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E. Gorbunova, A. Chertov Colorimetry of Radiation Sources

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E. Gorbunova, A. Chertov Colorimetry of Radiation Sources E. Gorbunova, A. Chertov COLORIMETRY OF RADIATION SOURCES St. Petersburg 2016 THE MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION ITMO UNIVERSITY E. Gorbunova, A. Chertov COLORIMETRY OF RADIATION SOURCES TEXTBOOK St. Petersburg 2016 2 E. Gorbunova, A. Chertov Colorimetry of radiation sources. Textbook. – SPb: ITMO University, 2016. – 124 pages Theoretical framework and calculation methodology for tristimulus values and source radiation chromaticity coordinates are given. General outline of vision physiological basis is also presented. In addition, colorimetry basic terms and definitions as well as principles of color space construction are given. Besides, rules for color temperature (and correlated color temperature) calculation and calculation of color rendering index for the radiation source are given. The textbook is intended for students majoring for a Master's degree 12.04.02 - "Optical Engineering". Recommended for publication by the Academic Board of the Laser and Light Engineering Department, Minutes No. 13 of December 13, 2016. ITMO University is the leading Russian university in the field of information and photonic technologies, one of the few Russian universities with the status of the national research university granted in 2009. Since 2013 ITMO University has been a participant of the Russian universities' competitiveness raising program among the world's leading academic centers known as "5-100". Objective of ITMO University is the establishment of a world-class research university being entrepreneurial in nature, oriented at the internationalization of all fields of activity. ITMO University, 2016 E. Gorbunova, A. Chertov, 2016 3 CONTENT ABBREVIATIONS ............................................................................................... 5 DESIGNATIONS .................................................................................................. 6 1 COLOR PERCEPTION ..................................................................................... 9 1.1 Constitution of the human visual apparatus ............................................ 9 1.2 The mechanism of light and color sensation ......................................... 15 1.3 Eye movements ..................................................................................... 19 1.4 Adaptation of visual perception ............................................................ 23 2 COLOR – CONCEPTS, DEFINITIONS AND PROPERTIES ...................... 27 3 COLOR REPRESENTATION AND COLOR REPRODUCTION SYSTEMS (COLOR SPACES) .......................................................................... 35 3.1 Methods for color mixing ..................................................................... 35 3.2 Grassmann's Laws ................................................................................. 37 3.3 Properties of color spaces ..................................................................... 39 3.4 Color measurement systems .................................................................. 40 4 PROPERTIES OF RADIATION SOURCES (ENERGETIC, SPECTRAL AND SPATIAL) .................................................................................................. 46 4.1 Basic values and units of measurement ................................................ 46 4.2 Emitting diodes characteristics ............................................................. 49 5 CALCULATION OF COLOR COORDINATES FROM THE SPECTRAL PROPERTIES OF RADIATION SOURCES ................................ 56 6 COLOR TEMPERATURE CONCEPT ........................................................... 64 7 RECALCULATION OF COLOR COORDINATES ...................................... 71 7.1 Calculation of color coordinates in CIE 2003 color space L*a*b* ...... 71 7.2 Color coordinates calculation in the CIE 1976 color space L*u*v* ..... 72 7.3 Color coordinates calculation in the CIE 1976 color space CIE LCH ............................................................................................................. 73 7.4 Conversion from XYZ color space into RGB color space ..................... 75 8 DETERMINATION OF SMALL COLOR DIFFERENCES .......................... 80 9 COLOR RENDERING INDICES OF RADIATION SOURCES ................... 86 9.1 Colour rendering index for radiation sources located on the Planck's curve .................................................................................................................... 89 9.2 Calculation of the colour rendering index for radiation sources located outside the Planck's curve ....................................................................... 91 10 MODELING OF RADIATION SOURCES WITH PREDEFINED CHROMATICITY .............................................................................................. 95 LITERATURE REFERENCES ........................................................................ 101 APPENDICES ................................................................................................... 103 4 ABBREVIATIONS CCT – correlated color temperature. CIE – International Commission on Illumination (Commission Internationale de l´Eclairage). CT – color temperature. ED – emitting diode. IR – infrared. L cones – visual receptor retina cells containing Rhodopsin 5 erithrolab pigment (photosensitive in the red spectral range). M cones – visual receptor retina cells containing Rhodopsin 7 chlorolab pigment (photosensitive in the green spectral range). S cones – visual receptor retina cells containing Rhodopsin 9 cyanolab pigment (photosensitive in the blue spectral range). UV – ultraviolet. 5 DESIGNATIONS A type source is a source with the relative spectral energy distribution in the visible portion of spectrum relevant to the radiation of a black body at the temperature equal to 2856°K (GOST 7721-89). A is the color. B type source is a source with the relative spectral energy distribution in the visible portion of spectrum relevant to the radiation of a black body at the temperature equal to 4874°K. It reproduces the conditions of direct solar lighting (GOST 7721-89). c is the speed of light in vacuum (3 108 m/s). C type source is a source with the relative spectral energy distribution in the visible portion of spectrum relevant to the radiation of a black body at the temperature equal to 6774°К. It reproduces the lighting conditions with diffused daylight (GOST 7721-89). CRI is complete color rendering index. CRIi is particulate color rendering index. d is the distance from the point characterizing the radiation source under study to the nearest isothermal line on the CIE 1976 color diagram. D65 type source is a source with the relative spectral energy distribution in the visible portion of spectrum relevant to the radiation of a black body at the temperature equal to 6504°K. It reproduces the lighting conditions with average daylight (GOST 7721-89). E is the illuminance. E is the color of a white surface illuminated with E type source. E type source is a source with the constant spectral radiant intensity in the visible portion of spectrum. fQB is the distribution of carriers in the allowed bands of a nongenerated semiconductor. h is Planck's constant (h 6,6262 1034 J·s). h is photon energy. I is radiation intensity (luminous intensity). K is the weighting factor. Km is maximum spectral luminous efficacy of radiation at 0,555µm ( Km 683lm/W). k is Boltzmann's constant (k 1,38067 1023 J/K). kc is the multiplier. kv is the quasi-wave vector. L is brightness. M is luminosity. 6 M () is spectral luminosity distribution of the radiation source. me is effective electron mass. mh is effective hole mass. mr is reduced mass. nair is air refractive index. ns is semiconductor refractive index. P () is distribution of source spectral radiant density according to the wave length. P max is maximum distribution of source spectral radiant density. Q is energy. QC is conduction band extremum energy. QE is electron energy in the conduction band. Qg is bandgap energy. QH is hole energy in the valence band. Q is valence band extremum energy. V RGB is the three-color system utilizing three major colors R , G and B . Ri () is radiation reflectivity spectral distribution of the i -th surface. r is the radius. r0 () , g0 () , b0 () are color match physiological curves. (,)rf are chromaticity coordinates for color space Lu v characterizing adaptive colorimetric shift of coordinates (,)uv when using the illumination source under consideration. T is temperature in Kelvin degrees. t is the tangent of the isothermal line inclination. Tc is the color temperature of the radiation source. Tc is correlated the color temperature of the radiation source. ts is the time. u , v are chromaticity coordinates on the CIE 1976 color diagram. V is the relative curve of eye visibility (relative spectral luminous efficiency of monochromatic radiation). x , y are chromaticity coordinates on the CIE 1931 color diagram. x , y , z are color coordinates of XYZ color space. x() , y() , z () are color match curves in XYZ color measurement system. xWWW,, y z are color coordinates of a white light source in XYZ color space. is the three-color system utilizing three major colors X , Y and Z . 7 c is the limiting angle of total internal reflection. is the wavelength. begin is the wavelength for the "beginning" of the spectral distribution. dom is the dominant wavelength. end is the wavelength for the "end" of the spectral distribution. max is the wavelength for the maximum spectral distribution. Q is the energy-dependent combined
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