We need some help from math wizards! - Home Theater Forum and Systems - HomeTheaterShack.com

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post #1 of 37 Old 09-18-09, 09:25 PM Thread Starter
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We need some help from math wizards!

Hi folks!

We are getting quite a database of reflectance data from different paints, but we mix developers don't have the mathematical skills required to accurately predict how two colors will interact when combined.

When someone has a color computer-matched at a paint store, what happens is that the color is measured by a spectrophotometer which breaks down the color into a range of spectral reflectance readings. The computer software then uses it's database of the same type of spectral readings of the tints available and the base chosen to mix the final color. For light to medium dark colors this process results in an amazingly close match (it has failed for VERY dark colors).

While the goal would be to ultimately be able to combine two or more colors via software and get a correct prediction of the color that would be produced, what we are starting out with is simply adding a gray paint to a white paint and getting the resulting gray shade correct. We are using an Excel spreadsheet to do the figuring.

EXAMPLE DATA

To show what we are up against, I will give a list of reflectance data for a white paint, a gray paint and then the REAL combination when joined in equal amounts.

The numbers on the left (400-700) represent the color of the light measured in nanometers; 400 nm is deep violet, 700 is deep red.
The numbers on the right are the percentage of reflectance (0-100) of that color.

Valspar Ultra Premium Enamel flat White

400 42.99
410 66.58
420 82.98
430 89.47
440 90.4
450 90.19
460 89.48
470 89.76
480 90.4
490 91.24
500 91.96
510 92.01
520 91.83
530 91.94
540 92.19
550 92.53
560 92.9
570 93.33
580 93.6
590 93.24
600 92.8
610 92.98
620 93.46
630 94.32
640 94.86
650 93.92
660 92.79
670 92.58
680 92.85
690 93.48
700 94.49

Behr #1850 in 'Reference Gray'

400 36.9
410 45.3
420 50.79
430 52.18
440 51.5
450 50.92
460 50.42
470 50.2
480 50.16
490 50.39
500 50.66
510 50.66
520 50.57
530 50.55
540 50.6
550 50.75
560 50.95
570 51.2
580 51.39
590 51.3
600 51.09
610 50.89
620 50.72
630 50.71
640 50.6
650 50.01
660 49.33
670 48.88
680 48.61
690 48.55
700 48.69


The measured combination mixed 1:1

400 40.27
410 52.92
420 61.26
430 63.46
440 62.6
450 61.99
460 61.5
470 61.36
480 61.38
490 61.5
500 61.63
510 61.65
520 61.63
530 61.65
540 61.68
550 61.65
560 61.68
570 62.02
580 62.35
590 62.24
600 61.96
610 61.77
620 61.62
630 61.59
640 61.46
650 60.91
660 60.3
670 59.89
680 59.65
690 59.58
700 59.67


While math is not my strong suite, I have tried taking the arithmetic mean, geometric mean and harmonic mean of the white and gray paints, but none of them match the measured result. I'm at the end of my rope and am stuck firmly in the mud.

I'm hoping someone out there has the ability and willingness to help us figure out how to do this. If those reading this don't have one or the other, but know someone that might, please ask them!
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post #2 of 37 Old 09-19-09, 12:29 AM
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Re: We need some help from math wizards!

Is 400-700 the total range of reflected color?

Could you post another range with a different gray?

I am good with math and algorithms, but not so knowledgeable wih paint/light color interactions.

Also - what are the pct of error on the values above? And how accurate do you need the resulting computations to be to be useful?

If the women don't find you handsome, they should at least find you handy - Red Green


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Last edited by seattle_ice; 09-19-09 at 12:54 AM.
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post #3 of 37 Old 09-19-09, 07:47 AM Thread Starter
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Re: We need some help from math wizards!

Quote:
seattle_ice wrote: View Post
Is 400-700 the total range of reflected color?
Thanks for the assist Darryn!

My older spectro (an X-rite DTP-22) only measures from 400 nm to 700 nm in 10 nm increments. Mech's newer X-rite I1 measures from 380 nm to 730 nm in 10 nm steps. Depending on the source you read the values below 400 nm are actually in the ultraviolet and above 700 nm gets into the infrared.

Quote:
Could you post another range with a different gray?
Here are two other combinations of the white and gray paints I gave data for before.

Valspar UPE Ultra White/Behr 1850 Reference Gray 1:3 (1 part white to 3 parts gray)

400 38.26
410 48.11
420 54.56
430 56.15
440 55.37
450 54.93
460 54.6
470 54.42
480 54.33
490 54.36
500 54.44
510 54.45
520 54.48
530 54.62
540 54.74
550 54.62
560 54.52
570 54.84
580 55.25
590 55.32
600 55.17
610 54.77
620 54.36
630 54.3
640 54.26
650 53.81
660 53.28
670 52.87
680 52.56
690 52.38
700 52.34

Valspar UPE Ultra White/Behr 1850 Reference Gray 4:1 (4 parts white to 1 part gray)

400 42.17
410 59.2
420 70.47
430 73.6
440 72.61
450 71.79
460 71.13
470 71.27
480 71.65
490 71.8
500 71.81
510 71.58
520 71.38
530 71.6
540 71.92
550 71.93
560 71.89
570 72.1
580 72.3
590 72.08
600 71.78
610 71.81
620 71.92
630 72.03
640 71.92
650 71.06
660 70.19
670 70.15
680 70.33
690 70.3
700 70.19


Quote:
Also - what are the pct of error on the values above? And how accurate do you need the resulting computations to be to be useful?
You know, I never really noticed! My DTP-22 has more variance between readings than Mech's I1. If you have seen the Spectral Reflectance Charts I post now and again (I'll make some up and post them in this thread later), I usually have to take 2 or 3 readings of the same spot of my paint sample before I get rid of "waves" that seem to be in the X axis line drawn from the reflectance data sent to the spreadsheet from the spectro. Mech's I1 doesn't have that problem. I would guess that these "errors" are usually less than 1 percent. I'll take multiple readings and find out; will also post the data if needed.

It would be nice to have the accuracy of the "predictions" as close as possible to the measured result, but I would guess that anything less than 3 percent would be usable, I may be wrong about that though and it could be more like 1 percent. I really haven't thought in percentages before in this area!

Thanks for taking a stab at this!
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post #4 of 37 Old 09-19-09, 11:10 AM
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Re: We need some help from math wizards!

After my initial glance, I see some small anomalies in the patterns. I think they are partly the 'waves' you mentioned. I need to know if those are 'real' or a measurement defect.



Although you could generalize over them and straighten the line out, I would rather not unless I knew it should be that way.

If you look at the variance in the differences between the measured reflections of the 1:1 mix, and the expected average and mean differences, there is a trend. The waves in the trend would make it much more difficult to quantize at a repeatable mathematical (formulaic) level


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post #5 of 37 Old 09-19-09, 01:51 PM
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Re: We need some help from math wizards!

Quote:
seattle_ice wrote: View Post
Is 400-700 the total range of reflected color?

Also - what are the pct of error on the values above? And how accurate do you need the resulting computations to be to be useful?
Thanks for any help you can offer Darryn!

400-700nm is the viewable wavelengths of color. Anything above is infrared and below is ultraviolet.

As for the accuracy, the only stat I know off the top of my head is that the i1pro has a .002 margin of error for x & y values. How that relates to the spectrum would be a guess as I'm uncertain of the Luminance margin of error. Otherwise you could punch it all into the XYZ formula and figure it out.... I think....


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post #6 of 37 Old 09-19-09, 05:31 PM
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Re: We need some help from math wizards!

Harp:

Could I get a reading with more in between values? Say every 5 NM instead of 10? And could you average out a few (4) passes? The 1:1 would be enough to start with.

Mech: Could you get me a similar chart from yours?

Darryn

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post #7 of 37 Old 09-19-09, 07:01 PM
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Re: We need some help from math wizards!

Chart or data? There are a lot of charts here, here, and here. If you want the numbers I could dig them up. But I've got a lot of readings so let me know which you'd want.


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post #8 of 37 Old 09-19-09, 07:07 PM
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Re: We need some help from math wizards!

Mechman:

I actually meant a direct comparison to harps chart from 400-700 on the 1:1 mix from the first post.

I have been reading a bunch of stuff on Spectrophotometry and colorimetry. Very interesting stuff.

Very complicated stuff, also.

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Last edited by seattle_ice; 09-19-09 at 07:17 PM.
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post #9 of 37 Old 09-19-09, 07:30 PM
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Re: We need some help from math wizards!

Then no, I don't have any charts of those three items. But I can get a measure of the white by Monday or Tuesday if need be. Let me know. I don't think I have any of the reference gray. I might. Some day I should take inventory...


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post #10 of 37 Old 09-19-09, 08:06 PM Thread Starter
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Re: We need some help from math wizards!

Quote:
seattle_ice wrote: View Post
Harp:

Could I get a reading with more in between values? Say every 5 NM instead of 10? And could you average out a few (4) passes? The 1:1 would be enough to start with.
Sorry no. Those values would have to be interpolated since my spectro only outputs spectral data in 10 nm increments.

Quote:
I have been reading a bunch of stuff on Spectrophotometry and colorimetry. Very interesting stuff.

Very complicated stuff, also.
Yeah, the math behind that is way over my head. As a math person you might enjoy Bruce Lindbloom's page. Check out the INFO and MATH links at the top of the page. http://www.brucelindbloom.com/index....alculator.html

I send the spectral data from my spectro to Lindbloom's spectral calculator spreadsheet to get the L*a*b* and RGB data (two different "color spaces") that goes into my Spectral Reflectance Charts.

BTW, I found most of the sample chits I made up to measure different ratios of VUPE (the white paint) and Reference Gray. I think it might help you if I sent 10 consecutive readings (or however many you want) of the 1:1 sample to you. That will mean posting 310 values. I could simply post them as I did the values in the above posts, or I could put them in an Excel spreadsheet and email it to you. Which would you prefer?
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