Film curve plotting and fitting

[Stephen Benskin]

Ron,

I agree flare always makes it impossible to be definitive about anything having to do with exposure. Here's a thought about flare and curve shapes. As flare is higher with exterior scenes than interior, in effect, it makes a short toe film shot outside have similar tonal relations as a long toe film shot inside. Maybe that was one of the reasons for keeping long toe films around.

It's sad to think that with the increasing loss of long toe films from the market, like TXP, the need for exposure distinctions is becoming more and more hypothetical.

 

[Photo Engineer]

Well, actually, from what I have seen, long toe films become mushy.

PE

 

[Nicholas Lindan]

I’m thinking that since long toe films are still being made ... there has to be a reason.

The now discontinued Plus-X and Tri-X 320 sheet films were a 'all toe' emulsions with an upswept HD curve. They were used for portraiture where lots of highlight contrast was needed to preserve detail in the hair. The lack of shadow speed wasn't an issue as there aren't any important deep shadows in a high-key portrait. All toe films also work well with snow scenes where snow texture is important.

I think some of the Efke emulsions are also all toe.

 

[Ray Rogers]

Conventions...

I think mushy or nice depends on how the coded data in the negative gets translated by the paper emulsion... and well, the whole output process (including method and chemistry).

Now, I would never doubt my own ability to recognize beauty (for example), despite the lack of my ability define and describe it adequately, nor would I seek to restrain the use of a term meant to represent the concept in conversation...
but doesn't it bother anyone, that, AFAIK, the terms "long" and "short" toe length remain unquantifed?

Could one of our resident mathematicians attempt to place a meaningful limiting definition on "long" and "short" in this context and propose either a sharp borderline or slightly fuzzy gray area for seperating the two from each other? This should not be that hard to do.

I am thinking this sort of thing must have precedent somewhere in the field mathematical analysis....

And while I am on the topic, how about an acceptable definition of "straight";

Are there no conventions?

 

[Photo Engineer]

Ray;

Yes there are and it is easly defined by using the curve I posted above. Straight = Straight. I used a straight edge to draw the 2.5 gamma portion of the curve. Anything above that line is toe and anything below that line is shoulder. The measurement points are on the graph. I used a similar overlay with marked points for film.

PE

 

[RalphLambrecht]

Ray;

Yes there are and it is easly defined by using the curve I posted above. Straight = Straight. I used a straight edge to draw the 2.5 gamma portion of the curve. Anything above that line is toe and anything below that line is shoulder. The measurement points are on the graph. I used a similar overlay with marked points for film.

PE

Ron

What what you call the midtone hump, I see in Tmax emulsions?

 

[Photo Engineer]

Ralph;

Page 9 here: http://www.kodak.com/global/en/professional/support/techPubs/f4043/f4043.pdf shows a variety of curves in different developers and different development times. In the main, you see a straight line, but at some condition you see the break in the curve (that is what we call it, or we call it a hump). These films are blends of emulsions and there is always going to be some condition under which a perfect curve is not achieved. This is as inevitable as it was with the older films, but just different.

With color, the break can be critical and that is why one developer is specified. I have seen tests though with other C41 developers that reveal breaks in the color negative curves. With B&W, such breaks are less critical. And, as you can see from the posted data, they are not very large.

However, if you look at page 15 here: http://www.kodak.com/global/en/professional/support/techPubs/f4016/f4016.pdf the breaks are much more pronounced and it is a judgment call as to which you would prefer. To me, the 400 in D76 looks very nice.

PE

 

[RalphLambrecht]

Ron

TMax-400 in D76 is my favorite combination (EI 250 by the way). When I saw these humps first, I questioned my data collection, but then I saw the Kodak TechPubs and knew it wasn't me.

Statisticians use a method called 'thick-pencil test' to check normality of a distribution. It basically says, if the line only deviates within the thickness of a pencil, it is a straight line. Not very scientific, but it works. Maybe something similar can be applied here too.

 

[Photo Engineer]

Ralph;

I took another look at the TriX 320 and thought how much it reminds me of the old style curves that we have been discussing. Wait, it is an old style curve! Yeah, 320 is the old style with the upswept shoulder. This increase in contrast is intended to be printed on the toe of the paper to even out the toe of the paper and give a longer toe to the print with any paper.

However, this works best with graded papers and even lighting as noted earlier in this thread. In fact, the curves mentioned by Nicholas, on his web site, demonstrate some of the problems with current VC papers. The article by Dickerson and Zawadski about 2 years ago in Photo Techniques illustrates VC curves from different manufacturers. This complicates printing on TriX 320, but is less of a problem on other films.

The bottom line here is that the paper may be more of a problem than the film in many cases.

PE

 

[RalphLambrecht]

... The bottom line here is that the paper may be more of a problem than the film in many cases. ...

Especially at soft grades!

 

[Kirk Keyes]

When I saw these humps first, I questioned my data collection, but then I saw the Kodak TechPubs and knew it wasn't me.

Ralph - do you use/test Acros? I always get a hump in it with XTOL and Pyro developers. I beleive I have good control on my densitometer so I believe it to be an artifact of the film and not the densitometer.

 

[RalphLambrecht]

Ralph - do you use/test Acros? I always get a hump in it with XTOL and Pyro developers. I beleive I have good control on my densitometer so I believe it to be an artifact of the film and not the densitometer.

Unfortunately, I have not tested Acros, but Fuji's curves show a bit of a hump with one developer on the last page of their data sheet:

http://www.fuji.fi/documents/13/neopan_100_acros_af3083e.pdf

To verify your densitometer readings, you could test it with a calibrated step wedge and conduct a repeatability and reproducibility study. This will tell you how reliable your readings are, but I don't recommend to take it that far as long you get the results you need from your testing.

 

[dpgoldenberg]

back to fitting functions

Hi,
As I indicated in my original post in this thread, the function that I proposed for fitting film curves was something I had made up, and I didn't think that it had any obvious relationship to the underlying physics. After reading one of the papers that Steve has circulated, I now realize that this function has a long and honorable history in sensitometry!

In the paper that lays out the "delta x" method that Steve favors (Nelson and Simonds, 1956, J. Opt. Soc. Am., 44, 324-333), "my equation" is described as "Luther's equation" and is used as the basis for the method (see page 326, eq. 1) The authors cite the following paper:

Luther, R., 1923, The under-exposure period of the characteristic curve, Trans. Faraday Soc. 19, 340.

I was able to find this paper. It doesn't actually present the equation, but it is clearly related and shows how far back the idea of fractional gradients goes. Luther found that the ratio of the slope of the curve at the "inertia point" to the slope of the linear region (gamma) was very close to 0.5 for many different films, with many different developing conditions (something like 700 combinations.) He then goes on to demonstrate that this relationship is predicted "on a partly theoretical basis" by the theories of the day, which were basically statistical.

A later paper (1945) by Silberstein shows that this relationship, referred to as "Luther's rule" can also be predicted with quantum mechanical models for exposure. Importantly, both the original treatment by Luther and Silberstein's show that the relationship holds even for emulsions made up of mixtures of grains with different sensitivities.

The connection between "Luther's rule" and the equation is that the functional form of the equation requires that the rule be satisfied. I suspect that there was a later, and harder to find, paper by Luther in which he presented the equation. It can also be shown that the Luther ratio is approximate 0.46 for the integrated Gaussian function discussed earlier in this thread. (This forms part of the basis for connecting the theory of exposure to the "rule")

In their paper on the delta-x method, Nelson and Simonds report that the equation worked well with all of the films they tested, developed to different contrasts, and then use it to derive the parameters for the delta-x method.

I doubt that this will convince anyone to adopt the properly renamed "Luther equation", but I was excited to find the historical connection. Robert Luther was a Professor at the University of Dresden, where he set up an institute of photographic science. His students there included Imogen Cunningham and Emanuel Goldberg, another fascinating person in the history of photography.

David

P.S. My apologies for going back to the original thread topic, which now seems to be in an off-topic phase!

 

[Stephen Benskin]

David,

In Minimum Useful Gradient as a Criterion of Photographic Speed, JOSA, v.25, Dec 1935, Jones sites two papers by Luther. The one you have and Interpretation of the Characteristic Curve, Photo. J, 49, 185 (1925).

Steve

 

[RalphLambrecht]

David

Does that mean I can call the following equation the Luther-Goldenberg equation?

y= a1*Log(1+Exp(a2*x+a3))/(a4+Log(1+Exp(a2*x+a3)))

 

[dpgoldenberg]

David

Does that mean I can call the following equation the Luther-Goldenberg equation?

y= a1*Log(1+Exp(a2*x+a3))/(a4+Log(1+Exp(a2*x+a3)))

Sure! But, is it working for you?

 

[RalphLambrecht]

Sure! But, is it working for you?

Perfect for film and paper up to grade 3.

 

[Photo Engineer]

Just some thoughts that struck me today....

There are basically 3 questions being asked here:

1. What equations best describe an H&D curve or does one equation fit all types?
2. How do I use the curve to determine speed?
3. Where do I place an actual exposure on that curve to get the best results?

Each of us has tried to answer one or more of these questions implicit in posts here and sometimes to cross purposes. I can only speak from my experience saying that I have evaluated literally tens of thousands of curves over 15 years of active product development and my answers were posted here.

They are:

1. Yes, EK uses a cubic spline to describe all curves for all products. We used either DEC or HP computers in a room full of automated Densitometers. They were plotting curves from several precision 1B Sensitometers. For color we used Status A, M and D for film and paper. M was used for negative, A for reversal and D for paper. This is basically grounded on the visual response of the human eye for reversal film and reflection prints and on print materials for color negatives. For B&W, they used a white light system. In all of my work I have never seen the spline fail!

2. Use the published ISO method for all films.

3. There is the most disagreement here, but I have found that almost all professionals and Kodak engineers agree with the plots and test results in Mees and Haist that the best exposures for negative films are 1/3 stop over ISO speed. This places the exposure on the straighter portion of the H&D curve. Thus, for negative films, I expose a 400 speed film at 320 to 400 and a 160 film at 100 to 160. This depends on my judgment of the scene and knowledge of the film. For reversal films I stick with ISO speed.

PE

 

[ic-racer]

Nice summary.

Here is a tangent question based on #2 above which can only be done with a calibrated sensitometer.

Just out of curiosity would you know or guess the 'box speed' of TMY or TMX to two or three significant digits? For example lens manufacturers always tell the actual focal length. So, what is the actual ISO test result for TYM or TMX to two or three significant digits? Did they really formulate it to be that close to 400 or 100 when ISO tested? Just curious.

 

[Nicholas Lindan]

EK uses a cubic spline to describe all curves for all products ...

1 cubic polynomial for the whole curve or 1 cubic polynomial between each set of data points with > 4 data points?

In all of my work I have never seen the spline fail!

I didn't know they could fail. What's the mechanism?

 

[Nicholas Lindan]

the 'box speed' ...to two or three significant digits?

ISO speed is a gross simplification of the film response. It says absolutely nothing about the shape of the HD curve. To quantify it to 3 significant digits - .1% or 0.0014 stops is - well, how shall I put this politely ... of course you can do it, but it would have no relevance.

For negative film it doesn't really matter what the exposure is as long as it is adequate.

To find the optimum exposure for slide film in a non-studio setting the only viable solution for most of us is to bracket in 1/3 stops and pick the 'least bad' result. If you have a movie producer's budget then you can control outdoor lighting, which you have to do to deal with the lack of any latitude in slide film.

 

[Photo Engineer]

IC;

Internally, we had the ISO rating of every emulsion to 3 figures such as 351 or 433 or the like, but for the life of me I cannot remember any of these figures for those emulsions. Sorry.

However, the release aim of 400 means just that and it is adjusted at coating time by the use of a trimmer dye to get an exact speed. You see this dye and the acutance dyes washing out of the coating during processing. The 3 digit internal speeds are used to determine the amount of trimmer dye to be used.

Nicholas;

We used 21 data points which were plotted and then the spline was used to draw the curve that best fit those points. Thus we had both the actual data and the best fit. AFAIK, only one equation was used to fit the whole curve.

Due to internal reflections in reflection products and the effect of angle of view on a reflection material, there is, to my understanding, a theoretical possibility of a failure of the spline function with reflection materials. I have seen wide variations in Dmax due to surface, thickness and backing whitening material. A goniophotometric study of density vs angle of "view" showed me that the densities could vary over a considerable range, but the spline still worked and gave us totally normal results. The surfaces tested in this experiment were designed to cause huge changes in reflection Dmax and shoulder scale from the same amount of silver, by changing coating conditions, and they did. We saw Dmax values for the first time that were over 3.0, but they were correct and plotted correctly at every angle. In other words, the individual data points and the spline best fit matched even though there was the possibility in some minds that they might not. Just as we have seen here, some curves do not exactly match the data points.

PE

 

[ic-racer]

ISO speed is a gross simplification of the film response. It says absolutely nothing about the shape of the HD curve. To quantify it to 3 significant digits - .1% or 0.0014 stops is - well, how shall I put this politely ... of course you can do it, but it would have no relevance.

I'm thinking of TMY (or really any reputable name-brand film product) as a cheap and dirty sensitometer calibration standard. I'm thinking it would be better than a 'standard candle' or as good as 'reflected sunlight at noon.'

Why? To give some ballpark reasonable numbers to the x-axis of any H&D curves I might post or share, rather than having just some generic log axis.

 

[ic-racer]

IC;


However, the release aim of 400 means just that and it is adjusted at coating time by the use of a trimmer dye to get an exact speed. You see this dye and the acutance dyes washing out of the coating during processing. The 3 digit internal speeds are used to determine the amount of trimmer dye to be used.

Ok, so for 'home use' I'll use it as 400. So, I can look through my curve database and find some examples developed to something similar to ISO standards and just define the 0.1 crossing point of the average of some of those curves as -2.69897 lux seconds on my logarithmic x-axis.


(assuming ISO speed = 0.8/Hm, where Hm is lux seconds at the 0.1 point under the appropriate conditions, bla, bla, bla)

 

[Stephen Benskin]

ISO speed is a gross simplification of the film response. It says absolutely nothing about the shape of the HD curve.

Maybe not the overall shape, but it does give the shadow gradient and average gradient.