Completion of density curves?

AbsurdePhoton

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Hi there,

the simulation of analog films I am writing uses film density curves, and I'm wondering about their representation.

Some curves are presented as a nice "S", while others often skip the shoulder part, and even some don't really show the entire toe part.

I read somewhere that the shoulder part is not very important, this is why it is not represented, but for me it still contains some information concerning the highlights. It is the same for the toe which is used for shadows.

My simulation uses D-min and D-max to use the full gray scale. So when I am using the curves to discretize them (i.e. save some curves coordinates in a file to simulate them later), should I complete what is missing ?
If I am not wrong, how much should I "add" to the curves, for the y axis (density)?

Here is an example with Fomapan 100, curve #2:


The red line would be the addition for the toe, and blue for the shoulder.

Does that make sense to you ?
 

xkaes

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You're correct that manufacturers don't give you the complete line(s) -- just what part they think is important. If you want a more complete line, you have options. Maybe there are expanded lines somewhere -- good luck with that.

My suggestion would be to create your own. That's much more work, but it more accurate because it uses your chemicals and gear instead of the manufacturer's lab.

Another is to use math to predict where the lines will go, but you have to have a way of getting all the data points on the line into the mathematical formulas -- and after that, there are many formulas that you need to choose from. They will all give you different results -- predictions of where the lines would go -- quadratic, cubic, etc.

So if you really, REALLY. REALLY have convinced yourself that you need the expanded lines, do your own tests.
 
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AbsurdePhoton

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Thanks for this. I already have the knowledge and the tools to perform basic maths. For the "real" thing, I don't have the equipment.

It is just that I have to decide how much should I go for the toe and shoulder on the density axis.
For the toe : in the case above it is not difficult to complete the line, the lowest curve (1) gives a hint to what D-min should be. But if I had only say the 3rd curve just to decide, it would be more difficult.
For the shoulder: surely the manufacturers cut the curve just at the end of the straight line, so there's no way to really know how much higher the curve should go?

I can also do stats, I already have entered many B&W density curves.

But if other people have hints to help me decide...
 

ic-racer

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It is usually not practical to measure the shouder, but it indeed is important.

The shoulder is represented by the faint and clear portions of the common 21 step wedge. The exposure of the film in that area can't increase without making the sensitometer light 20 to 100 times brighter to obtain the data to graph the shoulder.

Making the sensitometer light 20 to 100 times brighter, while maintaining exposure time and color temperature, is not usually practical. Thus, the shoulder of the curve is usually cut off as there is insufficient data.

To fit the curve on a control strip, most sensitometers have a way of adjusting the exposure for the ISO/ASA range in which one has an interest in graphing.
 
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koraks

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AbsurdePhoton said:
I read somewhere that the shoulder part is not very important, this is why it is not represented, but for me it still contains some information concerning the highlights.
Click to expand...

YMMV. Whether or not it's relevant depends on the application. I do a lot of carbon transfer printing and I develop to densities of 2.6logD and beyond. That's shoulder territory for most films. However, that's an extreme example; for silver gelatin, you're virtually never working in that area (or at least, you shouldn't). Even for an alt. process it's kind of extreme.

So "for all intents and purposes", I wouldn't feel too bad about chopping off the extreme shoulder. Yes, something happens there, but it's kind of extreme. Think also how much data it costs to represent this area; what if half your bit-depth is 'wasted' on densities that are virtually never used?

Also, what happens in the extremes can be...extreme. Consider that there's life to the right of the shoulder, too. You'll see the curve dipping again after it has peaked. The question becomes how far you want to take it.
 

xkaes

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koraks said:
Consider that there's life to the right of the shoulder, too. You'll see the curve dipping again after it has peaked.
Click to expand...

And no mathematical formula can predict that physical, chemical effect.
 

Bill Burk

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I wouldn’t trust curve fitting to extrapolate the toe and shoulder.

The shoulder information may extrapolate higher than it really is. You can quickly get a practical max density from anyone who can read the density of the section of film that was fully exposed while loading the camera.

The toe shapes also vary from an abrupt drop in density as in TMAX100 to a smooth curve as in Tri-X.

But you can’t really guess what changes in density occur between 0.15 log E exposure differences.

Maybe it’s time to use start using that glass wedge I found.
 

Bill Burk

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As exposure increases to a thousands of times greater exposure than normal, there is often reversal (and sometimes a cycle back and forth of reversal and re-reversal).

From Mees Theory of the Photographic Process. (that you can find in its entirety for free online)
 
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koraks

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Bill Burk said:
But couldn’t physical analysis predict it?
Click to expand...

I'm with @xkaes on this:
xkaes said:
Dunno.
Click to expand...

I assume that quite a bit of research was done to understand the effects and on that basis, I imagine it's to an extent possible to model it. But looking at the family of curves @Bill Burk has posted above makes it clear enough for me that it's probably darn complex.
 

Bill Burk

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Another stylized graph illustrating reversal and re-reversal. This from Todd-Zakia Photographic Sensitometry

Some film or paper is designed specifically to do this on purpose, for example photobooth paper where you sit still where bright light hit you and your friend in the face.

 
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AbsurdePhoton

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Solarization can be simulated on my system, I just have to enter the curve(s) coordinates and try them. The graph from Mees' book is perfect for that

All I need for the simulation is the spectral sensitivity chart (which can be set as neutral) and the density curve of a film - the MTF curve will also be simulated if provided, but this is a bonus.
Then all I have to do is load an image, choose the simulated film, adjust the exposure, and "take the photo" from a digital image/photo.

In this precise case, using a neutral spectral chart and Mee's curves will give a good idea of what's going with different curves at different exposures. I'll try it!

koraks said:
Think also how much data it costs to represent this area; what if half your bit-depth is 'wasted' on densities that are virtually never used?
Click to expand...
It won't be the case, because the shoulder in terms of density range doesn't represent much. and I am using a color space (OKHSL, derived from OKLAB) that simulates well a "real" grayscale.
Anyway, I'm already loosing some of the densities below D-min, but defining the shoulder will in fact extend the density range, so a little more in the highlights is welcome and will prevent a little more some banding in large zones of the photo in the extreme values.
 

Mr Bill

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DREW WILEY

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Yeah, truncated curves can be disappointing; but they're printed so small on the official tech sheets already that what is regarded as the most important portion would be even harder to read than now on a graph of the same allotted size. It really helps to make your own densitometer plots on a large sheet of paper or full computer screen. I still use the old translucent Kodak curve plotting graph paper.

And of course, curve shape can change when the developer regimen itself changes. Even with the same developer, it's better to think in terms of a "family of curves" rather than just a single profile.

Every portion of the curve has real-world printing and reproduction connotations - the toe, the straight line portion, and the shoulder. Sometimes at used book stores you can find old Kodak black and white film guidebooks. The later ones are most likely to show more recent films; but in general, they have an introductory section explaining how to read curves, and the differing practical implications of short-toed, long straight line films, versus long toe films with an upswept curve, versus films with a pronounced S-curve.
 

Romanko

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AbsurdePhoton said:
Then all I have to do is load an image, choose the simulated film, adjust the exposure, and "take the photo" from a digital image/photo.
Click to expand...
You should consider the dynamic range of digital cameras. Unless you are using some specialized sensors I doubt that you will need to know both the toe and the shoulder part of the film curve to do the simulation, even with older films.

Your projects sounds very interesting. Could you please share a bit more details on the system you are working on?
 
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DREW WILEY

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But where that Dmin actually is depends on the specific film and how you develop it. Zone System devotees sometimes tell you to place your lowest textural value on Zone 3 = 2 stops below mid-tone, or maybe 3 stops below. But with TMax films I routinely use the equivalent or Zone 1 due to its steeper drop down into the toe; and with old 200 soeed "straight line" films, even down to Zone 0 (five stops below). That requires careful metering, but the reward is a lot more linear real estate to work with in high contrast lighting situations before the curve starts shouldering off at the top.

Digital imagery is a whole different ballgame.

Mr Bill - there were certain changes between the early versions of both TMax 100 and 400 and the current versions, especially with respect to shoulder characteristics. And D76 never was an ideal developer in term of toe linearity. That was more of a marketing and advertising ploy - their most popular traditional developer used in conjunction with this new line of films.
 
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AbsurdePhoton

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Thanks to you all, what you wrote made me rethink the process of converting densities to grayscale.
In fact I had overlooked the transmittance factor.
What I did before was normalizing the HD curve on the density axis to [0..1], for negative films 0 being black and 1 pure white. It was a shortcut that seemed to work, I got pleasant results.
But... there was something wrong, that's why I opened this thread, and why I was using D-min and D-max. And it was a mistake.

Returning to fundamentals, I read again this page: http://ljoyeux.free.fr/univ-lr/public_html/sensit.html
And this image caught my eye:

I realized that density is NOT a finite scale. What I did then was computing the transmittance, then converting it to a [0..1] value: gray = log10( 1 / transmittance )

And it works! No need to normalize the density axis anymore, or complete the curves, I can now use the direct values from the graphs.

It solved the grayscale problem for b&w films simulation, and also my color films simulation that was a bit off. Woo-hoo!

Now I have to try the solarization case, but I know it will work as is. Stay tuned.
 
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AbsurdePhoton

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Solarization simulation test ! I saved the coordinates of the curve from Mee's book, used a flat spectral chart.

Here is the test image (her name is Typhaine), with a nice palette for reference:


This is what the simulated shot looks like with Mee's book's curve (ref exposure = 0)


+1 exposure = burned


+6 exposure = solarized


This is almost a negative! I reversed it in GIMP and it looks like a dark version of the "normal" processed photo.
+6 exposure is a LOT, the interface of my program was not ready for this, so I had to tweak it a little temporarily.
Blacks stayed white because they didn't get past the drop.

What do you think?
 

koraks

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Pretty neat!
I'm surprised that your +1 comes out so light - but then again, let's not forget you're starting with a high-gamma digital file, which is a bit like working with a slide instead of a negative.
The plain/straight B&W conversion is really pretty good although I wonder if the toe behavior is maybe a bit too abrupt. It feels like film being underexposed by 1-1.5 stops or so.
 
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AbsurdePhoton

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You're right!
In my program the exposure numbers are shifted to relative representation, and spectral charts are normalized, and on Mee's chart the curves starts at a negative number.
All in all in this precise case, I think you are right the 1st simulated photo base exposure must be around 1. The internal numbers used in my simulation are indeed weird.
I underexposed it a bit for the blacks to stay white when the solarization strikes, plus I added a little more exposure time with base exposure = 0 to boost even more the total exposure!


Here is the photo processed at exposure = 0.5, no added exposure time:

(so you can't compare, it was just to show how the simulation behaves)
 
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alanrockwood

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Let me ask a question first. Do you have a densitometer?
 
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