open at page → 70 Page 70 13 E. Calculations Based on Spectral Reflectance Factors The chromaticity coordinates and color space values can also be calculated directly from the spectral reflectance factor by substituting Eqs. (2.3) to (2.5) into t... Open at page → 71 Page 71 14 d. Calculate the uncertainty in Γ using the results from steps a, b, and c for each source of uncertainty. [Eq. (4.25)] 6. If using the spectral reflectance factor to calculate Γ a. Calculate the sensitivity coefficie... Open at page → 72 Page 72 15 Following the first two steps in Section IV.F, the sources of uncertainty are the same as those considered above and listed in Table 1. The standard uncertainties for each source are chosen to be representative of a h... Open at page → 73 Page 73 16 for the random effects and 002.0 )( c = i i R Ru (5.9) for the systematic effects. The fourth step in Section IV.F is to calculate the correlation coefficient between spectral reflectance factors at different waveleng... Open at page → 74 Page 74 17 .*)(*)(*)*,( * * * * 2 *)( * * *)( * * *)( abab 2 2 ab 2 2 ab ab 2 c buaubar C b C a bu C b au C a Cu ⋅⋅⋅ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⋅+ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = (5.12) To calculate the uncertainties is... Open at page → 75 Page 75 18 and b* being smaller. The uncertainties caused by random effects in the standard are simply reduced in magnitude from those caused by signal noise. The uncertainties caused by systematic effects in the standard are si... Open at page → 76 Page 76 19 References of Appendix B 1. Nimeroff I. Propagation of errors in spectrophotometric colorimetry. J Opt Soc Am 1953; 43: 531-533. 2. Shipley T, Walker GL. Chromatic significance of spectrophotometric errors. J Opt Soc... Open at page → 77 Page 77 20 Appendix A. Sensitivity coefficients for common chromaticity coordinates and color space values 1. Chromaticity coordinates a. x, y 2 )(ZYX ZY X x ++ + = ∂ ∂ (A.1) 2 )(ZYX X Y x ++ − = ∂ ∂ (A.2) 2 )(ZYX X Z x ++ − = ∂... Open at page → 78 Page 78 21 3 1 n 2 1 3 500* ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ∂ ∂ XXX a (A.14) 3 1 n 2 1 3 500* ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛− = ∂ ∂ YYY a (A.15) 3 1 n 2 1 3 200* ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = ∂ ∂ YYY b (A.16) 3 1 n 2 1 3 200* ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛− = ∂ ∂ ZZZ b (A.17) * * * *... Open at page → 79 Page 79 22 * * * * uv uv C v v C = ∂ ∂ (A.30) () 2 * * * * uv uvC v u h − = ∂ ∂ (A.31) () 2 * * * * uv uvC u v h = ∂ ∂ (A.32) Open at page → 80 Page 80 23 Tables Table 1. Correlation coefficients for common sources of uncertainty Correlation Coefficient Source of Uncertainty r(S i, Ss,i) r(R i, Rj) Signal Noise 0 0 Non-linearity One signal -- +1 Two signals +1 +1 a [Eq.... Open at page → 81 Page 81 24 Figure Captions Figure 1. Reflectance factor as a function of wavelength for the example specimens and the standard. The colors of the specimens are indicated. Figure 2. Weighting factors as a function of wavelength f... Open at page → 82 Page 82 25 300 400 500 600 700 800 900 1000 1100 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Green Deep Blue Red Gray Standard Reflectance Factor Wavelength [nm] Figure 1. 300 400 500 600 700 800 0 1 2 3 4 5 6 7 8 9 10 11 W z W... Open at page → 83 Page 83 26 300 400 500 600 700 800 900 1000 1100 0 10 20 30 40 50 Signal [mV] Wavelength [nm] Figure 3. Open at page → 84 Page 84 27 Noise Offset Stray WL Std (R)Std (S) 0.00 0.03 0.06 0.09 0.12 (c) Green Uncertainty Source of Uncertainty L* a* b* Noise Offset Stray WL Std (R)Std (S) 0.00 0.09 0.18 0.27 0.36 (d) Red Uncertainty Source of Uncertaint... Open at page →