Sandy, thanks for your post. You have very clearly layed out you thoughts on this! I really appreciate it.
I agree with the all calculations used to make your two graphs. The math is really striaghtforward. And you are right that the slope (gradient) of the curve will change based on the numbers that we use for the x-axis. It is a simple rise over run calculation. And you are right that if we change the values on the x-axis, all of our derived data (SBR, EFS) will change as well. I completely agree with this observation. It's simple mathamatics.
So what we need to figure out now is which set of data is the correct one!
"you will have noticed that values on the X axis are calibrated in LogE units, not meter-candle-seconds. They are in fact relative LogE units since their values are being determined relative to something else."
It does not matter if we have relative logE for our x-axis or absolute logE. The only difference is that you have not accounted for the actual amount of light that was used in the exposure. You could have easily used a light meter to measure the light, in say Lux and then multiply that by your exposure time for Lux-seconds (which are the preferred units). It does not really matter - it is actually a non-issue, but using relative logE is simpler but it works.
"If the units on the two axis are not determined by a measuring system with the same spectral response they may be different."
Well, it is not that the units are different. They are still exposure units to which the logarithm has been taken. We have not changed units. We may have had to change the color content of those units to match the material we are exposing, but we have NOT changed units.
"Now, assume that you have developed the test negatives ( made by exposure to the calibration step wedge). Now you measure them in UV mode because you plan to print in Pt./Pd. What is the unit of density? It is a relative unit of density determined by a specific measurment."
This is correct - to be more explicit, we have density units for our y-axis that are logE as measured with UV light.
"It would be different (because of the stain) if we measured in Visual mode."
Correct again, we would then have density units for our y-axis that are logE as measured with Visual light. But we do not want that for our y-axis data because the NEXT STEP in our process is to print on Platinum.
You are completely correct that the y-axis units when printing on Pt paper should be density units that are logE as measured with UV light. Correct.
"So we determine above that a given log density unit, say 0.3, will have a specific physical length on the Y axis."
Correct.
"It follows that the units of density that correspond to a given lenth on the y axis must be of the same length on the X axis. If they are not, the slope of the curve will be distorted."
Correct. If the actual spacing of the lines on the paper or computer screen are not equal, there will be a streching of one axis of the graph.
"Now look at the curves again. Notice that the curve plotted from the Visual step wedge begins at LogE 3.05, as we would expect from the Visual reading at Step 21. Now look at the graph plotted from the step wedge values read in UV begins at LogE 2.85, again as we would expect from the UV reading at Step 21. So which one should we use?"
Yes, now we are getting to our quesion.
"Obviously we need to use the one that represent a log density of 0.3 with the same physical density on the x axis as it is represented on the y axis."
This is where you are getting confused. There is no such thing as "physical density", unless you are talking about the actual spacing of the lines on our graph. And we have endured that - Our log units on the x-axis are exactly the same spacing as the log units on our y-axis. This is because we were diligent and precise in the spacing of our lines. The graph paper is not changing size here.
"That is only possible if we use the step tablet values read in UV."
No. Not correct. This is where you are incorrect.
LogE units are logE units the world around. LogE units do not change size because of the color of light that we used to generate them. As I said above, we should really be labelling our x- and y-axis with units like "density units = logE as measured with UV light" or "density units = logE as measured with Visual light" or "density units = logE as measured with IR light". The logE units are all the same size, and they do not "distort" the curve. They are quite simply the units with which our exposure was made.
"If you use the step tablet made in Visual mode you will expand what would be 2.85 units of density on the y axis into 3.05 units on the x axis, which makes any unit of a given value of different length on the x and y axis."
And this is incorrect as well, for the reason given in my paragraph above. You are not "expanding" units. Units are units. They do not expand, they cannot expand. You simply want to apply one set of data points for the x-axis (the value of the exposure that was given to the step tablet) to your measured y-axis data points (the values measured from the developed test film). They can be made with different channels on the densitometer (as long as they match the conditions that match the material).
Keep in mind, when graphing data like this, the x-axis contains what is called the "independant" data, the y-axis contains the "dependant" data. The values of y are dependant on x, not the other way around. In your system, you have the x dependant on the y which is incorrect.
This actually comes into play here - the exposure being made through the steps in our wedge are the independant data. We could expose for 1/10th, 1, or 100 seconds if we want. The f/stop on the enlarger can be anything we like, as can the enlarger head height. The color quality of our light source can be anything we want - blue light, IR light or UV light. It is completely up to us as to what we do here, the x-values are independant. There are many combinations that will not make any density on the test neg or it will be completely overexposed, but we are completely free to use those combinations if we want (which could waste a lot of film in the process). The x-values are independant.
The density that results on the film for which we will use on the y-axis are completely dependant on what we did to the value at the x-axis. Nothing in the y-axis results has any effect on our x-axis data. It doesn't work that way. That's what my esoteric information theory discussion above was all about. It does not matter if we measure the values on the y-axis with UV, visual, IR, blue...
But we should measure the the y-axis data based on our intended goal for the negative. And you are right with that - if you are going to be Pt printing, measure y-values in UV, if silver printing use blue or visual. It should be based on your intended use of the neg.
But let me say it again, the x-axis data is completely independant of the y-axis data. So your claim that we should use UV for measuring the step wedge if we are going to be Pt printing is completely without any basis. What we must do is measure the x-axis data based on the sensitometric properties of that initial piece of film and the light conditions under which we will be exposing it.
"As one would predict, and can prove by examination of the two graphs, this will reduce the slope of the curve and it will also have an impact on other values such as SBR and EFS."
What your two graphs prove is that since we know that both of them can not be correct, then one of them must be wrong. But that actually does not prove that the other one is correct by default, it may be wrong as well... If the data used to prepare the graphs is not appropriate for what we are trying to prove, then that does not help us make our proof.
Here's another conundrum for you. Let's look at your Pyrocat graphs over at unblinkingeye.com
http://unblinkingeye.com/Articles/PCat/pcat.html Your very first graph in your article, "Figure 1. A JandC 200 negative developed in Pyrocat 2:2:100", shows the densities measured from one neg in visual, blue, and UV channels. I suspect you measured all the values for the x-axis of this graph with the visual channel, right? Well, this is in contradiction to the advice you are giving above. What you are saying is that we will have to use a separate graph for the UV channel since we have to measure the x-axis data from the step wedge with UV light. Otherwise there will be distortion of our chart and data as you claim. If that is true, then all your graphs in this article are prepared incorrectly if you have both UV and visual data on it, because we know your step tablet has different values in UV vs. Visual. That is the conlusion that we must make from your claims above.
Well, I do not beleive that conclusion. Your graphs ARE prepared correctly (assumung you used the visual channel data for your x-axis). This is BECAUSE you were exposing a panchromatic film, and because of that, you selected a daylight source for the exposure. That's the reason that you should have used the visual channel for the x-axis. And you did (I think).
Sandy, if you are not convinced yet, could you take a look at the IR film/ Pt print scenario above? Could you tell me where my reasoning is incorrect on that? Would you use the UV channel to measure the step wedge in this situation even though the film is only going to be exposed to and pass IR light?
Thanks again for better stating your position.
Kirk