Profiling target sheet patch count

There is a question lingering in the background how many colors are necessary on a profiling target to get a (very) good (good enough) icm color profile; I made an attempt more than a year ago but did not come to a conclusion so I have a reason to make another attempt, and I like to post some of the findings here. I'm using the i1Profiler package by x-Rite with an i1Pro2 spectrometer and a i1io2 scanning table.
Let me start with

step 1 - I'm doing all these tests with an ET-8550 printer with Epson 106 inks and printed all targets on Aldi Netbit paper sheets. I'm varying the number of colors for these targets from 96 to 2880 - a pretty wide number range. The 96 patches just fit onto 4 x 6 inch photo paper, and the 2880 colors print on 4 A4 sheets. The i1Profiler software let you create easily targets with about any color count - starting at 400 colors minimum up to any higher number which processor and memory of the computer can handle. The bottom limit of 400 is probably an attempt to separate the i1profiler software from the lower end i1Studio software which uses similar target sizes as the previous ColorMunki package with 100 patches. But the i1Studio software - the user frontend etc actually - appears to be a kind of crippled i1profiler software. So how did I get a target with 96 patches working in i1Profiler software ? There is an age old stand alone X-Rite piece of software - Colorport - which let you define target sheets and export configuration parameters which can be imported into i1Profiler without limitation. This was already used this way with the previous GretagMacBeth Print Profiler software. So I printed target sheets with 96 - 400 - 720 - 2880 patches and created profiles from the scanned data; I scanned the targets 3 times and averaged them to smooth reading errors. These are the diagrams how the profile volumes overlap



The image on the right shows how the profile volumes overlap at mid luminance of L=50 - several of the border lines overlap pretty closely - for the profiles based on 96 - 400 720 2880 patches , and there is a red line escaping the bundle. This belongs to a profile made with 283 colors on the target, as well imported from a Colorport layout - I don't have an idea at this time what is causing this deviation.

The other profiles match very well as well at the dark end - at a luminance of L=15 , all profiles are very close together except for the mismatch with the 283 patches target.



And the same applies for the congruence at the lighter end - at L=80



All profiles shows a very similar shape and size regardless of the patch count varying from 96 to 2880 (except for the 283 profile). But the Shape and volume of the profile does tot tell the complete story how a profile performs - profiles reassign color values based on various parameters - like the rendering intent, and this cannot be shown that easily with some diagrams.

P.S. I found the reason for the above mentioned problem with the gamut plot based on 283 color patches - I used different driver settings - different to those printing all the other patch sheets - premium glossy paper selection vs. ultra glossy paper selection. I recreated the 0283 patch profile - it is identical with the other profiles.

So I did step 2 - I printed the 96 color target again - this time with the previously created profiles - I printed the 96 color target with the profiles created from the 96 - 2880 color targets - I scanned these prints and compare how the prints differ for these 96 patches and by how much.

The i1Profiler software offers a data analysis function which is a compare function for 2 scanned data sets, and the software displays various statistical parameters for this comparison, here an example


Numbers are shown as DeltaE values, the cursor is placed on the peak delta value of 37, the yellow marked patches are the 10% with the highest deltas.
It is abvious that deltas of such magnitude indicate a problem, I just will not use that target sheet setup anymore.

The other profiles in this comparison against the 2880 one perform like this table shows:



It is remarkable to see how close the 96 and 2880 based profiles perform - almost identical for the 96 colors of this test sheet. The profile based on 400 color patches performs almost as good.
This test shows that 96 or 2880 color patches on the profile target sheets don't make a difference in the accuracy of the profiles - in this test flow as reported above.

I'll run another test - I'll print a patch sheet with more color patches - 400 - and compare how much the printouts differ when printed with either a profile based on 96 color patches or the profile based on 2880 patches, this to evaluate whther there is any quality gain when creating and using these profiles. I'll print with the relative color rendering intent to bypass additional color changes by the perceptual rendering mode, and without blackpoint compensation.. I'll do this test on the same Netbit Aldi glossy paper as in the test above.

As described above I profiled the ET-8550 with patchsheets with different patch counts - from 96 to 2880. And I'm printing a target with 400 patches with the 0096 and 2880 patch profiles.

Where are these 400 color patches located - across the complete RGB color space in equal distance - the little ColorInspector Java applet pretty well can show this:



The corresponding profile looks like this plot - including the sRGB color space - in the Lab color space



The printer profile and the sRGB color space don't match very well - the sRGB color space is displayed in green. There are segments where the printer profile by far exceeds the sRGB gamut. You can go a step further and add the wider Adobe color space as well - rendered in yellow.



There is a segment where the ET-8550 gamut with the 106 dye inks even exceeds the Adobe color space.
But this is not the main subject - there is an assumption that higher patch counts in the profiling process create 'better' - more accurate profiles. I'm comparing here profiles created from 96 or 30x96=2880 patches, and print a 400 color target with either profile. The i1Profiler software let me compare scans of such prints and display various statistical data. I have scanned the prints 3x and let the software average the data, these are the results



The variations betweens these 2 prints - 400 patches/colors - are all displayed above and averaged to a value of 1.59 and a peak value of 5.24. I must admit that I'm surprised how good a profile based on 96 patches matches a profile created from 2880 patches , such a low delta indicates to me that such a low-count profile is as good as a high patch count profile - just with this very small DeltaE of 1.59 . This is a first run of such comparitive testing, I don't have an idea if a test with ArgyllCMS profiles is possible and would yield the same findings, and I don't know at this time if there are variables and parameters which may limit these findings just to a subset of profiles.