[Color] grayscale coefficient and dot increase

File: studydotgain.txt
Name: grayscale coefficient and dot increase
Author: zyl910
Version: V1.0
Updata: 2007-7-20

In the color Settings dialog box of Photoshop, you will find that the word "dot gain" frequently appears, such as "gray" and "special color" in the "color settings" dialog box ", in the dialog box of "Custom CMYK", click "increase outlet ". Especially in the drop-down lists of "gray" and "special colors", in addition to the predefined items, the "Custom dot correction" and "Custom gray coefficient" functions are also provided, so I suspect that the gray coefficient is related to the increase of the dot.
You can use "Custom gray level coefficient" to view the gray level coefficient of the pre-plan. The following figure shows the gray level coefficient of the pre-plan:

Dot Gain 10%	1.32
Dot Gain 15%	1.51
Dot Gain 20%	1.74
Dot Gain 25%	2.00
Dot Gain 30%	2.32
Gray gamma 1.8	1.80
Gray gamma 2.2	2.20
Black & white	1.80
Sgray	2.20

Note that the gray Gamma coefficient is the Gamma coefficient. Let's review the calculation method of Gamma Correction.
Set the Gamma coefficient to F, the source gray level to G, the current intensity of the display electron gun to I, the actual brightness to V, G, I, V are normalized to the [0, 1] range. When Gamma Correction is not performed, the actual brightness is:
I = g // use g directly as the current intensity without Gamma Correction
V = I ^ F = G ^ F
Because V = G ^ F is not equal to the source gray value g, Gamma Correction is required:
I = G ^ (1/F) // perform Gamma Correction
V = I ^ F = G ^ (1/F) ^ F = G

Now v = G.

On the network, I checked the description about the increase of the network:
Dot Gain (expanded outlets ). In photoshop5.0, there are two ways to expand the network point:
A. Standard (standard mode): the expansion of outlets has the greatest impact on intermediate adjustment, and the expansion rate of 50% outlets is the largest. The expanded outlet value set in the standard mode is the expanded outlet value of 59%. For example, setting a 20% outlet expansion rate means that the intermediate outlet will be printed as 70% (50% + 20% ). In addition, the dot expansion of the color printer also has a great impact on the color. Different paper, inkjet speed and printer models will bring about a very different dot expansion.
B. curves (curve mode): In this mode, you can use both the same (composite channel) and CMYK four-color channel to set the network expansion, it can set up to 13 levels of corresponding dot expansion value, its accuracy is higher than the standard mode. In the case of "all the same, the expansion rate of each CMYK channel is forcibly consistent, which is actually an extension of the standard mode, expand most outlets from 50% to the entire gray ladder range. This setting requires the gray ladder ruler, and the density meter is used to measure the dot values after the gray gradients at all levels on the gray ladder, respectively, and fill in the table. For example, if the original gray ladder 20% grayscale area is printed and the actual site is 30%, enter 30 in the 20% column of the dialog box.

Set the dot size to E, and the Gamma coefficient (gray level coefficient) to F. We can see from the above that the dot increase is calculated based on the intermediate color of 50%, that is, the source gray G is 0.5. The actual output is 0.5 + e, which is 1-(0.5 + E) in the color system ). Substituted gamma equation:
1-(0.5 + e) = 0.5 ^ F
Solution:
E = 0.5-0.5 ^ F
F = Log (0.5 + E)/log (0.5)

The numeric value is substituted into the formula for calculation, which is consistent with the predetermined constant of Photoshop:

Dot Gain	Gamma
10.00%	1.3219
15.00%	1.5146
20.00%	1.7370
25.00%	2.0000
30.00%	2.3219

Gamma	Dot Gain
1.32	9.95%
1.51	14.89%
1.74	20.06%
2.00	25.00%
2.32	29.97%