Film curve plotting and fitting

[RalphLambrecht]

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. ...

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.

 

[RalphLambrecht]

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.

 

[Photo Engineer]

Ralph;

I'll scan it in if it cools down here. Right now the sweat is pouring off me due to the heat and humidity and working in the garden.

It is in a paragraph that starts "When the ASA speed values....." It is about 3 sentences into that paragraph.

PE

 

[Stephen Benskin]

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.

Me too. I have the second edition published in 1966. The first edition was published in 1948 so the quote had to be referring to the Fractional Gradient Method.

Not that I disagree with adding a little extra exposure, but the quote appears to be part of a larger statement. Notice the quote says the ASA "relates" to the minimum exposure, not "is". The Fractional Gradient point was around the minimum useful point, but it was used to determine speed and the ASA of that time never intended for the exposure to fall on that point. 0.3G falls approximately one stop below today's fixed 0.10 density point, but the speeds were one stop slower than they are today. Added to that, in the mid 50s, it was confirmed that the safety factor was 2.5x.

So, I think that they were referring to the problem of using 0.3G in its purist form as the base exposure as it doesn't allow for error, lower than average flare, or larger than average luminance ranges. The ASA of 1948 never intended the 0.3G to be the base camera exposure.

BTW, I'm looking under the heading The Determination of Sensitivity, and I've notice a strange tendency for them to write about historical concepts in the present tense. For instance, they write that with "the small negatives that are increasingly common" there is "an increasing tendency to recommend exposure indices that are about 2.5 times as great as the American Standard Exposure Index." The quote falls within the section dealing with 0.3G, but without a very careful read, one would think it applies to current conditions. I got caught off guard with another statement about the inertia speed.

 

[Photo Engineer]

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

 

[Nicholas Lindan]

[Nicholas,] you are making this tougher than it really is. I don't understand why.

I was just reviewing this thread, er hawser, and came upon the above.

It seems that each of us is thinking the other is doing it the hard way and making it far more complicated than it needs to be.

Let's just stick to toe, midsection and shoulder, shall we? That's what's relevant!

We have very different ideas about what is and is not relevant.

The toe/mid/shoulder is what's relevant to you. And that's fine. Nobody is debating that is the part of the curve you are interested in.

But for me, I find it very limiting.

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. And if the system is to deal with flashing it has to be able to make some sense of exposure that may, on its own, not make a visible dent in the image.

De Gustibus non est disputandum, and all that.

My method doesn't work for you, and your method doesn't work for me. But as there is no requirement they have to, it would seem politic to let this impasse stand and be done with it.

I knew I should have stayed out of this thread. I knew it. I knew it. Learn all your life and you still die stupid.

 

[Stephen Benskin]

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).

 

[ic-racer]

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.

Of course, I missed that. Thanks. (I should have figured it out as that y(x) vs y(x) swap is how I am getting the 'inertia'.)

 

[dpgoldenberg]

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?

It took me a while to figure out DeltaGraph enough to do this, but I did get it to fit my function to the toe and linear regions of Ralph's paper curve. Here is a capture of the dialog boxes.

David

 

[RalphLambrecht]

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

I fully agree with that.

 

[RalphLambrecht]

... 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. ...

Of course, but you don't need a curve fit outside of that area, and that's why a single polynominal does work reasonably well for film and paper curves.

 

[RalphLambrecht]

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.

 

[Stephen Benskin]

Stephen

I need to see this. Maybe it helps me to understand better why you are so taken by this approach. Yes, please.

I'm not the only one taken. The Delta-X criterion is the current ISO speed standard.

BTW, check out Fig 11.3b on p 216 of Fundamentals of Photographic Theory.

 

[RalphLambrecht]

I can offer another curve fit option, which worked very very on Nicholas' smooth curve but did not work that well on my data. Still, an interesting approach.

 

[Lee L]

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

 

[Photo Engineer]

Guys;

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.

On another tack, 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. Therefore, you will end up with the wrong conclusions and perhaps poor photos from a bad batch of film or paper that looks smooth just because the curve is drawn that way.

This is an event that we always took precautions to avoid. We used individual points and drew the best curve through them so that we saw the data and the curve. If there were bumps that were not artifacts such as dust or scratches, then we repeated the test to see if the bumps in the real data was correct.

PE

 

[Lee L]

Very true Ron. But could you call a sine wave a good generalized model of modern emulsions? I haven't tried, and I don't know the answer, but can you push a negative film far enough over the top of a sine wave (so to speak) to render a positive image with the characteristics of the other half of the same sine form? I'll be interested to see any curve of a solarized image you can find. From the solarized images I've seen, I'd guess that you could push the midtones to the peak, but not the shadows.

Perhaps that's the real crux of the debate here, and differing takes on curve fits. The OP is hoping to find a good generalized equation for current films with a long straight line portion. That makes sense given how few of us actually hit the shoulder in practice on modern films.

Some of us are looking for 'good enough' fits that describe the part of the curve we use for analog printing. Others are looking for the best generalized mathematical model that describes the complete behavior of current emulsions. Those can easily be two different things, although they don't have to be.

Lee

 

[Nicholas Lindan]

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. Splining between the points didn't' add any practical accuracy - sheet to sheet variation (and even variation across a sheet) was greater than any error caused by using linear interpolation.

 

[Kirk Keyes]

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.

 

[Stephen Benskin]

That's exactly what I did when I wrote a spreadsheet/macro for film curves.

I'm curious as to what the benefit of curve fitting is over a straight x,y raw data plot. It seems to me like a lot of talk and effort to draw a pretty curve with little talk about interpreting the results.

 

[Kirk Keyes]

For me, point to point linear interpolation gave me enough to work with to figure the basics I needed for contrast and speed. Of course, I couldn't do any of the fractional gradient calcs as I did not have a formula to find the slope of the film curve as it runs into the base+fog region. So no fancy calcs like in your 4-quadrand program.

But to do basic BTZS calcs, it works well enough.

So I guess it's less precision but much easier calculation is the benefit.

 

[RalphLambrecht]

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

... or the curve just stretches out a bit more.

 

[RalphLambrecht]

... 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...

The new direct-positive paper from Ilford is an excellent example. It goes into solarization almost immediately after Dmax. At first I thought I messed up the test.

 

[RalphLambrecht]

That's exactly what I did when I wrote a spreadsheet/macro for film curves.

That's what Phil Davis did in his plotter software as well. I thought it was a bit rough, especially since it is (was) limited to a 21-step wedge.

 

[ic-racer]

Anyone that wants to join in this discussion over a few beers, come to the (there was a url link here which no longer exists)