Thread: Reciprocity formulas (for Ilford films)

1. Reciprocity formulas (for Ilford films)

I was looking for information on the reciprocity failure compensation for HP5+ and Delta (in particular Delta) and I found two formulas; and since Ilford claims that the reciprocity failure is the same for the two films I'm asking (given by the charts they post), then I found these two formulas:

1. Te=tm[4.03(log tm)2-5.24(log tm)+4.19] (this formula is on the side, on the first post); and
2. f(x)=0.105x2+0.2007x+0.821

I entered some times in seconds. I entered the time in seconds that appears on the Ilford chart (1 to 35 seconds), then I entered a couple of fractions of seconds, and then minutes (1 to 5 minutes, in seconds). Well, the data doesn't quite match. Check it out:

ilford rf table.zip

(The first caluculation is using formula 1 and the second one is using formula 2.)

The numbers don't quite match. At one second, according to the chart, there should be no adjustments, it should still be 1 seconds, yet, according to the formula, there needs to be an adjustment. The numbers become more different as the seconds increase, especially when we get to the minutes.

Does anyone have a more reliable formula to use? I know there are apps out there, but some of us don't have "smart" phones or iPads to carry around. Or, for the more mathematically inclined, how can one construct a formula from the data (the chart) given?

Thanks

2. Re: Reciprocity formulas (for Ilford films)

You may find this article interesting; it describes an empirical method for determining reciprocity characteristics for any selected film/developer. Since Ilford may at times make unannounced changes to a given emulsion, it's best to test the materials yourself.

And here is another article (recommend reading this first).

I, too, went down this path some time ago and found results reported from a number of other users and manufacturers to be all over the map. So it's best to do your own tests.

3. Re: Reciprocity formulas (for Ilford films)

I have been using the Delta 100 times provided by Howard Bond in the article referenced by Jerry above (the one he recommends reading first). I only recently began to use Bond's recommendations and so far, so good. They work rather nicely for me.

4. Re: Reciprocity formulas (for Ilford films)

Originally Posted by macandal
Does anyone have a more reliable formula to use?
Here’s a chart I've shared that's easier and more reliable (in my "KISS" experience).

Note that corrections start at 2 seconds.

It’s for traditional b/w films (such as HP5+ – not T-grain films like Delta), until one becomes more familiar w/ personal equipment & film, darkroom processing habits (such as “N-1” or “N-2”), and preferred results. As you learn more, adjust to your taste:

• Metered 2 sec. – use 4 sec (2x)
• 4 sec – use 12 sec (3x)
• 8 sec – use 32 sec (4x)
• 15 sec – use 75 sec (5x)
• 30 sec – use 3 min (6x)
• 60 sec – use 7 min (7x)
• 120 sec – use 16 min (8x)

Over time, my personal reciprocity charts for various films depart more and more from the chart above, and from manufacturing suggestions, but not by a very significant amount.

-----
Master’s note :
“This is commonly known as ‘failure of the reciprocity law’,” AA says in his book, The Negative, “but I prefer the term reciprocity effect as it is not actually a ‘failure.’ ”

5. Re: Reciprocity formulas (for Ilford films)

Originally Posted by macandal
I was looking for information on the reciprocity failure compensation for HP5+ and Delta (in particular Delta) and I found two formulas; and since Ilford claims that the reciprocity failure is the same for the two films I'm asking (given by the charts they post), then I found these two formulas:

1. Te=tm[4.03(log tm)2-5.24(log tm)+4.19] (this formula is on the side, on the first post); and
2. f(x)=0.105x2+0.2007x+0.821

I entered some times in seconds. I entered the time in seconds that appears on the Ilford chart (1 to 35 seconds), then I entered a couple of fractions of seconds, and then minutes (1 to 5 minutes, in seconds). Well, the data doesn't quite match. Check it out:
I cannot see the graphs or tables you've attached so I do not quite understand the nature of the error but you've copied equation #2 wrong (compared to the one mentioned in the link).

The post in the link states that the resultant equation was calculated using least squares regression....however, if we simply choose three points off of the graph supplied on the Ilford Data sheet and assume the relationship is quadratic, then a suitable equation can be determined fairly easily using linear algegra.

So, let us choose three different points from the graph in the Ilford data sheet and do the algebra....
the points (5,12.5), (22.5,100), (35,200) give the equation
ta = 0.1tm2 + 2.25tm - 1.25

This fits Ilford's graph perfectly at the three points we used to derive the equation but will diverge outside that region. I think it will do better at the high end and poorer at the low end.

Originally Posted by macandal
.... At one second, according to the chart, there should be no adjustments, it should still be 1 seconds, yet, according to the formula, there needs to be an adjustment. The numbers become more different as the seconds increase, especially when we get to the minutes.

Thanks
What chart are you looking at? The graph in the Ilford data sheet that I have has increments of 5 seconds on the horizontal axis and 25 seconds on the vertical. ???

6. Re: Reciprocity formulas (for Ilford films)

Also, many people are of the opinion that the reciprocity of Delta 100 is not correctly represented by the graph in the Ilford Data sheet. My own experience with thse two films also strongly suggests that the reciprocity characteristics of HP5+ and Delta 100 are quite significantly different (but the data sheets imply that they are the same).

7. Re: Reciprocity formulas (for Ilford films)

Also, many people are of the opinion that the reciprocity of Delta 100 is not correctly represented by the graph in the Ilford Data sheet. My own experience with thse two films also strongly suggests that the reciprocity characteristics of HP5+ and Delta 100 are quite significantly different (but the data sheets imply that they are the same).
I am mostly interested in Delta 100 data.

8. Re: Reciprocity formulas (for Ilford films)

Originally Posted by macandal
I am mostly interested in Delta 100 data.
Unfortunately, I do not believe that Ilford have supplied accurate reciprocity information for Delta 100.

9. Re: Reciprocity formulas (for Ilford films)

I think Heroique's approach is the most practical and is certainly more practicable for those of us without the mathematical chops you guys appear to possess.

I pretty much always just estimate long exposures (loosely based on Heroique's table) and usually get a usable negative.

10. Re: Reciprocity formulas (for Ilford films)

following up to my prior post...(slaps head) of course, the sane thing to do is to force the estimated curve through the origin...

choose the points (0, 0), (22.5, 100), (35, 200) and you get the equation:

ta = 0.1015873tm2 + 2.15873tm + 0

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