# Reciprocity Failure Correction - Gadget Gainer's Formula from '05 - EFKE PL100M?

Discussion in 'B&W: Film, Paper, Chemistry' started by holmburgers, Sep 8, 2011.

1. ### holmburgersMember

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Hi all,

In my quest for the proper reciprocity failure compensations for EFKE PL100M I've come up nearly empty handed. I did however come across this excellent thread from nearly 7 years ago that seems incredibly useful for any film.

The formula is Log(tc) = log(tc,1) + 1.62 log(tm), where tc,1 is the correction at 1 second indicated time.

Given the emboldened statement, I'm wondering if anyone can come up with a reasonable number to apply to Efke PL100M?

Or, if all that is required to come up with the right coefficient for a given film is based off 1 or 2 tests then I'd be more than glad to do it myself. The thing is, I need a bit of help understanding the formula and how to apply it; like where does that coefficient come from exactly?

tr = tc,1*(tm^1.62) + tm

tm = exposure time indicated by the meter
tc = amount to be added to indicated time
tc,1 = correction to be applied to a 1 second tm
tr = exposure time adjusted for reciprocity failure
__________________________________________

I've basically reposted the information here because it seems like a useful tool, and one that is perhaps forgotten(?)

2. ### michael_rSubscriber

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I don't know, I've never understood why a given reciprocity formula should work for all films. I prefer specific testing. For example, I tried using Howard Bond's rather exhaustive TMAX and Delta tests and found them pretty much spot on for my purposes.

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3. ### holmburgersMember

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Well, is this formula not derived from Bond's testing?

4. ### michael_rSubscriber

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But to answer your question about the coeficients, they come from experimental testing. In this case, the coeficients were based on the "brute force" tests Bond conducted - ie based on the experimental measurements/results, the coefficients are the additional amounts of exposure needed at 1 second (metered) to adjust for reciprocity departure. Howard Bond's testing was extremely labour intensive, exposing and developing hundreds of sheets of film to determine the reciprocity adjustments in small exposure increments out to 4 minutes (metered). But if you were going to do this for just a 1 second exposure to determine the coefficient, and then apply Gainer's formula to determine the adjustments for other metered exposure times, then yes presumably it would not take very much testing work for a given film.

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5. ### cougstarMember

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I've used the Reciprocity Chart for Bergger 200. Seems to work good. I found this on Michael Smith's Azo Forum a few years ago.
http://www.michaelandpaula.com/mp/azoforum/one.asp?ID=4918&PgNo=&GID=4918&CID=4

Meter Exposure Given (All times in seconds)

1sec = 2sec
2sec = 5sec
4sec = 15sec
8sec = 35sec
10sec = 50sec
20sec = 120sec
30sec = 195sec
40sec = 300sec
50sec = 405sec
60sec = 525sec
70sec = 600sec
80sec = 825sec
90sec = 1005sec
100sec = 1200sec

6. ### Lee LMember

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Using the data for Bergger 200 supplied by Ted from the Azo forum, I ran a regression with the Gainer formula using SciDAVis.

The coefficient should be around 0.6177. So the new exposure time with reciprocity compensation in seconds should be:

corrected time = 0.6177 * metered time ^ 1.62 + metered time

The attached chart shows the data in black (which appears a bit 'ragged', as one should probably expect), and the calculated fit in red.

Lee

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• ###### Bergger200reciprocity.png
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7. ### holmburgersMember

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This is great! Lee, it's nice to see you are still a whiz with this formula, just as you were 6 years ago! I had hesitated to follow the Bergger 200 times because in my search I saw somewhere a dissenting comment regarding those times. But as they say, 'good enough for jazz'.

Michael, indeed that seems to be the beauty of this formula; that one only needs the coefficient.

Now, I'm having a bit of trouble with the math here, to be honest... putting metered times into Lee's formula is getting me values that don't match the above Bergger times given by Ted. Are there some parantheses, or some order of operations I'm missing? And the time spit out should be the time, not the time to add, right?

8. ### Lee LMember

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I'd have to look at what you're doing more directly to comment on order of operations, but if you know the concept and apply it, you may be getting 'correct' numbers without realizing it. I'll attach a screenshot of a spreadsheet with metered times, Bergger data from the Azo forum, calculated exposure times with the Gainer formula and the coefficient I derived, and then the percentage difference between the Gainer and Bergger times. If you look at the adjustments given in the Bergger data for metered times below 30 seconds, you'll find that it's not a very smooth set of numbers, the 'ragged' stuff I referred to before.

However, even though there are differences between the proposed Bergger data and the derived Gainer formula, you can look at the last column and see that the Gainer formula differs by -0.5 stops at 4 seconds metered time, most of the time it agrees with the Bergger data to better than +/- 0.3 stops. I'd guess that the original work to generate the Bergger 'data' wasn't done with tolerances as tight as the supplied numbers might suggest.

Lee

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9. ### holmburgersMember

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Thanks Lee, that confirms that I was doing the math correctly, but indeed, I was thrown off by the discrepancies. I'll be using the data you generated and I'll report back if it works well or not.

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11. ### Lee LMember

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Patrick Gainer established his reciprocity formula based on data from this article:
http://www.phototechmag.com/index.php/archive/reciprocity/

Ilford hasn't changed it's reciprocity data for HP-5 for decades, but the film has changed. Here's a quote from Bond's article concerning HP5+.

You'd likely do much better with Bond's recommendations for reciprocity adjustment for HP5+ than with the data sheet from Ilford.

Lee