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While doing some tests on the effect of dilution of inks, I noticed some (to me) strange effects that might be of interest to others.
This post builds on the information presented in (http://www.nifty-stuff.com/forum/viewtopic.php?id=496), so you may want to start at the beginning if this is your first look at one of the FNO posts.
The attached image shows the effect of diluting yellow, red and magenta inks. The 100% yellow passes most light above about 540 nm and blocks most light below about 500 nm, getting progressively more effective at the shorter wavelengths.
At this point it is necessary to discuss the non-linear nature of light absorption, as it is necessary to understand what happens when the ink is diluted. Suppose that a certain ink absorbs 50% of the light (passing the remaining 50%), and that the ink's strength is then doubled. The new ink will not absorb 100% of the light, but only 75%! The reason is that we must look at the light that is allowed to pass - doubling the ink's strength will pass 50% of 50% (=25%) of the light. In a similar fashion, the following table gives the relative ink strength required to pass a certain percentage of light:
Relative strength % of Light Passed % of Light Absorbed
0.25x 84% 16%
0.5x 71% 29%
1x 50% 50%
2x 25% 75%
3x 12.5% 87.5%
4x 6% 94%
5x 3% 97%
6x 1.5% 98.5%
7x 0.78% 99.2%
8x 0.39% 99.6%
This table shows that the ink will have to be 5 times as "strong" to reduce the reflected light to 3% (typical for yellow and red at the shorter wavelengths). It also shows that if the strength is reduced by one (from 5x to 4x) it will only pass 3% more light (3% --> 6%). However, if the strength is reduced by the same factor of one (from 1x to 0x), it will pass 50% more light. This shows why dilution can cause a large change where the ink Is marginally effective, but very little change where the ink is very effective - as demonstrated on the image below. Diluting the yellow ink by a factor of 4 (25%) caused no difference in the absorption of short wavelengths - it just moved the thresholds where the absorption starts and ends. It is only when the ink was diluted by 8x (12.5%) that the shorter wavelengths began to get through! This is certainly not what I expected to see, but it does make sense if you consider inks as light filters and compare them to the behavior of electronic and acoustic filters.
Just below the yellow test are similar plots for the dilution of red ink. The most obvious thing that jumps out about the red spectrum is that it is almost identical to yellow's spectrum, only shifted about 50 nm to the right. It can also be seen that the red does not seem to be affected as much by dilution as the yellow was, but that dilution merely shifts the red toward yellow (as would be expected based on what was learned above).
The spectra for magenta are different in that they also allow a second band of light to pass (a "band pass" filter) at about 450 nm. This type of ink is obviously affected by dilution in a very different way than either the yellow or red.
The "Lab" color values for each color were converted to "HSB" and are given below:
H S B
100% R 30 100 94
50% R 33 100 97
25% R 36 90 98
100% Y 51 100 96
50% Y 57 85 95
25% Y 59 58 93
12.5% Y 63 32 95
100% M 329 100 75
25% M 316 65 87
Note that the Yellow and Red colors are very "bright" (they have Brightness values of about 95% - about the same as the paper) when compared to magenta, and this means that they will be affected by the addition of a darker ink much more than magenta (which has a Brightness of only 75%).
Why is this information of any interest? Two reasons:
1. If you decide to play with diluting your inks to adjust your overall color, you need to do a lot of research if you hope to get predictable results.
2. An understanding of this information is required to understand the next post in the series, dealing with some of the strange things that occur when inks fade.
This post builds on the information presented in (http://www.nifty-stuff.com/forum/viewtopic.php?id=496), so you may want to start at the beginning if this is your first look at one of the FNO posts.
The attached image shows the effect of diluting yellow, red and magenta inks. The 100% yellow passes most light above about 540 nm and blocks most light below about 500 nm, getting progressively more effective at the shorter wavelengths.
At this point it is necessary to discuss the non-linear nature of light absorption, as it is necessary to understand what happens when the ink is diluted. Suppose that a certain ink absorbs 50% of the light (passing the remaining 50%), and that the ink's strength is then doubled. The new ink will not absorb 100% of the light, but only 75%! The reason is that we must look at the light that is allowed to pass - doubling the ink's strength will pass 50% of 50% (=25%) of the light. In a similar fashion, the following table gives the relative ink strength required to pass a certain percentage of light:
Relative strength % of Light Passed % of Light Absorbed
0.25x 84% 16%
0.5x 71% 29%
1x 50% 50%
2x 25% 75%
3x 12.5% 87.5%
4x 6% 94%
5x 3% 97%
6x 1.5% 98.5%
7x 0.78% 99.2%
8x 0.39% 99.6%
This table shows that the ink will have to be 5 times as "strong" to reduce the reflected light to 3% (typical for yellow and red at the shorter wavelengths). It also shows that if the strength is reduced by one (from 5x to 4x) it will only pass 3% more light (3% --> 6%). However, if the strength is reduced by the same factor of one (from 1x to 0x), it will pass 50% more light. This shows why dilution can cause a large change where the ink Is marginally effective, but very little change where the ink is very effective - as demonstrated on the image below. Diluting the yellow ink by a factor of 4 (25%) caused no difference in the absorption of short wavelengths - it just moved the thresholds where the absorption starts and ends. It is only when the ink was diluted by 8x (12.5%) that the shorter wavelengths began to get through! This is certainly not what I expected to see, but it does make sense if you consider inks as light filters and compare them to the behavior of electronic and acoustic filters.
Just below the yellow test are similar plots for the dilution of red ink. The most obvious thing that jumps out about the red spectrum is that it is almost identical to yellow's spectrum, only shifted about 50 nm to the right. It can also be seen that the red does not seem to be affected as much by dilution as the yellow was, but that dilution merely shifts the red toward yellow (as would be expected based on what was learned above).
The spectra for magenta are different in that they also allow a second band of light to pass (a "band pass" filter) at about 450 nm. This type of ink is obviously affected by dilution in a very different way than either the yellow or red.
The "Lab" color values for each color were converted to "HSB" and are given below:
H S B
100% R 30 100 94
50% R 33 100 97
25% R 36 90 98
100% Y 51 100 96
50% Y 57 85 95
25% Y 59 58 93
12.5% Y 63 32 95
100% M 329 100 75
25% M 316 65 87
Note that the Yellow and Red colors are very "bright" (they have Brightness values of about 95% - about the same as the paper) when compared to magenta, and this means that they will be affected by the addition of a darker ink much more than magenta (which has a Brightness of only 75%).
Why is this information of any interest? Two reasons:
1. If you decide to play with diluting your inks to adjust your overall color, you need to do a lot of research if you hope to get predictable results.
2. An understanding of this information is required to understand the next post in the series, dealing with some of the strange things that occur when inks fade.
