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Standard Colorimetry
Current and future titles in the Society of Dyers and Colourists – John Wiley Series
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Standard Colorimetry: Definitions, Algorithms and SoftwareClaudio Oleari
The Coloration of Wool and Other Keratin FibresDavid M. Lewis and John A. Rippon (Eds)
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Theoretical Aspects of Textile ColorationStephen M. Burkinshaw
Natural Dyeing for Textiles: A Guide Book for ProfessionalsDebanjali Banerjee
Colour for Textiles: A User’s Handbook, Second EditionRoger H. Wardman and Matthew Clark
Giles’s Laboratory Course in Dyeing, Fifth EditionUzma Syed
Standard Colorimetry
Definitions, Algorithms and Software
Claudio OleariDipartimento di Fisica e Scienze della Terra, Università degli Studi di Parma, Italy
Software developed by Gabriele Simone-Dipartimento di Informatica, Università degli Studi di Milano, Italy
This edition first published 2016© 2016 John Wiley & Sons, Ltd
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ISBN: 9781118894446
Set in 10/12 pt in Times LT Std by Aptara, India
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To those who strive to be just
Contents
Society of Dyers and Colourists xvPreface xvii
1 Generalities on Colour and Colorimetry 11.1 Colour 11.2 Colorimetry 2References 4Bibliography 4
2 Optics for Colour Stimulus 52.1 Introduction 52.2 Electromagnetic Waves 72.3 Photons 112.4 Radiometric and Actinometric Quantities 112.5 Inverse Square Law 142.6 Photometric Quantities 142.7 Retinal Illumination 16References 16Bibliography 16
3 Colour and Light–Matter Interaction 173.1 Introduction 17
3.1.1 Luminous Colours 173.1.2 Non‐luminous Colours 183.1.3 Light Phenomena and Body Appearance 18
3.2 Light Sources 193.3 Planckian Radiator 203.4 Light Regular Reflection and Refraction 21
3.4.1 Snell’s Laws 223.4.2 Fresnel’s Laws 23
3.5 Light Scattering 243.5.1 Lambertian Diffusion 253.5.2 Light Scattering on a Rough Surface 253.5.3 Light Scattering in an Optically Heterogeneous Medium 26
3.6 Light Absorption and Colour Synthesis 283.6.1 Simple Subtractive Synthesis 283.6.2 Complex Subtractive Synthesis 28
3.7 Fluorescence 293.8 Transparent Media 30
3.8.1 Internal Transmittance of a Medium 303.8.2 Total Transmittance and Total Reflectance 32
viii Contents
3.9 Turbid Media 333.9.1 Two‐Flux Model of Kubelka–Munk 343.9.2 Saunderson’s Equation 363.9.3 Colorant Characterization and Formulation 38
3.10 Ulbricht’s Integration Sphere 41References 43Bibliography 44
4 Perceptual Phenomenology of Light and Colour 454.1 Introduction 454.2 Perceived Colours, Categorization and Language 464.3 Light Dispersion and Light Mixing 47
4.3.1 Newton’s Prism Experiment, Colour Wheel and Colour Attributes 484.3.2 Maxwell’s Disk Experiment 50
4.4 Unique Hues, Colour Opponencies and Degree of Resemblance 524.5 Colour Similitude 554.6 Unrelated and Related Colours 56
4.6.1 Relative Attributes 564.7 Colour Interactions 57References 65
5 Visual System 675.1 Introduction 675.2 Eye Anatomy and Optical Image Formation 685.3 Eye and Pre‐retina Physics 725.4 Anatomy of the Retina 74
5.4.1 Retina Layers 765.4.2 Fovea 775.4.3 Foveola 785.4.4 Extra Fovea 785.4.5 Macula Lutea 795.4.6 Rod and Cone Distribution 79
5.5 From the Retina to the Brain 805.5.1 Scotopic Vision 805.5.2 Photopic Trichromatic Vision 815.5.3 Rushton’s Univariance Principle and Photoreceptor Activation 825.5.4 Horizontal Cells 835.5.5 Bipolar Cells 835.5.6 Amacrine Cells 845.5.7 Ganglion Cells and Visual Pathways 845.5.8 From the Ganglion Cells to the Visual Cortex 85
5.6 Visual System and Colorimetry 87Bibliography 88References 88
6 Colour‐Vision Psychophysics 916.1 Introduction 91
6.1.1 Psychophysics and Physiology 916.1.2 Visual Judgement 92
Contents ix
6.1.3 Modes of Colour Appearance and Viewing Situations 936.1.4 Colour Stimuli 956.1.5 Colour‐Attribute Matching 986.1.6 Visual Detection Threshold and Sensitivity 996.1.7 Scaling of Colour Attributes 100
6.2 Adaptation 1036.2.1 Brightness Adaptation 1056.2.2 Threshold in Dark Adaptation 106
6.3 Absolute Thresholds in Human Vision 1086.4 Absolute Threshold and Spectral Sensitivity in Scotopic and Photopic Visions 108
6.4.1 Silent Substitution Method 1096.5 Luminous Efficiency Function 113
6.5.1 Abney Additivity Law and Luminance 1146.6 Light Adaptation and Sensitivity 1166.7 Weber’s and Fechner’s Laws 118
6.7.1 Contrast Sensitivity 1196.7.2 Fechner’s Scaling 119
6.8 Stevens’ Law 1196.8.1 Brightness Scaling and Stevens’ Law 119
6.9 Fechner’s and Stevens’ Psychophysics 1216.10 Wavelength Discrimination 1216.11 Saturation Discrimination and Least Colorimetric Purity 1236.12 Rushton’s Univariance Principle and Scotopic Vision 1246.13 Tristimulus Space 125
6.13.1 Rushton’s Univariance Principle and Grassmann’s Laws in Photopic Vision 126
6.13.2 Metamerism 1306.13.3 Chromaticity 1316.13.4 Reference Frames in Tristimulus Space 1326.13.5 Measurement of the Colour-Matching Functions in the RGB
Reference Frame 1346.13.6 Luminance and Exner-Schrödinger’s ‘Helligkeit’ Equation 1396.13.7 Dichromats and Fundamental Reference Frame 1416.13.8 Newton’s Centre‐of‐Gravity Rule and Chromaticity‐Diagram
Properties 1456.14 Lightness Scales 1496.15 Helmholtz-Kohlrausch Effect 1506.16 Colour Opponencies and Chromatic Valence 1536.17 MacAdam’s Chromatic Discrimination Ellipses 1556.18 Perceived Colour Difference 1566.19 Abney’s and Bezold-Brücke’s Phenomena 1616.20 Chromatic Adaptation and Colour Constancy 164
6.20.1 Asymmetric Colour Matching 1656.20.2 Empirical Data 1666.20.3 Von Kries’s Coefficient Law 1666.20.4 Retinex 168
6.21 Colour‐Vision Psychophysics and Colorimetry 170References 171
x Contents
7 CIE Standard Photometry 1777.1 Introduction 1777.2 History of the Basic Photometric Unit 1807.3 CIE 1924 Spectral Luminous Efficiency Function 1807.4 CIE 1924 and CIE 1988 Standard Photometric Photopic Observers 1817.5 Photometric and Radiometric Quantities 1827.6 CIE 1951 Standard Scotopic Photometric Observer 1857.7 CIE 2005 Photopic Photometric Observer with 10° Visual Field 1857.8 CIE Fundamental Photopic Photometric Observer with 2°/10° Visual Field 185
7.8.1 Photopic Spectral Luminous Efficiency Functions for the 2° Fundamental Observer 186
7.8.2 Photopic Spectral Luminous Efficiency Functions for the 10° Fundamental Observer 186
References 186
8 Light Sources and Illuminants for Colorimetry 1898.1 Introduction 1898.2 Equal‐Energy Illuminant 1908.3 Blackbody Illuminant 1918.4 CIE Daylights 1938.5 CIE Indoor Daylights 1958.6 CIE Standard Illuminants 1968.7 CIE Light Sources: A, B and C 1978.8 CIE Sources for Colorimetry 1988.9 CIE Illuminants: B, C and D 1998.10 Fluorescent Lamps 199
8.10.1 Typical Fluorescent Lamps 1998.10.2 New Set of Fluorescent Lamps 200
8.11 Gas‐Discharge Lamps 2048.12 Light‐Emitting Diodes 205References 208
9 CIE Standard Psychophysical Observers and Systems 2099.1 Introduction 2099.2 CIE 1931 Standard Colorimetric System and Observer 210
9.2.1 CIE 1931 RGB Reference Frame and WDW Chromaticity‐Coordinates Normalization 2119.2.2 CIE 1931 XYZ Reference Frame 214
9.3 CIE 1964 (Supplementary) Standard Colorimetric Observer/System (10°‐Standard Colorimetric Observer) 218
9.4 CIE 1989 Standard Deviate Observer/System 2219.5 Vos’ 1978 Modified Observer for 2° Visual Field 221
9.5.1 Smith–Pokorny’s Cone Fundamentals 2239.5.2 Vos’ 1978 2° Fundamental Observer Data and MacLeod–Boynton’s
Chromaticity Diagram 2239.6 CIE Standard Stockman‐Sharpe’s ‘Physiologically Relevant’ Fundamentals and
XYZ Reference Frame 2249.6.1 XFYFZF and XF,10YF,10ZF,10 Reference Frames 2269.6.2 MacLeod-Boynton’s Tristimulus Space and Chromaticity Diagram 229
Contents xi
9.7 CIE Colorimetric Specification of Primary and Secondary Light Sources 232References 234
10 Chromaticity Diagram from Newton to the CIE 1931 Standard System 23710.1 Introduction 23710.2 Newton and the Centre of Gravity Rule 23710.3 Material Colours and Impalpable Colours in the Eighteenth Century 24310.4 Physiological Intuitions and the Centre of Gravity Rule – Young, Grassmann,
Helmholtz, Maxwell and Schrödinger 24510.5 Conclusion 251References 251
11 CIE Standard Psychometric Systems 25311.1 Introduction to Psychometric Systems in Colour Vision 25311.2 CIE Lightness L* 25411.3 Psychometric Chromaticity Diagrams and Related Colour Spaces 255
11.3.1 CIE 1960 (u, v) UCS Psychometric Chromaticity Diagram 25511.3.2 CIE 1964 (U*, V*, W*) Uniform Colour Space – CIEUVW Colour Space 25711.3.3 CIE 1976 (u′, v′) UCS Psychometric Chromaticity Diagram 25711.3.4 CIE 1976 (L*, u*, v*) Colour Space – CIELUV Colour Space 25911.3.5 CIE 1976 (L*, a*, b*) Colour Space – CIELAB Colour Space 261
11.4 Colour Difference Specification 26411.4.1 Colour Difference Data 26411.4.2 CIE 1976 Colour‐Difference Formulae 26511.4.3 CMC(l : c) Colour‐Difference Formula 26611.4.4 CIE 1994 Colour‐Difference Formula 26711.4.5 CIEDE2000 Total Colour‐Difference Formula 26811.4.6 Small Colour Differences in OSA‐UCS Space 27011.4.7 Metamerism Indices 27011.4.8 Daylight‐Simulator Evaluation and ‘Special Metamerism Index: Change
in Illuminant’ 27311.5 Conclusion 276References 276
12 Instruments and Colorimetric Computation 27912.1 Introduction 27912.2 Reflection and Transmission Optical‐Modulation 282
12.2.1 Absolute Quantities of Optical‐Modulation 28212.2.2 Relative Quantities of Optical‐Modulation 283
12.3 Spectroradiometric and Spectrophotometric Measurements 29612.3.1 Introduction to the Spectrometer 29612.3.2 Instrumental Convolution 30312.3.3 Deconvolution 308
12.4 Colorimetric Calculations 30912.4.1 CIE Colour Specification 30912.4.2 Relative Colour Specification 31012.4.3 Deconvolution 31212.4.4 Interpolation 31312.4.5 Extrapolation 315
xii Contents
12.5 Uncertainty in Colorimetric Measurements 31512.5.1 Laws of Propagation of Uncertainty 31712.5.2 Uncertainty Computation 318
12.6 Physical Standards for Colour‐Instrument Calibration 320References 322
13 Basic Instrumentation for Radiometry, Photometry and Colorimetry 32513.1 Introduction 32513.2 Lighting Cabinet 32713.3 Visual Comparison Colorimeter 32913.4 Instruments with Power Spectral Weighting Measurement 330
13.4.1 Photometric Instruments 33013.4.2 Colorimetric Instruments 332
13.5 Instruments for Measurements with Spectral Analysis 33613.5.1 Spectroradiometer 33613.5.2 Spectrophotometer 33713.5.3 Multiangle Spectrophotometers 33713.5.4 Fibre‐Optic‐Reflectance Spectroscopy (FORS) 338
13.6 Glossmeter 34113.7 Imaging Instruments 343
13.7.1 Imaging Photometer 34313.7.2 Colorimetric Camera 34413.7.3 Multispectral and Hyperspectral Camera 344
References 346
14 Colour‐Order Systems and Atlases 34914.1 Introduction 34914.2 Colour Solid, Optimal Colours and Full Colours 351
14.2.1 MacAdam’s Limit 35414.3 Ostwald’s Colour‐Order System and Atlas 354
14.3.1 Ostwald’s Hue Circle with Temperate Scale 35514.3.2 Ostwald’s Semichrome 35614.3.3 Ostwald’s Blackness, Whiteness and Purity 35714.3.4 Ostwald’s Atlas 358
14.4 Munsell’s Colour‐Order System and Atlas 36014.4.1 Munsell’s Instruments 36214.4.2 Chromatic Tuning Fork 36214.4.3 Munsell’s Value and Grey Scale 36414.4.4 Munsell’s Hue 36514.4.5 Munsell’s Value in Coloured Scales 36714.4.6 Colour Sphere and Munsell’s Colour Specification 36714.4.7 Munsell’s Chroma 36914.4.8 Colour Tree 36914.4.9 Munsell’s System and CIE Chromaticity Specification 36914.4.10 Helmholtz-Kohlrausch’s Effect and Abney’s Hue Shift Phenomenon in the
Munsell Atlas 37114.4.11 Munsell’s Colour Atlas 371
14.5 DIN 6264’s Colour‐Order System and Atlas 372
Contents xiii
14.6 OSA‐UCS’s Colour‐Order System and Atlas 37414.6.1 OSA‐UCS’s Lightness 37614.6.2 OSA‐UCS’s (g, j) Coordinates 37714.6.3 OSA‐UCS’s Colour Difference Formula 37914.6.4 OSA‐UCS’s Metrics 379
14.7 NCS’s Colour‐Order System and Atlas 38014.7.1 NCS’s Axioms 38114.7.2 NCS’s Hue, Chromaticness and Nuance 38214.7.3 Production of the NCS System and Visual Situation 38414.7.4 Psychophysics and Psychometrics for NCS 38414.7.5 Luminance Factor and NCS’s Whiteness Scale 38514.7.6 NCS’s Atlas 387
References 387
15 Additive Colour Synthesis in Images 39115.1 Introduction 39115.2 Video Colour Image 392
15.2.1 RGB Colorimetry 39515.2.2 Video Signal and γ Correction 39715.2.3 Tristimulus Space and YIQ Reference Frame 40115.2.4 sRGB System 40415.2.5 Prints in the sRGB System 40615.2.6 Camera, Photo‐Site and Pixel 40615.2.7 Spectral Sensitivities of Digital Cameras 409
15.3 Principles of Halftone Printing 41215.4 Towards the Colorimetry of Appearance 419References 420
16 Software (Software developed by Gabriele Simone) 42316.1 Introduction to the Software 423
16.1.1 Software Installation 42316.1.2 Data Files 425
16.2 Monitor 42916.2.1 Monitor Setup 42916.2.2 Visual Evaluation of Gamma (γ) 430
16.3 Colour‐Vision Tests 43216.4 Visual Contrast Phenomena 440
16.4.1 Simultaneous Brightness Contrast and Crispening 44016.4.2 Simultaneous Brightness Contrast in Colour Scales 44116.4.3 Brightness and Chromatic Contrast 44216.4.4 After Image 442
16.5 Colour Atlases 44316.5.1 Ostwald’s Atlas 44416.5.2 Munsell’s Atlas 44416.5.3 DIN’s Atlas 44416.5.4 OSA‐UCS’ Atlas 44616.5.5 NCS’ Atlas 447
16.6 CIE 1976 CIELUV and CIELAB Systems 448
xiv Contents
16.7 Cone Activation and Tristimulus 45016.8 CIE Colorimetry 451
16.8.1 CIE Colour Specification 452 16.8.2 CIE Systems 456 16.8.3 Chromaticity Diagrams 459 16.8.4 Fundamental Observers 462 16.8.5 Dominant Wavelength and Purity 463 16.8.6 Tristimulus Space Transformations 463 16.8.7 Colour‐Difference Formulae ΔE 464 16.8.8 CIE 1974 Colour Rendering Index Ra 465
16.9 Black Body and Daylight Spectra and Other CIE Illuminant Spectra 47016.10 Additive Colour Synthesis 471
16.10.1 RGB Monitor, Additive Colour Mixture 472 16.10.2 Halftone CMY Printing 472
16.11 Subtractive Colorant Mixing 474 16.11.1 Two Pigment Mixture 475 16.11.2 Four Pigment Mixture 475
16.12 Spectral Data View and Download – Illuminant-Observer Weights 47816.13 Save File Opening 478References 480
Index 481
Society of Dyers and Colourists
Society of Dyers and Colourists (SDC) is the world’s leading independent, educational charity dedicated to advancing the science and technology of colour. Our mission is to educate the changing world in the science of colour.
SDC was established in 1884 and became a registered educational charity in 1962. SDC was granted a Royal Charter in 1963 and is the only organization in the world that can award the Chartered Colourist status, which remains the pinnacle of achievement for coloration professionals.
We are a global organization. With our Head Office and trading company based in Bradford, UK, we have members worldwide and regions in the UK, China, Hong Kong, India and Pakistan.
Membership: To become a member of the leading educational charity dedicated to colour, please email [email protected] for details.
Coloration Qualifications: SDC’s accredited qualifications are recognized worldwide. Please email [email protected] for further information.
Colour Index: The unique and definitive classification system for dyes and pigments used globally by manufacturers, researchers and users of dyes and pigments (www.colour-index.com).
Publications: SDC is a global provider of content, helping people to become more effective in the work-place and in their careers by educating them about colour. This includes text books covering a range of dyeing and finishing topics with an ongoing programme of new titles. In addition, we publish Coloration Technol-ogy, the world’s leading peer-reviewed journal dealing with the application of colour, providing access to the latest coloration research globally.
For further information please email: [email protected], or visit www.sdc.org.uk.
Preface
“Standard Colorimetry” is an ambitious title that comes from the project of a small book, already fully writ-ten and never published, entitled Concise Handbook of Standard Colorimetry. The reviewers, who certainly knew my scientific production, suggested to broaden the content of the book, pointing me to chapters and contents. The book has become bigger, but more personal. This produced the change of the title, which con-tracted as Standard Colorimetry.
The books published in recent years on colorimetry are all excellent, comprehensive and authoritative, and written by authors and experts, and surely many readers have not felt the need for the publication of a further book. However, the differences between these books, including this one, are obvious.
Each book highlights the author’s knowledge, expertise and experience, which are made of reliefs, accents that make the various points otherwise important and in this sense reveal the views of the author. These important features differentiate the various books.
I do not like to take possession of the sentences of others, so the text is full of quotations in inverted com-mas, indicating clearly the source. This is a way to go to the source and respect the authors.
A software that accompanies this book has the function of giving visual concreteness to the numbers that specify the colour and is a tool for all colorimetric calculations.
Today this book is the book I wish I had read in a sequential way, starting from the first row, when, at the age of about 45 years, the case led me to passionately study human colour vision.
I thank the unknown reviewers. I appreciate the quality of their work and their competence.I thank the many colleagues that through dialogue, often with very short conversations, e-mail exchanges,
or simply the seminars I attended, helped me to understand and know, led me to get a varied overview of col-our science. I cannot cite everyone. I feel obliged to mention one name among them all, Robert M. Boynton, because in 2003 in a very short workshop in La Jolla he made us understand that every formula is obtained by engineering, but its value lies in its capacity to explain the phenomena and not simply to fit the phenom-ena. He had a high conception of science. Today there are too many formulae in colorimetry that have only a practical value but are unsatisfactory and do not help us to understand the phenomena.
Thanks to the readers who want to tell me the darkness and the errors encountered in reading the book or just want to comment. Send me suggestions and questions through e-mail: [email protected].
Claudio Oleari2015
Standard Colorimetry: Definitions, Algorithms and Software, First Edition. Claudio Oleari. © 2016 John Wiley & Sons, Ltd. Published 2016 by John Wiley & Sons, Ltd.
1Generalities on Colour and Colorimetry
The Commission Internationale de l’Éclairage (CIE) is the official institution devoted to worldwide coopera-tion and the exchange of information on all matters relating to the science and art of light and lighting, colour and vision, photobiology and image technology.
CIE publications are the main reference for this book.1–3 This book is about colorimetry and has the defini-tions of colour and colorimetry as its starting point.
1.1 Colour
In non‐specialist language, the word ‘colour’ is ambiguous, because it is used to describe the quality of the objects, self‐luminous and non‐luminous, and to describe a quality of the viewing experience. These mean-ings of the same word ‘colour’ are different but they are not disjoint, because the first one is the stimulation of the visual experience and the other the visual experience itself. Between these two meanings there is a correspondence and colorimetry quantitatively describes this correspondence.
The colour of self‐luminous and non‐luminous objects is associated with a physical quantity, which is properly called colour stimulus and is measurable because it is external to the body of the observer:
“Colour stimulus – visible radiation entering the eye and producing a sensation of colour, either chro-matic or achromatic.”1
“Color consists of the characteristics of light other than spatial and temporal inhomogeneities; light being the aspect of radiant energy of which a human being is aware through the visual sensations which arise from the stimulation of the retina of the eye.”4
The definition of colour as an effect of the colour stimulus is given by the Optical Society of America (OSA) in the 1952 report:
2 Standard Colorimetry
Among the many definitions of colour, the most comprehensive, albeit in its brevity, is given by the American Society for Testing and Materials (ASTM),5 which with the definitions opens highly technical discussions, which are clarified later in the book:
The ‘perceived colour’ is defined using the names of the colours. This means that the names of the colours represent fundamental concepts, which are not definable in other words. The perceived colour is incommuni-cable. Humans evoke the perceived colour in the interlocutors with conventional words – red, yellow, green, blue, black, grey, white, so on –.
1.2 Colorimetry
Robert W. Hunt6,7 distinguishes between:
and
Psychophysical colour terms regard Psychophysical colorimetry and psychometric colour terms regard Psychometric colorimetry. Both definitions of psychophysical and psychometric colour refer to colour stim-uli, whose measurement and processing are same as those in the human visual system. The human visual system is a tool that measures the colour stimulus, as a camera, (psychophysics) and processes the signals produced quantifying the colour attributes according to a perceptive scale (psychometrics).
Psychophysical colorimetry is limited to the measurement of colour stimuli, attributing the same speci-fication to different colour stimuli which induce equal colour sensations. This is exactly what happens in a photographic camera.
The human eye, unlike the camera, has a sensor – the retina – that has not the same optical properties in all its parts. The central part, for acute vision, is different from the surrounding parts, for which, according to a simplified diagram, there are two different colorimetries. In 1931 the CIE defined a colorimetry for
“Psychophysical colour terms – terms denoting objective measures of physical variables that are eval-uated so as to relate to the magnitudes of important attributes of light and colour. These measures iden-tify stimuli that produce equal responses in a visual process in specified viewing conditions.”
“Psychometric colour terms – terms denoting objective measures of physical variables that are evalu-ated so as to relate to differences between magnitudes of important attributes of light and colour and such that equal scale intervals represent approximately equal perceived differences in the attribute considered. These measures identify pairs of stimuli that produce equally perceptible differences in response in a visual process in specified viewing conditions.”6
“Colour of an object – aspect of object appearance distinct from form, shape, size, position, or gloss that depends upon the spectral composition of the incident light, the spectral reflectance or transmittance of the object, and the spectral response of the observer, as well as the illuminating and viewing geometry.”5
1.
“Perceived colour – attribute of visual perception that can be described by colour names such as white, grey, black, yellow, brown, vivid red, deep reddish purple, or by combinations of such names.Discussion – perceived colour depends greatly on the spectral power distribution of the colour stimulus, but also on the size, shape, structure, and surround of the stimulus area, the state of adap-tation of the observer’s visual system, and the observer’s experience with similar observations.”5
2.
Generalities on Colour and Colorimetry 3
acute vision – observer with a visual field of 2° described in Section 9.2 – and in 1964 a colorimetry for non‐acute vision – observer with the field of view of 10° described in Section 9.3 –.
The distinctions between psychophysical and psychometric colorimetries, and between the 2° and 10° visual fields, have led to four different colorimetries, as summarized in Table 1.1.
Over time, the study of colour‐vision has led to improving the standard observers by adding new cases within the schema of Table 1.1, that is, Vos and fundamental observers described in Sections 9.5 and 9.6. These improvements are considered so small that the industries and laboratories continue to use the standard CIE 1931 and CIE 1964.
This distinction among different colorimetries corresponds to a distinction among the historical phases of colorimetry7:
Table 1.1 Scheme of the colour specification according to historical steps, stages of vision, visual fields and referred to the CIE standard systems.
Historical steps/stages of vision/systems
First stage of vision: transduction
Second stage of vision: colour difference and illuminant discounting
Third stage of vision: colour appearance and adaptation
Psychophysics (Chapter 9) Psychometrics (Chapter 11) Colour appearance
v i s u a l
Visual field < 4° CIE 1931 standard observer (X, Y, Z),
CIELUV system (L*, u*, v*) CIELAB system (L*, a*, b*)
CIECAM97 CIECAM02 Retinex
Vos observer2° CIE fundamental observer
f i e l d
10° visual field CIE 1964 supplementary standard observer (X10, Y10, Z10)
CIELUV system (L*10, u*10, v*10) CIELAB system (L*10, a*10, b*10)
10° CIE fundamental observer
The third phase of colour‐appearance colorimetry is in rapid progress and is a subject of debate; therefore, it is not considered in this book.
A third phase concerned with ‘what colours look like’ and is termed “colour appearance:
i. aspect of visual perception by which things are recognized andii. in psychophysical studies, visual perception in which the spectral and geometric aspects of a visual
stimulus are integrated with its illuminating and viewing environment.”1
A first phase concerned with ‘which colours match’ and is termed psychophysical in strict sense (Chapter 9) and also classical colorimetry or tristimulus colorimetry.
A second phase concerned with ‘whether colour differences are equal’ and is termed psychometric (Chapter 11).
4 Standard Colorimetry
References
1. ILV CIE S 017/E:2011, ILV: International Lighting Vocabulary, Commission Internationale de l’éclai-rage, Vienna (2011). Available at: www.eilv.cie.co.at/free access (accessed on 3 June 2015)
2. CIE 15:2004, Colorimetry, 3rd edn, Commission Internationale de l’éclairage, Vienna (2004).3. CIE Supplement No. 2 to publication No. 15, Colorimetry, Recommendations on Uniform Color Spaces, Color
Difference Equations, Psychometric Color Terms, Commission Internationale de l’éclairage, Vienna (1978).4. Committee on Colorimetry of the O.S.A., The Science of Color, OSA – The Optical Society of America,
Washington, DC (1963).5. ASTM E284 – 13b, Standard Terminology of Appearance, ASTM International, West Conshohocken, PA
(2013).6. Hunt RWG, The specification of colour appearance. I. Concepts and terms, Color Res. Appl., 2, 55–68
(1977).7. Hunt RWG, Colour terminology, Color Res. Appl., 3, 79–87 (1978).
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New York (1995).Committee on Colorimetry of the O.S.A., The Science of Color, OSA – The Optical Society of America,
Washington, DC (1963).Gegenfurtner KR and Lindsay TS, eds., Color Vision, From Genes To Perception, Cambridge University
Press, Cambridge, (1999).Gescheider GA, Psychophysics – The Fundamentals, 3rd edn, Lawrence Erlbaum Associates, London, (1997).Hunt RWG and Pointer MR, Measuring Colour, 4th edn, Wiley‐IS&T Series in Imaging Science and Tech-
nology, John Wiley & Sons (2011).Kaiser PK and Boynton RM, Human Color Vision, Optical Society of America, Washington, DC (1996).Kuehni RG, Color, An Introduction to Practice and Principles, John Wiley & Sons, New York (1997).Kuehni RG, Color Space, and Its Division, John Wiley & Sons, New York (2003).Kuehni RG and Schwarz A, Color Ordered, A Survey of Color Order Systems from Antiquity to the Present,
Oxford University Press, New York (2008).Le Grand Y, Light, Colour and Vision, 2nd edn, Chapman and Hall, London (1968).MacAdam DL, Color Measurement, Springer, Berlin (1985).MacAdam DL, ed., Colorimetry – Fundamentals, SPIE MS 77, SPIE – The International Society for Optical
Engineering, Washington, DC (1993).Malacara D, Color Vision and Colorimetry: Theory and Applications, Second Edition, SPIE Press (2011)McDonald R, eds., Colour Physics for Industry, Society of Dyers and Colourist, Bradford (1987).Ohta N and Robertson AR, Colorimetry – Fundamentals and Applications, John Wiley & Sons, New York (2005).Schanda J, ed., Colorimetry: Understanding the CIE System, John Wiley & Sons, New York (2007).Sève R, Physique de la couleur, Masson, Paris (1996).Shevell S, ed., The Science of Color, 2nd edn, OSA‐Elsevir, Amsterdam (2003).Valberg A, Light Vision Color, John Wiley & Sons, Chichester (2005).Wyszecky G and Judd DB, Color in Business, Science and Industry, John Wiley & Sons, New York (1975).Wyszecky G and Stiles WS Color Science, John Wiley & Sons, New York (1982).
Standard Colorimetry: Definitions, Algorithms and Software, First Edition. Claudio Oleari. © 2016 John Wiley & Sons, Ltd. Published 2016 by John Wiley & Sons, Ltd.
2Optics for Colour Stimulus
2.1 Introduction
This chapter has solely educational purposes and only recalls classical optical phenomena, therefore its bibliography consist of textbooks, manuals and tutorials.
This chapter considers the physical nature of colour stimuli.
“Colour stimulus – visible radiation entering the eye and producing a sensation of colour, either chro-matic or achromatic.”1–3
“Colour stimulus function ϕλ – description of a colour stimulus by the spectral concentration of a radi-ometric quantity, such as radiance or radiant power, as a function of wavelength.”1–3
“Relative colour stimulus function ϕ(λ) – relative spectral power distribution of the colour stimulus function.”1–3
“The psychophysical specification of a colour stimulus is termed again colour stimulus and is denoted by a symbol in square brackets, for example, [ϕ]”1–3 (the context avoids ambiguity). Since the psyco-physical colour stimulus is mathematically a vector, in this book the colour stimulus is always indicated in bold roman letters as scientific convention requires.
The colour stimulus function is a physical quantity measured in W/nm if it is the spectral distribution of the radiant power – also spectral flux –, or in W/(m2 sterad nm) if it is the spectral distribution of the radiance. The relative colour stimulus function is dimensionless and the spectral plots of this function and that of the colour stimulus function are proportional, that is, ϕλ = k ϕ(λ), where k is a constant with a suitable physical dimension. The colour stimulus functions must be used for the computations of absolute
6 Standard Colorimetry
quantities as, for example, the illuminance and the luminance, but generally the use of the relative colour stimulus function is more convenient and almost all the colour specification is made on a relative scale. [In colorimetry and photometry the absolute spectral distribution functions have dependence on the wave-length λ written as a subscript while the relative spectral distribution functions have dependence written in brackets (λ).]
These definitions of colour stimulus are merely radiometric (Section 2.4) and only physical operations on these quantities are considered, for example, addition of many colour stimuli.
Colour stimuli produce colour sensations, that usually continue to be called colour stimuli, which should not be confused with the previous colour stimuli (the context avoids ambiguity). Psychophysical opera-tions can be made on these last colour stimuli, for example, addition, comparison and colour matching, and in this case colour stimuli, which represent colour sensations, are written in square brackets [ψ] or as vectors.
The colour stimulus function characterized by a spectral power distribution constant is termed equal‐energy (or equi-energy) stimulus function and denoted by the relative spectral radiance EE(λ) = 1. The equal energy stimulus function often plays a role in the normalization of the tristimulus space, used for the psycho-physical specification of colour stimuli (Section 6.13).
Colour vision is a phenomenon triggered by colour stimulus, and it happens by the interaction between visible electromagnetic radiation (light) and the visual system. Activation consists of the absorption of radia-tion by typical molecules located inside photosensitive cells of the retina on the fundus of the eye. Everything that happens before the activation itself concerns the interaction between the electromagnetic radiation and matter. It is therefore necessary to have a theoretical framework that describes the generation, propagation and interaction of light with matter in order:
1. to have a basis for the understanding of the meaning of colour stimulus function and of colour perception and
2. to quantify and forecast the light phenomena, and connect them with the physical nature of matter.
Point (1) is considered in this introductory section. The physical phenomena related to the colours, often called colour physics, are described in Chapter 3, while the fundamental optical phenomena used in colour science are concisely recalled where necessary.
It is known that visible light is an electromagnetic radiation constituted by mutually orthogonal electric and magnetic fields that propagate in space and time, in a vacuum and in matter, with a velocity dependent on the nature of the medium.
Electromagnetic radiation shows a dual nature, corpuscular and wave nature: the processes in which light is generated or absorbed can be explained assuming that it consists of quanta, postulated by Einstein and called photons, while light propagation in space and time is well explained by a wave‐like behaviour, fully described by Maxwell’s equations.
Everyday experience suggests we consider light as consisting of rays. Geometrical optics is based on this assumption and is derivable from wave optics by an approximation, termed eikonal approximation. Geomet-rical optics is valid only when light interacts with objects, which are much larger than its wavelength.
All these descriptions of light radiation enter the representation of vision phenomena and the lab equip-ment:
● The image formation in the eye is well described by geometrical optics. ● The transduction of light radiation into an electrical phenomenon in the photosensitive cells of the eye is
a photochemical process and regards the quantum nature of light, that is, photons. ● The photo‐detection of solid state devices, generally used in radiometric, photometric and colorimetric
instruments, is often a quantum phenomenon and regards the quantum nature of light.
Optics for Colour Stimulus 7
● The emission of light radiation from a body – light source – is a quantum process, albeit divided into two different processes:1. transitions between electronic states of matter at different energy – responsible for the coloration of
many bodies and2. blackbody emission, a phenomenon dependent only on the temperature of the body (Section 3.3).
● The interaction of the electromagnetic radiation with matter is describable with one of the three descrip-tions (geometrical, wave and quantum optics) according to the phenomena involved.
Here we describe briefly the characteristics of light according to the wave and quantum model. (It is assumed that the reader is familiar with geometrical optics.)
2.2 Electromagnetic Waves
The wave hypothesis dates back to Huygens (1629–1695), but then there are the Maxwell equations (1873) that fully describe the light as electromagnetic waves. The electromagnetic properties of the matter, in which there are waves, are represented by the dielectric constant ε and magnetic permeability μ. In fact, these are precisely the electromagnetic properties of matter that determine the light velocity v = (εμ)1/2 and conse-quently the optical properties. The light velocity in the vacuum, denoted by c, is the maximum possible velocity and is an universal constant of physics. The refractive index n≡c/v, known in geometric optics, is a quantity that summarizes these properties. The refractive index is a function of the wavelength and is typical for any material.
The waves, solutions of Maxwell’s equations in an optically homogeneous medium, are represented by sinusoidal functions called wave functions, whose argument, the phase of the wave, is defined at the point x of the space along the direction of propagation and the time instant t by
x tx t2 0 0π
λ τϑ κ ω ϑ−
− = − − (2.1)
τ is the period;ν = 1/τ is the frequency;ω = 2πν is the pulsation;λ is the wavelength;κ = 2π/λ is the wave number (sometimes the wave number is simply the reciprocal of λ); andϑ0 is the initial phase.
The electromagnetic waves have the following properties:
● The quantities described by wave functions are the electric field vector E x t( )0
�κ ω ϑ− − and the mag-
netic field vector H x t( )0
�κ ω ϑ− − . A qualitative representation of a wave in space and time is given in
Figure 2.1. ● E� and H�
are perpendicular to each other and to the direction of propagation – transverse waves – (Figure 2.1). ● The waves associated with the electric filed are plane waves if the vectors E
� at any points of the propaga-
tion line belong to a plane. Since electric and magnetic fields are linked together by Maxwell’s equations, the vectors H
� of the magnetic field belong to a plane orthogonal to the plane of the electric field. The
surfaces on which the phase of the wave is constant are called wave fronts, and the planes tangent to these surfaces are perpendicular to the direction of propagation.
8 Standard Colorimetry
● A light wave is linearly polarized if the wave is a plane wave (Figure 2.1). Linear polarization and plane polarization are synonyms.
● Light polarization, represented in waves by the direction of the electric field, is a property with a role in the processes of reflection and refraction, and is therefore in part responsible for the surface appearance of bodies. Therefore, it has an important role in colorimetry and should not be ignored, especially in colori-metric measurements, in which the radiation reflected by a body is measured and the optical components of the instrument reflect light.
● An example of linearly polarized light is the light emitted by an LCD monitor. It can be easily checked with Polaroid sun glasses rotated on the screen, which operates as a polarization analyser.
● In the majority of cases, the light is not polarized and it is not possible to define a single plane for the oscillation of the electric field, but thanks to the superposition principle, it is possible to consider it as a sum of linearly polarized waves. The decomposition of a light beam in waves of different polarization facilitates the discussion of the phenomena of reflection and refraction. It is also of practical utility since many everyday devices polarize light as, for example, polaroid filters used in sunglasses.
● The flow of power ϕe of the electromagnetic radiation (energy per unit of time and area, measured in W/m2) proceeds in the direction orthogonal to the fields E
� and H
�.
● The electric and magnetic field magnitudes are proportional to each other H E( / )� �
ε µ= . ● The wave is coherent, which means when the phase is known at a point in space and at an instant in time,
then it can be determined at any other point and instant. ● The velocity at which the plane waves propagate in space is implicitly defined by the argument of the
wave functions (κ x – ω t –ϑ0), which takes the same value for different pairs of variables x and t. If we consider the wave function at the instants t1 and t2, it follows that this function has the same values at the points x1 and x2 such that (κ x1 – ω t1) = (κ x2 – ω t2), from which ω (t1 – t2) = κ (x1 – x2), and then the
x
(a)
(b)
(c)
x
t
H
E
λ
τ
H
E
Figure 2.1 (a) Plane electromagnetic waves represented in space at fixed time and (b) in the time in a fixed point in space. This graphical representation shows the wavelength and the frequency in space and time, respectively. (c) The third graph from the top represents a wave with ‘circular polarization’; here only the electric field is represented and the magnetic field is orthogonal to the electric field. The electric field and magnetic field are mutually perpendicular and together orthogonal to the propagation direction.
Optics for Colour Stimulus 9
wave advances rigidly with a velocity v =(x1 – x2)/ (t1 – t2) = ω/κ = λ/τ = λν. The velocity in the vacuum is c = 2.997925 × 108 m/s.
● The waves are classified by their wavelength λ or frequency ν = c/λ. Since the velocity depends on the medium, by convention the wavelength is considered in a vacuum and is very close to that in air. A clas-sification according to decreasing wavelength (Figure 2.2) distinguishes between radio waves (used in telecommunications), microwaves (typical of radar and microwave ovens), infrared radiation (IR), visible radiation (VIS), ultraviolet radiation (UV), X‐rays and γ‐rays. There are no precise limits for the spectral
Figure 2.2 Complete spectrum of electromagnetic radiation characterized by wavelength and frequency. The part of the spectrum related to visible light is expanded and a hue name is associated to each wavelength range. The colours printed here are only representative and approximate for many reasons, which will become clear on reading the book. For completeness, the non‐spectral hues (purple and magenta hues) are added, which are specified by the complementary wavelengths (Section 4.3). ‘c’ before the wavelength numbers in the extra‐spectral region means ‘complementary of’.
10 Standard Colorimetry
range of visible radiation since they depend upon the amount of radiant power reaching the retina and the responsivity of the photosensitive cells. Generally, the lower limit is taken between 360 and 400 nm and the upper limit between 760 and 830 nm. A finer subdivision of UV radiation distinguishes between UVC with 100 < λ < 280 nm, UVB with 280 < λ < 315 nm and UVA with 315 < λ < 400 nm, while in IR radiation we have NIR (near‐IR) with 0.8 < λ < 2.5 μm, and IR‐A with 0.78 < λ < 1.4 μm, IR‐B with 1.4 < λ < 3.0 μm and IR‐C with 3 μm < λ < 1 mm.
“Monochromatic radiation – radiation characterized by a single frequency or a single wavelength.
NOTE 1 – In practice, radiation of a very small range of frequencies can be described by stating a single frequency or wavelength (NB: In reality a radiation with a single wavelength cannot exist).
NOTE 2 – The wavelength in air or in vacuum is also used to characterize a monochromatic radiation. The medium must be stated.
NOTE 3 – The wavelength in standard air is normally used in photometry, radiometry and colorimetry.”1–3
A clarification is required: the radiation of a single wavelength is not selectable instrumentally (Section 12.3.1) and is theoretically definable only in an infinite optically homogeneous space. In a strict sense, the word ‘monochromatic’ is improperly used; anyway, it is used. This does not condition the science of col-our, and the monochromatic radiations can be considered as a language approximation. A radiation, which is non‐monochromatic but is defined within a narrow spectral range, is a spectral radiation defined within a band specified by its width (Section 12.3.1). In colorimetry, the bandwidth should be 1 nm (Section 6.10). In practice, often the spectral radiations used have a bandwidth up to 10 nm and Gaussian spectral distribution.
“Monochromatic stimulus – colour stimulus consisting of monochromatic radiation. Equivalent term: spectral stimulus.”1
Anticipating the description of the colour sensations, Figure 2.2 proposes the visible electromagnetic radiation associated with the various spectral hues (albeit approximated by the printing process) and the corresponding names. There are extra‐spectral hues provided by a mixture of radiation of short and long wavelengths with the intensity in a variable ratio. These extra‐spectral hues cannot be associated with a wavelength; however, the convention is to associate them with the complementary wavelengths, denoted by the letter ‘c’ followed by the value of the complementary wavelength.
The plane wave functions with different wavelengths are simultaneously solutions of Maxwell’s equations because these differential equations are linear. It follows that also a linear combination of these waves is a wave function solution of Maxwell’s equations. This is summarized in the superposition principle, so the sum of many solutions is still a solution. This latter property enables treating any light beam as a sum of monochromatic beams, which are defined by a single wavelength. This property is of particular importance in colour science.
Complementary wavelength to a light radiation is the wavelength of the spectral radiation, which when mixed with this in an appropriate ratio of intensity generates a light‐looking achromatic – without hue –.
Radiation defined by a superposition of different monochromatic waves is termed heterochromatic.
