We need some help from math wizards! - Page 3 - Home Theater Forum and Systems - HomeTheaterShack.com

Old 09-22-09, 04:43 PM Thread Starter
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Don

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Re: We need some help from math wizards!

Quote:
lcaillo wrote: View Post
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.
D65 is the color temperature that all HT projectors are supposed to be calibrated to. We design our screen mixes to be neutral at the D65 temperature which should mean that the image that is reflected off the screen is the same color image the PJ hit it with - the screen doesn't add any color of it's own to the image.

Final color temperature of a device is determined physically or mathematically. Neither the lamps of our spectros nor our projectors are naturally D65. In the case of the PJ lamps the color is adjusted by internal filters, voltage adjustments or some-such; as for the spectros, the color of the tungsten lamps is a known value and the firmware of the spectro, or the software used with the spectro, adjusts the color temp mathematically. The Lindbloom spectral calculator spreadsheet I use gives color values for a wide range of color temperatures. The only one we are interested in for our purposes is D65.

The reason we need to work with other colors than simply white and gray is that most, if not all, of the reflective elements that can be added to paint to increase their performance as a PJ screen are not color-neutral themselves which means the base paint they are added to must be of a compensating color to make the final mix neutral. If we could get these predictive color and luminance spreadsheets or programs working it would save us developers a LOT of time and money developing new mixes since it would eliminate a lot of the current trial and error that is part of the process.
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Old 09-22-09, 04:58 PM
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Re: We need some help from math wizards!

When you measure a color with your I1, you are using the tungsten lamp to illuminate that sample. When you get a reading, how does that relate to the D65 that should be coming from any projector? Like I said the differential values between colors are certainly useful, but predicting what a D65 projector will do on a sample measured with a tungsten lamp seems problematic.

With respect to the colorimeter vs spectrophotometer discussion, you are very much correct. I believe that much of the confusion on the matter comes from the idea that you can get any color within a given gamut by using some combination of the RGB primaries. This does NOT mean that you can reliably nor usefully MEASURE the color of a color with only a tristimulus colorimeter. The only way that that works is if the colors you are mixing have spectra that match the filters in the colorimeter. The measurements with the spectrophotometer give you much more information that can be useful.

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Old 09-22-09, 07:18 PM Thread Starter
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Don

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Re: We need some help from math wizards!

Thanks for the questions and input Leonard.

The way my DTP-22 works is the program that lets me interface it with Excel (an X-rite program called Toolcrib) allows me to define measured color temperature along with either a 2 degree or a 10 degree Observer. I select D65 and a 2 degree Observer. The program that comes with the basic i1 spectro (called i1Share) doesn't allow you to change from the default D50 setting; I have no idea why.

In consultation with Mech (who has been using an i1 for years now), it seems that the raw reflective data from either the DTP-22 or the i1 is at the default tungsten setting and the only time the temperature and Observer settings come into play is when using the respective software to produce RGB or L*a*b* data (or other "color space" data). Changing the color temp from D50 to D65 or D75 does NOT change the spectral values or the spectral chart, but only the RGB and L*a*b* numbers. It took quite a while for that to sink into my poor tiny brain!

There are a lot of surprises in color science! One of the ones that really threw us for a loop is that a perfectly neutral gray does NOT have a flat spectral curve, but rather a bump at the violet end of the spectrum and a dip at the red end! That is still a head-scratcher than makes me lose sleep at times.

To try and answer your last question, the tungsten reflectance curve doesn't directly relate to the D65 color of the PJ image, but rather the L*a*b* and xyY color space data DOES, and this data has been converted mathematically from the native color temp of the spectro to D65 either by the spectros firmware or the software it is used with.

Another benefit of being neutral in color is that the more neutral the color is the less difference there will be when the color is viewed at differing color temperatures (metamerism). An example of this is looking at a pair of navy blue socks in a department store under fluorescent lighting and then looking at them in bright daylight. The two socks might match under the fluorescent lighting, but be different colors in daylight (or the other way around). Another good example of this is the color component of the older versions of Silver Fire. In daylight it looked very blue, but under a 60 watt incandescent light bulb it looked green! My understanding is that a perfectly neutral gray looks the same no matter what color temperature the light is.
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Old 09-23-09, 04:05 AM
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Re: We need some help from math wizards!

Your last paragraph is exactly what I am questioning. What you are doing is looking at the sample with one color temp lighting to measure it and another when using a D65 projector. The question is whether the difference is significant.

Metamerism is when two colors look the same with different spectral densities, or different combinations of primary colors. You are correct that with less saturation, i.e. more neutral, this becomes easier to achieve. The question is, have you tested the difference between the tungsten lamp in the probe and actual projectors to see if it is significant? Have you established the degree of metamerism for these two kinds of light sources for any of the samples?

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Old 09-23-09, 09:02 AM Thread Starter
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Don

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Re: We need some help from math wizards!

The criteria we judge color neutrality of a screen mix by is the L*a*b* and xyY data from a sample; this data has been converted to D65 so, as I understand it, it would be the same values as if we used a D65 temperature light source to do the actual spectral measurement.

As for checking for metamerism, yes, Mech's software does have a function that checks and displays that information for a color. I just started using a program that will do this too.
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Old 09-23-09, 09:11 AM
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Re: We need some help from math wizards!

If you have the same x,y colorimetry, you have the same color (not necessarily the same brightness of a color). The point with metamerism is that there are different combinations of primaries that can produce the same color. This is the basis of how colors in photography, printing, video, and other media can produce the same color. Colorimetry also tells you nothing about reflectivity nor directivity though the color can be affected by the angular presentation of light.

Looking for me, just google my username. I have used the same one for most sites for many years.
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Old 09-24-09, 01:09 PM
colorblind

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Re: We need some help from math wizards!

Quote:
Harpmaker wrote: View Post
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.
Harpmaker, Thank you for the welcome.

Let me restate what I said in my first post. To match colors, paint matching systems use colorimetry, not colorimeters. The instruments are 20nm spectrophotometers. The spectrophotometer privides the precision to accurately and repeatedly measure color.

The software converts the spectral point data to colorimetric functions (XYZ, then L*a*b* or LCh) and matches colors using the colorimetric data. Colorimetric data, by definition, is light-source dependent. When you ask the paint vendor for a match, they will ask in which room you intend to use the paint (fluorescent in the bath and kitchen and incandescent in the living room and bedroom,)

The limitation, of course, is that the match is only good for the light source specified in the chosen colorimetric space (Daylight or incandescent or fluorescent.) That's usually not a problem for household paints until a patch needs to be repainted and the wrong illuminant is chosen to formulate the new paint batch.

Reading the subsequent posts to my first entry, I see that you are trying to create a neutral gray paint that would not flair in multiple light sources, a non-metameric formulation that would remain neutral in appearance whether in daylight, fluorescent or incandescent light. Colorimetrically, this paint would have some degree of lightness with zero Chroma (color strength) in a wide range of light sources. Not easy to concoct in the garage without very clean materials. A slight mis-tint in the dark gray might be exacerbated when mixed with white. A reflectance reading of the dark gray might not show the mis-tint because there is not enough light to show it.

In essence, Color is not linear and producing good color recipes requires a database with multiple concentrations of pigment. If you are indeed looking to match the color in multiple light sources, the math gets very complicated and I'm no mathematician. Good luck in your endeavors.

It sounds like you are having fun, but if you tire of the exercise, good neutral paint is available from Graphic Technologies in Newburgh, NY. I believe that you can also buy it from X-Rite's Munsell division.

PS: I don't know where you found the "neutral gray" with bumps and dips in the spectral curve. Either it isn't really neutral or you've got a problem with the measurement. At best, this curve would only look neutral in one light source. At most, I would expect to just see a tail off in the blue end (400-430 nm) with a very flat plateau along the rest of the curve.

Kind regards,
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Old 09-24-09, 05:06 PM
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Steve Mechelke -mech

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Re: We need some help from math wizards!

Hello colorblind and welcome!

We are using spectrophotometers, not colorimeters.

As for the spectral display, it actual does have bumps and dips. Here's a N8 direct from Bruce Lindbloom's page:

And here's my reading of a N5 direct from a X-Rite Color Checker photo card

The bumps in the second graph are a larger due to the software adjusting the Y axis to fill the chart. But there are bumps.

As for getting a neutral gray paint, we've done it. Granted there will always be slight variables due to inconsistencies from the store mixers. But if they are as accurate as you say they are, I'm feeling pretty good about our mix then!

We have never had a vendor ask us which room it was for? At least I haven't. Maybe it's because we tell them exactly what we want and what base to put it in? But for our purposes it has worked. And quite often. I haven't measured anyone's sample of our paint that hasn't been within our specifications for a neutral gray screen paint. And I've measured quite a few.

We have methods for adjusting paints and getting them where we want them. And then we test them. If all holds true, we release it. Otherwise, we do as I have done many, many times, we trash it.

As for what Harp is doing here and what he wants to accomplish, I can honestly say I haven't a clue. But it's important to him and that's important to me. But I can not honestly tell you what he's trying to do. (that's me being the dumb crazy one!!) But I think I answered a couple of your thoughts on this... maybe?
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Old 09-25-09, 09:49 AM Thread Starter
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Don

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Re: We need some help from math wizards!

Quote:
colorblind wrote: View Post
Harpmaker, Thank you for the welcome.

Let me restate what I said in my first post. To match colors, paint matching systems use colorimetry, not colorimeters. The instruments are 20nm spectrophotometers. The spectrophotometer privides the precision to accurately and repeatedly measure color.

The software converts the spectral point data to colorimetric functions (XYZ, then L*a*b* or LCh) and matches colors using the colorimetric data. Colorimetric data, by definition, is light-source dependent. When you ask the paint vendor for a match, they will ask in which room you intend to use the paint (fluorescent in the bath and kitchen and incandescent in the living room and bedroom,)
I guess I'm still a bit unclear as to why a spectrophotometer is used to simply gather colorimetric data. Are you saying that while only colorimetric data is required to match paint color, colorimeters are not used because they are not precise and accurate enough?

I have had many different paints matched over the years at Lowe's and Home Depot and not once was I asked what color temperature I wanted the color matched to either by name (daylight, fluorescent, tungsten) or use (kitchen/bath, living room, exterior). I do understand why this question should be asked, but I guess they either assume a color temp for you or expect that you have used the "light booths" to make sure your color looks right in a given lighting environment.

Since this thread is of a technical nature I'll provide data from the spectral calculator spreadsheet I use and try to explain a bit about it. The data below is from a sample of Black Widow I made using an artist paint color to make the mix neutral instead of using tinted latex house paint.

I enter the spectral reflectance data from my spectro, which is: (color in nanmeters, percentage of reflectance of that color)

Code:
```400	0.3889
410	0.4814
420	0.5429
430	0.5608
440	0.5565
450	0.5534
460	0.5502
470	0.5484
480	0.5473
490	0.5472
500	0.5474
510	0.5468
520	0.5459
530	0.5453
540	0.5453
550	0.5465
560	0.5487
570	0.5524
580	0.5558
590	0.5561
600	0.5541
610	0.5498
620	0.5454
630	0.5441
640	0.5425
650	0.5362
660	0.5285
670	0.5212
680	0.5153
690	0.5125
700	0.5123```
The spreadsheet then converts that data to colorimetric data. Explaining everything below in detail would take awhile and bore most folks to tears, but in a nutshell, the data is given for both standard Observers (2 and 10 degree), a range of different Illuminants which represent different standards of color temperature (D has been set at the D65 setting of 6503), and then data is given for the values X, Y, Z, x, y, L, a, and b (RGB data is given elsewhere in the sheet). More data than this is given in the sheet, but this portion is what I use for screen mix development.

Notice the "L", "a", and "b" values for 2 degree D (highlighted in red) are 78.95, 0.03, -0.06. A perfectly neutral color would have 0.0 for both the "a" and "b" values since these represent color data and a perfectly neutral gray would have none ("L" represents the "Lightness" of the color - 100 is pure white and 0 is pure black). We try to keep our screen mixes below 1.0 for "a" and "b" (plus or minus doesn't usually matter, long story). You can see that "a" and "b" values are still well below 1.0 (ignore +-) for ALL Illuminants. As "a" and "b" values get larger there is a greater difference in their values in the different Illuminants; when these differences become large enough the color starts to be seen as a different color under the various color temperature Illuminants.

Code:
```Observer	Illuminant	X	Y	Z	x	y	L	a	b
2-Degree	A		0.6007	0.5483	0.1954	0.4468	0.4078	78.94	-0.31	-0.13
B		0.5433	0.5485	0.4687	0.3481	0.3515	78.95	-0.03	-0.14
C		0.5381	0.5485	0.6496	0.3099	0.3159	78.95	0.07	-0.15
D		0.5212	0.5484	0.5973	0.3127	0.3290	78.95	0.03	-0.06
E		0.5479	0.5484	0.5478	0.3333	0.3336	78.95	-0.10	0.03
F2		0.5446	0.5502	0.3074	0.3884	0.3924	79.05	0.23	-0.06
F7		0.5206	0.5489	0.5348	0.3245	0.3421	78.98	0.18	-0.15
F11		0.5668	0.5483	0.2844	0.4050	0.3918	78.94	0.32	-0.36
Blackbody	0.5380	0.5485	0.4728	0.3450	0.3517	78.95	-0.06	-0.02
Custom		0.5479	0.5484	0.5478	0.3333	0.3336	78.95	-0.10	0.03
10-Degree	A		0.6087	0.5483	0.1934	0.4507	0.4060	78.95	-0.18	-0.11
B		0.5443	0.5485	0.4636	0.3497	0.3524	78.95	0.03	-0.11
C		0.5341	0.5485	0.6383	0.3103	0.3187	78.96	0.10	-0.11
D		0.5203	0.5484	0.5889	0.3139	0.3309	78.95	0.07	-0.02
E		0.5483	0.5484	0.5480	0.3334	0.3335	78.95	-0.03	0.05
F2		0.5665	0.5501	0.3123	0.3964	0.3850	79.05	0.24	-0.04
F7		0.5233	0.5489	0.5264	0.3274	0.3434	78.98	0.20	-0.12
F11		0.5812	0.5483	0.2876	0.4101	0.3869	78.95	0.30	-0.36
Blackbody	0.5406	0.5485	0.4712	0.3465	0.3515	78.95	0.01	0.00
Custom		0.5483	0.5484	0.5480	0.3334	0.3335	78.95	-0.03	0.05```

Quote:
Reading the subsequent posts to my first entry, I see that you are trying to create a neutral gray paint that would not flair in multiple light sources, a non-metameric formulation that would remain neutral in appearance whether in daylight, fluorescent or incandescent light. Colorimetrically, this paint would have some degree of lightness with zero Chroma (color strength) in a wide range of light sources. Not easy to concoct in the garage without very clean materials. A slight mis-tint in the dark gray might be exacerbated when mixed with white. A reflectance reading of the dark gray might not show the mis-tint because there is not enough light to show it.
We have found that with the proper testing equipment (a spectrophotometer) it isn't that difficult to color-correct a mix so that it does become neutral, but if one simply wants a neutral gray paint that isn't necessary. There is a formula for making a neutral gray paint that Bill got from X-rite that has come to be known as "Reference Gray" (which is not an official name). This color is very neutral and IIRC is it about a Munsell N7.6 in Lightness. I have found that this paint can be mixed with the "ultra white" paints from Behr and Valspar in ratios up until the result is about N9 and the mix will still fall within our neutrality standards.

Quote:
In essence, Color is not linear and producing good color recipes requires a database with multiple concentrations of pigment. If you are indeed looking to match the color in multiple light sources, the math gets very complicated and I'm no mathematician. Good luck in your endeavors.
For our purposes we only need to find neutrals or colors for D65.

While this little exercise began as a quest to see if it was possible to accurately predict the L* value (just listed as L in the table above) when two neutral, or near-neutral, paints are mixed; depending on the difficulty of doing so we might try to branch out into predicting color combinations.

Quote:
PS: I don't know where you found the "neutral gray" with bumps and dips in the spectral curve. Either it isn't really neutral or you've got a problem with the measurement. At best, this curve would only look neutral in one light source. At most, I would expect to just see a tail off in the blue end (400-430 nm) with a very flat plateau along the rest of the curve.

Kind regards,
Mech addressed this in his post.

Thanks for sharing your knowledge colorblind. It sounds like you have some experience in this area, looking forward to hearing more from you!
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Old 02-08-13, 09:12 AM
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SGA

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Re: We need some help from math wizards!

I just caught this thread. Is the quest for a model to predict "L" values dead? I am optimistic that we can do a reasonable curve fit if we can get more data (e.g., response curves for 25/75 and 75/25 white/grey mix).

There are alot of limitations here - margin of error in readings, accuracy/repeatability of the mix from the store and at home, etc. - but this could be useful and would be "fun" to try.

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