Color Vision and Physics PDF

What is color? Color is a highly multi-faceted phenomenon in nature, biology, and culture. There are meanings related to physics (light, emission, absorption, spectrum, coloration etc.) and to our perceptual response to such physical effects. Color a multi...

What is color? Color is a highly multi-faceted phenomenon in nature, biology, and culture. There are meanings related to physics (light, emission, absorption, spectrum, coloration etc.) and to our perceptual response to such physical effects. Color a multidisciplinary approach, Zollinger  Color is associated to light properties Plane electromagnetic wave The electric and magnetic vectors E and H are perpendicular to one another, and, in addition, mutually perpendicular to the propagation direction inidicated by the wave vector k. Colour and the Optical Properties of Materials, Wiley  Transverse electromagnetic (TEM) waves Monochromatic wave 2𝜋𝜋 𝐸𝐸𝑦𝑦 = 𝐸𝐸0 cos[ 𝑥𝑥 − 𝑣𝑣𝑣𝑣 ] 𝜆𝜆 In vacuum v=c=300,000 km/s Part of a light wave travelling along x. The curve represents the magnitude E of the electric field vector as a function of position. The distance between the crests or troughs is the wavelength l. Any point on the wave moves with a speed v  Transverse electromagnetic (TEM) waves If the electric field vector remains in the plane of the paper, as drawn, the light is linearly polarised. If the orientation of the electric field with respect to the plane of the page varies at random so that the curve continually adopts differing angles with the plane of the paper, the light is unpolarised The term E0 is the amplitude of the wave (the maximum value that the electric field vector takes) and is a constant. The speed v at which any point on the wave, say a peak or a trough, travels is called the phase speed or phase velocity. The velocity of an electromagnetic wave in vacuum, denoted by the speed of light c, is an important physical constant.  Phase and interference The argument of the cosine function, is called the phase of the wave. A beam of light is said to be monochromatic when it is comprised of a very narrow range of wavelengths and it is coherent when all of the waves which make up the beam are completely in phase; that is, the crests and troughs of all the waves are in step. 2𝜋𝜋 φ=[ 𝑥𝑥 − 𝑣𝑣𝑣𝑣 ] 𝜆𝜆 If two identical waves are exactly in step then they will add to produce a resultant wave with twice the amplitude by the process of constructive interference. If the two waves are out of step, then the resultant amplitude will be less, due to destructive interference  Phase and interference constructive interference destructive interference  Color and wavelength The electromagnetic spectrum covers an enormous range of wavelengths λ from, for example, values such as λ ≈ 1 fm (1 fm corresponds to 10–15 m) for cosmic radiation to λ ≈ 10 km for radio waves, therefore a range of around 19 orders of magnitude. The visible range of humans is only a small part of the spectrum of electromagnetic waves. Merely wavelengths in the very small interval from 380 to 780 nm.  Photons When light is absorbed by or emitted from a material, say a gemstone such as ruby, energy changes are paramount. In this case, light is best regarded as a stream of photons; the energy of each photon being defined as: semiconductors molecule The absorption of light by isolated atoms or molecules involves a change in energy of the electrons surrounding the atomic nuclei. These occupy a series of atomic or molecular orbitals, each of which can be assigned a precise energy. Color and wavelength  Visual color impression/perception The visual color impression of non-self- luminous object ultimately due to three independent components: the light source, the optical properties of the object, and the observer. The color perception depends on: – the spectral power distribution emitted of the light sources used; – the light interactions with the object especially the resultant absorption, scattering, reflection, transmission, as well as interference or diffraction; (possible light emission from the object – the color perception capability of the observer Black-Body Radiation Spectral irradiance What is color?  Color vision Light is perceived by the eye brain combination, and colour is a description of this perception.  Color vision The cornea is only 0.5 mm thick and of fixed focal length of 25 mm, the iris has a lightness-dependent aperture ratio of 28:1, and the crystalline lens is of variable focal length. This focal length amounts about 50 mm for the resting eye when relaxed for distant vision. For an eye of normal vision, these optical elements provide a clear and focused image on the retina in the area of the fovea. In the retina are located two types of photosensitive receptors: first, the rods responsible for dusk vision and achromatic colors for luminance less than 0.01 cd/m2 (scotopic vision); second, the cones for color vision for luminance higher than 10 cd/m2 (photopic vision).  Color vision If the eye is fully adapted to darkness, just nine photons are required before a light stimulus is detected. In cases of middle illumination for luminance in the range of 0.01 and 10 cd/m2, rods and cones are simultaneously active (mesopic vision). The retina of the human eye contains altogether about 125 million visual cells, but only 5% consist of cones. In the small area of the fovea for visual angles of about ±0.5◦, there are only cones present. Here they are of maximum density and enable focused vision only at this spot of the retina. Cones and rods (a) All photoreceptors have inner segments containing the nucleus and other important organelles and outer segments with membrane arrays containing the photosensitive opsin molecules. Rod outer segments are long columnar shapes with stacks of membrane- bound discs that contain the rhodopsin pigment. Cone outer segments are short, tapered shapes with folds of membrane in place of the discs in the rods. (b) Tissue of the retina shows a dense layer of nuclei of the rods and cones. The photochemistry of vision  The photochemistry of vision Opsin pigments are actually transmembrane proteins that contain a cofactor known as retinal. Retinal is a hydrocarbon molecule related to vitamin A. Photons cause some of the double-bonded carbons within the chain to switch from a cis to a trans conformation. This process is called photoisomerization. Before interacting with a photon, retinal’s flexible double-bonded carbons are in the cis conformation. This molecule is referred to as 11-cis-retinal. A photon interacting with the molecule causes the flexible double-bonded carbons to change to the trans- conformation, forming all-trans-retinal, which has a straight hydrocarbon chain. Cones sensitivity  Additive color mixing Additive color mixing occurs when two or more beams of differently colored light combine (i.e. overlap on a perfectly white surface, or arrive at the eye simultaneously). Colors on television screens are produced by additive coloration, as the screen is composed of small dots of three different phosphors each of which shines with one of three primary colors when activated.  The trichromatic principle All color stimuli can be simulated by additively mixing only three selected color stimuli (trichromatic principle). It has been found that colors can be produced by mixing just three additive primary colors, red, green and blue. (Strictly speaking, any fairly monochromatic light near to these colors will suffice). Moreover, mixing equal quantities of these three primary color lights will produce white light. There are a number of ways of quantifying the amounts of each primary color light present, which can represented by the values, r of the red component, g of the green component and b of the blue component; thus: Use of these three additive primaries is called the RGB colour model.  The RGB color model A simple colour space can be constructed by using Cartesian axes to represent the amount of the three primary colours, red, green and blue, while the diagonal represents the transformation from black to white. Sections through this colour space allow one to represent colours by a planar figure. Such representations are called chromaticity diagrams. A simple example is given by taking the triangular sheet running diagonally through the cube normal to the black white diagonal and cutting the corners of the cube that represent pure red, green and blue.  The CIE 1931 system The study of light mixing has been quantified by the Commission Internationale de l’Eclairage (CIE), Industrial color testing, Wiley The CIE 1931 system A colour is specified by a pair of x- and y- coordinates. The spectral colours are arranged around the outer edge of the shape and colours not seen in the spectrum, the purples and browns, are found to lie between the red and violet ends of the curve. The colours are fully saturated along the outer edge of the curve and become less and less saturated as the centre of the diagram is approached. Standard daylight white is represented by a point close to the coordinates x=y=0.33  Complementary colors If a straight line is drawn through the point W and extended to the boundaries of the curve, the pair of colors reached, when mixed, will give white light. The proportions of the end colors red and blue green light needed to produce white light is given by the lever rule. The colors at the ends of a line through the point W are called a complementary pair of colors. If one of these colors is subtracted from white light then the colour remaining is called the complementary color to the first.  Limits of CIE 1931: other color spaces As with the colour triangle, all planar chromaticity diagrams represent hue and saturation, but not the exact value of lightness, which must still be added as a third axis perpendicular to the chromaticity diagram if this information has to be displayed. Colors can then conveniently be represented by points in a three-dimensional coordinate system. There are many diagrammatic ways of representing the three attributes, and these are called color spaces. The way in which the coordinates of any colour in the colour space are derived is called a colour model. One widely used colour model takes as initial parameters the three attributes hue, saturation and brightness to give the HSB model, HVC (hue, chroma, value), HSL (hue, saturation, luminance), HIS (hue, intensity, saturation) and HCL (hue, chroma, luminance).  The HSB model 1. Hue, which corresponds to the wavelength or frequency of the radiation. The hue is given a colour name such as red or yellow. 2. Saturation or chroma, which corresponds to the amount of white light mixed in with the hue and allows pale ‘washed out’ colours to be described. 3. Brightness, lightness, luminance, or value, which describes the intensity of the colour, the number of photons reaching the eye.  The CIELAB system This system uses the three spatial coordinates a* (red-green axis), b* yellow-blue axis), and L* (lightness axis) for brightness. In order to calculate the CIELAB coordinates, X, Y, and Z are first converted to the "value functions" X*, Y*, and Z* (Xn, Yn and Zn are the CIE tristimulus values for the illuminant used) The CIELAB system  The Interaction of Light with a Material As a beam of light passes through a material it gradually loses intensity, a process generally called attenuation (formerly extintion). Attenuation is due to the interaction of light with a material in two basic ways: scattering or absorption  Light attenuation When attenuation takes place in a homogeneous solid the amount of light transmitted by a semitransparent plate of thickness x is given by 𝐼𝐼𝑥𝑥 = 𝐼𝐼0 𝑒𝑒 −𝛼𝛼𝑒𝑒𝑥𝑥 where Ix is the irradiance leaving the plate, Io is the incident irradiance and αe (m-1) is the (Napierian) linear attenuation coefficient (formerly extinction coefficient). Equation is known as Lambert’s law or Beer’s law, More often, extinction is associated with a dilute concentration of centers distributed throughout the bulk phase. In this case, the degree of extinction is often taken to be a function of the concentration of these centers. This is taken into account in the Lambert- Beer law. 𝐼𝐼𝑥𝑥 𝑙𝑙𝑙𝑙𝑙𝑙 = −𝜀𝜀𝜀𝜀𝜀𝜀 𝐼𝐼0 The dimensionless product A=εcx is called the absorbance (sometimes the optical density) and the ratio Ix/Io is the transmittance or transmissivity T 𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = −𝐴𝐴 𝐼𝐼0 = 𝐼𝐼𝑟𝑟 + 𝐼𝐼𝑠𝑠 + 𝐼𝐼𝑎𝑎 + 𝐼𝐼𝑡𝑡 1 = 𝑟𝑟 + 𝑠𝑠 + 𝑎𝑎 + 𝑡𝑡 where r is the fraction of light reflected, s is the fraction of light scattered, a is the fraction of light absorbed and t is the fraction of light transmitted and the quantities measured are the appropriate irradiance values. Subtractive coloration  Subtractive coloration Combination of three subtractive primary colors to produce the whole range of subtractive colors. These subtractive primary colors are: cyan, which absorbs red and transmits blue and green; magenta, which absorbs green and transmits blue and red; and yellow, which absorbs blue and transmits green and red. If the three subtractive primaries are mixed in equal amounts we obtain black, as one primary will absorb red, one will absorb green and one will absorb blue, thus removing the whole of the visible spectrum. Colour construction using these three subtractive primary colurs is described as employing the CMY model