Standard Colorimetry

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4 Current and future titles in the Society of Dyers and Colourists John Wiley Series Published Standard Colorimetry: Definitions, Algorithms and Software Claudio Oleari The Coloration of Wool and Other Keratin Fibres David M. Lewis and John A. Rippon (Eds) Forthcoming Theoretical Aspects of Textile Coloration Stephen M. Burkinshaw Natural Dyeing for Textiles: A Guide Book for Professionals Debanjali Banerjee Colour for Textiles: A User s Handbook, Second Edition Roger H. Wardman and Matthew Clark Giles s Laboratory Course in Dyeing, Fifth Edition Uzma Syed

5 Standard Colorimetry Definitions, Algorithms and Software Claudio Oleari Dipartimento 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

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7 To those who strive to be just

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9 Contents Society of Dyers and Colourists Preface xv xvii 1 Generalities on Colour and Colorimetry Colour Colorimetry 2 References 4 Bibliography 4 2 Optics for Colour Stimulus Introduction Electromagnetic Waves Photons Radiometric and Actinometric Quantities Inverse Square Law Photometric Quantities Retinal Illumination 16 References 16 Bibliography 16 3 Colour and Light Matter Interaction Introduction Luminous Colours Non luminous Colours Light Phenomena and Body Appearance Light Sources Planckian Radiator Light Regular Reflection and Refraction Snell s Laws Fresnel s Laws Light Scattering Lambertian Diffusion Light Scattering on a Rough Surface Light Scattering in an Optically Heterogeneous Medium Light Absorption and Colour Synthesis Simple Subtractive Synthesis Complex Subtractive Synthesis Fluorescence Transparent Media Internal Transmittance of a Medium Total Transmittance and Total Reflectance 32

10 viii Contents 3.9 Turbid Media Two Flux Model of Kubelka Munk Saunderson s Equation Colorant Characterization and Formulation Ulbricht s Integration Sphere 41 References 43 Bibliography 44 4 Perceptual Phenomenology of Light and Colour Introduction Perceived Colours, Categorization and Language Light Dispersion and Light Mixing Newton s Prism Experiment, Colour Wheel and Colour Attributes Maxwell s Disk Experiment Unique Hues, Colour Opponencies and Degree of Resemblance Colour Similitude Unrelated and Related Colours Relative Attributes Colour Interactions 57 References 65 5 Visual System Introduction Eye Anatomy and Optical Image Formation Eye and Pre retina Physics Anatomy of the Retina Retina Layers Fovea Foveola Extra Fovea Macula Lutea Rod and Cone Distribution From the Retina to the Brain Scotopic Vision Photopic Trichromatic Vision Rushton s Univariance Principle and Photoreceptor Activation Horizontal Cells Bipolar Cells Amacrine Cells Ganglion Cells and Visual Pathways From the Ganglion Cells to the Visual Cortex Visual System and Colorimetry 87 Bibliography 88 References 88 6 Colour Vision Psychophysics Introduction Psychophysics and Physiology Visual Judgement 92

11 Contents ix Modes of Colour Appearance and Viewing Situations Colour Stimuli Colour Attribute Matching Visual Detection Threshold and Sensitivity Scaling of Colour Attributes Adaptation Brightness Adaptation Threshold in Dark Adaptation Absolute Thresholds in Human Vision Absolute Threshold and Spectral Sensitivity in Scotopic and Photopic Visions Silent Substitution Method Luminous Efficiency Function Abney Additivity Law and Luminance Light Adaptation and Sensitivity Weber s and Fechner s Laws Contrast Sensitivity Fechner s Scaling Stevens Law Brightness Scaling and Stevens Law Fechner s and Stevens Psychophysics Wavelength Discrimination Saturation Discrimination and Least Colorimetric Purity Rushton s Univariance Principle and Scotopic Vision Tristimulus Space Rushton s Univariance Principle and Grassmann s Laws in Photopic Vision Metamerism Chromaticity Reference Frames in Tristimulus Space Measurement of the Colour-Matching Functions in the RGB Reference Frame Luminance and Exner-Schrödinger s Helligkeit Equation Dichromats and Fundamental Reference Frame Newton s Centre of Gravity Rule and Chromaticity Diagram Properties Lightness Scales Helmholtz-Kohlrausch Effect Colour Opponencies and Chromatic Valence MacAdam s Chromatic Discrimination Ellipses Perceived Colour Difference Abney s and Bezold-Brücke s Phenomena Chromatic Adaptation and Colour Constancy Asymmetric Colour Matching Empirical Data Von Kries s Coefficient Law Retinex Colour Vision Psychophysics and Colorimetry 170 References 171

12 x Contents 7 CIE Standard Photometry Introduction History of the Basic Photometric Unit CIE 1924 Spectral Luminous Efficiency Function CIE 1924 and CIE 1988 Standard Photometric Photopic Observers Photometric and Radiometric Quantities CIE 1951 Standard Scotopic Photometric Observer CIE 2005 Photopic Photometric Observer with 10 Visual Field CIE Fundamental Photopic Photometric Observer with 2 /10 Visual Field Photopic Spectral Luminous Efficiency Functions for the 2 Fundamental Observer Photopic Spectral Luminous Efficiency Functions for the 10 Fundamental Observer 186 References Light Sources and Illuminants for Colorimetry Introduction Equal Energy Illuminant Blackbody Illuminant CIE Daylights CIE Indoor Daylights CIE Standard Illuminants CIE Light Sources: A, B and C CIE Sources for Colorimetry CIE Illuminants: B, C and D Fluorescent Lamps Typical Fluorescent Lamps New Set of Fluorescent Lamps Gas Discharge Lamps Light Emitting Diodes 205 References CIE Standard Psychophysical Observers and Systems Introduction CIE 1931 Standard Colorimetric System and Observer CIE 1931 RGB Reference Frame and WDW Chromaticity Coordinates Normalization CIE 1931 XYZ Reference Frame CIE 1964 (Supplementary) Standard Colorimetric Observer/System (10 Standard Colorimetric Observer) CIE 1989 Standard Deviate Observer/System Vos 1978 Modified Observer for 2 Visual Field Smith Pokorny s Cone Fundamentals Vos Fundamental Observer Data and MacLeod Boynton s Chromaticity Diagram CIE Standard Stockman Sharpe s Physiologically Relevant Fundamentals and XYZ Reference Frame X F Y F Z F and X F,10 Y F,10 Z F,10 Reference Frames MacLeod-Boynton s Tristimulus Space and Chromaticity Diagram 229

13 Contents xi 9.7 CIE Colorimetric Specification of Primary and Secondary Light Sources 232 References Chromaticity Diagram from Newton to the CIE 1931 Standard System Introduction Newton and the Centre of Gravity Rule Material Colours and Impalpable Colours in the Eighteenth Century Physiological Intuitions and the Centre of Gravity Rule Young, Grassmann, Helmholtz, Maxwell and Schrödinger Conclusion 251 References CIE Standard Psychometric Systems Introduction to Psychometric Systems in Colour Vision CIE Lightness L* Psychometric Chromaticity Diagrams and Related Colour Spaces CIE 1960 (u, v) UCS Psychometric Chromaticity Diagram CIE 1964 (U*, V*, W*) Uniform Colour Space CIEUVW Colour Space CIE 1976 (u, v ) UCS Psychometric Chromaticity Diagram CIE 1976 (L*, u*, v*) Colour Space CIELUV Colour Space CIE 1976 (L*, a*, b*) Colour Space CIELAB Colour Space Colour Difference Specification Colour Difference Data CIE 1976 Colour Difference Formulae CMC(l : c) Colour Difference Formula CIE 1994 Colour Difference Formula CIEDE2000 Total Colour Difference Formula Small Colour Differences in OSA UCS Space Metamerism Indices Daylight Simulator Evaluation and Special Metamerism Index: Change in Illuminant Conclusion 276 References Instruments and Colorimetric Computation Introduction Reflection and Transmission Optical Modulation Absolute Quantities of Optical Modulation Relative Quantities of Optical Modulation Spectroradiometric and Spectrophotometric Measurements Introduction to the Spectrometer Instrumental Convolution Deconvolution Colorimetric Calculations CIE Colour Specification Relative Colour Specification Deconvolution Interpolation Extrapolation 315

14 xii Contents 12.5 Uncertainty in Colorimetric Measurements Laws of Propagation of Uncertainty Uncertainty Computation Physical Standards for Colour Instrument Calibration 320 References Basic Instrumentation for Radiometry, Photometry and Colorimetry Introduction Lighting Cabinet Visual Comparison Colorimeter Instruments with Power Spectral Weighting Measurement Photometric Instruments Colorimetric Instruments Instruments for Measurements with Spectral Analysis Spectroradiometer Spectrophotometer Multiangle Spectrophotometers Fibre Optic Reflectance Spectroscopy (FORS) Glossmeter Imaging Instruments Imaging Photometer Colorimetric Camera Multispectral and Hyperspectral Camera 344 References Colour Order Systems and Atlases Introduction Colour Solid, Optimal Colours and Full Colours MacAdam s Limit Ostwald s Colour Order System and Atlas Ostwald s Hue Circle with Temperate Scale Ostwald s Semichrome Ostwald s Blackness, Whiteness and Purity Ostwald s Atlas Munsell s Colour Order System and Atlas Munsell s Instruments Chromatic Tuning Fork Munsell s Value and Grey Scale Munsell s Hue Munsell s Value in Coloured Scales Colour Sphere and Munsell s Colour Specification Munsell s Chroma Colour Tree Munsell s System and CIE Chromaticity Specification Helmholtz-Kohlrausch s Effect and Abney s Hue Shift Phenomenon in the Munsell Atlas Munsell s Colour Atlas DIN 6264 s Colour Order System and Atlas 372

15 Contents xiii 14.6 OSA UCS s Colour Order System and Atlas OSA UCS s Lightness OSA UCS s (g, j) Coordinates OSA UCS s Colour Difference Formula OSA UCS s Metrics NCS s Colour Order System and Atlas NCS s Axioms NCS s Hue, Chromaticness and Nuance Production of the NCS System and Visual Situation Psychophysics and Psychometrics for NCS Luminance Factor and NCS s Whiteness Scale NCS s Atlas 387 References Additive Colour Synthesis in Images Introduction Video Colour Image RGB Colorimetry Video Signal and γ Correction Tristimulus Space and YIQ Reference Frame srgb System Prints in the srgb System Camera, Photo Site and Pixel Spectral Sensitivities of Digital Cameras Principles of Halftone Printing Towards the Colorimetry of Appearance 419 References Software (Software developed by Gabriele Simone) Introduction to the Software Software Installation Data Files Monitor Monitor Setup Visual Evaluation of Gamma (γ) Colour Vision Tests Visual Contrast Phenomena Simultaneous Brightness Contrast and Crispening Simultaneous Brightness Contrast in Colour Scales Brightness and Chromatic Contrast After Image Colour Atlases Ostwald s Atlas Munsell s Atlas DIN s Atlas OSA UCS Atlas NCS Atlas CIE 1976 CIELUV and CIELAB Systems 448

16 xiv Contents 16.7 Cone Activation and Tristimulus CIE Colorimetry CIE Colour Specification CIE Systems Chromaticity Diagrams Fundamental Observers Dominant Wavelength and Purity Tristimulus Space Transformations Colour Difference Formulae ΔE CIE 1974 Colour Rendering Index R a Black Body and Daylight Spectra and Other CIE Illuminant Spectra Additive Colour Synthesis RGB Monitor, Additive Colour Mixture Halftone CMY Printing Subtractive Colorant Mixing Two Pigment Mixture Four Pigment Mixture Spectral Data View and Download Illuminant-Observer Weights Save File Opening 478 References 480 Index 481

17 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 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 members@sdc.org.uk for details. Coloration Qualifications: SDC s accredited qualifications are recognized worldwide. Please edu@sdc.org.uk 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 ( Publications: SDC is a global provider of content, helping people to become more effective in the workplace 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 Technology, 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 info@sdc.org.uk, or visit

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19 Preface Standard Colorimetry is an ambitious title that comes from the project of a small book, already fully written 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 contracted 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 commas, 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, exchanges, or simply the seminars I attended, helped me to understand and know, led me to get a varied overview of colour 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 phenomena. 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 claudio.oleari@fis.unipr.it. Claudio Oleari 2015

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21 1 Generalities on Colour and Colorimetry The Commission Internationale de l Éclairage (CIE) is the official institution devoted to worldwide cooperation 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 definitions 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 meanings 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 chromatic or achromatic. 1 The definition of colour as an effect of the colour stimulus is given by the Optical Society of America (OSA) in the 1952 report: 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 Standard Colorimetry: Definitions, Algorithms and Software, First Edition. Claudio Oleari John Wiley & Sons, Ltd. Published 2016 by John Wiley & Sons, Ltd.

22 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: 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 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 adaptation of the observer s visual system, and the observer s experience with similar observations. 5 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 incommunicable. 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. Hunt 6,7 distinguishes between: and Psychophysical colour terms terms denoting objective measures of physical variables that are evaluated so as to relate to the magnitudes of important attributes of light and colour. These measures identify 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 evaluated 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 Psychophysical colour terms regard Psychophysical colorimetry and psychometric colour terms regard Psychometric colorimetry. Both definitions of psychophysical and psychometric colour refer to colour stimuli, 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 specification 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

23 Generalities on Colour and Colorimetry 3 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), Vos observer 2 CIE fundamental observer CIELUV system (L*, u*, v*) CIELAB system (L*, a*, b*) CIECAM97 CIECAM02 Retinex f i e l d 10 visual field CIE 1964 supplementary standard observer (X 10, Y 10, Z 10 ) 10 CIE fundamental observer CIELUV system (L* 10, u* 10, v* 10 ) CIELAB system (L* 10, a* 10, b* 10 ) 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 This distinction among different colorimetries corresponds to a distinction among the historical phases of colorimetry 7 : 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). A third phase concerned with what colours look like and is termed colour appearance: i. aspect of visual perception by which things are recognized and ii. 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 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.

24 4 Standard Colorimetry References 1. ILV CIE S 017/E:2011, ILV: International Lighting Vocabulary, Commission Internationale de l éclairage, Vienna (2011). Available at: 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, (1977). 7. Hunt RWG, Colour terminology, Color Res. Appl., 3, (1978). Bibliography Berns RS, Billmeyer and Saltzman s Principles of Color Technology, 3rd edn, John Wiley & Sons, New York (2000). Billmeyer F Jr and Saltzman M, Principles of Color Technology, 2nd edn, John Wiley & Sons, New York (1981). Brainard D, Colorimetry, in OSA Handbook of Optics, 2nd edn, Bass M, ed., Vol. 1, Chap. 26, McGraw Hill, 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 Technology, 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).

25 2 Optics 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 chromatic or achromatic. 1 3 Colour stimulus function ϕ λ description of a colour stimulus by the spectral concentration of a radiometric 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 psycophysical 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/(m 2 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, ϕ λ = 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 Standard Colorimetry: Definitions, Algorithms and Software, First Edition. Claudio Oleari John Wiley & Sons, Ltd. Published 2016 by John Wiley & Sons, Ltd.

26 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 wavelength 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 operations 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 equalenergy (or equi-energy) stimulus function and denoted by the relative spectral radiance E E (λ) = 1. The equal energy stimulus function often plays a role in the normalization of the tristimulus space, used for the psychophysical 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 radiation 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. Geometrical 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 equipment: 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.

27 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 and 2. 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 descriptions (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 ( ), 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 consequently 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 t π ϑ κx ωt ϑ λ τ = (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); and ϑ 0 is the initial phase. The electromagnetic waves have the following properties: The quantities described by wave functions are the electric field vector E( κ x ω t ϑ0 ) and the magnetic field vector H( κ x ω t ϑ0 ). 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 propagation 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.

28 8 Standard Colorimetry (a) E H λ (b) E H (c) τ x t x 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. 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 colorimetric 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 ϕ e of the electromagnetic radiation (energy per unit of time and area, measured in W/m 2 ) proceeds in the direction orthogonal to the fields E and H. The electric and magnetic field magnitudes are proportional to each other H = ( ε / µ ) E. 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 ϑ 0 ), which takes the same value for different pairs of variables x and t. If we consider the wave function at the instants t 1 and t 2, it follows that this function has the same values at the points x 1 and x 2 such that (κ x 1 ω t 1 ) = (κ x 2 ω t 2 ), from which ω (t 1 t 2 ) = κ (x 1 x 2 ), and then the

29 Optics for Colour Stimulus 9 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 extraspectral region means complementary of. wave advances rigidly with a velocity v =(x 1 x 2 )/ (t 1 t 2 ) = ω/κ = λ/τ = λν. The velocity in the vacuum is c = 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 classification 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

30 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 ) 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 colour, 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 ). 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. 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. 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. Radiation defined by a superposition of different monochromatic waves is termed heterochromatic.