Digital BW, The Print

Just one more thought for the evening.  If QTR or IJC/OPM linearizes LAB
values from (0, 0.04) to (1, 1.68) for EEM, as an example, then I believe
this function is defined as y = -0.04 + 1.64x where x=log10(normalised pixel
value) = -Density. If I am not mistaken this is a gamma of 1.64.  This also
means 50% grey is printed with a density of 0.5337.  This is much lighter
than what we want.  A 60% step (norm. pixel value 0.4) prints at 0.6926.  So
a step from 50% to 60% was a change in density of 0.16.  Yet LAB would
prescribe a change of 0.73-0.55=0.18.  So if I wanted to print a simple
picture of 2 squares, one 50% grey and the other 60% grey this curve would
not print them properly, even though they are well within the tonal range of
the printer.


> From: Steve Kale <stevekale@...>
> Reply-To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
> Date: Mon, 06 Dec 2004 21:17:18 +0000
> To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
> Subject: Re: [Digital BW] Tonal range and linearization
> 
> 
> Tyler
> 
> Ever narrowing circles of misunderstanding! We are getting closer - I think.
> I wish I we had a white board - I think we would be done in about 10
> seconds.
> 
> 
>> From: Tyler Boley <tyler@...>
> 
> 
> 
>> Steve, my wording above was perhaps confusing. I did not mean to imply
>> LAB makes sense as a working or editing space, but as an output
>> standard for linearization.
>> 
> 
> I understood you.  I guess I was raising the counter question that if there
> is little difference in grey scale between 2.2 gamma and LAB (see Bruce's
> curves) then what is gained by output at LAB?  But as I noted later in my
> post, as the error rate between 2.2 gamma and LAB is low, I could tolerate
> the difference if we solve the issue below:
> 
>> ...
>>> With reference to my point above, do you linearize over 0 to 1 or
>> over the
>>> dynamic range for that curve?
>> 
>> I still don't see the logic in your previous assertions. an input
>> value of 0 will always map to "no ink", paper white. It's density will
>> always be determined by the particular paper. 1 (one) will always be
>> the dmax capable from the particular hardware/workflow/materials.
>> There are no input values "outside" that range. I don't see how any
>> other approach can be useful. Put in a different paper, less white or
>> with a coating that can't print as black, and everything changes. But
>> I still want the full linearized range between, so why would I clip
>> info or whatever?
>> I'm not challenging what you have been saying, I've just not carefully
>> followed it due to brain constraints on my end.
>> StudioPrint is linearizing between paper white and ink black, though I
>> can select where that black point is based on what the readings are
>> telling me (there may be a better black point than max ink load).
>> But I still want to send the RIP ALL the values of the file.
>> 
> 
> OK let me try to explain what I am thinking.
> 
> Let's assume we do our step wedges like Paul does: 100% black (pixel value
> 0) on the left, 0% black ie white (pixel value 1) on the right.
> 
> First of all, I suspect we can agree that we both want to use the full range
> of the printer and I think we can also agree that since the tonal range of
> the printer is less than the tonal range of the image file (assuming the
> image has been adjusted to fill or spread pixel values from 0 to 1, either
> naturally, with a curve or with a levels adjustment) there must be some
> compression of tonal range - either by the RIP or before it gets to the RIP.
> Let's leave which to one side for now! Let us also agree that we don't want
> any clipping.  So we have a necessary compression from perfect black (pixel
> value = 0) to printer dMax and from pure white (pixel value = 1) to paper
> white, and some function in between.
> 
> Do you agree that we can measure and test the results of our linearization
> ie we have an empirical test as to whether we have done things right?  This
> can be done by printing another step wedge with linearization "in place"
> measuring the densities, calculating their luminosity equivalents, plotting
> log10(luminance), ie -Density, against log10(pixel value), and comparing
> this versus the same figures for the gamma 2.2 space.  The two graphs should
> overlap as straight lines for the range of log10(pixel value) which are
> within the tonal range of the printer.  If they do not then we have not then
> we have not linearized to our chosen space.
> 
> The target values for gamma 2.2 are in 11 steps:
> 
> Norm. Pixel Val   log10(pixel value)  log10(luminance)
> 0.0     -infinity   -infinity
> 0.1     -1.00    -2.20
> 0.2     -0.70   -1.54
> 0.3     -0.52   -1.15
> 0.4     -0.40   -0.88
> 0.5     -0.30   -0.66
> 0.6     -0.22   -0.49
> 0.7     -0.15   -0.34
> 0.8     -0.10   -0.21
> 0.9     -0.05   -0.10
> 1.0      0.00    0.00
> 
> 
> The log10(luminance) or -Density figures for LAB would, I believe, be
> -infinity, -1.95, -1.52, -1.21, -0.95, -0.73, -0.55, -0.39, -0.25, -0.12,
> 0.00.
> 
> Now unless I am mistaken, a linearized RIP like QTR when it receives a
> normalised pixel of 0 puts down max ink and gets dMax, around 1.68 for EEM,
> and when it gets a normalised pixel value of 1 it puts down zero ink and
> gets dMin (paper white), around 0.04 for EEM.  Fine, but what about points
> in between?  Let's look at normalised pixel value = 0.1 (25.5 in 8 bit).
> Gamma 2.2 wants 2.20 and LAB wants 1.95 but the max the printer can produce
> is 1.68. I believe QTR would give it even less than 1.68. I think we can
> already see that our empirical test will fail.  There will be no overlapping
> of the curves and they will not necessarily cross at 0.5.  Put another way,
> the have a completely different gamma.  It may be linear (I haven't tested
> it) but it isn't gamma 2.2 and it isn't LAB.
> 
> If on the other hand, I recognised that the printer can't begin to record
> changes in tone until dMin and that this equates to our linerization target
> norm. pixel value equivalent of just over 0.9 and that it stops recording
> changes in tone at dMax and that this equates to our linearization target
> norm. pixel value of just under 0.20 and I put dMin and dMax in these places
> and linearized between them then I would have a solid overlap from dMin to
> dMax in my empirical test chart.  I would have linearized to my target.
> Outside of this range my printer can't register tonal range but within it I
> have a rate of change of values consistent with gamma 2.2 or LAB, whichever
> I chose.
> 
> (As an aside, what if I had a photographic paper which was as white as EEM
> and could only record the same dMax as EEM and a contrast of 2.2, how would
> Kodak plot it's "characteristic curve"?  It would begin flat at a density of
> 0.04 then turn upwards at a linear slope until it hits 1.68 reflection
> density and turn flat again. The horizontal axis LOG Exposure is equivalent
> to LOG normalised pixel Value.  Only the chart in the second case has the
> same profile as that which would be drawn by Kodak.)
> 
> So putting off to one side for the moment the issue of editing in one space
> and linearizing to another, I do not see how you can linearize to LAB or
> gamma 2.2 except in the manner I have described.  You linearize I guess but
> not the way you intend to.  And if LAB more closely matches the way the "eye
> sees" then I would want to be sure that I matched it. Starting at the mid
> and moving left seeing increasingly darker shades at the correct rate of
> change (and vice versa to the right).  If I linearize the way I am
> suggesting and I used LAB, I also get my Kodak grey card reading for all
> pixels at the mid point of 0.5 (K=50%, LAB=50) if I read their density in
> the final print.
> 
> I am really not sure that I can explain myself more clearly.  If you believe
> in LAB then you want to linearize to LAB.  LAB says that if I have a 20%
> change from 50 to 60 in my range I get a defined change in tone.  As you get
> better paper white and better inks then the range around LAB=50 gets wider -
> we reach further out on our step wedge ALWAYS AT THE SAME RATE AS LAB...not
> some other rate of change.
> 
> I hope this helps and would welcome any comments
> 
> Steve
> 
> 
> 
> 
> 
> 
> 
> 
> 
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