Nicholas
Let's just stick to toe, midsection and shoulder, shall we? That's what's relevant!
Oh yes, polynomials can do that, and so can simple nonlinear equations. No need to patch up curve fits.
Well, we have a disagreement, that appears will never be settled, as to what is relevant. I find the HD curve goes from no exposure through to and past solarization and reversal. Exposure past that which results in DMax is common, as is exposure under the DMin point. The sections of the HD curve that deal with under and over exposure do exist and do have to be dealt with. As an example, we all make flashing exposures below the DMin exposure. ...
It is "The Determination of Sensitivity" and is located right under figure 11.2d, the idealized characteristic curve divided into 3 portions based on exposures given to pictures on another page. It is the 7th page in the chapter.
They begin the discussion of average gradient on the page following.
If you have a problem, I can scan the page in.
PE
Ron
I found fig.11.2d on page 213 of my edition, and it seems to be the figure you're referring to, but I just cannot find the quote.
[Nicholas,] you are making this tougher than it really is. I don't understand why.
Let's just stick to toe, midsection and shoulder, shall we? That's what's relevant!
Maybe I can help. Deltagraph can solve for y=f(x) and x=f. So, if you are willing to put up with a mediocre x=f fit, you'll get your answer by solving the attached equation for 0.1, using Nicholas data as an example. But, you could always do it graphically with the y=f(x) function.
However (Ralph, correct me if I am wrong) I could not get DeltaGraph to do a "user specified" curve fit like the one mentioned in the original post (D(x) = a1*ln(1+exp(a2*x + a3)) ) to get the a1, a2 and a3 values. Did you try it also?
Steve, Ralph;
I mentioned before the danger of using these older texts. I have fallen into doing it myself because of the lack of more modern texts which deal with more modern emulsion curves.
But they do seem to agree on one thing. Exposure on the straight line, as much as possible, is best and slight overexposure from the ASA (or ISO) value is best.
To be sure, this is even more important with color films, especially if the 3 layers are unbalanced for speed. I have seen films from some manufacturers that were supposedly 400, but were actually 320 absolute, and probably needed about 280 to really be up on the curve and "neutral".
PE
... If I have a system that reads exposure and spits out the density then I have to deal with parts of the curve that are outside the normal image forming range. ...
I now have available for anyone interested Simple Methods for Approximating the Fractional Gradient Speeds of Photographic Materials, by C.N. Nelson and J.L. Simonds. This paper changed my perception of film speed. It describes the Delta-X Criterion and w method (which was never implemented).
Stephen
I need to see this. Maybe it helps me to understand better why you are so taken by this approach. Yes, please.
curve smoothing is sometimes not desirable. Some of these equations will smooth out the real bumps in curves of films and papers made of poorly blended emulsions.
I found it was best, when one needed the curve with warts and all, to just use the raw data points and do a linear interpolation between them.
That's exactly what I did when I wrote a spreadsheet/macro for film curves.
That's a half cycle of a sine wave Ralph. Give a few stops under or over exposure and you'll get a positive image with that model. With the right exposure (x-axis shift), you could make both highlights and shadows match density with midtones being the brightest part of the image, or both shadows and highlights bright with dark midtones. And you could keep sliding exposure up and down infinitely with alternating image characteristics.
In other words, it may fit the data over a very short range, but it's not a good model of how an exposed emulsion behaves.
Lee
... A film curve can be a sine wave. Remember solarization? If you overexpose a film, you get a reversal curve which appears to be a sine wave. Modern films are built to repress this effect. It was there in older films and some of those texts show the reversal portion of the curve. If I run across one, I will post it...
That's exactly what I did when I wrote a spreadsheet/macro for film curves.
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?