# Reciprocity misbehavior.

Discussion in 'B&W: Film, Paper, Chemistry' started by gainer, Jan 8, 2005.

1. ### gainerSubscriber

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As a result of analyses of reciprocity correction determined by Howard Bond
through painstaking experiment, I found that the time to be added to iindicated exposure to correct for reciprocity misbehavior is expressed by the following equation.

Log(tc) = log(tc,1) + 1.62 log(tm)

where tc,1 is the correction at 1 second indicated time.

The factor 1.62 is accurate for all the films tested which were 400TX(0.169),
TMY(0.061), TMX(0.069), HP5+(0.101) and 100Delta(0.046). The numbers in
parentheses are the values of tc,1. This equation is easily plotted on Log-Log
graph paper, or calculated on most pocket calculators. On such a plot, all the
lines are parallel.

Howard found that the factors supplied by manufacturers were not accurate,
possibly because they were not updated with changes in emulsions. 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. The graphical solution is very easy. Plot the correction time at any indicated time on log-log paper and draw a line through that point with a slope of 1.62 vertical inches for each horizontal inch. As you see, the grphical solution does not need the correction at 1 second, and if you plan to do any experimenting, it will be better to use a greater indicated time given the very small corrections required at 1 second for most current films.

Remember, there are no negative coordinates on log-log paper. Negative logs are logs of reciprocals, as log (1/10) = -log(10). If your line goes off the bottom of the graph before it gets to 1 second, just add another piece of paper to give you more cycles. You should be able to get Log-Log graph paper at a college bookstore. If you cant and want to try this approach, I can mail you some sheets. I wrote a program to print the stuff. You can make as many copies as you want without infringing on a copyright.

2. ### David A. GoldfarbModeratorStaff MemberModerator

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Pat, that's really interesting. Thanks for doing the analysis!

Have you tried it for color slide films, some of which seem to need no reciprocity correction out to 2 minutes or more (or so the manufacturers claim--I don't seem to do many exposures this long in color myself)?

3. ### wfwhitakerMember

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Yes, that is interesting. Thanks for the work.

Just to clarify the notation, is (tm) the exposure time indicated by the meter?

4. ### Lee LMember

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This is very interesting to me as well. Is the Bond information on method and/or your analysis published anywhere? I'd love to see it.

Robert Reeves, in chapter 7 of "Wide-Field Astrophotography", (ISBN 0-943396-64-6) offers a technique for determining reciprocity law failure characteristics of film. You set up a gray card (and gray scales/color patch charts as preferred) to shoot at 1/8 second, then put on an ND 3.0 filter and shoot exposures for 128 seconds at varying apertures with the same illumination. You find the amount of failure by measuring negative density on the long exposures relative to the baseline 1/8 sec exposure. This obviously works off failure factor data much further out than 1 second, and perhaps is more applicable to pinhole shooters and astrophotographers. But the method is sound and interesting. The aim in astrophotography is to find suitable films that have the least reciprocity failure and least color shift in the very long exposures used. Spectral sensitivity is also an issue in that application.

I'm curious about the method used by Bond, and the range of exposure lengths covered.

Lee

5. ### Peter SchragerSubscriber

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Bond Article

Lee-the Howard Bond article was published in Photo-Techniques magazine. See if you can get a back issue from them. If not you can PM me and I will dig it out for you. Mr. Bond also did an article on Reciprocity several years ago on the older films; i.e. Tri-x,Tmax,Hp5 etc. His basic conclusion on the new films is that they don't increase nearly as much as the older films. They do increase as the times get longer though. See if you can find the article......if not then contact me.
Regards Peter

6. ### Bob CarnieSubscriber

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Gaget Gainer

I knew there were some brainiacs on this forum.

So I want to do a night exposure my meter tells me 8 sec f16 , triX film to be developed normal PMK.
What should my new exposing time be???

7. ### gainerSubscriber

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13 seconds should do it. On my TX-30X calculator I did ,169*(8^1.62)+8. the .169 is the reciprocity correction for 400TX at 1 second indicated exposure and 1.62 is the same for all tested films.

8. ### gainerSubscriber

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My article in Photo Techniques was in the next issue after Howards, I believe. It was called "Reciprocal Trade Disagreement". I always try to be humorous, probably because we were not allowed to at NASA.

9. ### gainerSubscriber

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Yes indeed it is.

10. ### Bob CarnieSubscriber

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gaget gainer

Does this reciprocity factor hold at 1.62 for all long exposures, ie. 10 minutes equals 16.2 minutes, or 30 minutes equals 48.6???
thankyou for your insight

11. ### gainerSubscriber

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Look again at the equation. The log of the indicated time is multiplied by 1.62 and added to the log of the correction at 1 second indicated time to get the log of the correction. The answer is "No".

To convert that equation to one that can be solved quickly on a TI-30 pocket calculator (cost about \$20) : tm is indicated exposure time. tc is amount to be added to indicated time. tc,1 is correction to be applied to a 1 second tm. tr is exposure time adjusted for reciprocity failure. Then,

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

The * is what shows when you press the multiply key. The ^ means "raised to the power"

12. ### MikeKMember

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Mr. Gadget - this is cool stuff. Do you have any words of wisdom on the change in development that would ne need as the exposure time is increased to maintain a consistent contrast?

I had an old Kodak Technical document from the late 1970's that had a set of tables showing the percentage development time change needed as the exposure time increased. But I have no clue where it is and I suspect the information is way out of date for today's emulsions.

Mike

13. ### Peter SchragerSubscriber

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Reciprocity

Mr. Gainer-or you could just carry the little chart that Mr. Bond so kindly published! I rather photograph than do calculations but that's why your known as Gadget Gainer!
Peter

15. ### gainerSubscriber

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Lee, you said "I'm curious about the method used by Bond, and the range of exposure lengths covered."

Howard's experiments covered up to 240 indicated seconds by factors of 2: 1,2,4,8 etc. He found the exposure for 400TX to be 1006 seconds at 240 indicated. This is about 1/2 stop less than I would calculate by fitting the whole range of data, but 1/2 stop is not much when you get down to it. I often find when I am metering a scene that I have to average readings with a greater spread than that, and even if I do three exposures at +/- 1/2 stop, I cannot see much difference in the final results.

If you find my article in Photo Techniques (sorry I don't remember the issue) you will see tables and graphs that illustrate what I am saying here.

16. ### Bob CarnieSubscriber

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My questions are simple ,as I only was able to get to grade 9 math before my teacher threw me out of class . He did not realize my mother language Moronica.
My interest is in very long exposures for some night photography as well as being able to correct very long times in the darkroom. I have been PM by someone else on this matter so I hope not lower the scope of this thread.

17. ### MikeKMember

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If anyone is interested I could make an Excel Spreadsheet/Chart Available. I have made up a quick and dirty chart you can see here - limitations of converting Excel to HTML with GIF image. Adjustments for HP5, TMX and TMY

http://home.pacbell.net/mkirwan/Reciprocity.htm

- Mike

18. ### Lee LMember

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For convenience of interested parties, the Phototechniques web site lists:

Vol. 24, No. 5 Reciprocal Trade Agreement - Gainer
Vol. 24, No. 4 B&W Reciprocity Departure Revisited - Bond

These would be the July-Aug (No. 4) and Sept-Oct (No. 5) issues for 2003 if I'm calculating correctly.

To answer in part the questions Bob Carnie and Mike K have about adjusting development;

When you make a long exposure in the range where a film has reciprocity law failure, you'll probably have a range of a number of stops, probably a minimum of 5-7 stops or often much greater, especially in a night shot with manmade lighting and dark areas. If you took the darkest area and calculated the necessary exposure with reciprocity compensated for, then did the same with the lightest area, you'd find that the dynamic range (# of f-stops) of the scene has just expanded tremendously because of the differential in reciprocity failure between the light and dark areas. To compensate in part for this, development times are sometimes decreased to keep the contrast of the negative down, but that means marginally lower "film speed" as well. This gets out of hand rather quickly, and you often just have to accept some loss in highlights, shadows, or both. Or you can explore the stand development and other techniques used by the photographers who do cathedral interiors.

My advice is to bracket either side of your calculated exposures if the shot is important to you. I've found that bracketing with the Fibonacci series works well. That series is 1, 2, 3, 5, 8, 13, 21... each subsequent number is the sum of the previous two numbers, and I do this in either seconds or minutes. I do this because in my experience a half stop bracket is too little and a full stop is too much. It works for me in time exposures of under a minute up to a half hour or so. I started using the Fibonacci series when I was doing 2000 custom B&W prints a month using two hand-operated Omega D-V enlargers with no meter or analyzer. (Luckily I had a roller-processor for the paper.) I could eyeball the exposure and be right 95% of the time, and could always nail the second by going up or down to the next number in the sequence. It was also handy because I'd often get requests for reprints, and within the tolerance of the materials, I could always get a reasonably exact duplicate print without having written down exposures.

When you take the ratios of any two sequential numbers in the Fibonacci series, you get 1.618, which is coincidently, the golden mean ratio, and the number by which the log of the indicated exposure is multiplied in Mr. Gainer's reciprocity equation.

Lee L

19. ### gainerSubscriber

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If you had made these plots on log-log paper, you would see straight, parallel lines.

20. ### gainerSubscriber

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If someone will tell me how, I will send the log charts with raw data superimposed. I have it as a jpg file of around 300 K. These are the charts that were used in my PT article.

21. ### MikeKMember

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In the Excel charting function I can only apply a log scale to the y-axis

This has been a useful mental exercise for me on this wet and miserable Saturday afternoon. I have printed a little booklet from the Excel Tables and have stuck it in the back of my field notebook.

- Mike

22. ### David A. GoldfarbModeratorStaff MemberModerator

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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.

23. ### Bob F.Member

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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...

Cheers, Bob.

24. ### Lee LMember

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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.

Lee L

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25. ### MikeKMember

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Lee, just redid my chart and we match 100% (tables and Chart)

- Mike

26. ### Bob F.Member

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Thank Gawd for that - our graphs agree. I can stop sweating now....

Cheers, Bob.