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In color science the perception of colors is divided as the interaction of three different, independent elements: i) light source ii) object iii) observer The two first elements can be described in pure physical terms, the light source by through its spectral intensity distribution, the object by its reflectance spectrum i.e. the fraction of light intensity reflected within a certain spectral region. The observer imposes limitations since the electrical signals generated at the eye are processed in the brain through unknown process into the final color sensation. Here lies the psychochromatic origin of color sensation, a point that we always must bear in mind when dealing with color assessment. Color science distinguishes also three different steps approaching color assessment: i) quantification of color ii) color differences iii) color interaction Color quantification is quite straightforward; the problem posed by the observed is solved by defining an average observer through experimentally determined response functions. Color quantification relies on a number of conventions and definitions given by the CIE (Commission Internationale de lEclairage) that form the basis for color quantification and communication. Any color can be characterized by three numbers, the set of all possible triples define certain color solid that contains all possible colors detected by the human eye. Depending on the system used to quantify color the three numbers receive different names, in general one can speak that a color can be characterized by its saturation, its hue and its luminosity. After the reflectance values of samples have been measured, they are weighted with those of a light source and of the observer leading to saturation, hue and luminosity (or lightness). Two colored samples with exactly the same values for the color coordinates are said to be equivalent and they are perceived as equal by the eye under observation conditions. Bear in mind however that a change in illumination conditions will lead to different color coordinates and the color coordinates of color samples may change in different extent and not be equivalent under the new conditions (they are said to build a metameric pair). Color differences is a pure industrial problem and can be stated as to which extent color coordinates of two samples can differ and still be assessed as the same by the trained eye; this is the typical color matching problem. There are many formulas to express color differences but none of them has universal character i.e. they must be calibrated to the color region where assessment is conducted. Color interaction is a problem of design and appreciation, very difficult to cope in terms of mathematical simulation and models. Every color and color combination triggers an emotional flash that interacts deeply with the color assessment of each color by itself; as a result color assessment must be conducted in environments with controlled conditions and under isolation to avoid possible interactions that may lead to false judgments. The color white is defined in colorimetric terms as a color with the highest luminosity, no hue and no saturation. In spectroscopic terms this color is represented by a body with the property of reflecting light at all relevant wavelengths without any loss and represented by a horizontal line on its reflectance spectrum.
The key for making a surface to appear white is to cover it with a layer of white pigment, this is actually done with paints or by adding a filler to plastic or paper. It must be understood that in the latter case what is done is just a dilution of the original color of substrate and the process has limitations of the white obtained. A large part of the materials used in the textile industry and almost all of the paper industry is cellulose from natural resources (wool, cotton, wood, etc.) with colors form brown to light yellow. The traditional method for obtaining substrates with high lightness values is by chemical bleaching i.e. the chemical destruction of colored substances present in the substrate; the result of extensive bleaching however is at best an off-white substrate with a light yellow tint. Bleaching is however limited in terms of fiber destruction (prolonged bleaching affects fiber properties) and in terms of money. An alternative way of increasing perceived whiteness is by mixing complementary color of the substrate in order to shift the resulting color coordinates closer to the black-white axis. Since in general substrate color is yellow, the complementary color to be mixed is blue. Color mixing can be conducted in two different ways, subtractive and additive mixing. Subtractive color mixing is known as shading and consists in the addition of a dye that absorbs the complementary wavelength region to the one leading to yellowness. Since substrates normally already have a high value of whiteness the complementary color is more a violet than a blue (this is strictly dependent on the lightness of the substrate). Specially care must be given to the election of the shading agent since it introduces a new color and also a metameric element towards the color to be matched. One must bear in mind that although the shading agent will increase the perceived whiteness, being a dye it will decrease the overall value of the lightness; the substrate will appear in fact whiter compared to the non-shaded one (and it will be preferred over it), the perceived white is however dull. It is extremely critical to reach the point at which the substrate will appear colored and not white to the eye. Additive color mixing involves the addition of light to that reflected by the substrate; in the present case this is really blue light. Since the amount of light is now higher than for the original substrate, the value of the lightness increases leading to the perception of a vivid and dazzling white substrate as compared to the original one. The blue light is originated by a molecule (fluorescent whitening agent) added to the substrate by the phenomenon of fluorescence. Certain classes of molecules are capable to emit the energy absorbed as light, if the time scale is very short the light is called fluorescence. Fluorescent Whitening Agents (FWA) contain a fluorescent molecule that emits light in the region 380 to 480 nm with a maximum at about 440 nm, they are specifically tailored to compensate yellowness occurring with cellulose materials. The corresponding absorption occurs at higher energies typically with a maximum (actually a minimum in the reflectance) at 350 to 360 nm. The total perceived whiteness consists thus of three different elements: i) Base white: this is the contribution to the whiteness by the substrate itself, it is a pure reflectance with a small absorption of blue light that produces a yellow tint. The extent of the base white is the most important since it dictates the extent to which the yellowness can be compensated by physical means. ii) Shaded white: is the amount of whiteness increase due to the compensation of yellowness by subtractive color mixing. Whiteness is increased but the lightness decreases. iii) Fluorescent white: whiteness increase due to additive color mixing. The increase of whiteness is accompanied by an increase of the lightness as well.
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No losses means that the reflectance values
are 1 for the whole wavelength range (or 100%); this defines the ideal white, a body rarely encountered in nature. Continuous and regular losses at each wavelength define
ideal grays depending on the lightness value; zero lightness corresponds to the ideal black color. Any absorption in a limited wavelength region leads to a color. The axis from ideal
black to ideal white builds a natural whiteness axis that is in accordance with the definition given before as zero saturation and zero hue. Objects with reflectance spectra corresponding to a horizontal line are
extremely rare in nature, certain pigments like Titanium dioxide, Calcium carbonate, China clay, Magnesium dioxide, Barium sulfate, Zinc
oxide, etc. can be produced (or extracted from natural resources) and refined in such a way that their spectra approximate the one of ideal white (or in general a light gray).
The eye is not in position to distinguish the different
origins of the perceived whiteness, the light coming from the substrate is detected and perceived as a whole. The fact of whiteness multiplicity poses a formidable problem to color matching since the
metamerism is increased threefold; only pairs with equivalent color coordinates for each of the processes can be regarded as non-metameric.