Fully Automatic Two-Dimensional Spectrophotometric Colorimeter (2048 Pixels)
High-precision spectrocolorimeter, 2048 pixels. Conventional instruments have only 24 or 256 pixels; 2048 pixels improve color reproduction. Measurements: 380-780nm spectra at 1nm intervals versus conventional 10nm, repeatability 99%, CIE1931, XYZ, sGRB, LCH, HSV, Yxy, CYMK, xyz and color-rendering index. Colorimetry has 2 types: emissive objects, such as displays/lamps, are measured directly with a spectrometer; nonemissive objects depend on the illuminating source. Pink market lamps make pork look fresh, while sunlight at home changes its appearance. Colors of fabric, cards, paints and coatings therefore require a defined source, typically white 6500K D65 daylight or yellow illuminant A from a halogen bulb. An incorrect source gives inaccurate color. Color printing, physical specimens and automatic colorimeter results are shown. The following figure shows human responses to the three primaries at different wavelengths, representing color sensitivity. 1) 1924 luminous-efficiency function V(λ): λ means wavelength. Before foundational colorimetry, CIE published V(λ) for daylight spectral sensitivity. Two beams at 550nm and 400nm may have equal radiometric intensity but different apparent brightness. If green and blue look equally bright, the blue is brighter. The 1924 function was later found inadequate at the blue spectral end. 2) 1931 RGB color matching: CIE 1931 includes three RGB matching functions. Imagine red, green and blue lamps at precisely known single wavelengths aimed at one wall spot: can their powers be adjusted to match 540nm? The functions answer this, giving the amount of each fixed primary needed in the mixture. Their primary wavelengths are 700nm, 546.1nm and 435.8nm, with r(λ), g(λ), b(λ) plotted below. R, G and B are tristimulus values, the test-light brightnesses needed for a match. A diagram is given instead of the colorimetric equations. Because blue is negative, it cannot physically be used; therefore these primaries cannot exactly match 610nm, though positive red and green can approximate it. Negative values are discussed next. Lowercase rgb gives proportions: matching 400nm requires more blue than red or green. Uppercase RGB gives absolute amounts: almost no primary light is needed to match 400nm. Plotting each rgb value in 3D produces the spectral locus, a curve of chromaticity for each spectral wavelength. 3) CIE XYZ: Congratulations if you are still following; this is the final stage. The 1931 XYZ functions are linear transforms of 1931 RGB, giving convenient mathematical properties. RGB CMFs are rarely used directly in practical modern colorimetry; modern spaces are defined from XYZ. XYZ/RGB are different transforms of the same data: operations and colors can transfer between them. A key idea transforms one function to closely match the 1924 V(λ), so a color's luminance follows from one primary value. Before computers, manual CMF calculations were difficult, motivating functions without negative values. The difficulty is that an all-positive transform requires imaginary primaries unrelated to real colors. In the preceding rg diagram, enclosing every real color in a triangle requires primary coordinates outside real colors. XYZ does this by choosing new X, Y and Z primaries, so Y maps to V and all values are positive. Consider the preceding rg chromaticity space:
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