Mike, if I read your math right, the small "p" is off my 21 step chart. Those are fixed whole numbers so Step 1 is p1, Step 2 is p2 etc. on the X-axis.
If I do the table I get this:
P0: p0 = 0
P1: p1*0.75 + p2*0.25 = (0.75)+(0.50) P1=1.25 i.e. (Step 1*0.75) + (Step 2*0.25) for a Qimage LOC # = 1.25
Can't input that into QU. Rounds down to 1 only.
P2: p2*0.50 + p3*0.50 = (1.0)+(1.50) P2=2.50 Drops down to LOC=2
P3: p3*0.25 + p4*0.75 = (0.75)+(3.00) P3=3.75 Drops down to LOC=3
P4: p5 = = P4 or LOC4 = Step 5
P5: p6*0.75 + p7*0.25 = (4.5)+(1.75) P5=6.25
... etc.
Seems to be dependent on some other step than the single one I want to address, and also altering its neighbor, aside from the decimal part?
Somehow I can't see how 21 'whole numbers' off a step wedge reading can be fitted to 17 'whole number' LOC steps without some sort of decimal in the mix too?
Was trying to do this in a spreadsheet and got a math headache. Ugh!
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Aside:I'll attach a sample 21 step wedge (converted) JPG, but I need to reverse the Black to Zero and White to 21 for use in Qmage. What usually happens with some cheap printers the blacks get bunched up around the 18-21 scale in the JPG. I think my Canon 9000 II falls into the "cheap" category (Hence the need to do a quick bump off the left side of the Curve in QU as above), and the Epson 3880 addresses the issue a bit better with more balck shades of in. Tuning the black shadows so they separate in the cheap Canon is a problem, and the i1 spectrometer tells me its blocked up too. Just cannot refine it as well since the QU LOC range/scale is too compressed.
Don't know why 51 gray scale wedges is some big deal either, but those are out there. Might be the 8-9 blacks in piezo inks may make the same "bunching up of black shadows" issue with a smaller 3 black inks 'color' printer; Somewhat like Canon 9000 II is to 3-black ink 3880 (Excluding the other Epson 3880 Photo Black or Matte Black since only one can be used at a time, along with the other Light Black and Medium Black.).
Keith Cooper's newest B&W Test Image has the 51 step wedge that is capable of being scanned with the i1 ColorPort software which might make it easier than reading all 51 steps individually. Should be easier to dump the readings into a CRV file to read in the software or a spreadsheet that shows the linearization curve. He also did a 21 step as well maybe for manual entry or the cheaper ColorMunki Photo. Must be some standard since Kodak had 21 step wedge for decades, and Stouffer in the printer biz both.
Mack