Probably a dumb question about graphs

michael_r said:

On the x-axis each 0.3 log exposure is 1 stop.

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Is it? I've never found any way to use these graphs in practice, but I always assumed that the x-axis was log to base 2, so that each whole unit was double the exposure, which would seem sensible. I realise now that it must be base 10 because a 4 stop range would be absurd.

But whether log10 or log2, I still have a problem understanding what the equally-spaced half-units actually mean. How much more exposure is 2.5 compared with 2.0? My maths isn't up to it. Does anyone have the definitive answer?

radiant said:

Nothing else. It is not related to anything else.

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That is the problem with your approach. If I tell you something is 1.2 meters long, anyone in the world will know how long it is. If I tell you it it's twice as long, you'll need to ask "twice as long as what?" Without a reference, it's useless. Think of density as measuring in meters, it's a known quantity. A stop is always relative to something else, which then needs to be defined in order to have a useful scale. Density is a unit in it's own right, a stop isn't.

Craig said:

That is the problem with your approach. If I tell you something is 1.2 meters long, anyone in the world will know how long it is. If I tell you it it's twice as long, you'll need to ask "twice as long as what?" Without a reference, it's useless. Think of density as measuring in meters, it's a known quantity. A stop is always relative to something else, which then needs to be defined in order to have a useful scale. Density is a unit in it's own right, a stop isn't.

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Ilford's relative x-axis seems reasonable to me. It's relative to the point of inflexion where increasing exposure leads to a detectable change in film density above film-base+fog. In other words, increase or decrease in image-forming exposure.

Since we usually increase exposure by doubling it, plotting curves against log2(exposure) would also make sense to me.

Craig said:

That is the problem with your approach. If I tell you something is 1.2 meters long, anyone in the world will know how long it is. If I tell you it it's twice as long, you'll need to ask "twice as long as what?" Without a reference, it's useless. Think of density as measuring in meters, it's a known quantity. A stop is always relative to something else, which then needs to be defined in order to have a useful scale. Density is a unit in it's own right, a stop isn't.

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Well, what does density of 1.23 mean then?

radiant said:

Well, what does density of 1.23 mean then?

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Density = log10(Opacity)
Opacity = 1/T
Transmittance = Transmitted light / Incident light


Unless you mean Density range.

Actually, it's not so much about Density as it is about using logs. They work for Density, exposure, and Luminance Range.

For instance the LER of a grade 2 paper is around 1.05. LER is the log exposure of the paper from 0.04 over paper base plus fog to 90% of D-max. The statistically average scene is 2.20. You have the input of the 2.20 scene (minus flare) onto the negative and the output resulting Density range needs to be 1.05. The film average gradient can be determined using rise over run from the output / input numbers.

michael_r said:

Each 0.3 increment on the log H (log exposure) axis is one stop (ie a doubling of exposure). An interval of 1.0 is a 10x increase in exposure.

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Thank you!

radiant said:

YIf I look from X-axis that linear part of the curve is for example 10 stops and look where this sets into Y-axis; I see that it translates to density range of for example 2.0 in logarithmic scale, I know that it just fits the paper density range at grade 2?

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I've been a little under the weather this week. I knew something was a bit off this this statement. I just had to wait to long enough for my brain to start to work again. Don't get me wrong, asking questions and challenging ideas is the way to learn. Keep it up.

Here's the thing. A grade two paper does have a density range of around 2.0. But this is the output. The log exposure range (input from the negative) is a lot smaller. The idea is that once you know the printing conditions (enlarger, paper), you can adjust any scene through development of the negative to fit.

As I wrote earlier, the paper LER is determined by the log-H range between 90% of paper Dmax and 0.04 about paper base plus fog. Obviously, this doesn't cover the full range of the paper. The reason it is used is because they are two points of density that are distinguishable from Dmin and Dmax.



The two LER points is where S and H in the example below fall. A statistically average scene has a Subject Luminance Range of 2.20 This is what Normal development is based on. Like the paper, it measures what is considered to be the important points where tonal separation is generally desired. But it doesn't represent the full range of a scene as a scene frequently contains specular highlights and what the example calls "Cavity shadows." I usually refer to them as accent blacks. These will reach into Dmin and Dmax of the paper but are not part of determining the paper LER or Negative Density Range (NDR).



To determine the gradient of the developed film, take the Paper LER and divide by the Subject Luminance range - Flare.

1.05 / (2.20 - 0.40) = 0.58

Develop the film to an average gradient of 0.58 and you will get a negative with a negative density range of 1.05, excluding the density from the accent black and specular highlight. Side note: As the end results of photography are subjective, the LER isn't a hard and fast rule. It is simply a range that will produce acceptable prints to a higher frequency.

So you start with a scene having 7 1/3 stops and reduce it down to a negative with a density range of just over 3 1/3 stops if you want to measure Density in stops. This can get confusing using stops for Density.

Stephen Benskin said:

... the paper LER is determined by the log-H range between 90% of paper Dmax and 0.04 about paper base plus fog. Obviously, this doesn't cover the full range of the paper. The reason it is used is because they are two points of density that are distinguishable from Dmin and Dmax. ...

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As part of my LED controller project, I've been measuring the density for Zone II, which is the highest density at which texture is visible (according to AA). Ralph Lambrecht uses a density of 1.89 as this point, which is 90% of Dmax. Dmax is 2.1 for typical paper. But in my experiments, I have found that under EV 7 lighting (at ISO 100), that point is more like 1.80. That is the first density which is easily distinguishable from Dmax when I am placing a Dmax patch next to the test patch. That definition is not the same as "texture", which seems to me to be an imprecise definition. But perhaps texture is easier to distinguish than Dmax. To readily distinguish a Zone II patch from Dmax, I find the print must be illuminated at EV 9 or 10. In fact, I'm finding that this might be a good definition of Zone II: "The lightest tone that is *not* distinguishable from Dmax under EV 8 lighting."
Do you have any comments about how to determine Zone II (and the corresponding Zone VIII)?

Thanks, and I hope you feel better.

Mark Overton

Stephen Benskin said:

I've been a little under the weather this week. I knew something was a bit off this this statement. I just had to wait to long enough for my brain to start to work again. Don't get me wrong, asking questions and challenging ideas is the way to learn. Keep it up.

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Hope you are fine. But no rush here. Film stays the same even a bit of wait..

First of all thanks again for good detailed explanation. I think that is a *really* good explanation of the film->paper transfer and why exposing/developing to certain standards is a good idea. I would add to this that personal preferences should be considered by everyone; if one likes contrasty prints, then develop the film accordingly. I think this is not underlined well enough. But that is another story.

And it is good to understand my questioning is out of positive curiosity and to have some kind of response to my never ending questions. So thanks for listening so far Maybe I'm a bit stubborn but I try to digest everything with neutral attitude.

I think we are talking still about a bit different things; the traditional film->paper characteristic fitting should be done as it has been done. Reason is that you don't need stops for that - and traditional ways are better as these formulas and methods have been used for ages. I think we could use stops for this as it is just linear conversion, maybe I try it here (basically what you wrote in last sentence):

LER of paper : 3.5 stops
Average scene: 7.3 stops
Flare: 1.3 stops
So: 3.5 / (7.3 - 1.3) = 0.58

How I read this is:
- LER of paper.. ok pretty low actually, I have to take this into account. I need to make sure my negative has enough contrast. Low contrast scenes might be just 2 stops.
- Average scene .. nice, fits to any negative B&W film because I know how many stops my film can take.
- Flare: quite a huge decrease in the contrast actually, I haven't never realized it is so big. Damn flare, do not eat my contrast!
- Both together: hmm, the translation from film->paper needs some squeezing.

But the result (0.58) is of course out of this discussion, because my first point was not to change this calculation using stops at all. My point is just to make the characteristic graphs more user friendly because I assume stops are more understandable. Maybe why we are talking a bit different things is that typically characteristic curves are used exactly to purpose you are describing here. My criticism is more towards film manufacturer curves which are hard to read because of the units used. "Average" consumer do not understand those but maybe they could understand better if everything was presented in stops.

I probably also understand why you don't like the idea of showing density in stops. It might be just me but I remember these numbers in stops; to print at normal grade, the information which I want to print must be inside 3 stops of density. But I really start to understand why you don't want to use stops as unit for density, because it is still a bit irrational, as density in log is too. It really doesn't "mean" anything, it is just a calculation unit. Of course one can remember that normal grade print is about 1 range in density. But you could say it is 3 stops too. You need to measure the density anyways and I'm doing it in stops, but commonly it is measured in log density.

Maybe I can accept (big grin here) density in log, but for sure it could help readability of these graphs if X-axis was in stops. Or both?

Radiant,

Using stops is just adding a level of work that you don't need. All the conversion and rounding can also introduce error.

As for the negative density range, while it might be DΔ 1.05, it still represents a 7 1/3 stop Luminance range.

In my opinion, gradient is the key.

If you work out what Kodak considers Normal development (it actually fluctuates between 0.56 and 0.58) is only possible when flare is factored in. Basically Normal development is processing for an effective 6 1/3 stop Luminance range and not the statistical 7 1/3 stops.

The problem with published charts is that they aren't detailed enough to do any real work with. Take a look at the graph from the above LER example. You can determine the density value at any point on the graph. This style of graph comes from the type used by Kodak techs for hand drawn curves. The moral of the story, create you own curves.

I find guides to be an effective way to convey how the process modifies the original scene. Here is a two quad without flare. A four quad will include a curve that compares the original scene with the print. Adding quads can also include anything else you want, but mostly they include viewing conditions.



Two Quad with flare.

radiant said:

I would add to this that personal preferences should be considered by everyone; if one likes contrasty prints, then develop the film accordingly. I think this is not underlined well enough.

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I certainly hope I'm not giving the impression that all these technical concepts interferes with creativity. Just the opposite. They are tools to better achieve your ideas.

Stephen Benskin said:

I certainly hope I'm not giving the impression that all these technical concepts interferes with creativity. Just the opposite. They are tools to better achieve your ideas.

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That is so right and I understand it of course.

albada said:

As part of my LED controller project, I've been measuring the density for Zone II, which is the highest density at which texture is visible (according to AA). Ralph Lambrecht uses a density of 1.89 as this point, which is 90% of Dmax. Dmax is 2.1 for typical paper. But in my experiments, I have found that under EV 7 lighting (at ISO 100), that point is more like 1.80. That is the first density which is easily distinguishable from Dmax when I am placing a Dmax patch next to the test patch. That definition is not the same as "texture", which seems to me to be an imprecise definition. But perhaps texture is easier to distinguish than Dmax. To readily distinguish a Zone II patch from Dmax, I find the print must be illuminated at EV 9 or 10. In fact, I'm finding that this might be a good definition of Zone II: "The lightest tone that is *not* distinguishable from Dmax under EV 8 lighting."
Do you have any comments about how to determine Zone II (and the corresponding Zone VIII)?

Thanks, and I hope you feel better.

Mark Overton

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Hi Mark,

You're noticing why it's impossible to have absolutes in photography and something very few people take into consideration: psychophysics. Munsell's grey scale isn't about equally space tonal values between black and white, but about visually equally spaced values. Studies such as Munsell's or the Committee of Colorometry's 10 plus year study of color requires laborious controls in order to obtain accurate results such as how long does it take the eye to adjust to a light level, or how does the surrounding areas influence the perception of the target. You have already identify some of these.

A print of an exterior scene not only doesn't have the same range of the original subject, but the illuminance of the print is frequently many times less that the value of illuminance striking the original subject. Yet we still perceive it as a exterior lit scene. What is the point where the eye can no longer compensate?

Along with the level of illuminance in which you are viewing the test patches, a possible influence is with the surround. Simultaneous contrast , local inhibition, and adaptation can change how tones appear. What is the tone of the surface you are viewing the patches on. Here is an example of simultaneous contrast. The background is a gradient but the strip is a solid tonal value.



You place a value on Zone VII and it will look lighter if the surrounding tones are darker and darker if the surrounding tones are lighter.

Graph of dark and light surround.



And Inhibition and Adaptation. The value of the tones that surround and by how much.



And now what print densities should Zone I, II, and VIII be. There isn't a set value. The type of paper (glossy or matte) and the photographic process used make a difference. Flare and the film curve also add to the mix. But keeping with a nice silver print, you can generally consider 90% of Dmax as Zone I and 0.04 over paper base plus fog as Zone VIII. It's the paper LER equation.

The placement of Zone II is dependent on the degree of camera flare, and the film and paper curve. The higher Zones are less influenced by flare and more by the film and paper curves. Here are Jack Holm's "Preferred" Zone value. Also something to consider, you can only see texture when it's a range and not a single tonal value.



Here is an example of how the Zones will tend to fall. Notice how the difference between Zone I and II is not as large in practice as is preferred.



This example places the Zones in contact with a three quadrant Reproduction Diagram



I hope my brief comments and over compensation with graphs can help to point you in the right direction.

Stephen

This might help some. This is the chart from Jack Holm's paper "Exposure Speed Relations and Tone Reproduction". For some reason Holm uses 128% for highlight Reflectance instead of 100% Reflectance. This might skew some of the values.

Where I see an important distinction is in Zone VIII not falling on 0.04 above paper base plus fog. 0.04 might be too light for a Zone VIII, but the difference of 1/3 stop range between the Zone System and statistically average ranges can account for a slightly darker value than 0.04 for the statistically average placement.

While you're at it, take a look at the Scene Tone notes for Zone 4.5 and 5.

Wow for the first reply. And another wow for the second. I read your responses closely enough to understand them. In fact, I downloaded Jack Holm's paper and read parts of it. Holm's work is impressive, and as you hinted, texture/detail has differing contrasts, such as shade-lit versus side-lit by sun, so using it as a definition of a zone is inaccurate.
Also, Holm's paper referred to (and footnoted) Ansel Adams' Zone System, and then he (Holm) proceeded to change the definitions of the zones without telling anyone. That explains the significantly different preferred zone-densities.
The image below shows another observation I made:



The left group of bands are the densities given in Way Beyond Monochrome 2nd ed (Ralph Lambrecht), which are very close to the measurements you provided. The right group is perceptually uniform. The comparison shows that AA's zones are compressed into the left- and right- ends, giving fine control over shadows and highlights, and coarse control over midtones. I can think of two reasons for defining zones in this manner:

1. Accidental: These densities resulted from the long toes and shoulders of the media AA was using in the 1930's and 1940's.
2. Deliberate: Highlights and shadows are more important to control accurately than midtones, so compressing them provides sufficient control over them.

I defined a zone I call "apparent black" as follows: "The lightest dark tone that is indistinguishable from Dmax when viewed under EV 7 light." On ordinary paper, this definition results in a density of about 1.90, which coincidentally is the same as AA's zone 2, which is also the same as point "S" in the ISO standard for determining exposure-range (LER). My LED controller controls contrast based on LER (in units of stops), so I want a zone at point "T" also, which is AA's zone 8. So I decided to stay with AA's zones and Lambrecht's published densities for them, resulting in this table:

Zone	Density	My Remarks
1	2.04	Deeper black supresses most texture/detail.
2	1.89	Apparent black. Threshold of texture. Point "S".
3	1.61	Very dark.
4	1.19	Dark.
5	0.75	18% middle gray.
6	0.40	Light.
7	0.19	Very light.
8	0.09	Threshold of texture. Point "T".
9	0.05	Paper-white threshold. Any exposure-boost prints a tone.

I changed zone 9 slightly to be "paper-white threshold" instead of "hint of tone" because this definition is precise, so I can easily calibrate the controller for this zone.

Anyway, you can see that I've synthesized plenty of information about zones and the entire three-quadrant process you showed, went full circle, and ended up with AA's zones.

Mark Overton

The compressed scale looks like what I use on my Zone System stickers for light meters. I make them up from actual test negatives printed on my enlarger. For me these show “WYSIWYG” (what you see is what you get).

I am often surprised what the needle says I would get on my print, mostly how quickly a scene in real life drops to shades of black.

Skies getting blown out are not as surprising.

Mark,

A good argument can probably be made for a Zone scale consisting of visually uniform steps. It could be used as a reference guide for where the tonal values fall. Anyone who is familiar with tone reproduction theory is aware the level of precision the Zone System suggests isn't possible. Flare makes precise control impossible. A good amount of control is achievable but how and where the shadows fall on the film plane has too many variables to accurately predict. The best one can do is accept a certain range of variance. With printing tools and techniques, the placement of the highlights and shadows can be adjusted, but only a relative relationship between the negative and paper is practical.

Good thing photography doesn’t really have a definitive link between the negative density range and paper log exposure range. Paper LER will tend to produce acceptable results in a large percentage of situations. The reason why you don’t have to be a scientist to do photography and why so many “systems” work is because there isn’t a hard and fast rule connecting the physical properties of the photographic materials with perception and the further the print moves away from an accurate depiction of the subject, the interrelationship is further reduced.

This example shows a paper curve with the negative density range from images judged as high quality superimposed.over it. We don’t know the subject matter or intent of the photograph, but in many cases, the negative density range exceeds or is less than the paper LER.



There are two basic rules that tend to accurately apply to quality photographs. They are lighter than the original. If the density range of the print matched the original scene, it would universally appear dark. The second is that viewers can accept compression of the highlights and shadows, but usually require the mid-tones to have a higher gradient that the original subject. Usually above 1.08.

Here is a four quadrant reproduction diagram. The fourth quadrant compares the original subject to the print creating the reproduction curve. Many reproduction curves have a reference curve that depicts a perfect 1:1 reproduction. Truthfully, I don’t believe Adams knew this let alone incorporated it into his scale.



Finally, some fun. Your scale examples against a white and a gray background.



Stephen

I like Bill Burk's idea of taping the zones to the meter dial. Clever.

Four quadrants: I thought of a fifth quadrant, which would make it five pentants? It is flare inside and outside the enlarger. Inside the enlarger, flare comes from the bellows, surrounding metal, and lens. Outside, it comes from light that reflected off the paper and then reflected off something else and back onto the paper. Avoiding such flare is why some folks surround enlargers with black curtains. Anyway, enlarger flare will have a curve similar to camera flare, but affecting the highlights by effectively flashing the paper a little.

The graph of first-choice prints has many lines extending to the left of the paper-curve. I'll guess that some of those white areas were burned in the prints, moving them rightward. Likewise, some of the dark lines on the right were probably dodged, moving them leftward. These modifications make me suspect that negative density-range is not a good measure of the light-range that struck the paper. Nonetheless, I suspect the conclusions won't change: People like prints that are a bit lighter with high midtone contrast.

Mark Overton

Thanks Mark, I think it’s a hybrid idea. Obviously based on Minor White’s Zone Sticker, but I got the idea of using real print tones from Phil Davis’ “Wonder Wheel” in an early Beyond the Zone System.

I don’t think when they did the studies they dodged or burned prints. The skies are probably just blank white in those cases.

albada said:

I like Bill Burk's idea of taping the zones to the meter dial. Clever.

Four quadrants: I thought of a fifth quadrant, which would make it five pentants? It is flare inside and outside the enlarger. Inside the enlarger, flare comes from the bellows, surrounding metal, and lens. Outside, it comes from light that reflected off the paper and then reflected off something else and back onto the paper. Avoiding such flare is why some folks surround enlargers with black curtains. Anyway, enlarger flare will have a curve similar to camera flare, but affecting the highlights by effectively flashing the paper a little.

The graph of first-choice prints has many lines extending to the left of the paper-curve. I'll guess that some of those white areas were burned in the prints, moving them rightward. Likewise, some of the dark lines on the right were probably dodged, moving them leftward. These modifications make me suspect that negative density-range is not a good measure of the light-range that struck the paper. Nonetheless, I suspect the conclusions won't change: People like prints that are a bit lighter with high midtone contrast.

Mark Overton

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The number of quadrants can vary and easily increase depending on the aspects covered and what is integrated into a single quadrant or separated out into multiples. You may notice in the paper information section it refers to printing with a diffusion enlarger. The step tablet was enlarged and not contacted, so I was able to incorporate flare in the printing phase without an increase in quadrants. And since it was my enlarger under my printing conditions, it tended to apply to the results I would be expecting. With the Ilford papers, they are either from the enlarges where I used to work or from Herb Ritt's darkroom from when I consulting with his team. The more tests, the more examples available that fit more situations.



The Theory of the Photographic Process, 3rd Edition has examples of fine detail reproduction, effects of masking, and viewing conditions. It can get very granular and beyond my understanding.



Jones admits in a paper that there is no absolute correlation. We are ultimately dealing with a subjective experience after all. Even though matching the negative DR to the paper LER isn’t a perfect criterion, it is good enough to produce quality images in most situations, or at least with only a slight contrast adjustment. Jones made a large number of prints on different grades and exposures from each of around 170 different negatives (most are from the First Excellent Print Test). They were judged for quality from best to worst. The test wasn’t about creating specific criteria for paper grades, but to determine the best approach to objectively determine sensitometrically the paper grade that will consistently produce high quality prints. Jones concluded, “because of the influence of the brightness distribution and subject matter in the scenes photographed, an accurate prediction cannot always be made of the exposure scale (Log Exposure Range) of the paper which will give a first-choice print from a negative of known density scale (Density Range)… But what other course is there to follow? Either we must make the best of a somewhat imperfect relationship or face the prospect of having no criterion whatever for choosing the paper contrast grade.”

Jones also found “for the soft papers, the density scales of the negative (DR) should in most cases exceed the sensitometric exposure scale of the paper (LER), whereas, for the hard papers, the density scales of the negatives should in most cases be less than the sensitometric exposure scale of the paper (LER).”

Jones, L.A., and Nelson, C.N., Control of Photographic Printing: Improvement in Terminology and Further Analysis of Results, Journal of the Optical Society of America, V. 38, No. 11, 1948.

These two realizations are significant when considering the expectations and practicality of placing Zones. The thinking needs to be more in terms of tendencies and guidelines.