Patrick--To upload the files first I'd recommend making them something like 650 pixels on the long dimension and save as JPEG compression level 4 or so to keep the file size reasonable (since these are graphs, they don't need to be maximum image quality).
Then enter your reply in "advanced" mode and scroll down a bit, and click on "manage attachments." You'll get a pop-up with a number of boxes for uploading attachments. You can click on "browse" for each box to find the JPGs on your hard drive. When you've located all of them, click "upload" and wait until it says it's finished, then you can close the box, and when you "submit reply" in the reply screen, your images will be attached.
I have used RJSGraph (http://www.rjsweb.net/) graphing software to plot on log/log axis.
The software runs on Windows and is free. I use Excell to generate the numbers for the Y-Axis and cut&pasted them in to RJS Graph.
Example Plot here (I tried scrunching it down to fit APUG but it lost too much resolution).
[Edit: Spelt Pat's name right this time...]
I'd be interested if they fit other's curves just to make sure I have not boo-booed too much...
Reciprocity test chart
I don't have the article at hand, but I'll attempt to upload a "test" chart to be checked for accuracy as far as my math is concerned. Please inform me of errors and I'll make necessary changes and repost.
Times for the main chart are only out to 100 seconds metered times.
(BTW, for this type of graphic, .gif .png or some other lossless type of file is far superior to .jpg in both space savings and viewing quality.)
I added .png graphs for each range from 1-10, 10-100, and 100-1000 seconds to make them easier to read.
Oh, yeah, I also changed the order of the legend on the right hand side so that it matches the order of the curves from top to bottom on the three .png charts, just in case you want to print in B&W and carry along and still make sense of it.
Last edited by Lee L; 01-08-2005 at 11:13 PM. Click to view previous post history.
Lee, just redid my chart and we match 100% (tables and Chart)
Originally Posted by MikeK
Thank Gawd for that - our graphs agree. I can stop sweating now....
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Gainer "...Due to the fact that the factor 1.62 works for these diffeent films of different manufacturers, it is my opinion that it will work for any current emulsion to acceptable accuracy. That is to say that I expect it to be within the spread among readings of indicated exposure made by a number of proficient photographers of the same scene. If this is the case, all one needs to know is the reciprocity correction to one indicated exposure to find the correction for any other indicated exposure"
This is tremendously helpful. I'd like to chime in my vote of thanks for sharing your work also Mr Gainer.
I do have one question, and pls accept my apologies if the implication is already clear.
From your statement we can assume the 1.62 to be a constant factor for all current emulsions (then it would make sense for it to apply to FP4 and 320TXP OK). I guess if we wished to establish the reciprocity correction for different emulsions from those established by Howard Bond, we would need to do our own experimentation?
I did try it on the corrections Kodak supplied for the old Tri-X and it worked, with a different intercept at 1 second of course.
You only need to find the reciprocity correction for one indicated exposure time, but two would be better. The problem is that these experiments are quite tedious, as Howard Bond pointed out. I think it was several months after that project before he could stand to hear the word "reciprocity".
My reciprocity charts.
That last attempt didn't go so well.
Gainer reciprocity compared to Schwarzschild
Well, I couldn't let this go without comparing the results of Gainer's equations based on Bond's testing with the old standard Schwarzschild formula and tests done by Covington and Reeves.
For those unfamiliar with the Schwarzschild exponent, I'll just briefly explain it (using "spreadsheet mathematical notation"). Let p be the Schwarzschild exponent and t equal to exposure time in seconds. For a given effective film speed to be corrected in the range where the reciprocity law fails, the following equation applies:
Effective speed = Standard speed * t^(p-1)
Covington (page 180, Astrophotography for the Amateur, 2nd ed. ISBN 0-521-62740-0) says the following is more accurate, especially nearer the range where long exposure reciprocity is just beginning to fail:
Effective speed = Standard speed * (t+1)^(p-1)
This equation can be reworked to give revised exposure times as opposed to film speed:
Corrected exposure time = (Metered exposure time+1)^(1/p)-1
I've picked one film tested by both Covington and Bond, Ilford Delta 100, which Gainer gives a reciprocity factor of 0.046 using his equation. Covington's 1996 tests on Delta 100 assign an approximate Schwarzschild exponent of 0.85. Covington's tests are approximations to about 1/3 stop. I haven't read the Bond article, so I don't know his method, but from his other work, I expect accuracy and meticulous testing to be the norm, probably to a higher degree than Covington for several reasons. Astrophotographers are plagued by a host of other factors that rapidly overtake attempts to be very highly accurate when calculating exposure times, so it's pointless in that application to be overly careful with such testing. They mostly do this for relative comparsion of emulsions in deciding which film to use, not to nail down exposure times to a fraction of a stop with a particular film. Covington tests with this in mind and warns against using his results for elaborate calculations.
Given all that, I forged ahead and graphed the results from Covington's 1996 emulsion test and Bond's 2003 tests on Ilford Delta 100, using the appropriate Covington revision of the Schwarzschild formula and the Gainer formula describing Bond's data. The attached graph is the result. Covington's results run about 1/3 stop more correction early on, but Gainer's formula crosses over at a bit over 400 seconds metered exposure time. In practical terms the difference in using either equation in this instance is about 1/3 stop or less. Covington reports that reciprocity failure variations from batch-to-batch emulsion changes can be greater than this.
Covington (and Reeves in Wide-Field Astrophotography, ISBN 0-943396-64-6) list Schwarzschild exponents for a number of films in their books, but all on pre-2000 emulsions. Reeves includes 45 film tests, 12 of them B&W.
As Pat Gainer says, the testing is time consuming, but you could use the methods of Covington (also adopted by Reeves) to do some rough testing using a few frames on each roll during "normal" photography to get a data point for determining a Gainer film factor, or a Schwarzschild exponent for a given film. As always, doing this with sheet film will require more work, and very consistent processing methods.