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Comparative reciprocity failure of available sheet films

  1. While I have read that Kodak TMY-2 has good reciprocity characteristics and the Fomapan films show very significant reciprocity failure; the ILFORD data sheets for HP5+, FP4+, and Delta 100 all seem to show the same reciprocity characteristics through a rather imprecise and limited graph.

    A photo.net contributor has published a formula to calculate reciprocity failure of Delta 100 'Corrected time = 1.15567 x (Metered time)^1.4379'; however, I have seen little in way of comparison between HP5+, FP4+, and Delta 100. Does a lack of comparison indicate these films all have the same reciprocity characteristics, which seems unlikely...?

  2. Howard Bond published an article on this with some very useful information. I believe it was Photo Techniques in 2003. I don't have a copy on hand, unfortunately.
    It included Tri-X 400, Tmax 400, Tmax 100, 100 Delta, and HP5+. That was the old version of Tmax 400, of course.
    Tmax 100 and 100 Delta were the most linear of the bunch. But TMY is two stops faster... HP5 and Tri-X were the worst performers. Another conclusion was that no compensation in development needed to be done, which is good news.

    100 Delta and HP5 definitely did not have the same reciprocity characteristics, according to Bond's test.

    You'll have to locate the article somehow.

    - Thomas
  3. Thanks Ulrich, that's the most useful article I've seen in a long while. I'll make a precis of the data to keep with my lenses.

  4. Tom,
    In case you are interested, Fuji's boast that Acros 100 shows very little reciprocity failure seems to have something to it--which I found out quite by accident. I don't recall whether the sheet included with the box of 4x5 provides extensive information for it, though, although that may be available elsewhere.
  5. I recently suggested in a German forum already to collect data on reciprocity-failure. It seems to me more valuable than information on developing times in respect to certain developers, as it's inherent to the respective film, largely independent from individual influences and moreover difficult to test without the proper equipment.

  6. Search www.unblinkingeye.com for "LIRF is Lurking at Your F-stop" by Patrick Gainer. It shows some interesting facts about reciprocity obtained by analyzing Howard Bond's data in an unusual manner.

  7. I've tested this film for astrophotography and it does have very good reciprocity characteristics. I could see that density of nebula was still building against background in test exposures up to 32 minutes. For terrestrial shooting this just goes to show that it does indeed have excellent performance, likely the best on the market with LIRF in mind. Fuji boasts no reciproity adjustment for exposures up to two minutes. I plan further tests but I'm a little concern about how easily it seems to scratch; I'm going to have to track that down.
  8. I just did a quick check with some data for HP5 from the Bond article. It really seems to work.


  9. Thanks for the article-

    using your graph for all films, the corrected exposure for an indicated time of 1 sec is 1.3 sec, for a time of 10 sec is 14 sec? am I doing this correctly? seems kind of low corrections for Tri-X in my experience- or I have been over-correcting...
  10. 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.
  11. 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.
  12. 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)

    100 Delta
    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.

  13. 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
    Coefficient Data:
    a = 0.72538705
    b = 1.06559210
    correlation coeff: 0.99999128

    Linear Fit: y=a+bx
    Coefficient Data:
    a = -36.07858400
    b = 1.20142490
    correlation coeff: 0.9997068

  14. 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!
  15. Pat,

    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.

  16. 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.
  17. Tom,

    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.

  18. Pat,

    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.

  19. 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.
  20. As I said in an earlier post, #13, kinda buried under the list of equations,

    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 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.

  21. 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
  22. Lee:

    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.
  23. 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.

  24. 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.
  25. 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.
  26. 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.
  27. Pat,

    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/LunarLight/moonlight_gallery/technique/reciprocity.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.

  28. Thanks for the correction- I was simply using your chart to add numbers- it's obviously way more complicated than that.

    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 :sad: - how does one perform the function "^"?
  29. 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.

    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.
  30. I've been playing around with Bond's data a bit more today, and moved from Curve Expert to QtiPlot under linux (it's also freely available for Mac and MS Windows if you install the necessary QT environment on those platforms).

    I've been looking at the consequences of adding the metered time to a log equation as Gainer does in his formula.

    Covington notes that the Schwarzschild formula accommodates the approximate logarithmic character of reciprocity failure, but is a good fit only at longer exposures. So Covington modifies the formula as follows.

    where t = time in seconds
    and 'p' is the Schwarzschild exponent, which varies between about 0.50 and 1.00, with 1.00 being perfect reciprocity.

    actual speed = rated speed * t^(p-1)

    actual speed = rated speed * (t+1)^(p-1)

    When this equation is manipulated to produce adjusted exposure times, one gets

    corrected time = (metered time +1)^(1/p)-1

    In the same way, Gainer's formula , where 'a' is a coefficient dependent on film type,

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

    is a better fit than the straight log fit because it makes the correction relative to the initial value.

    Gainer's formula can be rewritten as


    where 'b' is a constant with a value of 1.62
    and 'a' is a variable coefficient, dependent on the film behavior

    compare this to a straight log fit


    where 'a' is a variable coefficient
    and 'b' is a variable exponent

    Taking the cue from Covington and Gainer, one can add the value of x (which is the metered exposure time) to the straight log fit as follows



    corrected time in seconds = a * metered time ^ b + metered time

    The only difference between this model and Gainer's is that 'b' becomes a variable exponent rather than a constant exponent equal to 1.62, and this equation can be plugged into a curve fitting program like QtiPlot and regressed. So this is just a more generalized form of Gainer's equation to accommodate films that might not "believe in" Gainer's constant (as Pat puts it) for the exponent. BTW, it hasn't been mentioned in this thread, but that constant is also known as phi, the golden ratio, and is also the ratio in the Fibonacci series and many natural phenomena.

    Making the Gainer adjustment (adding in the metered time) to a standard log fit generally makes for a better fit to the Bond data, especially with time exposures at the shorter end of the spectrum.

    Doing just that with QtiPlot produces the following values when regressing Bond's data using the formula y=a*x^b+x All values but one hit within +/- 20% of Bond's data. TMY is actually a somewhat better fit to a straight log function. (R^2 and Chi^2 values are shown, but one must keep in mind that tweaking to optimize R^2 with data containing sufficient randomness can lead to silly numbers. See http://www.statisticalengineering.com/r-squared.htm )

    Bond Data Modified Power fits using QtiPlot

    using function: y=a*x^b+x
    where: y = adjusted time in seconds
    x = metered time in seconds

    a = 0.040427011642017
    b = 1.7298680795766
    Chi^2/doF = 3.5603085938797e+00
    R^2 = 9.9995145162988e-01

    a = 0.18601192358624
    b = 1.3478556218539
    Chi^2/doF = 1.9330084508589e+00
    R^2 = 9.9994757744607e-01

    100 Delta
    a = 0.056981442009898
    b = 1.5754970970282
    Chi^2/doF = 2.4755726666553e+00
    R^2 = 9.9993698631413e-01

    a = 0.029331463486986
    b = 1.8845746981645
    Chi^2/doF = 1.8558446352135e+02
    R^2 = 9.9883106078538e-01

    a = 0.20711252730778
    b = 1.5186636391859
    Chi^2/doF = 9.3638439358780e+01
    R^2 = 9.9936933497974e-01
    I'll attach a revised .pdf with the modified log regressions from Bond's data. You can easily build your own chart in a spreadsheet using your own data and regressions.

    For those without much spreadsheet experience, the following functions are standard in spreadsheets and flat ascii representations of formulae:

    the carat ^ in y^x means "raised to the power", y raised to the power of x
    the asterisk * is a multiplier, e.g. 3*2=6 This is to avoid confusion between any variable 'x' and the common handwritten "x" as a multiplier.
    Don't include spaces in your spreadsheet formula. I've only done that in this post for human readability.

    If you can't afford MS Office, openoffice.org has a completely free office suite that runs natively in linux, under MS Windows, and the new version 3.0 is now native on the Mac OS-X. openoffice will also create .pdf files.


    P.S. After posting I went back and calculated the average value of the exponent b in the regressions of Bond's data using the modified power equation.
    It's 1.61113 :smile:
  31. What you did is essentially the process I used: finding the best fit for each film to Bond's data and averaging the exponent of all the films. I plotted the resulting individual curves (the exponential part) on log-log paper. Sometimes the visual experience is more meaningful than the mathematical. The scatter about a straight line when 1.62 (or 1.61 for that matter) was used for all the films tested was as aceptable as the scatter about the optimum line for each film. The conclusion may thus be drawn that the average exponent obtained from all the films might have been obtained for rach film if enough repetitions of experiments were available. You may find as much scatter when a number of experienced photographers measure the lighting of the same scene. Each one may yet get a satisfactory negative.
  32. Is there anyway this could be put into a nice little Excel workbook where you plug in your metered exposure and out pops the corrected exposure?:D Or am I dreaming here? You could win the APUG Nobel prize and be heroes with such a product...I forsee fame, endorsment deals, talk shows, ...groupies...
  33. The chart attached to post #32 in this thread does that in 1/3 stop increments for the films with Bond data.

    You could do your own spreadsheet with the Bond data and information already posted, but you'd need to test reciprocity for other films that you might want to include.

    You could use Gainer's approach and use a pocket calculator with his formula and a list of films and appropriate coefficients.

    If you want to regress data that you have or get from someone else against a given formula, you could download CurveExpert for MS Windows, or QtiPlot for Win, Mac, or linux. Several good formulae are in this thread for the copying.

    Are you asking if you could do the regressions in Excel?

  34. As a matter of curiosity, I was trying to find where I had used the magic number in a report. I thought I had mentioned it in "LIRF is Lurking at YOUR F-Stop". Any way, it involves the square root of 5. Using the theorem of Pythagoras and a compass and straight edge, one can construct a line that is the square root of 5 time the length of whatever length you set the compass for. You can, of course, construct the perpendicular to a line and lay off 2 units one the line and one length on the perpendicular. The line forming the right triangle with those two sides has a hypotenuse = square root of 5. Use the compass and straight edge to add one unit to an end of that hypotenuse. Bisect the resulting line and each part is of length 1.618... units.

  35. dude- you guys are so far over my head....but yes- this chart is awesome- now...how do I use it- are the numbers under each film time corrected exposures (mm:ss?), OR adders, or multiplyers to get corrected exposure? this is an awesome tool- thanks in advance
  36. The times under the films are corrected times in mmm:ss (minutes: seconds) They are corrected from the metered times in seconds in the first column. The tinted times are the full stop numbers shown most often on light meters. The mmm:ss format for the corrected times is used to make it easier than converting hundreds or thousands of seconds to minutes. No adjustment of the corrected mmm:ss times is necessary, use as read. The data up to 240 seconds metered is within Bond's experimental range. Times adjusted from longer than 240 seconds metered are extrapolated beyond the experimental data.

    The latest version I posted uses the more generalized form of Gainer's power formula, where his constant 1.62 is made a variable, and regressed from the data Bond found for those films.

  37. A basic requirement of any equation describing reciprocity characteristics, it seems to me, is that it's constants for any given film should allow for a fairly general reciprocity curve. An equation that attempts to do so by the form:

    tc = a*tm^b

    does not meet that requirement. In fact, if the meter reading is assumed to be an inaccurate analog of the film's response, it would be more reasonable to say that the corrected meter response is tm + tc which then more closely matches the film's response. The the basic equation becomes:

    tc = tm + a*tm^b

    Now there are many more possibilities. One is that the constant b may in fact be a constant for all films and yet each film may require a different value of a.
  38. I asked basically the same question on the Ilford website some months ago, and the eventual answer coming back from their technical people was simply that they "stood by their curves". After reading all of this I'm getting a little annoyed at their simplistic and misleading answer to me.
  39. Thanks for all your hard work on this guys, I will be using the chart for my long exposures moving forward- I'll let you know how it works out.
  40. Patrick,

    Is there any advantage to the TI30X compared to any other scientific calculator one might own? I see from the specifications that the TI30X has an equation recall function but as this is a short equation I assume a adhesive label on the back of the calculator would sufficient.


  41. It just happened to be the one I found at my local drugstore that would do those functions. There is now a TI-30XIIS which I bought when I mislaid the other. More streamlined looking but otherwise about the same. Handy to have around in any case.