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Essentials of Optical Radiation Metrology

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Blackbody Radiometry

Abstract

The basic concepts of optical radiometry and definitions of radiometric quantities are discussed. The main ideas of metrology are considered in connection with the metrological aspects of optical radiometry. An approach to evaluation of measurement uncertainties described in the Guide to the expression of Uncertainty of Measurements (GUM) is outlined and conditions for its applicability are indicated. The basics of the Monte Carlo simulation of measurement uncertainties (the method of propagation of distributions) is briefly considered and some suitable examples are provided.

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Notes

  1. 1.

    American National Standards Institute, a private, non-profit organization dedicated to supporting the voluntary standards for products, services, processes, systems, and personnel in the United States and coordinates U.S. standards with international standards so that American products can be used internationally.

  2. 2.

    In remote sensing, the name of sensors is used traditionally to designate various types of indicating radiometric instruments, including multi-element ones, often together with optics, scanning devices, devices performing spectral selection, etc.

  3. 3.

    Depletion layer is a region around the metal–semiconductor junction, where recombination of electrons and holes has reduced substantially the number of equilibrium majority carriers (for details, see any textbook on semiconductor physics).

  4. 4.

    Imperial Physical Technical Institute (German).

  5. 5.

    Bureau International des Poids et Mesures (Fr.)—International Bureau of Weights and Measures (https://www.bipm.org/en/about-us/).

  6. 6.

    International Electro-technical Commission (https://www.iec.ch/).

  7. 7.

    Organisation Internationale de Métrologie Légale (Fr.)—International Organisation of Legal Metrology (https://www.oiml.org/en).

  8. 8.

    CIE standard illuminant A has the relative spectral power distribution is that of a Planckian radiator at a temperature of approximately 2856 K and mimics typical indoor tungsten-filament lighting.

References

  1. C.G. Abbot, F.E. Fowle, Part I. Determination of the intensity of the solar radiation outside the Earth’s atmosphere, otherwise termed “the solar constant of radiation.” Ann. Astrophys. Observ. Smith. Inst. II, 11–158 (1908)

    Google Scholar 

  2. A. Allard, N. Fischer, Sensitivity analysis in practice: providing an uncertainty budget when applying supplement 1 to the GUM. Metrologia 55, 414–426 (2018)

    ADS  Google Scholar 

  3. K. Anhalt, A. Zelenjuk, D.R. Taubert et al., New PTB setup for the absolute calibration of the spectral responsivity of radiation thermometers. Int. J. Thermophys. 30, 192–202 (2009)

    ADS  Google Scholar 

  4. ANSI/IES RP-16-10, Nomenclature and Definitions for Illuminating Engineering (Illuminating Engineering Society of North America, New York, 2010)

    Google Scholar 

  5. A. Araújo, S. Silvano, N. Martins, Monte Carlo uncertainty simulation of surface emissivity at ambient temperature obtained by dual spectral infrared radiometry. Infrared Phys. Technol. 67, 131–137 (2014)

    ADS  Google Scholar 

  6. A. Araújo, N. Martins, Monte Carlo simulations of ambient temperature uncertainty determined by dual-band pyrometry. Meas. Sci. Technol. 26, 085016 (2015)

    ADS  Google Scholar 

  7. K. Ångström, Ueber absolute Bestimmungen der Wärmestrahlung mit dem elektrischen Compensationspyrheliometer, nebst einigen Beispielen der Anwendung dieses Instrumentes. Ann. Phys. 303, 633–648 (1899)

    Google Scholar 

  8. S. Bell, A beginner’s guide to uncertainty of measurement. Measurement Good Practice Guide No. 11 (Issue 2) (NPL, UK, 2001), https://www.npl.co.uk/publications/a-beginners-guide-touncertaintyin-measurement. Accessed 21 Jan 2019

  9. K. Berka, Scales of measurement, in Language, Logic, and Method, ed. by R.S. Cohen, M.W. Wartofsky (D. Reidel Publ. Co., Dordrecht, Holland, 1983), pp. 1–73

    Google Scholar 

  10. L. Birgé, Y. Rozenholc, How many bins should be put in a regular histogram. ESAIM: P&S 10, 24–45 (2006). https://doi.org/10.1051/ps:2006001

  11. BIPM, The International System of Units (SI), 9th ed. (2019), https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf. Accessed 5 Jan 2020

  12. G.E.P. Box, M.E. Muller, A note on the generation of random normal deviates. Ann. Math. Statist. 29, 610–611 (1958)

    MATH  Google Scholar 

  13. R.W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983)

    Google Scholar 

  14. S. Briaudeau, F. Bourson, O. Kozlova et al., The synthetic double wavelength technique: a simple robust method for thermodynamic temperature determination. Metrologia 57, 025014 (2020)

    ADS  Google Scholar 

  15. E. Bründermann et al., Terahertz Techniques (Springer, Berlin, 2012)

    Google Scholar 

  16. R.A. Chipman, Polarimetry, in Handbook of Optics, Volume I: Geometrical and Physical Optics, Polarized Light, Components and Instruments, 3rd ed., ed. by M. Bass (McGraw-Hill, New York, 2010), pp. 15.1–15.46

    Google Scholar 

  17. C.J. Chunnilall, E. Theocharous, Infrared hemispherical reflectance measurements in the 2.5 μm to 50 μm wavelength region using a Fourier transform spectrometer. Metrologia 49, S73–S80 (2012)

    Google Scholar 

  18. CIE, Methods of Characterizing the Performance of Radiometers and Photometers. CIE Publ. No 53. (International Commission on Illumination, Vienna, 1982)

    Google Scholar 

  19. CIE, Methods of Characterizing Illuminance Meters and Luminance Meters. CIE Publ. No 69. (International Commission on Illumination, Vienna, 1987)

    Google Scholar 

  20. F.J.J. Clarke, D.J. Parry, Helmholtz reciprocity: its validity and application to reflectometry. Light. Res. Technol. 17, 1–11 (1985)

    Google Scholar 

  21. W.W. Coblentz, Instruments and methods used in radiometry. Bull. Bur. Stand. 4, 391–460 (1907–1908)

    Google Scholar 

  22. W.W. Coblentz, Instruments and methods used in radiometry II. Bull. Bur. Stand. 9, 7–63 (1913)

    Google Scholar 

  23. W.W. Coblentz, Methods and apparatus in spectroradiometry. J. Opt. Soc. Amer. 7, 439–454 (1923)

    ADS  Google Scholar 

  24. R.R. Cordero, G. Seckmeyer, S. Riechelmann et al., Monte Carlo-based uncertainty analysis of UV array spectroradiometers. Metrologia 49, 745–755 (2012)

    Google Scholar 

  25. J.M. Cowley, Diffraction Physics, 3rd edn. (Elsevier, Amsterdam, 1995)

    Google Scholar 

  26. M.G. Cox, M.P. Dainton, A.B. Forbes et al., Use of Monte Carlo simulation for uncertainty evaluation in metrology, in Advanced Mathematical and Computational Tools in Metrology V, ed. by P. Ciarlini, M.G. Cox, E. Filipe et al. (World Scientific Publishing Co., River Edge, NJ, 2001), pp. 93–105

    Google Scholar 

  27. M.G. Cox, B.R.L. Siebert, The use of a Monte Carlo method for evaluating uncertainty and expanded uncertainty. Metrologia 43, S178–S188 (2006)

    ADS  Google Scholar 

  28. M.G. Cox, P.M. Harris, Validating the applicability of the GUM procedure. Metrologia 51, S167–S175 (2014)

    ADS  Google Scholar 

  29. R.U. Datla, A.C. Parr, Introduction to optical radiometry, in Optical Radiometry, ed. by A.C. Parr et al. (Academic Press, Amsterdam, Netherlands, 2005), pp. 1–34

    Google Scholar 

  30. J. De Lucas, J.J. Segovia, Uncertainty calculation of the effective emissivity of cylinder-conical blackbody cavities. Metrologia 53, 61–75 (2016)

    ADS  Google Scholar 

  31. J. De Lucas, J.J. Segovia, Measurement and analysis of the temperature gradient of blackbody cavities, for use in radiation thermometry. Int. J. Thermophys. 39, 57 (2018)

    ADS  Google Scholar 

  32. C. DeCusatis (ed.), Handbook of Applied Photometry (AIP Press, Woodbury, NY, 1998)

    Google Scholar 

  33. L. Devroye, Non-Uniform Random Variate Generation (Springer, New York, 1986)

    MATH  Google Scholar 

  34. R.H. Dieck, Measurement Uncertainty: Methods and Applications, 5th ed. (ISA—The Instrumentation, Systems, and Automation Society, Research Triangle Park, NC, 2017)

    Google Scholar 

  35. W.L. Dunn, J.K. Shultis, Exploring Monte Carlo Methods (Academic Press, Amsterdam, 2012)

    MATH  Google Scholar 

  36. K. Entacher, Bad subsequences of well-known linear congruential pseudorandom number generators. ACM Trans. Model. Comput. Simul. 8, 61–70 (1998)

    MATH  Google Scholar 

  37. T.J. Esward, A. de Ginestous, P.M. Harris et al., A Monte Carlo method for uncertainty evaluation implemented on a distributed computing system. Metrologia 44, 319–326 (2007)

    ADS  Google Scholar 

  38. L. Finkelstein, Fundamental concepts of measurement: definition and scales. Meas. Control 8, 105–111 (1975)

    Google Scholar 

  39. G.S. Fishman, Monte Carlo. Concepts, Algorithms, and Applications (Springer, New York, 1996)

    Google Scholar 

  40. A.T. Friberg (ed.), Selected Papers on Coherence and Radiometry. SPIE Milestone Series, MS 69 (SPIE Press, Bellingham, WA, 1993)

    Google Scholar 

  41. C. Fröhlich, History of solar radiometry and the world radiometric reference. Metrologia 28, 111–115 (1991)

    ADS  Google Scholar 

  42. J.L. Gardner, Partial coherence and practical radiometry. Metrologia 30, 419–423 (1993)

    ADS  Google Scholar 

  43. J.L. Gardner, On the use of the term “scale(s)” in radiometric and photometric metrology. Metrologia 37, 547 (2000)

    ADS  Google Scholar 

  44. J.E. Gentle, Random Number Generation and Monte Carlo Methods, 2nd edn. (Springer, New York, 2003)

    MATH  Google Scholar 

  45. T.A. Germer et al. (eds.), Spectrophotometry: Accurate Measurement of Optical Properties of Materials (Academic Press, Amsterdam, 2014)

    Google Scholar 

  46. C.E. Gibson, B.K. Tsai, A.C. Parr, NIST Measurement Services: Radiance Temperature Calibrations (NIST Spec. Publ. 250-43. NIST, U. S. Dept. of Commerce, Washington, DC, 1998)

    Google Scholar 

  47. J.W. Goodman, Statistical Optics, 2nd edn. (Wiley, Hoboken, NJ, 2015)

    Google Scholar 

  48. T. Goodman, W. Servantes, E. Woolliams et al., Final Report on the EURAMET.PR-K1.a-2009 Comparison of Spectral Irradiance 250–2500 nm. NPL Report OP 12 (National Physical Laboratory, Teddington, UK, 2015), https://www.bipm.org/utils/common/pdf/final_reports/PR/K1/EURAMET-PR-K1.a-Final-Report.pdf. Accessed 16 Jan 2020

  49. M. Grabe, Measurement Uncertainties in Science and Technology, 2nd edn. (Springer, Berlin, 2014)

    Google Scholar 

  50. B.G. Grant, Field Guide to Radiometry (SPIE Press, Bellingham, WA, 2011)

    Google Scholar 

  51. F. Grum, R.J. Becherer, Radiometry (Academic Press, Orlando, FL, 1979)

    Google Scholar 

  52. G. Grynberg, A. Aspect, C. Fabre, Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light (Cambridge University Press, Cambridge, UK, 2010)

    Google Scholar 

  53. S.V. Gupta, Measurement Uncertainties: Physical Parameters and Calibration of Instruments (Springer, Berlin, 2012)

    Google Scholar 

  54. Hamamatsu: Si photodiodes. Selection guide. Hamamatsu Photonics K.K. (2020), https://www.hamamatsu.com/resources/pdf/ssd/si_pd_kspd0001e.pdf. Accessed 11 Jun 2020

  55. T.P. Heavner, E.A. Donley, F. Levi et al., First accuracy evaluation of NIST-F2. Metrologia 51, 174–182 (2014)

    ADS  Google Scholar 

  56. P. Hellekalek, Good random number generators are (not so) easy to find. Math. Comput. Simul. 46, 485–505 (1998)

    MathSciNet  MATH  Google Scholar 

  57. H. von Helmholtz, Handbuch der physiologischen Optik, Band 1, S. 169 (Verlag von Leopold Voss, Leipzig, 1856)

    Google Scholar 

  58. W. Hormann, J. Leydold, G. Derflinger, Automatic Nonuniform Random Variate Generation (Springer, Berelin, 2004)

    MATH  Google Scholar 

  59. K. Horne, A. Fleming, B. Timmins et al., Monte Carlo uncertainty analysis for photothermal radiometry measurements using a curve fit process. Metrologia 52, 83–792 (2015)

    Google Scholar 

  60. J.M. Houston, J.P. Rice, NIST reference cryogenic radiometer designed for versatile performance. Metrologia 43, S31–S35 (2006)

    ADS  Google Scholar 

  61. P. Howarth, F. Redgrave, Metrology—In Short, 3rd ed. (EURAMET, 2008), https://www.euramet.org/publications-media-centre/documents/metrology-in-short/. Accessed 21 Jan 2019

  62. ILV, International Lighting Vocabulary. CIE S017/E:2011 (CIE Central Bureau, Vienna, 2011)

    Google Scholar 

  63. ISO 20473:2007, Optics and Photonics—Spectral Bands (International Standard, ISO, Geneva, 2007)

    Google Scholar 

  64. ISO 23539:2005 (CIE S010/E:2004), Photometry—The CIE System of Physical Photometry (International Standard, ISO, Geneva, 2005)

    Google Scholar 

  65. ISO 28640:2010, Random Variate Generation Methods—Specifies Methods for Generating Uniform and Non-uniform Random Variates for Monte Carlo Simulation Purposes (International Organization for Standardization, Geneva, 2010)

    Google Scholar 

  66. ISO 5725-1:1994, International Standard. Accuracy (Trueness and Precision) of Measurement Methods and Results—Part 1: General Principles and Definitions (International Organization for Standardization (ISO), Geneva, 1994)

    Google Scholar 

  67. ISO 5725-2:1994, International Standard. Accuracy (Trueness and Precision) of Measurement Methods and Results—Part 2: Basic Method for the Determination of Repeatability and Reproducibility of a Standard Measurement Method (International Organization for Standardization (ISO), Geneva, 1994)

    Google Scholar 

  68. ISO 5725-3:1994, International Standard. Accuracy (Trueness and Precision) of Measurement Methods and Results—Part 3: Intermediate Measures of The Precision of a Standard Measurement Method (International Organization for Standardization (ISO), Geneva, 1994)

    Google Scholar 

  69. ISO 5725-4:1994, International Standard. Accuracy (Trueness and Precision) of Measurement Methods and Results—Part 4: Basic Methods for the Determination of The Trueness of a Standard Measurement Method (International Organization for Standardization (ISO), Geneva, 1994)

    Google Scholar 

  70. ISO 5725-6:1994, International Standard. Accuracy (Trueness and Precision) of Measurement Methods and Results—Part 6: Use in Practice of Accuracy Values (International Organization for Standardization (ISO), Geneva, 1994)

    Google Scholar 

  71. ISO 5725-5:1998, International Standard. Accuracy (Trueness and Precision) of Measurement Methods and Results—Part 5: Alternative Methods for the Determination of the Precision of a Standard Measurement Method (International Organization for Standardization (ISO), Geneva, 1998)

    Google Scholar 

  72. ISO/CIE 17166:2019, Erythema Reference Action Spectrum and Standard Erythema Dose (International Organization for Standardization (ISO), Geneva, Switzerland, 2019)

    Google Scholar 

  73. JCGM 100:2008, GUM, Evaluation of Measurement Data. Guide to the Expression of Uncertainty in Measurement. (GUM 1995 with Minor Corrections) (BIPM Joint Committee for Guides in Metrology, Paris, 2008)

    Google Scholar 

  74. JCGM 101:2008. GUM, Evaluation of Measurement Data—Supplement 1 to the “Guide to the Expression of Uncertainty in Measurement”—Propagation of Distributions Using a Monte Carlo Method (BIPM Joint Committee for Guides in Metrology, Paris, 2008)

    Google Scholar 

  75. JCGM 102:2011. Evaluation of Measurement Data—Supplement 2 to the “Guide to the Expression of Uncertainty in Measurement”—Extension to any Number of Output Quantities (BIPM Joint Committee for Guides in Metrology, Paris, 2011)

    Google Scholar 

  76. JCGM 104:2009, Evaluation of Measurement Data—An Introduction to the “Guide to the Expression of Uncertainty in Measurement” and Related Documents (BIPM Joint Committee for Guides in Metrology, Paris, 2009)

    Google Scholar 

  77. JCGM 200:2012, International Vocabulary of Metrology—Basic and General Concepts and Associated Terms (VIM), 3rd ed.—2008 Version with Minor Corrections. (BIPM Joint Committee for Guides in Metrology, Paris, 2012)

    Google Scholar 

  78. B.C. Johnson, H. Yoon, J.P. Rice, A.C. Parr, Principles of optical radiometry and measurement uncertainty, in Optical Radiometry for Ocean Climate Measurements, ed. by G. Zibordi, C.J. Donlon, A.C. Parr (Academic Press, Amsterdam, 2014), pp. 13–67

    Google Scholar 

  79. S.F. Johnston, A History of Light and Colour. Measurement Science in the Shadows (Institute of Physics Publishing, Bristol, UK, 2001)

    Google Scholar 

  80. R. Kacker, K.-D. Sommer, R. Kessel et al., Evolution of modern approaches to express uncertainty in measurement. Metrologia 44, 513–529 (2007)

    ADS  Google Scholar 

  81. T. Keawprasert, K. Anhalt, D.R. Taubert, A comparison of absolute calibrations of a radiation thermometer based on a monochromator and a tunable source. AIP Conf. Proc. 1552, 682–687 (2013)

    ADS  Google Scholar 

  82. B. Khlevnoy, CCPR S1 supplementary comparison. Final Report on CCPR-S1: Spectral Radiance 220 nm to 2500 nm. Metrologia 45, 02001 (2008), https://www.bipm.org/utils/common/pdf/final_reports/PR/S1/CCPR-S1.pdf. Accessed 16 Jan 2020

  83. G.R. Kirchhoff, Über die Verhältnis zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht. Ann. Phys. 109, 275–301 (1860)

    Google Scholar 

  84. L. Kirkup, R.B. Frenkel, An Introduction to Uncertainty in Measurement Using the GUM (Guide to the Expression of Uncertainty in Measurement) (Cambridge University Press, Cambridge, UK, 2006)

    MATH  Google Scholar 

  85. K.H. Knuth, Optimal data-based binning for histograms and histogram-based probability density models. Digital Signal Processing 95, 102581 (2019)

    Google Scholar 

  86. H.J. Kostkowski, F.E. Nicodemus, An introduction to the measurement equation, in Self-Study Manual on Optical Radiation Measurements: Part I—Concepts, Chapters 4 and 5. NBS Technical Note 910-2, ed. by F.E. Nicodemus (NBS, U.S. Dept. of Commerce, Washington, DC, 1978), pp. 58–92

    Google Scholar 

  87. H.J. Kostkowski, Reliable Spectroradiometry (Spectroradiometry Consulting, La Plata, MD, 1997)

    Google Scholar 

  88. D.P. Kroese, T. Taimre, Z.I. Botev, Handbook of Monte Carlo Methods (Wiley, Hoboken, NJ, 2011)

    MATH  Google Scholar 

  89. P. L’Ecuyer, R. Simard, TestU01: A C library for empirical testing of random number generators. ACM Trans. Math. Softw. 33, article 22, 1–40 (2007)

    Google Scholar 

  90. P. L’Ecuyer, Uniform random number generators, in International Encyclopedia of Statistical Science, ed. by M. Lovric (Springer, Heidelberg, 2011), pp. 1625–1630

    Google Scholar 

  91. B. Lane, E. Whitenton, V. Madhavan et al., Uncertainty of temperature measurements by infrared thermography for metal cutting applications. Metrologia 50, 637–653 (2013)

    ADS  Google Scholar 

  92. L. Laurencelle, F.-A. Dupuis, Statistical Tables. Explained and Applied (World Scientific Publ, River Edge, NJ, 2000)

    Google Scholar 

  93. J. Mandel, The Statistical Analysis of Experimental Data (Interscience Publ, New York, 1964)

    Google Scholar 

  94. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, UK, 1995)

    Google Scholar 

  95. J.M. Mantilla, M.L. Hernanz, J. Campos et al., Monochromator-based absolute calibration of a standard radiation thermometer. Int. J. Thermophys. 35, 493–503 (2014)

    ADS  Google Scholar 

  96. G. Marsaglia, W.W. Tsang, Some difficult-to-pass tests of randomness. J. Stat. Software 7, 1–9 (2002)

    Google Scholar 

  97. M. Matsumoto, T. Nishimura, Mersenne Twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8, 3–30 (1998)

    Google Scholar 

  98. J.C. Maxwell, A dynamical theory of the electromagnetic field. Phil. Trans. R. Soc. Lond. 155, 459–512 (1865)

    ADS  Google Scholar 

  99. K.D. Mielenz, R.D. Saunders, J.B. Shumaker, Spectroradiometric determination of the freezing temperature of gold. J. Res. Natl. Inst. Stand. Technol. 95, 49–67 (1990)

    Google Scholar 

  100. K.D. Mielenz, “Wolf shifts” and their physical interpretation under laboratory conditions. J. Res. Natl. Inst. Stand. Technol. 98, 231–240 (1993)

    Google Scholar 

  101. A. Migdall, S. Polyakov, J. Fan, J. Bienfang (eds.), Single-Photon Generation and Detection (Academic Press, Amsterdam, 2013)

    Google Scholar 

  102. G.J. Myatt, Making Sense of Data. A Practical Guide to Exploratory Data Analysis and Data Mining (Wiley, Hoboken, NJ, 2007)

    MATH  Google Scholar 

  103. F.E. Nicodemus, H.J. Kostkowski, Distribution of optical radiation with respect to position and direction—radiance, in Self-study Manual on Optical Radiation Measurements: Part I—Concepts, Chapters 1 to 3. NBS Tech. Note 910-1, ed. by F.E. Nicodemus (NBS, U.S. Dept. of Commerce, Washington, DC, 1976), pp. 10–44

    Google Scholar 

  104. K.A. Nugent, J.L. Gardner, Radiometric measurements and correlation-induced spectral changes. Metrologia 29, 319–324 (1992)

    ADS  Google Scholar 

  105. G.D. Nutter, Radiation thermometers: design principles and operating characteristics, in Theory and Practice of Radiation Thermometry, ed. by D.P. DeWitt, G.D. Nutter (Wiley, New York, 1988), pp. 231–337

    Google Scholar 

  106. E.L. O’Neill, Introduction to Statistical Optics (Dover, Mineola, NY, 1992)

    Google Scholar 

  107. Y. Ohno, Basic concepts in photometry, radiometry, and colorimetry, in Handbook of Optoelectronics, Volume 1: Concepts, Devices, and Techniques, 2nd ed., ed. by J.P. Dakin, R.G.W. Brown (CRC Press, Boca Raton, FL, 2018), pp. 265–279

    Google Scholar 

  108. Y. Ohno, Photometry, in Optical Radiometry, ed. by A.C. Parr et al. (Academic Press, Amsterdam, 2005), pp. 327–366

    Google Scholar 

  109. ÅA.F. Olsen, R.A. Bergerud, Traceable calibration of a radiation thermometer in the range 100 °C to 300 °C by model fitting. Int. J. Thermophys. 36, 1803–1812 (2015)

    ADS  Google Scholar 

  110. R. Palenčár, P. Sopkuliak, J. Palenčár et al., Application of Monte Carlo method for evaluation of uncertainties of ITS-90 by standard platinum resistance thermometer. Meas. Sci. Rev. 17, 108–116 (2017)

    Google Scholar 

  111. F.O. Panneton, P. L’Ecuyer, P. Matsumoto, Improved long-period generators based on linear recurrences modulo 2. ACM Trans. Math. Softw. 32, 1–16 (2006)

    MathSciNet  MATH  Google Scholar 

  112. A.C. Parr, The candela and photometric and radiometric measurements. J. Res. NIST 106, 151–186 (2000)

    Google Scholar 

  113. A.C. Parr, B.C. Johnson, The use of filtered radiometers for radiance measurement. J. Res. Natl. Inst. Stand. Technol. 116, 751–760 (2011)

    Google Scholar 

  114. J.V. Pearce, P.M. Harris, J.C. Greenwood, Evaluating uncertainties in interpolations between calibration data for thermocouples. Int. J. Thermophys. 31, 1517–1526 (2010)

    ADS  Google Scholar 

  115. J. Piotrowski, Theory of Physical and Technical Measurement (Elsevier, Amsterdam, 1992)

    Google Scholar 

  116. M. Planck, The Theory of Heat Radiation (P. Blakiston’s Son & Co., Philadelphia, PA, 1914)

    MATH  Google Scholar 

  117. M. Planck, Theory of Light (Macmillan and Co., London, 1932)

    MATH  Google Scholar 

  118. T. Poikonen, P. Kärhä, P. Manninen et al., Uncertainty analysis of photometer quality factor. Metrologia 46, 75–80 (2009)

    ADS  Google Scholar 

  119. T. Poikonen, P. Blattner, P. Kärhä et al., Uncertainty analysis of photometer directional response index using Monte Carlo simulation. Metrologia 49, 727–736 (2012)

    ADS  Google Scholar 

  120. W.H. Press, S.A. Teukolsky, H.A. Bethe et al., Numerical Recipes: The Art of Scientific Computing, 3rd ed. (Cambridge University Press, Cambridge, UK, 2007)

    Google Scholar 

  121. M. Priel, From GUM to alternative methods for measurement uncertainty evaluation. Accred. Qual. Assur. 14, 235–241 (2009)

    Google Scholar 

  122. A. Prokhorov, V. Sapritsky, B. Khlevnoy, Alternative methods of blackbody thermodynamic temperature measurement above silver point. Int. J. Thermophys. 36, 252–266 (2015)

    ADS  Google Scholar 

  123. S.G. Rabinovich, Evaluating Measurement Accuracy. A Practical Approach, 3rd ed. (Springer, Cham, Switzerland, 2017)

    Google Scholar 

  124. C. Ratcliffe, B. Ratcliffe, Doubt-Free Uncertainty in Measurement. An Introduction for Engineers and Students (Springer, Cham, Switzerland, 2015)

    Google Scholar 

  125. P. Rosenkranz, Uncertainty propagation for platinum resistance thermometers calibrated according to ITS-90. Int. J. Thermophys. 32, 106–119 (2011)

    ADS  Google Scholar 

  126. A. Rukhin, J. Soto, J. Nechvatal et al., A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. NIST Spec. Publ. 800-22 Revision 1a (U.S. Dept. of Commerce, NIST, 2010)

    Google Scholar 

  127. P. Saunders, Analysis of the potential accuracy of thermodynamic measurement using the double-wavelength technique. Int. J. Thermophys. 35, 417–437 (2014)

    ADS  Google Scholar 

  128. SCHOTT, KG5 Data Sheet. SCHOTT North America, Inc. (2014), https://www.sydor.com/wp-content/uploads/2019/06/SCHOTT-KG5-Shortpass-Filter.pdf. Accessed 11 Jun 2020

  129. D.W. Scott, Sturges’ rule. WIREs. Comput. Stat. 1, 44–48 (2009)

    Google Scholar 

  130. D.W. Scott, Histogram. WIREs. Comput. Stat. 2, 203–306 (2010)

    Google Scholar 

  131. K.D. Sommer, B.R.L. Siebert, Systematic approach to the modelling of measurements for uncertainty evaluation. Metrologia 43, S200–S210 (2006)

    ADS  Google Scholar 

  132. H.-J. Song, T. Nagatsuma (eds.), Handbook of Terahertz Technologies. Devices and Applications (CRC Press, Boca Raton, FL, 2015)

    Google Scholar 

  133. S.S. Stevens, On the theory of scales of measurement. Science 103, 677–680 (1946)

    ADS  MATH  Google Scholar 

  134. B.N. Taylor, C.E. Kuyatt, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results. NIST Technical Note 1297 (1994 Edition.) (NIST, U.S. Dept. of Commerce, Washington, DC, 1994)

    Google Scholar 

  135. D.B. Thomas, W. Luk, P.H.W. Leong et al., Gaussian random number generators. ACM Comput. Surv. 39, 11 (2007)

    Google Scholar 

  136. A.S. Tistomo, D. Larassati, A. Achmadi et al., Estimation of uncertainty in the calibration of industrial platinum resistance thermometers (IPRT) using Monte Carlo method. MĀPAN—J. Metrol. Soc. India 32, 273–278 (2017)

    Google Scholar 

  137. B.K. Tsai, B.C. Johnson, Evaluation of uncertainties in fundamental radiometric measurements. Metrologia 35, 587–593 (1998)

    ADS  Google Scholar 

  138. F. Vignola, J. Michalsky, T. Stoffel, Solar and Infrared Radiation Measurements (CRC Press, Boca Raton, FL, 2012)

    Google Scholar 

  139. J.H. Walker, R.D. Saunders, A.T. Hattenburg, The NBS scale of spectral radiance. Metrologia 24, 79–88 (1987)

    ADS  Google Scholar 

  140. L. Werner, H.-W. Hübers, P. Meindl et al., Towards traceable radiometry in the terahertz region. Metrologia 46, S160–S164 (2009)

    Google Scholar 

  141. W. Wien, Temperatur und Entropie der Strahlung. Ann. Phys. 288, 133–165 (1894)

    MATH  Google Scholar 

  142. R. Willink, On using the Monte Carlo method to calculate uncertainty intervals. Metrologia 43, L39–L42 (2006)

    ADS  Google Scholar 

  143. R. Willink, A generalization of the Welch-Satterthwaite formula for use with correlated uncertainty components. Metrologia 44, 340–349 (2007)

    ADS  Google Scholar 

  144. E. Wolf, Selected Works of Emil Wolf With Commentary (World Scientific Publishing, Singapore, 2001)

    Google Scholar 

  145. W.L. Wolfe, Introduction to Radiometry (SPIE Press, Bellingham, WA, 1998)

    Google Scholar 

  146. E.R. Woolliams, R. Winkler, S.G.R. Salim et al., The double-wavelength technique—an alternative technique to determine thermodynamic temperature. Int. J. Thermophys. 30, 144–154 (2009)

    ADS  Google Scholar 

  147. E.R. Woolliams, Uncertainty analysis for filter radiometry based on the uncertainty associated with integrated quantities. Int. J. Thermophys. 35, 1353–1365 (2014)

    ADS  Google Scholar 

  148. G. Wyszecki, W.R. Blevin, K.G. Kessler, K.D. Mielenz, Principes régissant la photométrie/Principles Governing Photometry (BIPM, Sèvres, France, 1983), https://www.bipm.org/utils/common/pdf/monographies-misc/Monographie1983-1.pdf. Accessed 28 Mar 2017

  149. Y. Yamaguchi, Y. Yamada, J. Ishii, Supercontinuum-source-based facility for absolute calibration of radiation thermometers. Int. J. Thermophys. 36, 1825–1833 (2015)

    ADS  Google Scholar 

  150. H.W. Yoon, C.E. Gibson, P.Y. Barnes, Realization of the National Institute of Standards and Technology detector-based spectral irradiance scale. Appl. Opt. 41, 5879–5890 (2002)

    ADS  Google Scholar 

  151. H.W. Yoon, C.E. Gibson, NIST Measurement Services: Spectral Irradiance Calibrations. NIST Spec. Publ. 250-89 (NIST, Gaithersburg, MD, 2011)

    Google Scholar 

  152. S. Yurtseven, O. Pehlivan, H. Nasibov, Size-of-source (SSE) effect of broadband and interference filters for double wavelength thermometers. J. Phys. Conf. Ser. 1065, 122015 (2018)

    Google Scholar 

  153. E.F. Zalewski, Radiometry and photometry, in Handbook of Optics. Volume II: Design, Fabrication, and Testing; Sources and Detectors; Radiometry and Photometry, 3rd ed., ed. by M. Bass (McGraw-Hill, New York, 2010), pp. 34.3–34.47

    Google Scholar 

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Sapritsky, V., Prokhorov, A. (2020). Essentials of Optical Radiation Metrology. In: Blackbody Radiometry. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-57789-6_2

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