Dear Stephen,
thanks for your reply. I am not much of a programmer and opted to go with the btzs plotter. Could you elaborate on what you mean by produces approximate results? Do you mean the linearization of the actual measurements to create smooth curves? As far as I am aware, extra calculations, such as flare, are optional. I am a bit fuzzy about the actual difference between relative and absolute testing. Why would this tool not be useful for absolute testing? I can't enter lux seconds as an x-axis? Why would Delta X calculations be approximate in this case?
Phil Davis is probably one of the few authors of any general purpose photography book who is generally correct and accurate concerning photographic theory. The reason I don't use the BTZS program isn't because it's not good, but because I have different requirements. It's excellent for the needs of most photographers.
On pages 93-94 of BTZS 3rd edition, Davis explains the theory for the fractional gradient method and his method to approximate it. "Because the fractional gradient method of speed point location is difficult to implement in practice (you can't find the speed point until you know the average gradient, and you can't calculate the average gradient until you've located the speed point), it was important to find some simpler calibration procedure. Finally, researchers concluded that when a realistic safety factor of about 1 stop is included I the fractional gradient measurement procedure and when the film is developed to an average gradient value of about 0.7, the fixed density and fractional gradient methods are in close agreement." I just want to point out that I have a slight problem with that last sentence. While Davis correctly states the average gradient is approximately 0.62 in a following sentence which some what covers the 0.70 value, it's the 1 stop safety factor part that I find questionable. While the fixed density of 0.10 is effectively 1 stop over the fractional gradient point when the film has an average gradient of approximately of 0.62, the one stop difference isn't a safety factor. Calling it a safety factor can be misleading. It is possible this was a simplification on Davis' part to explain the range difference without getting into the weeds. He continues, "The current ANSI and ISO standards approximate this condition by specifyi8ng an exposure range of 1.30 and a density range of 0.80, with the speed point located at the 0.10 over Fb+f level. The average gradient of this standard curve is approximately 0.62."
The first sentence in the next paragraph is an important statement that is rarely found. "It's important to understand that the ISO speed point is only a point of reference from which the official film speed number is calculated." This distinction was clear with the ASA values before the 1960 standard, where there was an ASA Speed and an ASA Film Exposure Index value as indicated in this excerpt from Safety Factors. Notice the difference between the equations for the Exposure Index and American Standard Speed is the constant k (not the same constant as the K factor).
And this is from an old Kodak Data book.
The difference between the "Kodak Speeds" (ASA Speeds) and EI are approximately 2 stops. The difference between the fractional gradient speed and the fixed density of 0.10 in the ISO standard is approximately 1 stop. That is where the one stop difference between film speeds prior to and after the 1960 standard is from. Not from moving away from the fractional gradient speed, but from a change in the constant for the EI. Both standards use the fractional gradient speed as the foundation.
Continuing with Davis, "Furthermore, it approximates the point of optimum minimum image density for only that one exposure/development condition - that is when the subject range happens to be suitable for development that will produce an average gradient value of 0.62. The ISO speed point location and therefore the official film speed are not necessarily appropriate for use with other subject range of development conditions." The reason for this is the fractional gradient speed point is derived as it's name suggests, from a fraction of the average gradient. As the film gradient changes, so does the fractional gradient speed point. A fix density doesn't not shift in the same way. This is also a distinction left out of most speed discussions.
Further down on page 94. "As mentioned previously, it's quite difficult to locate fractional gradient speed points by using ordinary mechanical drawing techniques, so several methods have been proposed for approximating them." Davis then list a few methods, but interesting enough, not the Delta-X Criterion which is the very method adopted to replace the fractional gradient method. "This reinforces the conclusion we reached earlier: We can relate the density of the speed point - rather than the value of the curve gradient at the speed point - to the average gradient of the curve itself. In other words, it's practical (and convenient) to consider the speed point density to be equal to the curve gradient divided by some constant factor. You can get good results by using a factor number between about 7 and 10; temporarily, I'll suggest 8.5." Later on the page, he gives an example, "Because the "normal" average G is typically about 0.50, we'll apply the factor (8.5) to find a "standard IDmin" for this first average gradient measurement: 0.50 / 8.5 = 0.059, or 0.06." From the equation, a film with an average gradient of 0.50 has the approximate fractional gradient speed point at the the density point of 0.06.
My first reaction is why not use the Delta-X equation?
ΔD is easy to determine and the equation gives a fairly close approximation under all conditions to the fractional gradient speed point. A speed value can then be determined using a constant with either relative or actual log-H. The question with Davis method is how approximate is it and under what conditions is it more and less accurate? The fraction gradient method itself is a sensitometric approximation to the print-judgement speeds from the psychophysical first excellent print tests. Here is a comparison of various sensitometric methods of determining speed as compared to the print-judgement speeds. For me, even if Davis' method satisfactorily relates to the fractional gradient or ΔX method, unless you do a comparison between its results with the other methods, it's an unknown variable.
As far as I remember, the BTZS program is only able to do relative log-H.
Producing a curve is just the first step. The important part is how it is interpreted, and I believe the above speed discussion is a good example of how involved it can be. Understanding flare is critical in determining a development model. Determining an accurate LER is also important. This is where most mistakes are made and is something that can be discussed later.
Stephen
. We have a 7 filter reverse osmosis system in our Lab and create the chemicals from scratch (or use one-shot). We have air-conditioning and follow the exact same processes. Not only that, but we have machines who rotate the drums for us. 
