ColorimetryFundamentals and

Applications

Noboru OhtaRochester Institute of Technology, USA

Alan R. RobertsonNational Research Council of Canada, Ottawa, Canada (retired)

Innodata0470094737.jpg

Colorimetry

Wiley–IS&T Series in Imaging Science and Technology

Series Editor:Michael A. Kriss

Consultant Editors:Anthony C. LoweLindsay W. MacDonaldYoichi Miyake

The Reproduction of Colour (6th Edition)R. W. G. Hunt

Color Appearance Models (2nd Edition)Mark D. Fairchild

Colorimetry: Fundamentals and ApplicationsNoboru Ohta and Alan R. Robertson

Published in Association with the Society for ImagingScience and Technology

ColorimetryFundamentals and

Applications

Noboru OhtaRochester Institute of Technology, USA

Alan R. RobertsonNational Research Council of Canada, Ottawa, Canada (retired)

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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-13 978-0-470-09472-3ISBN-10 0-470-09472-9 (cloth : alk. paper)1. Colorimetry. I. Robertson, Alan A. II. Title. III. Series.QC495.8.038 2005535.6—dc22

2005013963

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Contents

About the Authors ixSeries Preface xiPreface xiiiIntroduction xv

1 Light, Vision and Photometry 11.1 Light 11.2 Mechanism of the Human Eye 41.3 Adaptation and Responsivity of the Human Eye 71.4 Spectral Responsivity and the Standard

Photometric Observer 91.5 Definition of Photometric Quantities 171.6 Photometric Units 211.7 Calculation and Measurement of Photometric

Quantities 261.8 Relations Between Photometric Quantities 31

Note 1.1 Luminous Exitance, Illuminance, andLuminance of a Perfect Diffusing Plane LightSource 34

Note 1.2 Luminance and Brightness 36

2 Color Vision and Color Specification Systems 392.1 Mechanism of Color Vision 392.2 Chemistry of Color Vision 462.3 Color Specification and Terminology 482.4 Munsell Color System 522.5 Color System Using Additive Color Mixing 57

Note 2.1 Colorfulness, Chroma and Saturation 61

3 CIE Standard Colorimetric System 633.1 RGB Color Specification System 633.2 Conversion into XYZ Color Specification System 68

vi CONTENTS

3.3 X10Y10Z10 Color Specification System 713.4 Tristimulus Values and Chromaticity

Coordinates 743.5 Metamerism 763.6 Dominant Wavelength and Purity 783.7 Color Temperature and Correlated Color

Temperature 823.8 Illuminants and Light Sources 853.9 Standard and Supplementary Illuminants 92

Note 3.1 Derivation of Color Matching Functions fromGuild and Wright’s Results 96

Note 3.2 Conversion between Color Specification Systems 99Note 3.3 Conversion into XYZ Color Specification System 101Note 3.4 Imaginary Colors [X] and [Z] 105Note 3.5 Photometric Quantities in the X10Y10Z10 Color

System 108Note 3.6 Origin of the Term ‘Metamerism’ 109Note 3.7 Simple Methods for Obtaining Correlated Color

Temperature 110Note 3.8 Color Temperature Conversion Filter 111Note 3.9 Spectral Distribution of Black-body Radiation 113

4 Uniform Color Spaces 1154.1 Uniform Chromaticity Diagrams 1154.2 Uniform Lightness Scales (ULS) 1224.3 CIE Uniform Color Spaces 1274.4 Correlates of Perceived Attributes 1324.5 Comparing CIELAB and CIELUV Color Spaces 1344.6 Conversion of Color Difference 1404.7 Color Difference Equations Based on CIELAB 143

Note 4.1 Calculation of Munsell Value V from LuminousReflectance Y 144

Note 4.2 Modified CIELAB and CIELUV Equations forDark Colors 146

Note 4.3 Other Color Difference Formulas 147Note 4.4 Direct Calculation of Hue Difference �H* 150

5 Measurement and Calculation of ColorimetricValues 1535.1 Direct Measurement of Tristimulus Values 1535.2 Spectral Colorimetry 1565.3 Geometrical Conditions for Measurement 1585.4 Calculation of Colorimetric Values 161

CONTENTS vii

5.5 Colorimetric Values in CIELAB and CIELUVUniform Color Spaces 167

Note 5.1 Spectral Colorimetry of Fluorescent Materials 172Note 5.2 Reference Standard for Reflection

Measurements 173

6 Evolution of CIE Standard Colorimetric System 1756.1 Additive Mixing 1766.2 Subtractive Mixing 1806.3 Maximum Value of Luminous Efficacy and

Optimal Colors 1846.4 Chromatic Adaptation Process 1886.5 von Kries’ Predictive Equation for Chromatic

Adaptation 1916.6 CIE Predictive Equations for Chromatic

Adaptation 1946.7 Color Vision Models 1976.8 Color Appearance Models 1986.9 Analysis of Metamerism 204

Note 6.1 Color Mixing Rule 211Note 6.2 Lambert–Beer Law 213Note 6.3 Method for Calculating the Maximum Value of

the Luminous Efficacy of Radiation 214Note 6.4 Method for Calculating Optimal Colors 215Note 6.5 Method for Obtaining Fundamental Spectral

Responsivities 216Note 6.6 Deducing von Kries’ Predictive Equation for

Chromatic Adaptation 221Note 6.7 Application of von Kries’ Equation for Chromatic

Adaptation 223Note 6.8 Application of CIE 1994 Chromatic Adaptation

Transform 225Note 6.9 Theoretical Limits for Deviation from

Metamerism 226

7 Application of CIE Standard Colorimetric System 2297.1 Evaluation of the Color Rendering Properties of

Light Sources 2297.2 Evaluation of the Spectral Distribution of

Daylight Simulators 2377.3 Evaluation of Whiteness 2427.4 Evaluation of Degree of Metamerism for Change

of Illuminant 244

viii CONTENTS

7.5 Evaluation of Degree of Metamerism for Changeof Observer 249

7.6 Designing Spectral Distributions of Illuminants 2557.7 Computer Color Matching 261

Note 7.1 Computation Method for Prescribed SpectralDistributions 268

Appendix I Basic Units and Terms 271AI.1 SI Units 271AI.2 Prefixes for SI Units 272AI.3 Fundamental Constants 272AI.4 Greek Letters 272

Appendix II Matrix Algebra 275AII.1 Addition and Subtraction of Matrices 276AII.2 Multiplication of Matrices 277AII.3 Inverse Matrix 277AII.4 Transpose Matrix 278

Appendix III Partial Derivatives 281

Appendix IV Tables 285

References 321Bibliography 327Index 329

About the Authors

Noboru Ohta

Noboru Ohta earned hisB.Sci., M.Sci., and Dr.Eng.from the University ofTokyo. In 1968, he joinedFuji Photo Film and from1973, he spent three yearsunder Gunter Wyszeckiat the National ResearchCouncil of Canada.He has taught colorime-

try and color reproductionat a variety of universities.He joined Rochester Insti-tute of Technology in 1998,and is associated there withthe 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 suchas the Japanese Industrial Standards (JIS), the American NationalStandards Institute (ANSI), and the International Commission onIllumination (CIE).

x ABOUT THE AUTHORS

Alan R. Robertson

Alan Robertson earned hisB.Sc and Ph.D. from theUniversity of London, wherehe studied under DavidWright. He then joinedGunter Wyszecki at theNational Research Coun-cil of Canada and spent35 years there before retir-ing in 2000. He has pub-lished over 50 papers injournals and conferenceproceedings and has givenmore than 60 invited talksin 10 countries. He is for-mer President of the Inter-national Color Association(AIC) and Vice Presidentof the International Com-mission on Illumination(CIE). In 2005, he receivedthe Godlove Award of theInter-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 earlychildhood that an apple is red, a banana is yellow, a lime is greenand an orange is orange. Hence, our introduction to colour is alearning process whereby we relate a ‘colour stimulus’ to a descrip-tive term (which changes with language, of course) supplied by ourparents, siblings or teachers. Probably the biggest introduction tocolour is the 64 or 128 pack of Crayons® or the 16-colour set ofwatercolors. Invariably we were told about the primary colours ofred, blue, green and yellow or some other set that was popularwith those teaching art in elementary schools. There was no con-cept of additive and subtractive primaries let alone the concepts ofhue, chroma and value. Outside of those of us who were artisticallygifted or inclined, the biggest issue with colour was matching thepaint chips for the living room walls with the choice of fabric for thedrapes or the colour of the new car. Our ability to define a colourto 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 easyway to define a colour short of having a physical example of whatyou wanted (and then in a given illuminant). How many times didone buy a matching skirt and blouse or sweater and slacks in astore illuminated by tungsten or fluorescent light sources only tofind 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 isColorimetry, Fundamentals and Applications. This text provides asystematic and unambiguous exposition of how colour is defined,measured and seen by human observers under different viewingconditions. In the seven chapters and four appendices of Colorime-try the reader will find both a logical and historic exposition of howcolour is physically measured, themethods used to incorporate how

xii SERIES PREFACE

the human observer sees the physical stimulus and some practicalapplications 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 andmanager in the Fuji Research Laboratories, where early in his careerhe focused on the colour aspects of conventional photographic filmsand image structure. Dr Ohta made the transition to electroniccolour imaging systems during the later years at Fuji and has con-tinued his research in electronic colour imaging systems at theMunsell Color Science Laboratory in the Chester F. Carlson Centerfor Imaging Science at RIT. Dr Robertson has had a long, active anddistinguished career in all facets of colorimetry at the NRC, wherehe rose from a post doctorate fellow to senior research officer todirector over his 35 years of service. He has had a major role in thegrowth of the International Commission on Illumination (CIE) andthe International Color Association (AIC), where his efforts resultedin the CIE having the ability to publish colour standards in coop-eration with the International Organization of Standardization. In2005, Dr Robertson received the Godlove Award from the Inter-Society Color Council (ISCC) for his long and distinguished serviceto 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 atthe NRC, he met Dr Robertson, thus beginning their long collabora-tion and friendship. Their combined research in colour, colorimetryand applications of colorimetry and teaching of colorimetry hasresulted in this lucid, concise and practical text. When combinedwith Mark Fairchild’s Color Appearance Models (2nd Edition) andRobert Hunt’s The Reproduction of Colour (6th Edition), the Wiley-IS&T Series in Imaging Science and Technology provides the studentand practitioner of imaging science a comprehensive treatment ofcolour and colour science.

MICHAEL A. KRISSFormerly of the Eastman Kodak Research Laboratoriesand the University of Rochester

Preface

The original version of this book was published in Japanese by thefirst author. It has had a wide variety of readers in Japan rang-ing from undergraduate and graduate students in universities toengineers in industries. Due to its success in the Japanese lan-guage, Chinese and Korean versions were published soon after theJapanese one.Considering the nature of the book, which covers basic knowl-

edge for novices, practical applications for industrial engineers, andadvanced developments for researchers, we have decided to publishan 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 truncatedobsolete sections, extensively expanded others, incorporated recentknowledge and added new material that has emerged since the firstpublication.In writing the book, we employed a variety of materials from

books, journals, standards, etc. We gratefully acknowledge themany publishers who kindly gave us citation permission for usingtheir material. We also would like to express our deep apprecia-tion to our friend, the late Dr Heinz Terstiege of the Bundesanstaltfür 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 originalJapanese version, who kindly gave us permission to translate theJapanese version into the present English one.

Noboru OhtaAlan R. Robertson

Introduction

Color can be perceived by anyone as long as the person has soundeyesight. Nevertheless, most people find it extremely difficult toexplain what ‘color’ is. A typical dictionary definition of color mightbe ‘a visual perception that enables one to differentiate otherwiseidentical objects by the intensity and the wavelength of light’. Thisis not a very satisfactory definition because it describes the phys-ical stimulus that causes the perception rather than describingthe perception itself. It would not be very helpful to someone whohad never experienced color. Furthermore, the definition can leadto confusion because the word ‘color’ is also used to refer to thephysical stimulus itself. In this book, we have accepted the com-mon practice of using the word with both its meanings, but wherewe think there might be confusion, we have used the more explicitterms ‘perceived color’ and ‘color stimulus’.The difficulty of finding a convincing definition of perceptions

without referring to the physical stimuli that evoke them is notconfined to color. It occurs with all five senses by which humansdetect external stimulation. These five senses are vision (includingcolor), hearing, smell, taste and touch. In the case of the verb ‘smell’,for example, a typical dictionary might define it as ‘to perceive theodor or scent of stimuli affecting the olfactory sense organs of thenose’. Clearly this definition would not mean much to someonewho did not have the sense of smell, nor does it offer a distinctionbetween the perception and the stimulus.It is said that 80% of the external stimuli we detect are visual. In

fact, there are 217 kanji characters for types of ‘visual perception’,which is a far greater number than the 18 characters that signify‘auditory perception’. It is clear from this that vision provides a fargreater amount of information than the other four senses.This book relates to vision, the most important of the five

senses, and, in particular, it describes methods for expressing color

xvi INTRODUCTION

quantitatively. The quantitative expressions comprise numericaldescriptions of color. By analogy, a quantitative expression says;‘the distance between Tokyo and Osaka is 550km’, or ‘the distancebetween Tokyo and Aomori is 740km’, instead of saying ‘Osaka isfar from Tokyo’, or ‘Aomori is very far from Tokyo’. By using suchquantitative expressions, the two distances can be accurately com-pared with the conclusion that: ‘Aomori is 190 km farther fromTokyo than is Osaka’. Similarly, for example, the red circle of theJapanese flag might be described as ‘a red circle with R equal to 16’instead of using a description with adjectives, such as ‘a slightly ver-milion red color, similar to the color of the rising sun’. A Japaneseflag must have a length-to-width ratio of 2:3, and the circle mustbe located at the center, with a diameter equal to 3/5 of the length.Thus the relative dimensions of the flag are always the same. Onthe other hand, at present, the color of the red circle is not welldefined. However, if the color were to be described quantitativelyas, for example, R = 16, flags having the same red color could beproduced and used at any place as desired.The quantification of color belongs to the field of colorimetry, and

that of light belongs to the field of photometry. In this book, the fun-damentals of photometry necessary for understanding colorimetryare described first, and then the principles and formulation of col-orimetry are explained and recent progress in the field is described.Finally, some fields in industry to which colorimetry is effectivelyapplied are introduced.The book provides a comprehensive background for color engi-

neering, and encompasses the basic principles, development, andapplication fields of colorimetry. It is intended for students or engi-neers who are beginners in the field and who want to apply col-orimetry, or to those who are already practicing color engineeringand want to learn more. The authors hope that those people canacquire the fundamentals of color engineering by reading throughthe book. For further understanding, important items are describedin detail in notes at the end of each section.

Noboru OhtaAlan R. Robertson

1Light, Vision and

Photometry

1.1 LIGHT

Light is radiation in the form of electromagnetic waves that makevision possible to the human eye. Electromagnetic radiation can beclassified by its wavelength or frequency, as shown in Figure 1.1.The wavelength of light is confined to a very narrow range lim-ited by a short-wavelength edge between 360 and 400nm (1nm =10−6 mm; see Appendix I) and a long-wavelength edge between 760and 830nm. Infrared radiation and ultraviolet radiation, which arenot visible to human eye, are sometimes included in the category oflight and referred to as infrared light and ultraviolet light. However,it is better to call these categories infrared radiation and ultravioletradiation. When it is necessary to distinguish light from radiationnot visible to human eye, it is referred to as visible light or visibleradiation.Newton (Figure 1.2) showed experimentally that white light, such

as sunlight, is composed of various types of colored light. Morespecifically, he demonstrated the following facts by introducingsunlight into a prism (Figure 1.3).

1. White sunlight incident on a prism is separated into seven com-ponents differing in color, as observed in a rainbow. The sevencolors are red, orange, yellow, green, blue, indigo, and violet (seeColor Plate 1).

Colorimetry: Fundamentals and Applications N. Ohta and A. Robertson© 2005 John Wiley & Sons, Ltd

2 LIGHT, VISION AND PHOTOMETRY

2. The spectrum (i.e., the seven components of light differing incolor) can be reunited to give the original white light by focusingthe components back through a reversed prism.

3. If one color component alone is incident on a prism, it cannot befurther separated into the seven colors.

We now know that, when observed in detail, the spectrumincludes an infinite range of components of different wavelengthsthat cannot all be given different color names. The classificationinto seven named components is based on a simple set of basic

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Figure 1.1 Wavelengths of electromagnetic radiation and light

LIGHT 3

Figure 1.2 Isaac Newton (1643–1727)

Prism

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Spectrum

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te li

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Light shield

VioletIndigoBlueGreenYellowOrangeRed

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Figure 1.3 Prismatic dispersion of white light

color names. On detailed examination, other colors can be named.For example, reddish orange colors appear between the pure redand pure orange parts of the spectrum.Monochromatic light is light that cannot be separated into compo-

nents.White light suchassunlight ispolychromatic, i.e., amixtureofmonochromatic lights. A spectrum is a band of color observed whena beam of white light is separated into components of light that arearranged in the order of their wavelengths. The approximate corre-spondence betweenwavelengths and colors is shown in Figure 1.1.If one or more components is decreased in intensity and the

components are recombined, colored light is obtained instead ofthe original white light. Thus, if an object illuminated with whitelight reflects the components with differing reflectance dependingon the wavelengths, the human eye sees the object as colored. Forexample, a red object does not reflect much in the range from vio-let to yellow, but reflects the red component strongly. Thus, it is

4 LIGHT, VISION AND PHOTOMETRY

perceived to have a red color. In general, color is generated wheneverwhite light is modified by reflection or transmission by an object.

1.2 MECHANISM OF THE HUMAN EYE

The visual system is very similar to a photographic system in thatboth respond to light and, in particular, to images. The humaneyeball is a sphere about 24mm in diameter, and its mechanismresembles that of a camera and photographic film. Figure 1.4 showsschematically an eye and a camera. The corresponding componentsare as follows:

Camera EyeBlack box Sclera and choroidLens Cornea and lensShutter EyelidDiaphragm IrisFilm Retina

Cornea

Ear side

Optical axis

Nose side

Blind spot

Iris

Diaphragm

Vitreous body

Fovea centralis

Optic nerve

Sclera

Choroid

Black box

Retina

Film

Lens

Photographic lens

Shutter

Figure 1.4 Structure of eye and camera

MECHANISM OF THE HUMAN EYE 5

Light incident on the eye induces a photochemical reaction inthe retina, which corresponds to the photographic film The nerveimpulse generated by the reaction is transmitted to the brain to givea visual sensation. The retina covers about two-thirds of the inter-nal surface of the eyeball, and is a transparent film about 0.3mmin thickness, with a complicated structure comprising several typesof cell (Dowling and Boycott 1966). This is illustrated in Figure 1.5.The incident light enters the retina in the direction indicated bythe arrows, and reaches the photosensitive neuroepithelial layer.The optic nerve layer, which is located in front of the neuroepithe-lial layer, performs various types of signal processing. It should benoted that the incident light reaches the neuroepithelial layer afterit passes through the transparent optic nerve layer.The photosensitive neuroepithelial layer, which corresponds to

the fine photosensitive silver halide (e.g., AgCl, AgBr, or AgI) grainsincorporated in a photographic film, consists of two types of cell.These are rods, which perceive brightness or darkness in relativelydark environments, and cones which perceive color in relativelybright environments. The names ‘rods’ and ‘cones’ are derived fromthe shapes of the cells. There are three types of cone cell, presentin the ratio of about 32:16:1, which respond to long-, medium- andshort-wavelength light, respectively. Thus, the eye can be thought

[Image not available in this electronic edition.]

Figure 1.5 Structure of retina (Dowling and Boycott 1966). Reproducedby permission of The Royal Society

6 LIGHT, VISION AND PHOTOMETRY

of as being constructed of a high-speed black-and-white film (therods) and a medium-speed color film (the cones).There are about a hundred million rods and about seven million

cones in a human retina. The end of each neuroepithelial cell (thehatched portion in Figure 1.5) is called the external node and con-tains a photosensitive pigment. The diameter of the external nodeis between 1 and 2�m for a rod and between 1 and 5�m for a cone.It can be seen therefore that the diameter of the external node isabout the same as that of a photographic silver halide grain, whichis between 0.05 and 3�m. The human eye has about 60000 ele-ments per mm2 at the center of the retina, an electronic camera hasabout 20000, and a color photograph about 30000.The distribution of neuroepithelial cells in the retina is shown in

Figure 1.6 (Pirenne 1948). The cones are concentrated in the vicin-ity of the optical axis in the fovea centralis. The fovea centralis isa narrow portion of the retina, about 1.5mm in diameter, in whichapproximately 100000–150000 cones are concentrated. Maximumresolution is therefore achieved in this narrow portion. In contrastto the cones, rods are rarely found in the vicinity of the fovea cen-tralis, and are distributed over a wide region of the retina. Becausethe rods, and not the cones, function in dark environments, stars inthe sky at night are seen more easily obliquely, i.e., with squintingeyes.The signals generated by the photosensitive pigments in the

neuroepithelial cells are processed by various cells, shown inFigure 1.5, and the processed signals are then transmitted tothe brain through about one million optic nerves. Because no

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Figure 1.6 Distribution of rods (solid line) and cones (broken line) (Pirenne1948)

ADAPTATION AND RESPONSIVITY OF THE HUMAN EYE 7

Figure 1.7 Detection of blind spot

neuroepithelial cell is present in the portion of the retina wherethe optic nerve penetrates, this portion cannot sense light and iscalled the blind spot. The blind spot is located at an angle of 15�

from the line of sight (optical axis) and is about 5� wide. This canbe confirmed readily by a visual experiment using Figure 1.7. If theobserver fixates his/her right eye on the cross while closing his/herleft eye and adjusting the distance between the eye and the crossto about 20 cm, the solid circle disappears from sight. This occursbecause the solid circle is imaged on the blind spot.

1.3 ADAPTATION AND RESPONSIVITY OF THEHUMAN EYE

The brightness (more correctly the illuminance) provided by naturaland artificial light sources used in daily life ranges widely, as shownin Figure 1.8 (Shoumei Gakkai 1967). The human eye can see anobject in direct sunlight where the illuminance is about 100 000lx, or at night without moonlight at an illuminance of about 0.0003lx (as described in Section 1.6, the unit of illuminance is the lux,abbreviated lx). To adapt the eye over such a wide range of illumi-nance, the pupil adjusts the quantity of light reaching the retina bychanging its size. Thus, the pupil functions like the diaphragm of acamera. Because the pupil changes its diameter in a range from 2to 7mm, the quantity of light adjustable in this way covers a rangeof only a factor of 12.Thus the change in pupil diameter is insufficient for full con-

trol of the quantity of light. Accordingly, the rods and cones sharethe function by changing the responsivity of the retina. In a rela-tively bright environment, the cones alone function to give what is

8 LIGHT, VISION AND PHOTOMETRY

10–310–2

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Figure 1.8 Approximate values of brightness (illuminance) (ShoumeiGakkai 1967). Reproduced by permission of Shoumei Gakkai

called photopic vision. In a relatively dark environment, the rodsalone function to realize what is called scotopic vision. In environ-ments having an intermediate brightness between photopic visionand scotopic vision, both the cones and the rods function to pro-vide what is called mesopic vision. Photopic vision is distinguishedfrom scotopic vision by the luminance range in which it operates.Photopic vision occurs for luminances of about 3 cd/m2 or higher(see Sections 1.5 and 1.6 for the definitions of photometric quanti-ties and units), and scotopic vision occurs for luminances of about0.003cd/m2or lower. These numbers depend somewhat on otherconditions, such as the color of the stimuli.When one enters a bright environment from a dark one, one’s

vision changes from scotopic to photopic via mesopic. This changeis completed in about 1min, and the eye readily adapts to the brightenvironment. On the contrary, when one enters a dark environ-ment from a bright one, vision changes from photopic to scotopicmuch more slowly. As shown in Figure 1.9, it takes about 30minto completely accomplish the adaptation (Chapanis 1947).In photopic vision, the photochemical reaction in the rods satu-

rates, and they become inert to light and the cones alone are leftactive. The photochemical reaction in the cones continues to anupper limit of about 106 cd/m2. If this limit is exceeded, the result isa blinding and uncomfortable sensation that can damage the eyes.Referring to Figure 1.9, the detectivity of the eye (the minimumluminance sensed as light) for white light changes from curve A tocurve B as the rods take over from the cones upon transfer fromlight adaptation to dark adaptation.

STANDARD PHOTOMETRIC OBSERVER 9

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Figure 1.9 Progress of dark adaptation

The ordinate of Figure 1.9 is luminance in units of millilambert(mL). These can be converted to cd/m2 by using a conversion factorof 1mL=3�183�=10/��cd/m2. In the initial stage of dark adaptation(about 10min), cones function to give curve A but, in the laterstages, rods with their higher responsivity take over to yield curveB. However, under red light, the portion of curve B in which the rodsfunction does not appear. This is because the rods do not respondto high (red) wavelengths.In scotopic vision, rods are active and exhibit a relatively high

response to light. With decreasing luminance, however, even therods finally become insensitive. Depending on the experimentalconditions, the luminance limit at which the rods lose sensitivity isabout 10−6 cd/m2. Taking into account absorption and scatteringof light inside the eye and the absorption efficiency of the retina,this limit corresponds to about 5–14 photons incident on the rods.Cones on the other hand require about 100–1000 as many pho-tons before they respond. By comparison, four or more photonsare necessary to induce a reaction in the fine silver halide grainsof high-speed photographic film. It can be seen that rods have adetectivity that compares well to that of photographic film.

1.4 SPECTRAL RESPONSIVITY AND THE STANDARDPHOTOMETRIC OBSERVER

The output of a photodetector divided by the radiant energy inputis called its responsivity. The term can be applied to the humaneye as well as to physical detectors. For the eye, the output is abrightness response. In the past, the term sensitivity was used,but responsivity is now preferred. The higher the responsivity, the

10 LIGHT, VISION AND PHOTOMETRY

higher is the output for a given input. When the responsivity isexpressed as a function of wavelength, the curve is called the spec-tral responsivity. Equal amounts of radiant energy become lessvisible to the human eye with decreasing or increasing wavelengthon either side of a maximum. Outside the visible region, whichextends from about 380 to 780nm, radiation becomes invisible.Thus the spectral responsivity of the eye is a function of wavelength,decreasing gradually to zero in the ultraviolet and infrared regions.Furthermore, since the manner of transfer from light adaptation todark adaptation in white light differs from that in red light, it is clearthat the spectral responsivity of rods differs from that of cones.In general, the spectral responsivity of a photoreceptor is deter-

mined for each wavelength by introducing a monochromatic light ofknown radiant energy and then measuring the response in the formof a photocurrent, for example. The response of the eye, however, isnot determined by a physical measurement, but rather in terms ofa brightness sensation. Thus, to obtain the spectral responsivity ofthe eye, a means such as matching is employed. More specifically,in the matching method, a predetermined reference light having acertain wavelength is used, so that the brightness �v of a test lighthaving an arbitrary wavelength may be matched with that of thereference light. By measuring the radiant energy �e of the test lightin the match, �v can be expressed as

�v =K �e (1.1)

where K is a measure of the brightness per unit radiant energy.Thus, K is the responsivity of the eye. (At this stage, the quantitiesand units of brightness and radiant energy have not been definedso the units of K are arbitrary. These matters are discussed laterin this chapter.)The brightness of two different lights can be matched by any of

the following methods:

1. Direct comparisonmethod. This method comprises directly com-paring a test light of wavelength �2 with a reference light of wave-length �1. In principle it is the simplest method, but it is verydifficult experimentally to match, for example, the brightness ofa red light with that of a blue light. Consequently, the resultsfluctuate and the method suffers from poor precision.

2. Step-by-stepmethod.Althoughit isdifficult tocomparethebright-nesses of lights differing greatly in color, those having similar col-ors can be readily compared. Thus, by using a test light havinga wavelength �2 near the wavelength �1 of the reference light,

STANDARD PHOTOMETRIC OBSERVER 11

the responsivity for a wavelength �2 can be determined. Then theresponsivity for a light having a wavelength �3 near �2 can beobtained by using the previous test light as the reference light. Byrepeating this process sequentially, the spectral responsivity forthe whole spectrum can be obtained, step-by-step.

3. Flicker method. By alternately introducing a reference light hav-ing a wavelength of �1 and a test light having a wavelength of�2 into the visual field, the color can be made to flicker, forexample, between red and green. On increasing the frequency ofrepetition, the two colors merge into one at a frequency of about30Hz. Above this frequency, no color change is perceived. In theexample given, the red and green lights merge to yield yellow.However, if the two lights differ in brightness from each other,the difference in brightness remains as a flicker even if the colorsmerge into one. On further increasing the frequency to a valuehigher than 50Hz, the brightness as well as the color merges toyield a uniform visual field. By utilizing the frequency region inwhich the flicker attributed to brightness remains, but that forcolor disappears, the brightness of the test light can be matchedwith that of the reference light.

In the direct comparison method, results cannot be determinedwith high precision. However, a relatively stable result can beobtained by the step-by-step method or by the flicker method.By setting the reference light sufficiently dark and performing theexperiment in scotopic vision, the spectral responsivity of the rodscan be measured. On the other hand, if the reference light is setsufficiently bright, photopic vision operates and the responsivitycurve of the cones can be measured. The spectral responsivity ofthe cones can also be obtained by narrowing the observation fieldto about 2�, because no rods are present in the fovea centralis.As described above, the value of K in Equation 1.1 corresponds

to the responsivity of the eye. The value of K is called the luminousefficacy of the radiation. The spectral luminous efficacy, K���, canbe determined by varying the wavelength, � and observing K as afunction of �. The maximum value, Km, of K��� is called the max-imum luminous efficacy, and the ratio of K��� to Km, is called thespectral luminous efficiency, V���. The maximum luminous effica-cies, Km and K

′m, are related to the spectral luminous efficacies,

K��� and K′���, by the following equations

K���=KmV��� (1.2a)K ′���=K ′mV ′��� (1.2b)

12 LIGHT, VISION AND PHOTOMETRY

where V��� and V ′��� are the spectral luminous efficiencies inphotopic and scotopic vision, respectively. Because K���≤Km andK ′���≤K ′m, the maximum values for V��� and V ′��� are 1.0.Once the spectral responsivity for brightness is known, the

brightness of lights differing in color can be treated quantita-tively. However, to compare brightness on a worldwide basis, it isnecessary for everyone to use the same spectral responsivity func-tion. The Commission Internationale de l’Élairage (CIE) is an inter-national organization that researches and recommends standardsrelated to light. The CIE has established two spectral responsivitycurves that are universally used.In 1924, the CIE established the spectral luminous efficiency for

photopic vision, V���, based on the average observed values from7 studies involving 251 people with normal color vision. Similarly,in 1951, it established the spectral luminous efficiency for scotopicvision, V ′��� (Figure 1.10 and Table 1.1). The responsivities thusestablished are the average values for a large number of observers.Although a real observer does not necessarily exist with exactly thespectral responsivities illustrated in Figure 1.10, virtual observerswith these responsivities are known as the CIE Standard Photomet-ric Observers.The spectral luminous efficiency functions recommended by the

CIE were determined by the step-by-step method and the flickermethod described above. These experimental methods use specialconditions for the evaluation of brightness whereas direct compar-ison is usually employed in practical situations. However, as isillustrated in Figure 1.11, the fluctuation of the values obtained bydirect comparison is too large (Ikeda et al. 1982). Hence, results ofthe direct comparison method are not used as basic data for estab-lishing spectral luminous efficiency. However, numerous observed

400 5000

0.2

0.4

0.6

0.8

Scotopic vision V ′(λ)

Photopic vision V (λ)

1.0

600Wavelength (nm)

700

Lum

inou

s ef

fici

ency

Figure 1.10 Spectral luminous efficiency in photopic and scotopic vision