# 48:1 ratio equals 9 f/stops????

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### #1 Giles Rais

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Posted 14 August 2006 - 06:01 AM

Dear friends:

Perhaps you can help me wrap my head around this. I have read in a couple of books (Brown's "Cinematography" and Viera's "Lighting for Film" that the grayscale goes from about 2% reflectance from the lower black to 96% to the brighter white. If you shine 100 fc, you then would get 2 footlamberts from the black and 96 footlamberts from the white. If you divide these figures to get the luminance ratio, you get a 48:1 (96 divided by 2).

This is what I don't get: a 48:1 brightness ratio does not equal the 8 zones of brightness that go from Zone 1 to Zone 9...the difference in brightness between zones equal those between f/stops, meaning that 8 zones would equal a ratio of 256:1, not 48:1. Yet those books show a grayscale with reflectance values that go from 2% to 96% across the entire 9 steps of the graycale...how can a 48:1 ratio accomodate for 8 steps in the scale, when 8 steps equal 256:1 ratio? (2, 4, 8, 16, 32, 64, 128, 256). PLease point out where I am making a mistake here. Thanks.

Giles.
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### #2 John Pytlak RIP

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Posted 14 August 2006 - 11:24 AM

Dear friends:

Perhaps you can help me wrap my head around this. I have read in a couple of books (Brown's "Cinematography" and Viera's "Lighting for Film" that the grayscale goes from about 2% reflectance from the lower black to 96% to the brighter white. If you shine 100 fc, you then would get 2 footlamberts from the black and 96 footlamberts from the white. If you divide these figures to get the luminance ratio, you get a 48:1 (96 divided by 2).

This is what I don't get: a 48:1 brightness ratio does not equal the 8 zones of brightness that go from Zone 1 to Zone 9...the difference in brightness between zones equal those between f/stops, meaning that 8 zones would equal a ratio of 256:1, not 48:1. Yet those books show a grayscale with reflectance values that go from 2% to 96% across the entire 9 steps of the graycale...how can a 48:1 ratio accomodate for 8 steps in the scale, when 8 steps equal 256:1 ratio? (2, 4, 8, 16, 32, 64, 128, 256). PLease point out where I am making a mistake here. Thanks.

Giles.

Although reflectances of most "real" objects ranges from about 2% to about 96%, most scenes contain brighter highlights and "speculars", and dark objects may be in the shadows (fill light only), so the range of luminances you want to capture may be much greater.

Kodak did much research in this area. Kodak researchers Jones and Condit found that the AVERAGE luminance range of scenes was 160:1 (2.2 log exposure, or just over 7 stops), but many outdoor scenes could have a greater luminance range.

Fortunately, modern color negative films can capture a luminance range much greater than this, giving film tremendous latitude. And print films like KODAK VISION Premier Color Print Film can display a density range of over 5.0 density (100,000:1):

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### #3 Hal Smith

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Posted 14 August 2006 - 12:57 PM

Kodak did much research in this area. Kodak researchers Jones and Condit found that the AVERAGE luminance range of scenes was 160:1 (2.2 log exposure, or just over 7 stops), but many outdoor scenes could have a greater luminance range.

Forgive me but the old Physics Teacher in me just got activated. Sometimes one just can't leave one's Master's Degree in the Teaching of Physic behind. It pops up from time to time.

To convert log exposure to fstops: fstops = (log exposure ratio / log 2)

For instance (from Kodak curve) I estimate about 1.8 log exposure from 2% to 96% density on the curve.

Plugging in: fstops = (1.8 / Log 2) = (1.8 / .3010) = 6 stops (actual number 5.9795 rounded)

[I used my calculator's answers to not confuse the subject with issues of precision - I'm mixing numbers with 2 digits of precision with numbers with 4 and 5 digits of precision, not a good practice but so that if someone tries to run the example on their calculator they'll get numbers that look like mine]

Underlying formula: To convert log base (A) to log base (B ) for number N

log base B (N) = ( log base A (N) / log base B (A) ) [fstops are logs to base 2]

The numerical ratio is found by raising the log base number to the log.

2^fstops = numerical ratio from fstops

10^log (N) = numerical ratio from log exposure.
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### #4 Hal Smith

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Posted 14 August 2006 - 01:33 PM

Kodak researchers Jones and Condit

John,

I tried searching for "Jones and Condit" on the Kodak website and didn't get a hit, nor did I get a hit on Amazon with them as authors.

Is there somewhere I can one find a list of their publications? There's a lot of technical stuff about photography I've been interested in from time to time and found that it's real hard to find scientific level information on photography.
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### #5 John Pytlak RIP

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Posted 14 August 2006 - 03:20 PM

John,

I tried searching for "Jones and Condit" on the Kodak website and didn't get a hit, nor did I get a hit on Amazon with them as authors.

Is there somewhere I can one find a list of their publications? There's a lot of technical stuff about photography I've been interested in from time to time and found that it's real hard to find scientific level information on photography.

Loyd A. Jones and H. R. Condit worked in the Kodak Research Labs during the 1940's. One key paper was "Sunlight and Skylight as Determinants of Photographic Exposure II", Journal of the Optical Society of America, 39: 94-135, February 1949. They were key researchers in the science of Tone Reproduction, with the method of doing graphical prediction of tone reproduction now known as a "Jones Diagram". My Laboratory Aim Density (LAD) control method was developed using some of their methods.

On your earlier post, don't forget that we are talking about the camera negative film, not the print film when we speak of latitude:

The density scale of the negative becomes the exposure scale on the print film (graphical tone reproduction ala a "Jones Diagram").
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### #6 Hal Smith

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Posted 14 August 2006 - 04:11 PM

Loyd A. Jones and H. R. Condit worked in the Kodak Research Labs during the 1940's.
The density scale of the negative becomes the exposure scale on the print film (graphical tone reproduction ala a "Jones Diagram").

Thanks John.

I can probably get some of their work from Oklahoma State University's library through interlibrary loan here in Edmond at the University of Central Oklahoma, I'm a consultant there and have library privileges.
I wasn't aware that latitude as a technical term refers only to negative films, but I do now.

Sincerely,

Hal

PS: I found a PDF of "Sunlight and Skylight as Determinants of Photographic Exposure II" on the web at http://www.opticsinf...f...77557&seq=0 . Unfortunately it's \$22 for a non-OSA member - not much less for a member. But if I can't finagle a loan copy I just might splurge and buy it.

Thanks again!
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### #7 Giles Rais

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Posted 16 August 2006 - 12:12 PM

Thank you John. However, I am not referring to the overall luminance range, which, as you point out, can easily exceed the 9 f/stop range of the grayscale.

What I am trying to find out is why several books equate a ratio of 48:1 (obtained by going from 2% to 96% luminance) to all the 9 steps in a grayscale, whereas that ratio could not be lower than at least a 256:1 ratio. It seems there is somehting fundamentally wrong if a 48:1 is presented as the whole range and yet it does not match a 256:1 ratio (which should be since zones equals f/stops equals doubling/halving of brightness values, therefore 2, 4, 8, 16, 32, 64, 128, 256...or 256:1 ratio equals a range of 8 zones or f/stops).

Both Brown and Viera quote this 48:1 ratio but I am trying to see why it does not fit with their own interpretation of a ratio for a grayscale with 9 steps. Hopefully my question is clearer now. Thanks.

Giles

Although reflectances of most "real" objects ranges from about 2% to about 96%, most scenes contain brighter highlights and "speculars", and dark objects may be in the shadows (fill light only), so the range of luminances you want to capture may be much greater.

Kodak did much research in this area. Kodak researchers Jones and Condit found that the AVERAGE luminance range of scenes was 160:1 (2.2 log exposure, or just over 7 stops), but many outdoor scenes could have a greater luminance range.

Fortunately, modern color negative films can capture a luminance range much greater than this, giving film tremendous latitude. And print films like KODAK VISION Premier Color Print Film can display a density range of over 5.0 density (100,000:1):

Edited by Giles des Rais, 16 August 2006 - 12:14 PM.

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### #8 John Pytlak RIP

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Posted 16 August 2006 - 04:20 PM

Thank you John. However, I am not referring to the overall luminance range, which, as you point out, can easily exceed the 9 f/stop range of the grayscale.

What I am trying to find out is why several books equate a ratio of 48:1 (obtained by going from 2% to 96% luminance) to all the 9 steps in a grayscale, whereas that ratio could not be lower than at least a 256:1 ratio. It seems there is somehting fundamentally wrong if a 48:1 is presented as the whole range and yet it does not match a 256:1 ratio (which should be since zones equals f/stops equals doubling/halving of brightness values, therefore 2, 4, 8, 16, 32, 64, 128, 256...or 256:1 ratio equals a range of 8 zones or f/stops).

Both Brown and Viera quote this 48:1 ratio but I am trying to see why it does not fit with their own interpretation of a ratio for a grayscale with 9 steps. Hopefully my question is clearer now. Thanks.

Giles

As I said, they evidently assume that the darkest black found in normal objects is about 2%, and the whitest white is near 96%. With completely flat lighting (1:1 lighting ratio), 48:1 would be the tonal range of the scene (1.68 log exposure, or only about 5.5 stops). But real scenes rarely have flat lighting, so the shadow areas may only be illuminated by fill light. There are blacks darker than 2% (think black velvet fabric), and whites whiter than 96% (think fabric or paper with optical brighteners), so the 160:1 average found by Jones and Condit would be a much better starting point, and I'm sure you can find scenes where you would want to capture over a 1000:1 brightness range (3.0 log exposure, or 10 stops).

"Stretching" a low contrast scene with only a 48:1 brightness range to fill a 9 stop grayscale is akin to turning up the contast.
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### #9 Giles Rais

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Posted 16 August 2006 - 05:35 PM

As I said, they evidently assume that the darkest black found in normal objects is about 2%, and the whitest white is near 96%. With completely flat lighting (1:1 lighting ratio), 48:1 would be the tonal range of the scene (1.68 log exposure, or only about 5.5 stops). But real scenes rarely have flat lighting, so the shadow areas may only be illuminated by fill light. There are blacks darker than 2% (think black velvet fabric), and whites whiter than 96% (think fabric or paper with optical brighteners), so the 160:1 average found by Jones and Condit would be a much better starting point, and I'm sure you can find scenes where you would want to capture over a 1000:1 brightness range (3.0 log exposure, or 10 stops).

"Stretching" a low contrast scene with only a 48:1 brightness range to fill a 9 stop grayscale is akin to turning up the contast.

Dear John:

But they are not saying that the 48:1 tonal range would equal 5.5 stops. If they did, I wouldn't be scratching my head trying to understand this. They list the following reflectances as equaling the 9 or 10 zones in a grayscale, which makes no sense to me because of the reasons I explained before. What you are saying makes complete sense to me. a 48:1 ratio should only equal about 5.5 stops. Take a look at what is included in their books:

This is what Viera writes:

black velvet = 2%
black face = 10%
green leaves= 14%
brown face = 16%
midgray = 18%
caucasian face= 36%
light grays = 70%
off-whites = 80%
white chalk = 96%

"The typical range of natural reflectances-from whitest white to blackest black-is about 96% to 2%, usually expressed as the ratio 48:1"

As you can see, he equates the steps in the grayscale to these reflectance values, and goes on to say that the "typical range" is about a 48:1 ratio. What I am continuing to ask, is how can a 48:1 ratio equal 9 steps in the grayscale when doubling a value every steps would make for at least a 256:1 ratio? (2,4,8,16,32,64,128,256=8 stops not copunting the one we began with). I am sorry to keep asking the same question, but I don't think my particular point has been adressed.

In fact, this is the breakdown Brown uses:

Zone 0= 3.5%
Zone 1= 4.5%
Zone 2= 6%
Zone 3= 9%
Zone 4= 12.5%
Zone 5= 17.5%
Zone 6= 25%
Zone 7= 25%
Zone 8= 50%
Zone 9=70%
Zone 10= 100%

and he writes:

"A very shiny surface can reflect up to 98% of the light that falls on it. Black velvet reflects about 2% of the light that fall son it. Thsi is a brightness ratio (BR) of 1:48"

If I shine 100 footcandles FLATLY on a grayscale with these reflectances, I would get a ratio of only 28:1 (the brightest value divided by the darkest value to obtain a luminance range). I am not asking about real life values here, or the overall luminance range, but just the rationale they are using in their books. Since every zone equlas an f/stop, a 28:1 ratio makes no sense whatsoever according to the reflectances given.

If somebody understands my question and can point out how to reconcile what these books are showing (or where my error lies), please let me know. Thanks.

Giles
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### #10 John Pytlak RIP

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Posted 17 August 2006 - 02:58 PM

Did you contact the authors/publishers to ask the basis for their statement?
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### #11 Giles Rais

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Posted 17 August 2006 - 03:09 PM

Did you contact the authors/publishers to ask the basis for their statement?

Dear John:

Mr. Viera unfortunately passed away. Mr. Brown I have not contacted yet. I've seen this information repeated in many other books as well, so I thought there must be something I am not getting. I will try asking Brown himself. Thanks again for all your help.

Giles
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### #12 Dominic Case

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Posted 17 August 2006 - 07:08 PM

I think this is easy to explain, and the difficulty probably comes from a basic misunderstanding - possibly the authors you quote have not explained their point clearly.

The Zone System, devised by Ansel Adams in the 1930s, is basically sensitometry without the maths. In fact it is so averse to using numbers and calculations that it numbers the zones with roman numerals I to IX. (Sometimes 0 to IX with 0 as pure black - but the Romans didn't have a 0 so that's a bit crook )

Now, most explanations that I have read of the Zone system (including Adams' own work), start with the fact that on paper (that is, in a print), the reflectance can go from pure white to pure black. To introduce numbers, that is from 0% to 100%. In fact, to see any shadow detail at all you need a percent or so of reflectance, and usually you are lucky to get 100% white. So the paper print has a brightness range of 2% to 90% or 45:1.

This range of tones in the print is used to represent the full range of tones that are in the original scene - which, because of the variation in light and shade, is far greater than 45:1. As John has pointed out, Kodak researchers decided that an average exterior might be 160:1. Perhaps they never left Rochester: it's usually a lot more here . I guess 8 or 9 stops (between 256 and 512 to 1) is a good range - and that gives you, of course, the 9 zones at a stop each. (It can get a lot more, especially if you are setting up tests to compare film and digital cameras )

The skill of the emulsion maker, the photographer, and the lab or the darkroom printer, lies in fitting the 9 stops into 5 or so. That is where the characteristic curves come in, and the gamma of the mid-range combined with the extent of the toe and shoulder. Mid-range contrast may be compressed to accomodate more highlight and shadow detail, or expanded at the expense of shadows or highlights. But invariably there is a creative compromise.

In fact I just found almost exactly the same explanation at http://www.luminous-...ne_system.shtml, as follows:

In a scene ? in the field ? each zone represents a doubling or halving of the luminance ? the light reflected from the subject ? or equivalently, a difference of one f-stop. The eight steps between the nine zones in the chart (1-9) represent a luminance range of 256 (28). On paper surfaces, this difference is considerably compressed. On good photographic paper, pure white is about 90% reflectance and pure black is about 2% reflectance. The maximum tonal range is around 45, equivalent to about 5.5 zones (log245). Reflectance differences between zones are less than a factor of two. The difference between zones at the ends of the scale (1 and 2 or 8 and 9) is much less than between zones in the middle (4, 5, and 6).

Values will be different again for cinematography, as it's possible to have a wider range of brightnesses on a screen than it is on a paper print.
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