# Discussion on the practical application of the hot

2022-08-17
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Discussion on the practical application of printing density II

II analysis of color separation algorithm based on density space

▲ 1. Electronic color separation and addition principle of black and white originals

electronic color separation machine is based on density space for color separation. This is essentially different from the color separation of Photoshop. It can also be said that the color separation of electronic color separation machine is device related color separation, while the color separation of Photoshop is based on chromaticity space and is device independent color separation

there is no color separation in the reproduction of black-and-white originals, but only addition, that is, turn the continuous tone black-and-white originals into halftone printing brushes, and use halftone to express the continuous tone

scan each point on the original continuously with a scanner, and calculate the percentage of addition according to the concentration of each point. The scanner is essentially a black-and-white densitometer

Murray of point percentage and tone density is derived below_ Davis formula (as shown in Figure 2)

set the percentage of points as α， Then the percentage of blank part is 1- α。 Set the point concentration (equal to the full page concentration) to DV, and set the concentration of the blank part (paper) to o. Then the total reflectivity of the point area to the incident light (set the incident light as 1) is 1I = α×+ （1- α）× 1OO＝1- α× （O-DV）。 The step concentration (point area concentration) can be expressed as follows: D1 = lg1/[1- α× （）]。 Based on this, we can deduce α＝ （O.D1）/（）。 Among them, DV can be measured by measuring the full page concentration of printing, so as to know the relationship between step concentration and dot percentage. The scanner measures the concentration of each point on the original (called step concentration after printing), and its point percentage can be calculated through this formula

▲ 2. Color separation and addition principle of color originals

the scanning of color originals should be used to manufacture important components such as Aeroengine Blades and turbine disks, and collect red, green and blue signals at each point. Its principle is equivalent to a color densitometer, that is, the three color separation concentrations D1, DG and DB can be measured for each point. To restore the original correctly, it is required to produce the percentage of each point of the yellow, magenta and cyan color plates (assuming that only the three color plates are used to restore the original)

if the ink is an ideal ink, that is, the yellow material must be non cytotoxic, mutagenic and carcinogenic. The ink only absorbs blue light and reflects all red and green light, magenta ink only absorbs green light and reflects all red and blue light, and green ink only absorbs red light and reflects all green and blue light, the problem is very simple. For example, suppose that the color separation concentration D1 is measured, that is, the color separation concentration of red light. To restore D1, it has nothing to do with the dot percentage of the yellow version and the dot percentage of the product version, because these two color versions will all reflect red light (the same as white paper), so it is only related to the dot percentage of the green version. The higher the dot percentage of the green version, the more red light absorption, and the greater D1. Therefore, you can measure the full plate concentration DRS of the green plate (the greater the concentration value measured with the red filter, also known as the color concentration or full plate concentration), and replace it with mur5 above Yield ratio（ σ s/σ b）ray_ Davis formula, so that we can find the relationship between D1 and the percentage of green version points

it can be seen that the color separation of ideal ink is actually the application of Murray to the reflection concentration of each color light respectively_ Davis formula

this is not the case with actual inks. For example, although yellow ink absorbs most of the blue light, it does not reflect all of the red and green light. The same is true for the other two inks. We can actually measure the trichromatic concentration of three inks with a color densitometer, which is the measurement result of a certain ink (see Table 1)

therefore, the actual color separation must consider the factor of ink color deviation. For example, if only green ink is printed on the paper, and the spot printing is set to be 100%, it will produce D1, that is, the color separation concentration of red light is 1.50, while the color separation concentration of green light is 0.50 and the color separation concentration of blue light is 0.10. Let us assume that the following formula holds, that is, the proportion coefficient of the color separation concentration of each color light remains unchanged. For example, suppose that D1 produced by a certain percentage of blue ink is half of the original, that is, 0.75, then its DG and DB are also reduced by half, that is, 0.25 and 0.05 respectively. In this way, it can be calculated that K5 is 0.50/1.50 = 0.33, K6 = 0.10/1.50 = 0.06. For the other two inks, their proportion coefficients are also calculated and listed in the above table

set the three concentrations of dro, dgo and dbo at a certain point on the original. Then calculate the corresponding step concentration (referring to the step concentration corresponding to the color concentration or full page concentration) Dr, DG and DB of each ink after printing. Then the calculated step concentration is substituted into Murray_ Davis formula, you can calculate the percentage of each point

according to the principle of density superposition, the following equation can be listed:

Dr for the drop weight impact experiment of coherent experimental materials o = K1 × Db ＋K3 × Dg＋Dr

Dgo＝K2 × Db＋Dg＋K5 × Dr

Dbo＝Db＋K4 × Dg＋K6 × Dr

the above equation is a system of equations containing three unknowns Dr, DG, DB. In general, the equation will have a unique solution. Put the solved Dr, DG and DB into Murray respectively_ Davis formula, you can calculate the point percentage of each color version

in some cases, the equation will have no solution. This is because the color gamut of the dot original is beyond the range of the color gamut that can be represented by the superposition of three color inks. In this case, only the closest solution can be obtained

the actual printing needs to add the black version. After the black version is added, the color gamut will expand, and what was not solved may now become solved. After the black version is added, the equation becomes three equations and four unknowns, and there will be countless solutions, which means that there may be an array of yellow, magenta, cyan and black combinations on the original that are not very saturated, which can restore the color. Generally, in this case, to determine the number of black plates, you may first determine the number of black plates through UCR (background color removal) or GCR (non color structure), and then calculate the number of other three color plates

(to be continued)

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