Zone System Question - Help Me Out

[Michael Kadillak]

I am interested in determining if there is a mathematical correlation to determine the correct reflection densities of a nine zone range with Zone V (18% grey card) as middle grey. As a point of reference, I am getting a reflection density of 0.81 for Zone V.

My reference department is lacking in this department. My thanks in advance.

[Witold Grabiec]

Zone to zone is 0.3 density difference. I always use transmission densities of the negative to determine what's right or wrong with assumtpion that a density of 0.1 above film base + fog is Zone I. The above is based on the fact that in order to have ANY texture recorded in Zone I you must expose it to just above what film base + fog would be, which varies from film to film. Then a 0.3 difference doubles the exposue or takes you to the next zone up.

That is of course a starting point which you can then alter to your liking.

From above, if you add density of the film base + fog to your gray card reflection of 0.81 you should be getting a fairly close figure to what you should expect from a Zone V transimssion density of your negative. Ensure that your instruments are well calibrated, or at least have a consistent correction factor, so your readings are something you can trust.

[Donald Miller]

As I understand your question you are wanting to work up a correlation based on reflection densities using Zone V reflectance as the benchmark. I would need to answer no unless you want this for only a given paper/grade. I suppose that one could come up with the curve for a given paper and contrast grade. To do that I would contact print a calibrated step tablet on the film that I was using. I would then take that film negative and contact print it on the paper that I was using and read the reflection densities of each step. This would take into account the film characteristic curve and also the papers characteristic curve. Zone transmission densities are not linear .30 as they are represented on film. This belief disregards the characteristic curve of the film.

[Witold Grabiec]

Transimission densities are represented by logarithmic values, not linear. If the question here is with regard to getting a zone 5 in print FROM film then film density to get that value will have to be taken into account anyway.

Above values I've given come from well regarded publications.

[Joe Smigiel]

I would think there is a mathematical function that describes this, but I'm not sure where you'd find the information. I suspect searching/googling for psychophysiologic tests might turn up the answer somewhere. What you are seeking sounds like data on psychophysical response of the human visual system. You have a reference point, 18% gray reflectance, that is producing a subjective interpretation of "middle gray" halfway between black and white. That's quite a bit different than the visual effect a 50% gray produces.

If you could find or produce the tones that represent the various tones you interpret to be the different zones and measure them yourself, I would think that might provide more useful information to you than some table of numbers measured on a different material and application. In other words, a 36% gray might not be Zone VI for you but if you had a printed tone on the paper you normally use that gave you your own subjective Zone VI value, the reflection of that sample might be better applied to your own photographic practice.

Having speculated above I can also relate some reflection data from the gray scales patches in an old 1975 Kodak Professional Dataguide. They aren't "Zones", but are close:

step , Reflection , R Density , subject:

1, 84%, .08, whitest snow & clouds;

2, 42%, .38, white sand/white paint;

3, 21% , .68, Caucasian skin/light grass & foliage/deep sky/wet white sand/weathered wood;

(gray card, .78, 18%, gray side of a Kodak gray card);

4, 10.5%, .98, dark skin/foliage/earth/dark tree trunks;

5, 5.2%, 1.28, black fresh turned earth/dark clothes;

6, 2.6%, 1.58 most black objects;

7, 1.3%, 1.88 blackest objects;

8, 0.6%, 2.18, black velvet;



Hope this is what you are looking for,

Joe

[D Poinsett]

There is a mathematical basis but you will have to define what the zones mean and have reflection density values for the black and white end tones in the scale. Then simple proportion determines the reflection density of any zone. If in your example we presume that Zone V in the print is the mid-point tone between black and white, then the reflection density would be:

Zone V Density = Dlow + 0.5 * Dfullrange

where
Dlow = Dwhite + 0.04
Dhigh = 0.9 * Dmax
Dfullrange = Dhigh - Dlow

where
Dwhite = reflection density of unexposed developed paper
Dmax = reflection density of completely exposed developed paper

Using the typical values for the above variables and your 0.81 figure, we could work backwards and say that the Dfullrange would be 1.40 and that Dmax is 1.67.

0.81 - 0.11 = 0.70 (Dlow)
0.70 * 2 = 1.40 (Dfullrange)
(1.40 + 0.11) / 0.9 = 1.67 (Dmax)

A Dmax of 1.67 and Dfullrange of 1.40 for photographic paper is a bit weak. It sounds more like the values for an ink print.

If your Zone V is something other than the midpoint, use simple proportion to determine its place on the Dfullrange scale. (Notice the 0.5 multiplier in the first formula. It could also be 0.4, 0.6, etc. for other proportions.)

Dlow and Dhigh definitions are based on an ANSI standard test method. Using simple proportion presumes a linear relationship on a log-log scale between density and zone. This method is commonly accepted but other schemes using a non-linear relationship between density and zone could also be used.

[D Poinsett]

oops...

0.81 - 0.11(Dlow) = 0.70 (midpoint of Dfullrange)

[Witold Grabiec]

I have to say that 0.04 of density increase is not enough though. This is a kind of texture that may be noticeable under a magnifier yet, we're looking for a visible details with a naked eye. As Ansel and others suggested, the 0.1 above film base + fog is I think a more realistic figure.

While densities are given in logarithmic values, the film or paper response curve is mostly a straight line. It bends below zone 3 and above zone 7 (an approximation). A simple linear ratio should work just fine.

Again, I would work on the negatives to get the zones-by-densities first. Then do the printing and alter my zone definitions as needed.

I usually see little value in extensive testing of paper as the image itself may require a different approach and I may want to depress some detail in shadows or highlights. However, I do believe in having the detail available to me at time of printing. It is thus more important to test the film and what I need to do to expose it correctly.

[D Poinsett]

Mr. Grabiec, I could be mistaken but I believe that Mr. Kadillak is asking about reflection density of the paper rather than transmission denisty of film. Log 0.04 above white (b+f) is a reflection value used in the ANSI and ISO standards for determining the white end of the density range of paper. Did I misunderstand the question?

[Witold Grabiec]

I think you're fine Mr. Poinsett. And you're right about that other end of it. As I mentioned in my post the negative is the key to what I believe in, but I'm quite confident that a 0.04 density difference from a WHITE paper base, will be a hard sell for viewers. I may be wrong though.

I realize I may not have been unswering the actual question, yet there is always a correlation between the two, to me anyway.

[D Poinsett]

The log 0.04 value above paper white was chosen because it is close to the limit at which we can see tonal difference on typical papers at the bright end of the scale. The brighter the tone, the more sensitive we are to density differences. Darker tones require much greater density difference to be noticed.

I just did a quick test with a calibrated reflection densitometer. I have a contact print made from a Stouffer 0.1 step wedge using a a #00 Ilford filter on Ilford MG Warmtone paper. The base reflection density of white is log 0.07. In rather poor illumination (2.5m from a 40W frosted bare bulb), the first noticeable tone that I can clearly distiguish from white measures log 0.08 on the densitometer. The next band, which looks dramatically darker (relatively speaking), measures log 0.13. This implies that the log-0.04-above-white figure in the ANSI/ISO standard is reasonable in the conservative direction.

Doing the same quick test in the same illumination at the dark end of the scale requires a reflected density change of log 0.10 (from log 1.69 to 1.59) in order to see any distiguishable difference in tone.

[Michael Kadillak]

Just got back from a marvelous day shooting and was elated at finding all the thought provoking contributions. My sincere thanks for sharing your knowledge with all of us. Cheers!

[neil poulsen]

You take your reflection density value and switch the two numbers, multiply by 100%, and you'll find that you are right on target! (Just kidding.)

To speak only to the relationship between percent reflection and "RD", the reflection density reading from your reflection densitometer, you can use the following formula:

Percent = 100% x 10^(-RD)

where ^ means "taken to the power of". For your reflection density value of 0.81, I come up with a percent reflection of 15.5%. I would say that you are pretty close.

[D Poinsett]

For what it's worth, I just dug a gray card out of the drawer and measured its reflection density. It was, coincidentally, log 0.81.

Mr. Poulsen insightfully provided the commonly used formula for converting density change in log units to percent. This may be exactly what Mr. Kadillak was asking for.

Whether 18% really represents "middle gray" is an interesting consideration. In a perfect world, log 0.81 is the middle of a log 1.62 density range. If you fiddle with the effects of an imperfect world, a log 0.81 measurement is the middle of something around a 1.4 to 1.5 density range. In printed material, that's not a very deep black. A toned silver gelatin print could easily hit 2.40 if allowed to go full black. Black construction paper measured 1.38. If 18% gray is used for a refrence when taking a meter reading for a photograph, it's the middle only when the brightness range is about 5 stops.