Colorimetry Fundamentals and Applications Noboru Ohta Rochester Institute of Technology, USA Alan R. Robertson National Research Council of Canada, Ottawa, Canada (retired) Colorimetry Wiley–IS&T Series in Imaging Science and Technology Series Editor: Michael A. Kriss Consultant Editors: Anthony C. Lowe Lindsay W. MacDonald Yoichi Miyake The Reproduction of Colour (6th Edition) R. W. G. Hunt Color Appearance Models (2nd Edition) Mark D. Fairchild Colorimetry: Fundamentals and Applications Noboru Ohta and Alan R. Robertson Published in Association with the Society for Imaging Science and Technology Colorimetry Fundamentals and Applications Noboru Ohta Rochester Institute of Technology, USA Alan R. Robertson National Research Council of Canada, Ottawa, Canada (retired) Copyright © 2005 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. 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II. Title. III. Series. QC495.8.038 2005 535.6—dc22 2005013963 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN-13 978-0-470-09472-3 (HB) ISBN-10 0-470-09472-9 (HB) Typeset in 10/12pt Bookman by Integra Software Services Pvt. Ltd, Pondicherry, India Printed and bound in Great Britain by TJ International Ltd, Padstow, Cornwall This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production. Contents About the Authors ix Series Preface xi Preface xiii Introduction xv 1 Light, Vision and Photometry 1 1.1 Light 1 1.2 Mechanism of the Human Eye 4 1.3 Adaptation and Responsivity of the Human Eye 7 1.4 Spectral Responsivity and the Standard Photometric Observer 9 1.5 Definition of Photometric Quantities 17 1.6 Photometric Units 21 1.7 Calculation and Measurement of Photometric Quantities 26 1.8 Relations Between Photometric Quantities 31 Note 1.1 Luminous Exitance, Illuminance, and Luminance of a Perfect Diffusing Plane Light Source 34 Note 1.2 Luminance and Brightness 36 2 Color Vision and Color Specification Systems 39 2.1 Mechanism of Color Vision 39 2.2 Chemistry of Color Vision 46 2.3 Color Specification and Terminology 48 2.4 Munsell Color System 52 2.5 Color System Using Additive Color Mixing 57 Note 2.1 Colorfulness, Chroma and Saturation 61 3 CIE Standard Colorimetric System 63 3.1 RGB Color Specification System 63 3.2 Conversion into XYZ Color Specification System 68 vi CONTENTS X Y Z 3.3 10 10 10 Color Specification System 71 3.4 Tristimulus Values and Chromaticity Coordinates 74 3.5 Metamerism 76 3.6 Dominant Wavelength and Purity 78 3.7 Color Temperature and Correlated Color Temperature 82 3.8 Illuminants and Light Sources 85 3.9 Standard and Supplementary Illuminants 92 Note 3.1 Derivation of Color Matching Functions from Guild and Wright’s Results 96 Note 3.2 Conversion between Color Specification Systems 99 Note 3.3 Conversion into XYZ Color Specification System 101 Note 3.4 Imaginary Colors [X] and [Z] 105 X Y Z Note 3.5 Photometric Quantities in the 10 10 10 Color System 108 Note 3.6 Origin of the Term ‘Metamerism’ 109 Note 3.7 Simple Methods for Obtaining Correlated Color Temperature 110 Note 3.8 Color Temperature Conversion Filter 111 Note 3.9 Spectral Distribution of Black-body Radiation 113 4 Uniform Color Spaces 115 4.1 Uniform Chromaticity Diagrams 115 4.2 Uniform Lightness Scales (ULS) 122 4.3 CIE Uniform Color Spaces 127 4.4 Correlates of Perceived Attributes 132 4.5 Comparing CIELAB and CIELUV Color Spaces 134 4.6 Conversion of Color Difference 140 4.7 Color Difference Equations Based on CIELAB 143 Note 4.1 Calculation of Munsell Value V from Luminous Reflectance Y 144 Note 4.2 Modified CIELAB and CIELUV Equations for Dark Colors 146 Note 4.3 Other Color Difference Formulas 147 Note 4.4 Direct Calculation of Hue Difference H* 150 5 Measurement and Calculation of Colorimetric Values 153 5.1 Direct Measurement of Tristimulus Values 153 5.2 Spectral Colorimetry 156 5.3 Geometrical Conditions for Measurement 158 5.4 Calculation of Colorimetric Values 161 CONTENTS vii 5.5 Colorimetric Values in CIELAB and CIELUV Uniform Color Spaces 167 Note 5.1 Spectral Colorimetry of Fluorescent Materials 172 Note 5.2 Reference Standard for Reflection Measurements 173 6 Evolution of CIE Standard Colorimetric System 175 6.1 Additive Mixing 176 6.2 Subtractive Mixing 180 6.3 Maximum Value of Luminous Efficacy and Optimal Colors 184 6.4 Chromatic Adaptation Process 188 6.5 von Kries’ Predictive Equation for Chromatic Adaptation 191 6.6 CIE Predictive Equations for Chromatic Adaptation 194 6.7 Color Vision Models 197 6.8 Color Appearance Models 198 6.9 Analysis of Metamerism 204 Note 6.1 Color Mixing Rule 211 Note 6.2 Lambert–Beer Law 213 Note 6.3 Method for Calculating the Maximum Value of the Luminous Efficacy of Radiation 214 Note 6.4 Method for Calculating Optimal Colors 215 Note 6.5 Method for Obtaining Fundamental Spectral Responsivities 216 Note 6.6 Deducing von Kries’ Predictive Equation for Chromatic Adaptation 221 Note 6.7 Application of von Kries’ Equation for Chromatic Adaptation 223 Note 6.8 Application of CIE 1994 Chromatic Adaptation Transform 225 Note 6.9 Theoretical Limits for Deviation from Metamerism 226 7 Application of CIE Standard Colorimetric System 229 7.1 Evaluation of the Color Rendering Properties of Light Sources 229 7.2 Evaluation of the Spectral Distribution of Daylight Simulators 237 7.3 Evaluation of Whiteness 242 7.4 Evaluation of Degree of Metamerism for Change of Illuminant 244 viii CONTENTS 7.5 Evaluation of Degree of Metamerism for Change of Observer 249 7.6 Designing Spectral Distributions of Illuminants 255 7.7 Computer Color Matching 261 Note 7.1 Computation Method for Prescribed Spectral Distributions 268 Appendix I Basic Units and Terms 271 AI.1 SI Units 271 AI.2 Prefixes for SI Units 272 AI.3 Fundamental Constants 272 AI.4 Greek Letters 272 Appendix II Matrix Algebra 275 AII.1 Addition and Subtraction of Matrices 276 AII.2 Multiplication of Matrices 277 AII.3 Inverse Matrix 277 AII.4 Transpose Matrix 278 Appendix III Partial Derivatives 281 Appendix IV Tables 285 References 321 Bibliography 327 Index 329 About the Authors Noboru Ohta Noboru Ohta earned his B.Sci., M.Sci., and Dr.Eng. from the University of Tokyo. In 1968, he joined Fuji Photo Film and from 1973, he spent three years under Gunter Wyszecki at the National Research Council of Canada. He has taught colorime- try and color reproduction at a variety of universities. He joined Rochester Insti- tute of Technology in 1998, and is associated there with the Munsell Color Science Laboratory in the Center for Imaging Science. He has published more than 100 technical papers in Japanese and English, and several books on colorimetry and color reproduc- tion in Japanese, Chinese, and Korean. He has been active in a vari- ety of academic societies, and also in standards organizations such as the Japanese Industrial Standards (JIS), the American National Standards Institute (ANSI), and the International Commission on Illumination (CIE). x ABOUT THE AUTHORS Alan R. Robertson Alan Robertson earned his B.Sc and Ph.D. from the University of London, where he studied under David Wright. He then joined Gunter Wyszecki at the National Research Coun- cil of Canada and spent 35 years there before retir- ing in 2000. He has pub- lished over 50 papers in journals and conference proceedings and has given more than 60 invited talks in 10 countries.