### f/stop timing and partial stop calculation

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Good morning,

I am starting to play with f/stop timing for print exposure in my darkroom. I have read several papers on the subject and like the way it works. I have noticed in some tables of f/stop increments that, as expected, +1 stop is a doubling of the time. For instance base exposure of 16 sec +1 stop = +16 sec. So far so good. BUT for +1/2 stop the increment is +6.6 seconds. I am surprised it is not 8 sec which would be 1/2 of the full stop increment.

SO, there must be something I do not understand and perhaps a formula for figuring out fractional f/stop increments both up and down (+ and -).This, I am sure will help me understand the non linear nature of these f/stop increments.

My goal is to make my own tables of f/stop increments for the range of exposures I use, and understand the process.Can any of our large format math wizards help me?

Scott

-- Scott Jones (scottsdesk@attbi.com), January 29, 2002

You'll find your answer in a rcent issue of Photo Techniques magazine:

"Darkroom Tips and Tricks by Ctein (No. 6, pg. 46)"

I can't remember all of it so you're better off finding a copy and reading. I'm not at home or I'd look it up. There's a "+1" in the formula that we always forget (it gets subtracted out when you go backwards)

-- Jim Galli (jimgalli@lnett.com), January 29, 2002.

Thanks for the reply, but this article talks about changes in exposure with changes in enlargement. The article is fantastic and I use it extensively when trying to figure a new exposure for a new enlargment.

BUT, my question is about f/stop timing increments and how to calculate them. Still hoping to get some help from the group.

-- Scott Jones (scottsdesk@attbi.com), January 29, 2002.

You are comparing linear thinking for the time, with exponential for the stop. 16 sec + 1 stop = 16*2, as you found. 16 sec + 1/2 stop = 16 times the square root of 2 = 22.6 sec, or 22.6 - 16 = 6.6 sec longer. An easy way is to use the calculator on your lightmeter.

-- Jim Galvin (jegalvin@lbl.gov), January 29, 2002.

Scott, the reason the previous poster referred you to that article is that it makes the point that this is not simple arithmetic. The fact that one stop increase from 16 seconds is 32 seconds is not because you double the number 16. It is because 2^4 (16 seconds) plus one stop is 2^5 (32 seconds). You can write a simple spreadsheet to calculate the exponents in 1/10 or 1/8 stops or whatever precision you need. I did this and hang the chart on my wall next to the enlarger. Whatever time I am at I can look at the chart to see how much time a 1/4 stop increase would be.

I have fallen in love with my palm top for this type of stuff. I have a small spreadsheet that allows me to enter the current time and how many stop difference I want and it shows the new time. I can enter the two times and it shows the difference in stops. I can also calculate enlargement ratios and the change in exposures to go from one print size to another. A very handy device to have at hand in the darkroom. (There's a whole different set of programs and spreadsheets that go into the field when shooting).

-- Dave Schneider (dschneider@arjaynet.com), January 29, 2002.

```-1   stop = old_time * 2 ^ (1/1)
-1/2 stop = old_time * 2 ^ (1/2)
-1/3 stop = old_time * 2 ^ (1/3)
-1/4 stop = old_time * 2 ^ (1/4)
...
-1/N stop = old_time * 2 ^ (1/N)
```
For example, if your base exposure is 16 seconds at f/5.6, then -1/3 stop less would be `16 * 2 ^ (1/3)` which comes out to 20.2 seconds. To increase exposure you divide instead of multiply: `16 / (2 ^ (1/3))` gives +1/3 more exposure.

Ed Buffaloe has a much nicer explanation on his site: Test Exposures in Printing

-- Bong Munoz (bong@techie.com), January 29, 2002.

Well, looks like this last post is the answer except that the directions by Bong are stated backwards according to the excellent web link provided by Bong.

It turns out that to find a POSITIVE increment in seconds from any starting time one MULTIPLIES the original exposure by 2 raised to the power of the fractional f/stop increment. This gives the new total time with the increment in seconds added. If one wants to know the increment in seconds itself, then one subtracts the starting time to find the increment in seconds.

New Longer Total Time = (original exposure)(2^f/stop fraction)

Positve Increment in seconds = [(original exposure)(2^f/stop fraction)] - (original exposure)

It turns out that to find a NEGATIVE increment in seconds from any starting time one DIVIDES the original exposure by 2 raised to the power of the fractional f/stop increment. This gives the new total time with the increment in seconds subtracted. If one wants to know the increment in seconds itself, then one subtracts the starting time to find the increment.

New Shorter Total Time = (original exposure)÷(2^f/stop fraction)

Negative Increment in seconds = [(original exposure)÷(2^f/stop fraction)] - (original exposure)

Wow, I knew there had to be something "simple" that one could use to figure all this out. This way anyone can make a spread sheet of values any way they like with increments that make sense to them and a range of starting times and maximum times that make sense to them.

Scott

-- Scott Jones (scottsdesk@attbi.com), January 29, 2002.

Scott,

Thank you for catching my embarassing error. My only excuse is that I was thinking aperture instead of exposure time. For example, multiplying the aperture by 2^(1/4) decreases exposure by a half-stop. Cheers!

-- Bong Munoz (bong@techie.com), January 29, 2002.

isn't it easier to just do test strips at 2, 4, 8, 16, 32, and 64..? I mean, afterwards all you do is a test in between the ranges and you should have it very accurate, without having to do all than number crunching....heck if I had to do all that math in my darkroom I would hate going in there!

-- Jorge Gasteazoro (rossorabbit@hotmail.com), January 29, 2002.

F stops are logarithmic to the base 2, which makes fractional stops a bit difficult to work out. It also makes the translation to a time interval counter-intuitive, but there's really no need to go reaching for a calculator or slide-rule each time you want to convert from stops to linear increments.
For all practical purposes, we're not interested in anything less than one third of a stop, and it's easy to write down or remember 6 ratios.

+1/3rd of a stop is 1.26 times.
-1/3rd of a stop is 0.8 times.
+1/2 a stop is 1.4(142) times.
-1/2 a stop is 0.7(071) times.
+2/3rds of a stop is 1.5874 times (1.6 near enough).
And -2/3rds of a stop is 0.63 times.

Those are all the numbers you need, IMHO.

-- Pete Andrews (p.l.andrews@bham.ac.uk), January 30, 2002.

You might also note that in my article Test Exposures in Printing I provide a handy chart of exposure times in 1/4-stop intervals from 5 seconds to 160 seconds. All you have to do is print the chart and put it up next to your enlarger. I do note in the article that, if you are making exposures less than 30 seconds, 3 second test strips are almost as accurate and a lot less trouble. But if your exposures are above 30 seconds you may find that precise 1/4-stop test strips are more useful in finding the desired exposure quickly.

-- Ed Buffaloe (edb@unblinkingeye.com), January 30, 2002.

Another way to do long exposure test strips is to give the whole strip a basic exposure then add smaller increments. For instance, if I judge the required exposure to be "somewhere around 25 seconds", I will expose the whole strip for 20 seconds, then add 3 second incremental exposures. This would give sections of: 20, 23, 26, 29, 32, and 35 seconds. For longer basic exposures, I make the increments larger; and smaller increments for shorter exposures. Maybe not as "arithmetically correct" as f-stop timing, but (IMO) a heck of a lot easier.

-- Chris Ellinger (chris@ellingerphoto.com), January 30, 2002.

Well, what an amazing discussion this has started.

With the help from the above answers, I have created an excel 2000 spreadsheet that I have carefully formatted for readability and printability that has a complete table of f/stop timing intervals from 4 seconds to 128 seconds. It gives you intervals in ¼ stops that can be used for creating custom test-strip/print series to your liking. Each increment also has a full listing of "plus" and "minus" times in ¼, ½, ¾, &1 stops to use for burning and dodging or any other adjustment to exposure that you want to do in the f/stop style.

I have this available to anyone for free in either excel 2000 form or as a .pdf (adobe acrobat) file. Both are ready for printing. (There is nothing commercial about any of this).

Please contact me at the address below if you would like me to send you one or the other. It's fun to be able to share information...

Scott

-- Scott Jones (scottsdesk@attbi.com), January 30, 2002.