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

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Library of Congress Cataloging in Publication Data Ohta, Noboru. Colorimetry : fundamentals and applications / Noboru Ohta, Alan R. Robertson. p. cm. — (Wiley-IS&T series in imaging science and technology) Includes bibliographical references and index. ISBN-13 978-0-470-09472-3 ISBN-10 0-470-09472-9 (cloth : alk. paper) 1. Colorimetry. I. Robertson, Alan A. 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. He is for- mer President of the Inter- national Color Association (AIC) and Vice President of the International Com- mission on Illumination (CIE). In 2005, he received the Godlove Award of the Inter-Society Color Council (ISCC) for long-term contri- butions in the field of color. Series Preface

How do we define colour? For the most part we are told in our early childhood that an apple is red, a banana is yellow, a lime is green and an orange is orange. Hence, our introduction to colour is a learning process whereby we relate a ‘colour stimulus’ to a descrip- tive term (which changes with language, of course) supplied by our parents, siblings or teachers. Probably the biggest introduction to colour is the 64 or 128 pack of Crayons® or the 16-colour set of watercolors. Invariably we were told about the primary colours of red, blue, green and yellow or some other set that was popular with those teaching art in elementary schools. There was no con- cept of additive and subtractive primaries let alone the concepts of hue, chroma and value. Outside of those of us who were artistically gifted or inclined, the biggest issue with colour was matching the paint chips for the living room walls with the choice of fabric for the drapes or the colour of the new car. Our ability to define a colour to others was almost always limited to saying it is sort of sky blue, apple red, lemon yellow or lawn green. In short there was no easy way to define a colour short of having a physical example of what you wanted (and then in a given illuminant). How many times did one buy a matching skirt and blouse or sweater and slacks in a store illuminated by tungsten or fluorescent light sources only to find that the colours shifted (in an undesirable way) in daylight? The science of Colorimetry has evolved to help resolve the above shortcomings of our learned perceptions of colour. The third offer- ing in the Wiley-IS &T Series in Imaging Science and Technology is Colorimetry, Fundamentals and Applications. This text provides a systematic and unambiguous exposition of how colour is defined, measured and seen by human observers under different viewing conditions. In the seven chapters and four appendices of Colorime- try the reader will find both a logical and historic exposition of how colour is physically measured, the methods used to incorporate how xii SERIES PREFACE the human observer sees the physical stimulus and some practical applications of colorimetry. The authors, Dr Noboru Ohta, of Fuji Photo Film and the Rochester Institute of Technology (RIT), and Dr Alan R. Robertson, National Research Council (NRC) of Canada, have a combined expe- rience in colorimetry of over 70 years. Dr Ohta was a scientist and manager in the Fuji Research Laboratories, where early in his career he focused on the colour aspects of conventional photographic films and image structure. Dr Ohta made the transition to electronic colour imaging systems during the later years at Fuji and has con- tinued his research in electronic colour imaging systems at the Munsell Color Science Laboratory in the Chester F. Carlson Center for Imaging Science at RIT. Dr Robertson has had a long, active and distinguished career in all facets of colorimetry at the NRC, where he rose from a post doctorate fellow to senior research officer to director over his 35 years of service. He has had a major role in the growth of the International Commission on Illumination (CIE) and the International Color Association (AIC), where his efforts resulted in the CIE having the ability to publish colour standards in coop- eration with the International Organization of Standardization. In 2005, Dr Robertson received the Godlove Award from the Inter- Society Color Council (ISCC) for his long and distinguished service to the colour community. In the early 1970s, Dr Ohta spent several years at the NRC work- ing under the guidance of Dr Gunter Wyszecki. During his stay at the NRC, he met Dr Robertson, thus beginning their long collabora- tion and friendship. Their combined research in colour, colorimetry and applications of colorimetry and teaching of colorimetry has resulted in this lucid, concise and practical text. When combined with Mark Fairchild’s Color Appearance Models (2nd Edition) and Robert Hunt’s The Reproduction of Colour (6th Edition), the Wiley- IS&T Series in Imaging Science and Technology provides the student and practitioner of imaging science a comprehensive treatment of colour and colour science. MICHAEL A. KRISS Formerly of the Eastman Kodak Research Laboratories and the University of Rochester Preface

The original version of this book was published in Japanese by the first author. It has had a wide variety of readers in Japan rang- ing from undergraduate and graduate students in universities to engineers in industries. Due to its success in the Japanese lan- guage, Chinese and Korean versions were published soon after the Japanese one. Considering the nature of the book, which covers basic knowl- edge for novices, practical applications for industrial engineers, and advanced developments for researchers, we have decided to publish an English version to make the content available and, hopefully, useful to a much wider range of readers. However the present book is not merely a literal translation of the Japanese version since that is already more than 10 years old. Instead, we have thoroughly reviewed the content, partly truncated obsolete sections, extensively expanded others, incorporated recent knowledge and added new material that has emerged since the first publication. In writing the book, we employed a variety of materials from books, journals, standards, etc. We gratefully acknowledge the many publishers who kindly gave us citation permission for using their material. We also would like to express our deep apprecia- tion to our friend, the late Dr Heinz Terstiege of the Bundesanstalt für Materialforschung undprufüng, Germany, for the original pho- tographs of color scientists. Finally we would like to express our deepest thanks to Tokyo Denki Daigaku Shuppankyoku, the publisher of the original Japanese version, who kindly gave us permission to translate the Japanese version into the present English one. Noboru Ohta Alan R. Robertson