# Phase One IQ3 100MP Trichromatic vs Standard Back Linear Color, Part III

Over the last two posts we’ve been exploring some of the differences introduced by tweaks to the Color Filter Array of the Phase One IQ3 100MP Trichromatic Digital Back versus its original incarnation, the Standard Back.  Refer to those for the background.  In this article we will delve into some of these differences quantitatively[1].

Let’s start with the compromise color matrices we derived from David Chew’s captures of a ColorChecher 24 in the shade of a sunny November morning in Ohio[2].   These are the matrices necessary to convert white balanced raw data to the perceptual CIE XYZ color space, where it is said there should be one-to-one correspondence with colors as perceived by humans, and therefore where most measurements are performed.  They are optimized for each back in the current conditions but they are not perfect, the reason for the word ‘compromise’ in their name:

The ideal matrix would simply translate white balanced raw data, say (1,1,1) for (r,g,b), to the white point of the illuminant, which in this case we have estimated to be about D65 – so it would look like this:

The closer the diagonal terms in figure 1 are to those in figure 2, and the closer the off-diagonal terms are to zero, the closer the relative CFA would most likely be to ideal.   The negative off-diagonal terms are relevant to the SNR IQ metric because, as we know when we add two frames, signals add or subtract linearly according to the sign but noises go in quadrature so they always add.   The SB has better looking red and green diagonals but the TC has a more contained blue entry and lower negative terms off-diagonal, we’ll see the positive effect those have when we look at the Adobe RGB matrices.

#### CFA Color Differences

In the meantime we can use the matrices in Figure 1 to compute the XYZ coordinates of the raw data collected off the 24 ColorChecker patches from the two backs.   XYZ data is usually transformed to the more perceptually uniform CIELAB color space in order to compute color difference metrics like deltaE76 (dE) or the better and more recent deltaE2000.  Here are dE2000 color differences from the BabelColor ColorChecker 24 database for the Standard Back, higher values indicate worse linear ‘accuracy’:

and for the Trichromatic

Recall that a dE2000 difference of 1 is supposed to represent a just noticeable difference.   I think some neutral patches were probably compromised by direct reflection from overlayed scene objects (leaves, lemon).  All patches were used to compute the matrices but Sensitivity Metamerism Index (SMI) was calculated from just the 18 color patches, per dxomark.com and the relative standard.

#### The Standard Back is ‘More Accurate’

SMI for the Standard Back came out at 86.9, indicating very good linear color fidelity for this setup, while the Trichromatic produced a lesser but still good 81.   the Sensitivity Metamerism Index is a metric of color ‘accuracy’, with 100 being perfectly accurate (but unattainable in commercial practice today), 90 outstanding (I’ve never seen it), 85 good (my D610 under D50 light), 80 decent and less than 75 poor as far as current photographic equipment is concerned.  Here is a summary with the key statistics from both backs:

The Standard Back appears to be the more accurate of the two out of the box as setup, by a noticeable margin.  Of course much of the difference can be made up with a good profile and these figures say nothing about how well ‘accuracy’ generalizes outside of this very limited ColorChecker tone set.

#### The Trichromatic is More ‘Precise’

Nor do they speak to ‘ease of processing’.  Perhaps a hint comes from the full-trip matrices obtained by converting the ones in Figure 1 to  Adobe RGB.  These are individually optimized linear matrices that convert white balanced raw data to the Adobe RGB color space in one go in the given setting (around D65 as we saw):

Here we would want the diagonals to be all ones (white is 1,1,1 in Adobe RGB) and the off-diagonal terms all zero.  Note how much closer to that ideal is the matrix for the Trichromatic – and how its negative terms are smaller than the SB’s.  This does indeed point to ‘purer’ RGB colors, less corrupted by mixing once converted to their final color space.  Perhaps this is what Phase One marketing meant when they mentioned “astonishing color definition”.  And given the supposedly more symmetric and trimmer CFA sensitivity functions maybe that does indeed allow them to be more precise in the processing, if not more ‘accurate’ as we have seen.  I am not sure whether these differences will be perceivable after a Color Profile has been applied with all its non-linear tweaks but I am sure that the Medium Format gang will let us know.

#### Similar Gamut in Given Setting

By the way, the negative terms in the matrices can and do cause negative values in the final color space.  Since the minimum value in Adobe RGB is zero tones that end up being negative are out-of-gamut in that color space and are therefore necessarily blocked to zero.  There were about 260k such out of gamut pixels in the Standard Back capture and 227k in the Trichromatic’s, all blue – not a substantial difference out of tens of millions.  They are mainly in the citrus fruit and the darkest shadows of the musk (the blue ball is the orange, refer to the original images shown in the previous post):

For reference, both images had their brightness normalized in the raw data so that  patch 22[3] would be at 18% of full scale; raw brightness in both was then reduced 0.15 stops so that the Adobe RGB histogram just did not clip (the only clipping before that was in the highlights of the lemon touching the ColorChecker).  Patch 22 landed at around L*47/48 in Adobe RGB.

#### Disclaimer

There are a large number of provisos and non idealities in this investigation – lighting, different ISO and exposure, position of cc24 (probably resulting in contamination of some of the patches by reflectance from items in the scene), absence of direct spectral measurements, etc. – not least of which the fact that I am not a color scientist and prone to mistakes so take this for what it is worth.  Nevertheless I think there were many interesting observations that  came out of this exercise.  Let me know in the comments if you have additional insights.

#### Notes and References

1. Lots of provisos and simplifications for clarity as always.  I am not a color scientist, so if you spot any mistakes please let me know.