question about tristimulus devices (colorimeters) and tristimulus response function, and RGB colorimeters. - AVS Forum
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post #1 of 46 Old 09-14-2013, 09:24 AM - Thread Starter
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I've been learning, with great interest, about the differences between spectros and colorimeters, and about profiling. I've read both of the following:

http://www.curtpalme.com/docs/XriteDisplayCalibrationDevices.pdf

http://www.tlvexp.ca/2012/04/do-calibration-tables-really-work-for-tri-stim-devices/

There's still a gap or two in my understanding, and I'm hoping I can get some clarification here:

thought experiment: if a colorimeter had a set of filters that perfectly matched the tristimulus response function (TRF) of the human eye (based on the CIE standard), I'm assuming it would yield the correct XYZ values no matter what display was being tested, correct?

The limitation with colorimeters, as I understand it, is that in practice, the filters do not match the TRF. Even if the peaks of the filter responses match the peaks of the TRF, the shape of the filter functions may differ, and will not yield the same XYZ values as an ideal filter would.

Now given a consistent spectral signature that can only vary uniformly in amplitude, a particular filter will differ from the ideal TRF by a consistent amount. So offset tables (whether done in the EEPROM or in software) can compensate for this difference, and so long as you know the set of spectral signatures in advance, you can create tables for each of the three filters for each of the spectral signatures.

So my first question is whether my understanding so far is correct.

My second question is about RGB devices whose filters are tuned to the primaries of a particular display. Clearly, such a device will not directly yield correct XYZ values. Is, then, the idea that so long as you know the XYZ values of the device's primaries, it's a very simple step to convert the RGB output to XYZ? (RGB here can differ depending on the particular display used, for example different CRT phosphor sets. I don't mean some universal standard of RGB).
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post #2 of 46 Old 09-14-2013, 09:31 AM
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if I'm not mistaken there's something unique about the way the tables work in the SpectraCal C6 (their enhanced version of the D3 colorimeter)... which allows them to add tables via software updates as opposed to having to send the meter to them for the new tables to be added

of course, this doesn't mean that the tables always work (in fact, that article on Michael's page is about the C6 vs. two spectros)... it's just a new approach in implementing them
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post #3 of 46 Old 09-14-2013, 10:13 AM
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^^

All the i1D3 Series ship with generic EDR (Electronic Display Reference) files which have the data for the Spectral Power Distribution of each included source. The calculation of each set of calibration is performed at run-time based upon the spectral sensitivities of that specific i1D3 and that data from the EDR selected via the SDK and reference Standard Observer Color Matching Functions (CMFs)..

SpectraCAL is licensed to add new ones when needed for their C6 and may be the only company that can do this officially.

A generic i1D3 has the ability to save (and use) a custom EDR but X-Rite has not released the tools necessary.

EDIT: meant 'The calculation'.. not sure what happen during edit.

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post #4 of 46 Old 09-14-2013, 11:14 AM
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The other major difference is that the exposure time for the C6 is variable and will extend when light levels get low unlike the D3 which has fixed exposure times.
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post #5 of 46 Old 09-14-2013, 02:01 PM
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Quote:
Originally Posted by spacediver View Post

thought experiment: if a colorimeter had a set of filters that perfectly matched the tristimulus response function (TRF) of the human eye (based on the CIE standard), I'm assuming it would yield the correct XYZ values no matter what display was being tested, correct?
The more technically correct name for what you are talking about is a Color Matching Function or CMF. And yes if a tri-stim device had filters that perfectly matched the 1931 2-degree CMF, then it would match an equally accurate spectro on any display. Of course the 1931 CMF isn't the best, but it is the standard that everyone uses. CMFs, are created through an emperical process though, meaning they are created through testing of groups of people to create an average response. Everyones eyes are a little different, and the research that is going into the deficiencies of our in-use CMFs is fascinating, if you're into that sort of thing.
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The limitation with colorimeters, as I understand it, is that in practice, the filters do not match the TRF. Even if the peaks of the filter responses match the peaks of the TRF, the shape of the filter functions may differ, and will not yield the same XYZ values as an ideal filter would.

Now given a consistent spectral signature that can only vary uniformly in amplitude, a particular filter will differ from the ideal TRF by a consistent amount. So offset tables (whether done in the EEPROM or in software) can compensate for this difference, and so long as you know the set of spectral signatures in advance, you can create tables for each of the three filters for each of the spectral signatures.

So my first question is whether my understanding so far is correct.
That is exactly correct.

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My second question is about RGB devices whose filters are tuned to the primaries of a particular display. Clearly, such a device will not directly yield correct XYZ values. Is, then, the idea that so long as you know the XYZ values of the device's primaries, it's a very simple step to convert the RGB output to XYZ? (RGB here can differ depending on the particular display used, for example different CRT phosphor sets. I don't mean some universal standard of RGB).

That is in essence how tri-stims are calibrated. We measure XYZ for Red, Green, Blue and White with both the target tri-stim meter and the reference spectrometer and run the numbers through a few well known formulas to create a correction matrix that will correct the deficiencies of the target tri-stim for the display under test.

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post #6 of 46 Old 09-14-2013, 03:49 PM - Thread Starter
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excellent, thanks Sotti smile.gif
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post #7 of 46 Old 09-14-2013, 05:35 PM - Thread Starter
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just ordered a brand new i1 pro (rev D) for under $500 (price includes shipping). Can't wait to get started! (it's actually a EFI ES-1000 with the UV Cutoff).
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post #8 of 46 Old 09-14-2013, 05:44 PM
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just ordered a brand new i1 pro (rev D) for under $500 (price includes shipping). Can't wait to get started! (it's actually a EFI ES-1000 with the UV Cutoff).

great choice.
Good accuracy, compatible with everything.

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post #9 of 46 Old 09-14-2013, 05:57 PM
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Originally Posted by airscapes View Post

The other major difference is that the exposure time for the C6 is variable and will extend when light levels get low unlike the D3 which has fixed exposure times.

The D3 also has an adaptive integration mode.
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post #10 of 46 Old 09-16-2013, 02:32 PM
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Originally Posted by turbe View Post

^^

All the i1D3 Series ship with generic EDR (Electronic Display Reference) files which have the data for the Spectral Power Distribution of each included source. The calculation of each set of calibration is performed at run-time based upon the spectral sensitivities of that specific i1D3 and that data from the EDR selected via the SDK and reference Standard Observer Color Matching Functions (CMFs).
Michael Chen's test indicates that they don't work very well.

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post #11 of 46 Old 09-16-2013, 06:59 PM
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Michael Chen's test indicates that they don't work very well.

Michael's test also did not factor in critical variables like field of view, which are necessary to make such blanket statements. Also 2 new white LED EDRs have been added to the C6 since that review which could have easily altered the conclusion.

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post #12 of 46 Old 09-16-2013, 09:17 PM
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Greetings

Improving the tables is a good thing. Now if you read the article ... it does factor in field of view ... and has talked about that aspect for a long time now.

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May I ask where you found this deal? Have been on the fence about getting one of these and the $500 price might just do it for me.
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just ordered a brand new i1 pro (rev D) for under $500 (price includes shipping). Can't wait to get started! (it's actually a EFI ES-1000 with the UV Cutoff).
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post #14 of 46 Old 09-17-2013, 09:59 AM
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Originally Posted by sotti View Post

Michael's test also did not factor in critical variables like field of view, which are necessary to make such blanket statements. Also 2 new white LED EDRs have been added to the C6 since that review which could have easily altered the conclusion.

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Greetings

Improving the tables is a good thing. Now if you read the article ... it does factor in field of view ... and has talked about that aspect for a long time now.

regards

while FOV is already factored in, it would be nice to see if the tables have become significantly more accurate since the writing of the article... especially since there are more LED-LCD tables than before

it might also be nice to take a look at plasmas (perhaps one LG, one Samsung, and one Panasonic)... since there is only one table for them
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post #15 of 46 Old 09-17-2013, 11:23 AM
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it might also be nice to take a look at plasmas (perhaps one LG, one Samsung, and one Panasonic)... since there is only one table for them
There are no significant differences between plasmas that would affect the ability of colorimeters to read them accurately. Multiple plasma profiles just are not necessary.

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post #16 of 46 Old 09-17-2013, 11:39 AM
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There are no significant differences between plasmas that would affect the ability of colorimeters to read them accurately. Multiple plasma profiles just are not necessary.

it would be nice to see the data anyway
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post #17 of 46 Old 09-17-2013, 11:41 AM - Thread Starter
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May I ask where you found this deal? Have been on the fence about getting one of these and the $500 price might just do it for me.

on ebay
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post #18 of 46 Old 09-17-2013, 04:48 PM
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Quote:
Originally Posted by TomHuffman View Post

[quote name="PlasmaPZ80U" url="/t/1490609/question-about-tristimulus-devices-colorimeters-and-tristimulus-response-function-and-rgb-colorimeters/0_100#post_23744319"]it might also be nice to take a look at plasmas (perhaps one LG, one Samsung, and one Panasonic)... since there is only one table for them[/quote]There are no significant differences between plasmas that would affect the ability of colorimeters to read them accurately. Multiple plasma profiles just are not necessary.

I think this is probably true, the spectral distributions of common plasma phosphors are very similar, it would be nice to see data on the modified vt and zt red phosphors though.
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post #19 of 46 Old 10-09-2013, 02:03 PM - Thread Starter
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So I've been doing some more reading, and I'm revisiting the assumption that the spectral signature of the display will have an interaction with the accuracy of any given colorimeter.

Schanda cites the three empirical laws of color matching (in the context of additive mixtures). In particular, notice the second:

"For an additive mixture of color stimuli, only their tristimulus values are relevant, not their spectral compositions." (p 27).

In 1915, Herbert Ives wrote a paper titled: "The Transformation of Color-Mixture Equations from one system to another", showing how if you know the tristimulus values, as measured by tristimulus device A, of the primaries of tristimulus device B, then you can mathematically derive the linear transformations necessary to compute (rather than empirically measure) the color matching functions of device B, across the entire visible spectrum.

This property, in effect, is what allowed the derivation of the XYZ color matching functions, based off of the empirically based R G B functions.

So, as long as the transformations between two color spaces remains consistent (i.e. no drift), then it follows that for any given (visible) spectral source, one can derive the color matching functions for any given tristimulus device, so long as we know the mapping functions between that device and a reference device.

According to the x-rite white paper:
Quote:
The only difficulty with the production of an XYZ colorimeter is the filters. The XYZ response curves are complex. In order to create these complex filters, many separate filters must be stacked together to achieve the final curves. The filters achieved are never perfect matches to the XYZ curves. However they don’t need to be. By calibrating a colorimeter at the factory against reference sources, a mathematical correction called a “calibration matrix” is stored in the colorimeter. This corrects the minor errors that are introduced by inaccuracies of the filters. This does not create a device that can measure “any” color with perfect accuracy. Instead a colorimeter of this type will produce very accurate results from most sources. Certain sources that have very narrow bandwidths like lasers will not be as accurate.

Notice the bolded part. My take on this is that lasers, being so narrow, provide a low signal to noise ratio.

However, assuming that the tristimulus device in question was perfectly characterized (i.e. we knew exactly how it mapped onto a set of reference color matching functions), and had an arbitrarily high signal to noise ratio, it wouldn't matter what the color matching functions were on that device! In other words, the validity of such a device would not depend on how close the filters matched the XYZ reference functions, but rather on how well characterized the particular filters were.

At least this is my tentative understanding.

So why the need for different calibration matrices depending on the display source?
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post #20 of 46 Old 10-09-2013, 02:29 PM
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#1, hardware filters are not the color matching function, they do emulate them, but they are deficient. The matrix makes up for the deficiencies, but only for a given spectral distribution.

A colorimeter is a physical implementation of a color matching function and it's imperfect. There is no way around this, and the only way to correct for it is to know the spectral information about the light source (typically cooked into a correction matrix).


The other issue that is being omitted in the research you were viewing is viewer metamerism. Everyone's eyes are a little bit different and there is no color matching function that works for everyone. So it is not entirely accurate to say that only XYZ matters, although that is certainly one of the fundamental blocks which color science is based on.

The broader the primaries, the less sensitive we are to the physiology of the individual observer. IE. our color matching functions work more reliably.
The narrower the primaries the more sensitive we are to their personal differences, so you begin to see larger differences from one observer to the next.

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post #21 of 46 Old 10-09-2013, 02:35 PM
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Sotti can always give you an in depth answer, the simple answer is because of the very line you so carefully highlighted.
Some source lighting of displays have very spikey spectra and because the technologies are always in development and modification a one fit design will and only be generic, a reasonble estimate.

This is why pro calibrators tend to go for a narrow bandwidth spectro, although many still use the i1pro with a Klein. The 11pro is still good but it can miss detail if the spike does not fall near or on a sensor, I have generally found blue readings can be different to my jeti because the light levels fall into the noise floor of the i1pro, combine with a spikey spectra and it can be a little off. So profile with an off reading to an off reading and it may or may not be correct.

Although the above can be splitting hairs for absolute accuracy, more often than not the display limits means any differences in absolute accuracy are countered by limited control, ie because of the large steps in a control of a CMS you end up at the same setting because the reading is a reasonble estimate.
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post #22 of 46 Old 10-09-2013, 03:52 PM - Thread Starter
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Thanks for the replies.
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hardware filters are not the color matching function, they do emulate them, but they are deficient. The matrix makes up for the deficiencies, but only for a given spectral distribution.

But, based on what I understand, the hardware filters need not match the color matching function - they only need to be accurately characterized, and the calibration matrix should work for all spectral sources. The transformation of one color matching function (i.e. the deficient one) to another function (i.e. the standard color matching function) is independent of spectral source. From what I can understand, this is a consequence of Grassman's Laws of additivity. In other words, if a particular test color, C, is equal to r*R +g*G +b*G, and we know how R G B maps onto an arbitrary color space R' G' B', then we can derive the equivalent coefficents r' g' b' for that test color C. Importantly, this relationship should hold across all possible metamers of C.

Perhaps the matrices that are actually used in offset tables are not actually characterizations of the hardware filter's CMF, as mapped onto the standard CMF. If they were, they would be transformation matrices rather than "offset" matrices?


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The other issue that is being omitted in the research you were viewing is viewer metamerism. Everyone's eyes are a little bit different and there is no color matching function that works for everyone. So it is not entirely accurate to say that only XYZ matters, although that is certainly one of the fundamental blocks which color science is based on.

The broader the primaries, the less sensitive we are to the physiology of the individual observer. IE. our color matching functions work more reliably.
The narrower the primaries the more sensitive we are to their personal differences, so you begin to see larger differences from one observer to the next.

interesting.
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Sotti can always give you an in depth answer, the simple answer is because of the very line you so carefully highlighted.
Some source lighting of displays have very spikey spectra and because the technologies are always in development and modification a one fit design will and only be generic, a reasonble estimate.

This is why pro calibrators tend to go for a narrow bandwidth spectro, although many still use the i1pro with a Klein. The 11pro is still good but it can miss detail if the spike does not fall near or on a sensor, I have generally found blue readings can be different to my jeti because the light levels fall into the noise floor of the i1pro, combine with a spikey spectra and it can be a little off. So profile with an off reading to an off reading and it may or may not be correct.


I need to learn more about how colorimeters work (it's on my reading list), but based on the cursory descriptions I've encountered, I didn't realize they had a sampling resolution issue. A photodiode array based spectro samples the spectrum at discrete intervals, and thus can miss a narrow spike. But a colorimeter's filters are analogue aren't they?
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post #23 of 46 Old 10-09-2013, 04:04 PM
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Thanks for the replies.
But, based on what I understand, the hardware filters need not match the color matching function - they only need to be accurately characterized, and the calibration matrix should work for all spectral sources. The transformation of one color matching function (i.e. the deficient one) to another function (i.e. the standard color matching function) is independent of spectral source.
No you're simply wrong and don't understand this correctly. I don't have time to generate all the graphs that you'd need to see this, but stop for a second and think.

If you're right, then everybody datacolor, xrite, Klien, Konica Minolta, NIST are being stupid and using these correction tables. Here's the hint, they aren't wrong, you just haven't framed the problem in the right way for you to understand it correctly.

What you're effectively saying is that either the spectrum doesn't have any effect on the color or the color matching function doesn't have any effect on the XYZ.
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From what I can understand, this is a consequence of Grassman's Laws of additivity. In other words, if a particular test color, C, is equal to r*R +g*G +b*G, and we know how R G B maps onto an arbitrary color space R' G' B', then we can derive the equivalent coefficents r' g' b' for that test color C. Importantly, this relationship should hold across all possible metamers of C.

You're forgetting that in order to map them you have to give them x,y,Y values which means giving them XYZ values. XYZ values can only be created from spectral information. Everything, always must go back to the spectrum, you cannot abstract the only physical concrete part of color away.

The levels of abstraction go:
spectral (the only real thing in color)-> XYZ -> RGB

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post #24 of 46 Old 10-09-2013, 04:20 PM - Thread Starter
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No you're simply wrong and don't understand this correctly. I don't have time to generate all the graphs that you'd need to see this, but stop for a second and think.

If you're right, then everybody datacolor, xrite, Klien, Konica Minolta, NIST are being stupid and using these correction tables. Here's the hint, they aren't wrong, you just haven't framed the problem in the right way for you to understand it correctly.

Oh, I know I'm wrong, I just want to understand how smile.gif
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You're forgetting that in order to map them you have to give them x,y,Y values which means giving them XYZ values. XYZ values can only be created from spectral information. Everything, always must go back to the spectrum, you cannot abstract the only physical concrete part of color away.

So suppose you build a tristim (call it A):

Tristim A has three filters which don't even come close to matching the standard CMF. But, Tristim A has a color matching function of its own, and this is measured very carefully, by stimulating it with a series of monochromatic wavelengths, all the way across the visible spectrum. For each wavelength, each of A's three filter responses are recorded, and A's color matching function is now on record.

Keep in mind that A's CMF is derived from very fine measurements of monochromatic radiation (say a linear series of ten thousand different spectral wavelengths). This alone will ensure that A's response to any given spectral signature (which can be represented as a linear combination of these monochromatic wavelengths) can be predicted in advance.

You then do some fancy math to figure out how each of the three functions X Y Z can be derived as a linear combination of A's three functions, and you end up with a matrix that perfectly characterizes the relationship.

Won't you then be in a position to derive the X Y Z values from A's output, given any spectral input?

I suspect that the difficulty is that the bolded part is not always mathematically possible.
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post #25 of 46 Old 10-09-2013, 04:46 PM
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Go read the information on converting SPD to XYZ.

Once you understand that in a more complete way, you'll understand why the correction can't be constant.

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post #26 of 46 Old 10-09-2013, 05:49 PM - Thread Starter
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I'm gonna do a few matlab experiments. I suspect that if you had a linear transformation that perfectly maps a given tristim's cmf onto the standard cmf (xyz), you'd be golden. But I think that it would be very unusual for there to be a perfect mapping between two arbitrary sets of functions, hence the need for the cruder calibration offsets (which are indeed sensitive to spectral source).
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post #27 of 46 Old 10-09-2013, 06:53 PM
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Originally Posted by spacediver View Post

I'm gonna do a few matlab experiments. I suspect that if you had a linear transformation that perfectly maps a given tristim's cmf onto the standard cmf (xyz), you'd be golden. But I think that it would be very unusual for there to be a perfect mapping between two arbitrary sets of functions, hence the need for the cruder calibration offsets (which are indeed sensitive to spectral source).

Go find some raw spectra distributions and convert them to XYZ.

This is not a linear transform, it's an integration.

If you want to understand how a colorimeter works, first you need to understand how a spectrophotometer works. Once you understand that, you'll understand how a colorimeter is a shortcut and why you need offsets for it.

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post #28 of 46 Old 10-09-2013, 07:36 PM - Thread Starter
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yes I get the integration (or rather summing over small discrete wavelengths, as the function isn't defined analytically). I'm not talking about linearly transforming raw spectral information to get tristim values, but linearly transforming each discrete value before summing them).

I've just created the X Y Z distribution, gonna program the summing code right now so I can get x y Y values given a spectral input.
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post #29 of 46 Old 10-09-2013, 08:13 PM
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Originally Posted by spacediver View Post

I'm not talking about linearly transforming raw spectral information to get tristim values, but linearly transforming each discrete value before summing them)

Colorimeters never have spectral data.

The filters ARE the color matching function, in a tri-stim (hence why it's called a tri-strim). Since it's a bad CMF, the compensation depends on having the spectral data, which it doesn't have, so we use a more accurate meter to get the XYZ data and create a four color matrix.

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post #30 of 46 Old 10-09-2013, 08:25 PM - Thread Starter
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yes, but when simulating what a filter does, you can take the spectral input and model what happens to it when it gets filtered. Just got all the data, am compiling it now.
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