The formula should have lead you to these numbers:
The time to be added to 10 seconds indicated exposure for a film that has a correction of 0.3 seconds at 1 second indicated is:
tadd = 0.3*(10^1.62) = 12.51. .
Add 12.51 seconds to the indicated 10 seconds to get 22.5 seconds after correction for non-linear reciprocity. Your suspicion was correct. I don't know what you did to get 4 seconds instead of 12.5, but you surely didn't calculate 10^1.62 in the process!
Remember: the coefficient a in the equation is the amount of the reciprocity CORRECTION at the measured exposure time of 1 second, 0.3 seconds in the case at hand.
I forgot to emphasize that it appears from my analysis of Howard Bond's data that the value 1.62 is common to all films he tested within the accuracy of measurement. A change from 0.3 to 1.0 in the coefficient "a" is the difference between 621 and 1838 seconds at a measured exposure of 100 seconds.
Thanks to Ulrich for finding the Bond article online. I found it once, but the link to it disappeared and I thought it was gone.
I've been working on Bond's numbers off and on for a while. The best fit depends on the film, and is either a power or log fit. The following are best fits derived with CurveExpert, a MS Windows program that I run under linux. The formulae are presented as they would be typed into a spreadsheet to calculate a corrected time that takes reciprocity failure into account, and all times are in seconds in these formulae.
In practical terms, these would be within a small fraction of a stop of Gainer's method.
corrected time = EXP(1.2147591*LN(metered time)+0.19783161)
corrected time = EXP(1.2746481*LN(metered time)-0.18828707)
corrected time = EXP(1.0020463*LN(metered time)^1.0793326)
corrected time = EXP(1.1577419*LN(metered time)-0.076131411)
corrected time = EXP(1.0179975*LN(metered time)^1.0959838)
I'll also attach a .pdf chart I just made up before logging onto APUG using these formulae, as I just happened to be working on this again, having some time exposure ideas I want to try. I've also added columns for Plus-X as per the Pinhole Designer software, which is also a very close match for the old Kodak and Ilford generic corrections, which are also in a column on my chart. The format for corrected times in the chart is mmm:ss Please let me know if you see any mistakes, as I just finished this up. I should also mention that the Efke 25 times are derived from an internet post by Andrew O'Neill at photo.net, with his data interpreted as per Robert Reeves and Michael Covington in their respective books on astrophotography.
Last edited by Lee L; 03-27-2009 at 09:14 PM. Click to view previous post history.
While we're on it here are some formulae for Acros. If you plug in the linear and power fits, you'll find no significant difference in the results or the fit to the data, which was taken from an APUG post by André E.C. : http://www.apug.org/forums/392161-post2.html
Don't bother with corrections at times of 120 seconds or less.
Acros regressions from CurveExpert
Power Fit: y=ax^b
a = 0.72538705
b = 1.06559210
correlation coeff: 0.99999128
Linear Fit: y=a+bx
a = -36.07858400
b = 1.20142490
correlation coeff: 0.9997068
Last edited by Lee L; 03-27-2009 at 09:32 PM. Click to view previous post history.
Lee, please calculate the corrected exposure for Acros at a metered exposure of 1 second. I'm missing something here. It's not old age. I have plenty of that. If y is the answer, then the corrected time can never be less than 0. 7254 seconds by the power fit, or greater than 0 until metered time > 30.03 seconds by the linear fit. Something doesn't fit!
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Originally Posted by gainer
I have. That's exactly why I recommended not using any corrections below 120 seconds, where they aren't necessary with Acros. The fit is only good beyond that time.
I also logged back in to address the original question of Delta 100 reciprocity. Whatever method was used by the photo.net poster certainly doesn't agree with the behavior found by Howard Bond. It's more in line with the generic curves that manufacturers posted, which Bond found to be inaccurate or out of date.
Last edited by Lee L; 03-27-2009 at 10:24 PM. Click to view previous post history.
WHOOPS! Maybe it is old age. The computed time at one second metered time is 0.7254 by the power fit and -34.8773 by the linear fit. it still doesn't fit.
I found the expression you posted through google, and the post indicates that it was based on Ilford's leaflet information for reciprocity corrections, which Bond found inaccurate in his tests. If you read the Bond article that Ulrich posted earlier, you'll find how his results differ, and why he thinks that's the case. Kodak's and Ilford's generic recommendations appear to be for older films, and have remained basically unchanged for decades.
The expression you posted is also extremely close to that posted by Ilford reps on photo.net, where corrected exposure = metered exposure ^ 1.48 , which is again their generic curve of very long standing.
Last edited by Lee L; 03-27-2009 at 11:19 PM. Click to view previous post history.
Originally Posted by gainer
I ran the regressions only on the "data" from Andre's post starting with 120 seconds, the point at which failure kicks in, and longer. So both the power and linear equations only describe behavior beyond 120 seconds, and should only be applied there. Interesting that the power curve does describe behavior pretty accurately below the data to which it was fit.
Lee, I don't understand how your chart would be used in the field. I see metered times, and under each film the numbers do not look like corrected times.