As I said in an earlier post, #13, kinda buried under the list of equations,
Originally Posted by Chazzy
This is to make it easier to use with a watch or timer. I have a Gossen Digiflash meter that has a countdown timer that goes up to 30m 59s and does countdown beeps for the last 10 seconds with a long ending beep, so the chart was aimed at using that way. This chart is from a spreadsheet, and I didn't bother to type in a formula to convert times over 60 minutes to hh:mm:ss.
The format for corrected times in the chart is mmm:ss
The grayed lines are for the full stop times displayed on most meters: 1s, 2s, 4s ..... 1m, 2m, 4m, etc. The others are approximately 1/3 stop steps because my most used meters are marked that way and non-linear interpolation "in my head" between full stops can be a brain bender.
Last edited by Lee L; 03-28-2009 at 09:48 AM. Click to view previous post history.
If you have a pocket calculator such as the T1-30XIIS, you need only know 1 number for each film you use and one constant, 1.62, that is good for all films. The sequence of entries is as follows, where Af is the film constant, tm is the metered time, and tc is the corrected time.
tm^1.62*Af+tm = tc
Let's say that your film requires 0.5 seconds correction at tm=1 second. For that film, Af = 0.5. Now you're out shooting lumps of coal at in the deep woods (a common, though not often photographed, sight in West Virginia) and your meter tells you it will take 100 seconds. (Wish I had such a meter.). You whip out your TI30 and do:
100^1.62*.5+100 and the answer is 20424.9 seconds. But suppose you have another film with Af = 0.1. then:
100^1.62*.1+100 = 273.8
Assuming that your equation gives an accurate corrected value for Acros at 120 seconds metered, I calculate by your power fit numbers that the corrected exposure is 165 seconds. Working backwards, I calculate that the Af coefficient in my equation is 0.0193. Now I find that at 60 metered seconds, Acros need 75 seconds, at 30 seconds it needs 35, and at 1 second, it needs 0.019. I would say that the correction is negligible at 30 metered second or less.
I'm aware of only a few people who have published very good reciprocity data. Bond is the only one I've seen do the really heavy lifting, testing carefully at a wide range of times. Others use a long-standing, sometimes modified, Schwarzschild calculation, based on the necessary adjustments in stops between a 1/8th second (0.125 second) exposure and an exposure with a 3.0 log density (10 stops) filter at 125 seconds (sometimes at 128 seconds) to get equal density. You have to be careful here to get a really neutral filter. The B+W 110 and Wratten ND filters are often recommended, with the caveat that the Wratten gel is too leaky in the red for accuracy with some films. Covington and Reeves in their books on astrophotography outline the procedures for this method. The result is a Schwarzschiild exponent 'p', which can be used to calculate corrected exposures with the formula:
corrected time = (( metered time +1)^(1/p))-1
Covington notes that he has seen significant batch-to-batch differences in the same film. If anyone's interested, I can post Covington's and Reeves' films and Schwarzschild exponents. There is some significant variation between their results using exactly the same procedure and films, but a few years apart.
My point is that none of this is pinpoint accurate. Gainer's method, the power and log formulae, and the Schwarzschild formula can all be fit to any experimental data I've come across within about 1/3 stop or better. If anyone assumes that any experimental data they've seen has a margin of error of less than 1/3 stop at these extended times, they're probably fooling themselves. Most of the data floating around the web is not documented at all. Some people have posted fourth order polynomial expressions in an effort to model experimental error and hit each observation exactly.
The difference between the 120 and 165 second example in Gainer's last post for Acros is about 1/3 stop.
So my point is that you can just pick your mathematical poison among several reasonable models for reciprocity failure, and get within a fraction of a stop, assuming the models are built on decent data such as Bond's. I'm not interested in worrying about thirds of stops or less.
I like working with charts in the field, which is why I produced the one I did. It's only as good as the data, none of which I've confirmed by exhaustive work like Bond's, but I've tried to choose the data reasonably carefully.
When it comes to pinpoint accuracy, reciprocal behavior of film exposure-density is not a good place to look for it, not is it needed when one considers the logarithmic transformations used to get a nearly straight line of exposure vs density. Considering the personal equations involved in the processes that take one from exposure to print, it is a wonder any of our charts and tables come close to agreeing.
When it comes to simplicity of use, I'll put my equations and a TI-30XIIS against any set of charts for anyone who uses more than one film. I haven't seen any comment on my posting of the reverse engineering of Acros. If anyone has data for metered exposures between 1 and 120 seconds, please post it. I do not use the stuff yet.
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BTW, my method fits just about any reciprocity curve, but my observation that the correction for any film is a factor of tm^1.62 is limited to those films that believe in it. The factor happens to be the amount of correction required at 1 second of metered time. Any time anyone gets some additional experimental data, my equation and its assumptions can be tested. For instance, if you find that a particular film needs 200 seconds when the metered exposure is 100, the amount of correction is 100, and that is Af*(100^1.62), so Af*1738 = 100 and Af = .056. After a few such results, you can average AF and see how that average fits the trials that went into calculating it.
Lee, the value of corrected time, 165 seconds, that I calculated for 120 seconds metered time was by using your linear fit. I had ASSumed that your linear fit was good from that point up. I then went to the previously posted data and used the values 1920 metered and 2288 corrected to calculate the value 0.001766 for the Af coefficient which I then used in the calculation tc = tm^1.62*0.001766+tm to calculate the following:
te are the posted experimental values, tpf are the values I calculated by your power fit equation, tc= tm^1.06559*0.72538.
How on earth did you get correlations so close to 1.00000? I personally would rather see the mean square deviation.
The point I was making in posting the linear model for Acros was that there was very little difference in practice between working from the power or linear model with this film. The attached chart shows percentage error for each model over the range of the experiment that found any reciprocity correction necessary, i.e. above 120 seconds. The linear model is -6% to +5% and the power model from -2.5% to +0.58%. The power model and your model are obviously better fits, but the linear model is perfectly usable in practice.
I thought Andre's numbers looked familiar, and I found them at http://home.earthlink.net/~kitathome...eciprocity.htm where I'd seen them before. The page states that these numbers for Acros are preliminary, the third test roll that the author shot. He lays out his procedure there, and claims an accuracy of approximately 0.02 log density units with his Pentax spotmeter and a light table, and an ability to get within 1/15th of a stop in typical tests. However, the first three data points in his results, at adjustments for 80, 160, and 240 seconds, show variations of 5% or less from the base times. In other words, three of the six data points used for the curve fitting are below the accurate measurement threshold given by the author, so I don't see the point in belaboring a fit to marginal data.
You could find the author of CurveExpert and request that he change his choice of default quality of fit statistics. I wondered about that as well.
Thanks for the correction- I was simply using your chart to add numbers- it's obviously way more complicated than that.
Originally Posted by gainer
I'm ashamed because I'm supposed to be a reasonably competent person (I do instruments and calibration for a living)...but this math is just way over my head for use in the field- Maybe someone somewhere has come up with a simple additive chart that I could understand.
It sure is neat to have exposure to scientific people of this caliber on a board of mostly us "artsy" types- I salute your superior grey matter fellas!- but I have no clue - how does one perform the function "^"?
The ^ symbol means "to the power of". It is not something one can do with paper and pencil unless the number on the right is an integer. Thus, 2^2 means 2 raised to the power of 2 which is simply 4, but 2^1.62 is not so easy. The TI30XIIS pocket calculator and many others have a key with that symbol. Using it, I find that 2^2=4 and 2^1.62=3.073750363. I am glad I didn't have to design the circuitry in that little light-powered pocket calculator. I is capable of math operations that I could not do at my desk during the 30 years of work at NACA-NASA without laborious calculation of power series on an electromechanical Friden or Marchant desk calculator.
Originally Posted by ghost
We use our grey matter to pursue knowledge along paths which are mysteriously chosen from among many available ones. I consider myself lucky that others who have pursued other paths have shared the fruits of their pursuits, and am happy to be able to share what I have found along my path.