Algorithm to find characteristic curve

OldBikerPete said:

I may be a tad thick here but for computer usage, why try to generate a characteristic curve? Why not just put measured points in a lookup table and do a linear interpolation between the points?
Generating a characteristic curve may be necessary if you want four-figure accuracy or better, but for photography usage you dont need that sort of accuracy.

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That was going to be my fallback position. But if there is a simple algorithm that gives more accurate results then that is what I'm looking for. One of the main things I am looking for is .04 over paper white. Depending on if the curve is "curved" or straight line interpolated does give different results, and it looks like in a meaningful way.

If I was just doing this in Excel the curves generated there are adequate for my use. But I'm trying to write an app to do this automatically. So I don't want to rely on other programs to do the curve part.

Michel Hardy-Vallée said:

Stephen, does your explanation mean that the flare curve is calculated, and not measured?

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It's the only practical way to do it. The intention for the camera image quadrant is to model how the camera influences the values of the subject and their relationship to the film/paper. The calculations are based on real world observations. The value of flare can be changed to represent a higher or lower flare conditions and the luminance range can be adjusted to represent various luminance ranges.

I'm also with Kirk on the subject of curve fitting. Curves have been hand drawn up until recently which seems to have been good enough. For me, the importance of plotting curves is in the interpretation of the results.

I've attached what I think are two good examples of why I believe the importance for plotting curves should be in their interpretation. The first are three camera image/flare curves. They come from an article on middle gray. The paper consisted of three parts - the psychophysical middle gray, real world/camera image middle gray, and exposure meter middle gray. These examples are from the real world/camera image section.

In a no flare curve, the middle falls at 9% reflectance for a 7 stop range (not the statistically average 7 1/3 stop range) as stated in Dunn's book Exposure Manual. For that it falls closer to 8% reflectance . A no flare camera image is in reality impossible but it represents the real world average reflectance outside of the camera. A flare curve representing statistically average flare for a modern lens has the middle fall at 12% reflectance. And a flare curve of 2 1/3 stops has the flare fall around 18% reflectance. Since older uncoated lenses have a higher flare, this might account for the 18% gray card to 12% average reflectance discrepancy.

The second example is the comparison of three reproduction curves representing how the subject tones will reproduce when the film is processed to different CIs and printed on different paper grades so that the negative density ranges fit the paper log exposure ranges. The printed density ranges are the same in all three examples, but there are distinct differences on the tonal distribution between. Grade 2 comes closest to match the originals tonal distribution. Grade 4 has higher local contrast in the mids and upper shadow region, but flattens in the lighter tones. The mid-tone also falls on three different print densities. From a psychophysical standpoint, if the tones actually matched the original subject (as defined by the straight line), the print would appear too dark.

I just ran across this attached example. It shows the results from "pushing for speed." The film is underexposed. The processing was extended (CI 0.68) in order to produce a negative with a density range capable of printing on a grade two paper with an LER of 1.15. The speed resulting from the push wasn't significant enough to make up for the underexposure. The shadows fall low in the toe (0.10 is represented by the dot a little above where Zone II exposure falls).

The tone reproduction curve illustrates the results. Even though the print produces the full tonal range, the distribution of tones is far from optimum. Tone for tone, everything is darker than what would be considered a faithful reproduction. The shadows fall darker than the original subject and there is a reasonably high degree of compression. The mid-tones show a good deal of expansion with the greatest degree falling around Zone V with about 30% over subject unity.

For comparison to a normal looking tone reproduction curve, there's an example earlier in the thread.

Steve, thanks for showing that. One thing I have noticed with extended development times for some films is a nasty 'hump' before the shoulder. The H&D portion of your reproduction series shows a mild version of this. I have found that when I print negatives like this, when the highlights are acceptable, the mid and low values are too dark in the print. Or visa-versa. So, to emphasize your point, if I just look at the gamma or say Zone VIII value, it don't tell me there is a 'hump.' The only way to know (prior to printing) is to see the H&D curve.

I know what you mean. I was thinking it might not be so much as a bump (as can be seen in HP5P with Xtol) as the point before a highlight falloff. Perhaps they are one and the same. Maybe it has to do with approaching D-Max with a particular film/developer/time combination. Thoughts?

Bumps in characteristic curves come from at least two sources.

Older emulsions were polydisperse, that is they had many grain sizes. The predominant grain(s) could cause a bump up or a sag down wherever they appeared in the speed / density relationship.

Modern emulsions are more monodisperse, or more nearly the same grain sizes. They are therefore blended to get long straight line response curves. If the blending is off, bumps can appear at the "join" point of any two of these emulsions. Typically, a blend has 3 emulsions or more and therefore you can see as many as 2 in a poor example of a 3 emulsion blend.

Using bad processing can bring out either type of problem in an otherwise good film. I have seen "bumpless" films released in one developer, demonstrate them in another developer due to development rate problems or a variety of other sensitivities.

PE

Photo Engineer said:

Bumps in characteristic curves come from at least two sources.

Older emulsions were polydisperse, that is they had many grain sizes. The predominant grain(s) could cause a bump up or a sag down wherever they appeared in the speed / density relationship.

Modern emulsions are more monodisperse, or more nearly the same grain sizes. They are therefore blended to get long straight line response curves. If the blending is off, bumps can appear at the "join" point of any two of these emulsions. Typically, a blend has 3 emulsions or more and therefore you can see as many as 2 in a poor example of a 3 emulsion blend.

Using bad processing can bring out either type of problem in an otherwise good film. I have seen "bumpless" films released in one developer, demonstrate them in another developer due to development rate problems or a variety of other sensitivities.

PE

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P.E.

I have a follow-up question if you don't mind. I've attached a curve family which, I believe, shows the phenomena ic-racer and I are referring. It's most noticeable with the 16 minute curve. Do you think this represents the conditions you've described?

Steve

Stephen Benskin said:

I've attached a curve family which, I believe, shows the phenomena ic-racer and I are referring.

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I find negatives developed to print on #3 paper are the best. You previously demonstrated that (at least with the materials you used) the best 'scene-to-photograph' tonal fit was for negatives processed to print on #2 paper. I have a hunch that, at least in my own rotary-processed negatives, the presence of this type of hump at higher gammas leads me to a preference for lower gammas. I think (no proof) that this phenomenon is more likely to occur with rotary processing.

Again, just a hunch, as I don't have curves from my darkroom for any non-rotary processed negatives to compare.

Steve;

In a word, yes! If you look at the shorter development times, you will see a small bump in the lower portion of the curve and later a bump at the high end. If the lower bump, earlier in development is not an artifact, then it is a manifestation of mismatched development in slow, medium and fast components (or small, medium and large grains). The coarser grains develop more slowly and give a downward dip in the curve early on, but as all grains begin kicking in, it smooths out and the bump then is manifest at the higher end.

At least, that is how I would tentatively read those curves with no other data and assuming no artifacts.

PE

I get humps like Stephen shows for both TMax 100 and Acros (moreso than TMX). I find it interesting that that flagship films of both Kodak and Fuji have this behaviour.

Kirk Keyes said:

I get humps like Stephen shows for both TMax 100 and Acros (moreso than TMX). I find it interesting that that flagship films of both Kodak and Fuji have this behaviour.

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I have another theory that all the of experiences with T-max since the 80's regarding 'blown highlights' etc are from the highlights falling on the hump, not the shoulder. I supect this is the case, since the tonal scale is so long. With the effects of flare, etc, the shoulder is never reached at the recommended EI. The shoulder is like fourteen stops out there.

One way I have dealt with this is to 'expose beyond the hump.' Or place the scene so the low zones are up above the toe and the hump is in the middle and the highlights fall past the hump. You have to give enough exposure, because just a little can just move the highlights to the apex of the hump and make things even harder to print.

I used to get these humps and bumps all of the time in experimental coatings when I made up the wrong blend of the emulsions. You have to keep at it.

And, since Kodak (IIRC -- it may have changed) releases film using a D-76 test, it might be that developers change the effects even on good film. I have seen it happen. Look at the curves reported on Kodak's web site.

PE

This is from Kodak's website. I believe I see a hump in the 12 minute curve.

Steve;

I'm not sure. May be, or may be the shoulder. I would have to run it more than one time and perhaps look at more of the curve. If it is a bump, it may be due to overdevelopment kinking up things. Offhand, IDK the suggested development time in D-76.

PE

ic-racer said:

I have another theory that all the of experiences with T-max since the 80's regarding 'blown highlights' etc are from the highlights falling on the hump, not the shoulder.

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If the highlights fall just above the hump, as they do in the two films I mentioned above, doesn't that "flatten" the highlights, and not "blow" them? The curve above the hump is of lower contrast than the curve below the highlights, so you have relatively higher contrast shadows and relatively lower contrast highlights.

Can somebody post one or more scans of a real char. curve that contains
what we all can agree on is a hump or bump not caused by developer interaction?

thanks...

Kirk Keyes said:

If the highlights fall just above the hump, as they do in the two films I mentioned above, doesn't that "flatten" the highlights, and not "blow" them? The curve above the hump is of lower contrast than the curve below the highlights, so you have relatively higher contrast shadows and relatively lower contrast highlights.

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Exactly. Depending on were the hump is. In my tests with T-max the hump was out around 10 stops. But many factors could change that in other's hands.

Ray Rogers said:

Can somebody post one or more scans of a real char. curve that contains
what we all can agree on is a hump or bump not caused by developer interaction?

thanks...

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Ray;

Since all films are developed in developer, how do we prove that the bump is caused or not caused by developer interaction. In fact, we can say with certainty that if the bump is there, a developer interaction of some sort caused it.

It takes a lot of coating or developer experimentation to prove things either way.

PE

Ray Rogers said:

Can somebody post one or more scans of a real char. curve that contains
what we all can agree on is a hump or bump not caused by developer interaction?

thanks...

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Here is one. Both are T-max 400. Top is rotary processed in T-max developer. Bottom is Rotary Processed in Rodinal 100:1. Hump in that case fell in the mid tones.

Here is another example. Both are "Copex-like" unmarked slow 35mm cine negative film. Both in Rodinal 100:1 rotary processed with different, perhaps unnusual, conditions (like multiple changes of dilute developer and empty tank periods, etc).

Ron- I was looking for official Kodak curves that have been published.
processing w/D-76 or D-72 @20 C.

ic-racer- Thanks... Could you specify/identify the bumps?

Everyone-
I don't have any intention to dwell here on this, but I would just like to hear some comment (from several sources even) about experimental error and why it is a non issue in these discussions...

Do we have a workng definition of what constitutes a "bump"
It appears to me to a single "hump" requires 5 slope changes.... but by how much?

Here is one dated 1988. So it is from a T-max 2 generations ago. The hump is way out just before the shoulder. You could describe it many ways. May not look like a hump to some. My interpretation was that if the highlights fell on the steep part (and they likely would) you may be hurting, but if you exposed MORE and got the highlights on the shoulder results may be improved. Just an observation many years ago, trying to 'salvage' overexposed images on T-max. I found out they printed pretty well!

I have actually never used the latest T-max (I switched to Ilford) so I'm curious as to what others have found.

Ray Rogers said:

Do we have a workng definition of what constitutes a "bump"
It appears to me to a single "hump" requires 5 slope changes.... but by how much?

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My personal working definition is anyplace between toe and shoulder where it bulges beyond the slope of the linear regression of the first 11 points 0.1 and greater. Thats just because when I graph my results I have the software show this line as a routine. I happened to then notice when the datapoints fall above the line.
If there is a 'correct' nomenclature maybe PE knows.

You can have a hump (or bump) and a sag. One goes up and one goes down. They are usually present in either a mismatched emulsion set or blend or a mismatched emulsion / developer combination. The developer includes agitation and dilution effects.

To be defined properly, the data should be reproduced at least twice in the same spot in the curve, as statistical fluctuations can cause this as well. The t-max 2 is the clearest case to me on the data available of a bad curve caused by some effect not revealed by the data. The one in post 99 above is the most vague along with 96. Usually bumps and sags don't reverse direction to that extent.

I would have to see repeats.

PE