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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. :dizzy:

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! :praying:
 

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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?
 

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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.

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


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! :T
 

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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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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.... :nerd: :coocoo: :dizzy: :hide:
 

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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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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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Then no, I don't have any charts of those three items. :hide: 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. :scratch: Some day I should take inventory... :dizzy:
 

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Discussion Starter #10
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.

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.html?ColorCalculator.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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What do you use as a reference source for the measurements? I can't see the measurements being precise enough to treat statistically unless you are using a reference source that has been calibrated and held constant somehow.
 

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What do you use as a reference source for the measurements? I can't see the measurements being precise enough to treat statistically unless you are using a reference source that has been calibrated and held constant somehow.
Mech has his I1 recertified yearly since he has had it. I basically compare my reading with his of the exact same paint mix by measuring a sample and then sending it to him to measure. My spectro has matched his within the normal variance parameters of my spectro (off-hand I forget what those are now) . Any sample that MUST be read by a certified spectro is sent to Mech.

Each X-rite spectro comes with it's own calibration plaque that consists of a white ceramic tile embedded in a plastic holder. The spectro has been calibrated to this plaque during the manufacturing process and it is mated to the spectro sharing the same serial number. Periodically the spectros are recalibrated to their plaque by the user via software.

While X-rite recommends yearly recertification of their spectros, they say themselves it doesn't need to be done unless the device is providing erroneous readings of known test targets.
 

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Are you using an internal light source?
 

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Sorry no. Those values would have to be interpolated since my spectro only outputs spectral data in 10 nm increments.


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.html?ColorCalculator.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?
I went and read a fair amount of the stuff at that site. It seems that there are many ways of converting from one reading to another, or from one type of value to another. I have not come across anything about combining 2 or more colors and calculating the result accurately. Hence, this thread...:doh:

If you look at the charts I posted earlier showing the wavy distribution of the variance from average, it becomes fairly obvious there is no linear way to express the relationship, without averaging the averages, so to speak. This might be accurate enough. Of course you can always take the brute force method, but that means actually compiling the data and storing it ahead of time for every sample you might use, and that becomes almost worthless.

You can send anything to me at [email protected].
 

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Are you using an internal light source?
Yes. Both the DTP-22 and the I1 use an internal light source. I'm not sure how the I1 works, but the DTP-22 has 3 separate lamps that are located about 3/4 inch away from, and slightly above, the central photo sensor which is in a small black tube so no light from the lamps hits it directly. They are positioned approximately at 12 O'Clock, 4 O'Clock and 8 O'clock. This configuration is known as a "45/0" (or "0/45", I keep getting that mixed up) spectrophotometer. The light is hitting the sample at 45 degrees while the photo sensor is looking straight down at 0 degrees. This configuration disregards the gloss of a sample.

While I don't know this for a fact, I suspect the main reason to periodically recalibrate a spectro with the plaque is to adjust for "burn time" on the lamps thereby minutely changing their color temperature. The lamps are tungsten bulbs.
 

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Ok. Without getting real in depth yet, I ran some simulations using weighted averages and some derived correction values for the DTP. I will do some similar calcs for the values obtained from the i1 as soon as I have a base chart for it.

This is what my calculations say should be the reflectance values for a 1 part white to 6 part gray:

400 36.72372055
410 46.36428452
420 52.56839752
430 54.27557755
440 53.70901871
450 53.17456818
460 52.6975441
470 52.63184357
480 52.75711441
490 52.99478912
500 53.20762253
510 53.16742325
520 53.07267761
530 53.19044876
540 53.38132858
550 53.50988388
560 53.61512375
570 53.77667236
580 53.90454102
590 53.93193436
600 53.88892365
610 53.82398987
620 53.68208694
630 53.43977737
640 53.08813858
650 52.59375381
660 52.10113144
670 51.80996323
680 51.61162567
690 51.49236298
700 51.44984436
 

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I've been reading this thread and I think you guys are both over thinking the situation and missing some information.

First, paint matching (especially as done in hardware stores) is accomplished using colorimetric data, not spectral data. 5nm data will do nothing to solve your problem. You would just have data overload. You're trying to match color, not reflectance (or emission.)

In fact most paint matching systems that you see in Lowe's or Home Depot are 20nm instruments. (For the record, X-Rite did sell a variant of the DTP-22 for paint stores for a while.) The paint is matched for usually one of three light sources (daylight for exterior, and incandescent and fluorescent for interior.)

On the other hand, you don't have enough data about the physical characteristics of the colorants, base and substrate when you merely average the reflectances every 10 nm.

A large number of paint samples are prepared and then measured into a database that takes into account the actual physical properties of the paint components, mostly translucency and scatter due to particle size. The databases are built from a wide range of samples prepared to represent probable mixtures. For example, samples would be made with each base colorant at 1%, 5%, 10%, 25% 50% and 75% of "full strength". Selected mixtures of multiple colorants would then be made to measure how colorants interact when mixed together.

Once enough samples are measured, the software uses a variety of algorithms to produce color recipes for any measured target color. There may be different algorithms used for different levels of pigment load, because one math model might work better with lighter colors than those with heavier pigment concentrations.

All that being said, what are you actually trying to accomplish?
 

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I've been reading this thread and I think you guys are both over thinking the situation and missing some information.

First, paint matching (especially as done in hardware stores) is accomplished using colorimetric data, not spectral data. 5nm data will do nothing to solve your problem. You would just have data overload. You're trying to match color, not reflectance (or emission.)

In fact most paint matching systems that you see in Lowe's or Home Depot are 20nm instruments. (For the record, X-Rite did sell a variant of the DTP-22 for paint stores for a while.) The paint is matched for usually one of three light sources (daylight for exterior, and incandescent and fluorescent for interior.)

On the other hand, you don't have enough data about the physical characteristics of the colorants, base and substrate when you merely average the reflectances every 10 nm.

A large number of paint samples are prepared and then measured into a database that takes into account the actual physical properties of the paint components, mostly translucency and scatter due to particle size. The databases are built from a wide range of samples prepared to represent probable mixtures. For example, samples would be made with each base colorant at 1%, 5%, 10%, 25% 50% and 75% of "full strength". Selected mixtures of multiple colorants would then be made to measure how colorants interact when mixed together.

Once enough samples are measured, the software uses a variety of algorithms to produce color recipes for any measured target color. There may be different algorithms used for different levels of pigment load, because one math model might work better with lighter colors than those with heavier pigment concentrations.

All that being said, what are you actually trying to accomplish?

1. Of course we are all over thinking the situation. That is what you do as a DIYer!

2. Yes, I realize that any difference in bases, tints, etc, would almost render previous measurements invalid, and that all the places that have paint matching build very large databases where they store the data they have previously collected about every color they offer, so getting a close match and interpolating is much more accurate than guessing.

3. There are actually multiple algorithms being used for various difference in darkness level of paint bases by the paint stores. One model just cant accurately describe all the range of paint colors, even for a single manufacturer.

4. Reflectance is not emission - emission describes light from a self emitting source. Emissive colors add and subtract completely differently than reflected colors - compare Light and Paint for example. And I think that most of the machines do at least 3 different angle samples to help account for translucency and sheen.

5. I actually think that with enough samples, we can come up with a 'good enough' system to at least make educated guesses as to what a combination will yield.

Plus, I enjoy many different kinds of projects, and sometimes you even learn more from the ones that don't work in the end. Maybe it is because you spend more time trying to make it work, hence absorb more info. I dont know, but I sure like trying.

Keep your stick on the ice!
 

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Hi Colorblind, welcome to the forum!

I will respectfully have to disagree with you in that only a colorimeter is needed to properly match colors with paint. For those that don't know, colorimeters only read RGB data while spectrophotometers read the full visible spectrum. Colorimeters are much cheaper than spectrophotometers since they only need to read three color values and not the full spectrum (or many points in the spectrum). When I had a custom color (the tinted base for C&S #3) matched at Home Depot the resulting paint was almost a dead ringer spectrally when I measured it with my spectro, it would have been the wildest stroke of luck for a colorimeter to have matched that color that closely.

Spectrophotometers can give colorimetric data, but colorimeters can't give spectral data.

I believe you are correct in that most of the X-rite spectros actually read in 20 nm increments and interpolate to give the 10 nm data. This isn't something I can control, but it is built into the firmware of the spectro.

My friend that owns an Ace hardware store has an X-rite color-matching system that has a spectro that looks and acts exactly like my DTP-22, but is called a CA-22. Physically, the only difference I can tell is the CA-22 has a DB-9 serial connector for IBM PC clones while the DTP-22 has a Apple Macintosh serial connector that I had to find an adapter to use it with my PC.

You are correct that different tint formulae can make the same physical color, this is why there is more that one tint formula given for making PPG-Bermuda Beige in Valspar and Behr paints (this is the base color for making Black Widow), but these different formulae make the same spectral curve (or really close).

Since I have needed to send seattle_ice literally thousands of reflectance readings, we have been communicating more via email than in this thread of late. I'll try to sum up the immediate goal.

It may seem intuitive that one should be able to take the luminance value of two paints (the L* value in the L*a*b* data) and simply find the average or mean value and that would be the new L* value of the new mixture. Nope, that doesn't work. And this is only talking about white and gray paints. This was the primary goal of this thread - to calculate what shade of gray would be made by mixing white paint with a darker gray paint in various ratios.

If the above goal is reached then we will start trying to work with colors. This might not be practical, but you never know until you try.

I would like to thank seattle_ice again for even attempting this. :T I think that calls for a dancing banana! :dancebanana:

There might not be much activity in this project for awhile since I need to make up more samples, measure them and get the data to Darryn.
 

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What I don't understand is how you plan to get meaningful performance predictions for projectors that do not use the same light source as your meter. When you throw a different spectrum at it, you are going to get different results, aren't you? Hg lamps ain't tungsten...

Also, you don't illuminate a screen with a projector from 45 degrees, so how can you expect similar results with an actual application? The differential values may be useful but how they relate to actual performance is not clear to me.
 
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