Reciprocity formulas (for Ilford films)

[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:


Te=tm[4.03(log tm)2-5.24(log tm)+4.19] (http://www.flickr.com/photos/janokelly/6804638225/) (this formula is on the side, on the first post); and
f(x)=0.105x2+0.2007x+0.821 (http://www.flickr.com/groups/hp5/discuss/72157629336985208/)


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:

106912

(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

[Jerry Bodine]

You may find this (http://www.unblinkingeye.com/Articles/LIRF/lirf.html) 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 (http://www.willwilson.com/articles/0403Bond_Reciprocity2.pdf) 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.

[Harley Goldman]

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.

[Heroique]

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 :D:
“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.’ ”

[BradS]

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:


Te=tm[4.03(log tm)2-5.24(log tm)+4.19] (http://www.flickr.com/photos/janokelly/6804638225/) (this formula is on the side, on the first post); and
f(x)=0.105x2+0.2007x+0.821 (http://www.flickr.com/groups/hp5/discuss/72157629336985208/)


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.





.... 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. ???

[BradS]

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).

[macandal]

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.

[BradS]

I am mostly interested in Delta 100 data.

Unfortunately, I do not believe that Ilford have supplied accurate reciprocity information for Delta 100.

[Cletus]

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.

[BradS]

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

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

ta = 0.1015873tm2 + 2.15873tm + 0

[BradS]

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

This is certainly the more pragmatic approach. All of the graphs and math, although fun, amount to a grand guess.

[tgtaylor]

I've been using Ilford's reciprocity curve for Delta 100 with great success. Appears to be spot on in my experience.

Thomas

[Cletus]

This is certainly the more pragmatic approach. All of the graphs and math, although fun, amount to a grand guess.


Yes, indeed, but if ever there were an educated guess I will be the first to admit, your's is it!

[macandal]

I've been using Ilford's reciprocity curve for Delta 100 with great success. Appears to be spot on in my experience.

ThomasSo how do you estimate times that do not appear on the curve? When you get to times above 200 seconds/~3 minutes?

Thanks.

[BradS]

Here’s a chart I've shared that's easier and more reliable (in my "KISS" experience).



• 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)


This is actually in close agreement with Kodak's suggestion for Tri-X films (Kodak Data sheet F-4017, page 2) which says essentially:


metered - adjusted
1 sec - 2x (add one stop)
10 sec - 4x (add two stops)
100 sec - 8x (add three stops)


I think people have trouble extrapolating this to longer times and feel uncomfortable with the coarseness of the table.

It is easy to express this relationship in an simple equation...
ta = tm * 2(1 + log10(tm))

which can be re-written:
ta = 2 * tm (k + 1), where k = log10(2)

or, replacing k+1:
ta = 2 * tm (1.3)


This is probably a pretty good starting place for most films.

[macandal]

or, replacing k+1:
ta = 2 * tm (1.3)


This is probably a pretty good starting place for most films.Thanks. I'll use this.

[BradS]

Yes, indeed, but if ever there were an educated guess I will be the first to admit, your's is it!

Thanks. :)



Thanks. I'll use this.

Cool. Hope it works ok for you. :)

[Andrew O'Neill]

Formulas are nothing but a guesstamate. You really should do your own testing. I have found Ilford's data to be a bit over the top. I have been using my own tested data in the field for 16 years for HP5 and FP4 and have been satisfied. I also have data for Delta 100 somewhere. If I dig it up, I can post it if you like.

[macandal]

I also have data for Delta 100 somewhere. If I dig it up, I can post it if you like.That would be very much appreciated. The more information the better. Thanks.

[BradS]

Formulas are nothing but a guesstamate. You really should do your own testing. I have found Ilford's data to be a bit over the top. I have been using my own tested data in the field for 16 years for HP5 and FP4 and have been satisfied. I also have data for Delta 100 somewhere. If I dig it up, I can post it if you like.


I concur. I hope people understand that all that I have done is give an equation for the relationship provided by the manufacturer. In Ilford's case, by choosing three points from the graph in their datasheet and writing the equation for the parabola that passes through those three points and in the and similarily with the Kodak data, all I have done is express in an equation what they say in word and in the table. There is no magic to this. The equations are no better than the data from the respective manufacturer.

As with so many things in photography, take this stuff as a starting point and develop (pun?) numbers, tables, graphs, whatever that works for you...based upon your own empirical evidence.

[tgtaylor]

So how do you estimate times that do not appear on the curve? When you get to times above 200 seconds/~3 minutes?

Thanks.

Mathematically model it and write the equation - Ilford has done all the work for you. Then it's just a plug in problem quickly solved with a scientific hand calculator. Alternatively you can ask Ilford for the equation I'm sure that they will oblige.
Thomas

[BradS]

Mathematically model it and write the equation...
Thomas

Which is what this is...


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

ta = 0.1015873tm2 + 2.15873tm + 0

[jwaddison]

You can make an equation yourself by googling and downloading a free copy of Curve Expert. You provide data points from the graph.

[StoneNYC]

Get an iPhone...

Then get this...

https://itunes.apple.com/us/app/reciprocity-timer/id459691262?mt=8

Problem solved :)

Someone else did the work for you :)

He is also updating it soon, it's a member here on LFF, lots of new films coming. I have no affiliation other than I use this app all the time and can focus on thinking about the shot instead of doing math.

[Ed Bray]

One of the reasons I like using Adox 25 is its great anti reciprocity attributes, 1 sec = 1.2x, 10 secs = 1.3x and 100 seconds = 1.5x this compared to FP4+ where 10 seconds requires 30 seconds and 30 seconds requires 155 seconds and 100 seconds is off the graph by some large margin.

By the time you get to an exposure time of 30 seconds for FP4 you will be shooting at the same time as for 100 seconds with Adox 25 (both 150 seconds ish) from then on, you are better off using Adox 25 as it will give you a shorter exposure time regardless of the initial ISO.

[StoneNYC]

One of the reasons I like using Adox 25 is its great anti reciprocity attributes, 1 sec = 1.2x, 10 secs = 1.3x and 100 seconds = 1.5x this compared to FP4+ where 10 seconds requires 30 seconds and 30 seconds requires 155 seconds and 100 seconds is off the graph by some large margin.

By the time you get to an exposure time of 30 seconds for FP4 you will be shooting at the same time as for 100 seconds with Adox 25 (both 150 seconds ish) from then on, you are better off using Adox 25 as it will give you a shorter exposure time regardless of the initial ISO.

Fuji Acros100 can be exposed for 2 minutes before any reciprocity adjustments need to be made, FYI

[Ed Bray]

Fuji Acros100 can be exposed for 2 minutes before any reciprocity adjustments need to be made, FYI

Not available in 5x7 though :(

[StoneNYC]

Not available in 5x7 though :(

OH! Yes point taken... But isn't TMY-2 available in 5x7? I just looked at B&H and they only have TXP in 5x7 and TMX in 5x7 but not TMY-2... Hmm freestyle doesn't have it either...

Though I don't see ADOX 25 either... I see ADOX CHS II 100 but I can't imagine that's better than Ilford, but I also would guess that TXP doesn't have as good an anti-failure than Ilford, but I don't have the chart on hand to know for sure.

Anyway that app I listed does work ;)

[evan clarke]

Ok, All. Forget all this scientific calculating..GET ENOUGH EXPOSURE AND PHOTOGRAPH SCENES THAT WILL PRINT. Log . bs has no place in making fine prints.

[Jerry Bodine]

Ok, All. Forget all this scientific calculating..GET ENOUGH EXPOSURE AND PHOTOGRAPH SCENES THAT WILL PRINT. Log . bs has no place in making fine prints.

Point well taken. To each his own, but how do you know when exposure is ENOUGH? Open shutter, go have a few pitchers of beer, shoot some pool, come back the next day to see how we're doing?

[tgtaylor]

In Ilford's case, by choosing three points from the graph in their datasheet and writing the equation for the parabola that passes through those three points...

But Ilford's graph is not that of a parabola (Y=X^2). Suppose x=10 seconds then Y on the graph is around 30 seconds and not 100 as it would be if the curve was a parabola. From personal experience their graph is accurate. My last long exposure x=30 and from the graph Y=160 and that's what I shot it at and the negative came out well exposed.

Thomas

[Heroique]

Ok, All. Forget all this scientific calculating..GET ENOUGH EXPOSURE AND PHOTOGRAPH SCENES THAT WILL PRINT. Log . bs has no place in making fine prints.

As a devoted "KISS"-er, I feel some measure of sympathy for this reply, but certainly not 100% sympathy. ;^)

Photography is part math, and "It should be apparent how deftly logs represent arithmetic numbers," says Ansel Adams in The Negative. They are, he adds, "a form of mathematical shorthand."

AA explains how easy logs are to understand and how useful they can be here:

• The Negative, Appendix 5 (a splendid two page read!)
• The Print, Appendix 2

For example, a quick glance at Appendix 5 (above), and you'll understand why ND filters are described – mysteriously to most people – as .3, .6, .9, and so on.

Even more interesting, AA calls .3 "the one most important log value" for photographers since it represents the ever-recurring 1:2 relationship in our work.

[BradS]

But Ilford's graph is not that of a parabola (Y=X^2). Suppose x=10 seconds then Y on the graph is around 30 seconds and not 100 as it would be if the curve was a parabola. From personal experience their graph is accurate. My last long exposure x=30 and from the graph Y=160 and that's what I shot it at and the negative came out well exposed.

Thomas

The general equation of a parabola is y =ax2 + bx +c. The equation I gave in post #10 is in fact the equation of a parabola and if you try plugging in a few points, I think that you'll find that the equation agrees very closely with the graph given in the Ilford Datasheets.

[Ed Bray]

OH! Yes point taken... But isn't TMY-2 available in 5x7? I just looked at B&H and they only have TXP in 5x7 and TMX in 5x7 but not TMY-2... Hmm freestyle doesn't have it either...

Though I don't see ADOX 25 either... I see ADOX CHS II 100 but I can't imagine that's better than Ilford, but I also would guess that TXP doesn't have as good an anti-failure than Ilford, but I don't have the chart on hand to know for sure.

Anyway that app I listed does work ;)

No, unfortunately manufacture of Adox CHS 25 has ceased. Luckily for me I managed to buy some of the last few boxes of 5x7 and have 6 full boxes left plus 1 half box.

[tgtaylor]

The general equation of a parabola is y =ax2 + bx +c. The equation I gave in post #10 is in fact the equation of a parabola and if you try plugging in a few points, I think that you'll find that the equation agrees very closely with the graph given in the Ilford Datasheets.

I stand corrected - it does model as a parabola! Thanks for the equation.

Thomas

[Vaughn]

One of the reasons I like using Adox 25 is its great anti reciprocity attributes...

That should be great pro reciprocity attributes... (or great anti reciprocity failure attributes, if one prefers the double negative)

Sorry, I have the flu and claim the right to be a bit of an ass-hole tonight...

Vaughn

[StoneNYC]

That should be great pro reciprocity attributes... (or great anti reciprocity failure attributes, if one prefers the double negative)

Sorry, I have the flu and claim the right to be a bit of an ass-hole tonight...

Vaughn

Have you been sick all year? ;)

(That's a bit if a joke).

[Vaughn]

Have you been sick all year? ;) (That's a bit if a joke).

Careful how you joke with a sick guy...if you were anywhere near, I'd breathe on you...

[StoneNYC]

Careful how you joke with a sick guy...if you were anywhere near, I'd breathe on you...

Haha!! Well, I'll be cautious, but I'm not that worried, I dated a doctor for over a year, that ended and now I'm dating a funeral director/embalmer... So I'm basically immune to germs now... Haha ;)

Happy Holliday's man, and feel better!

[Jim Fitzgerald]

Vaughn, get better and Merry Christmas!!

[Jerry Bodine]

Vaughn, way back in my college days I quickly broke the WORST cold I've ever had by getting in a shower so hot I could hardly stand it to get the body temp up, then two shots of straight whiskey, then rolled up wool blankets with head covered, and sweated it out. Woke up and it was gone in no time. Just thought I'd mention it.

Happy Holidays to you and all here.

Jerry

[Colin D]

I'm ressurecting this discussion from a different angle, I think. What about adjustments for developing after doing long exposures with these films, is there a formula for working this out? I did read somewhere once, can't quote it verbatim though, that if you double the time, halve the development, or triple the time, one third the development, which sounds more like the KISS theory than a mathematical standard.

[StoneNYC]

I'm ressurecting this discussion from a different angle, I think. What about adjustments for developing after doing long exposures with these films, is there a formula for working this out? I did read somewhere once, can't quote it verbatim though, that if you double the time, halve the development, or triple the time, one third the development, which sounds more like the KISS theory than a mathematical standard.

Makes no sense, if you adjust properly for reciprocity you develop as normal....

[Colin D]

On face value that makes good sense SNYC, I must try and track down the article that suggested otherwise. Whoever wrote it had what seemed valid reasons for their rationale, but on reflection there is an element of uncertainty. If I find it I'll post it.

[StoneNYC]

On face value that makes good sense SNYC, I must try and track down the article that suggested otherwise. Whoever wrote it had what seemed valid reasons for their rationale, but on reflection there is an element of uncertainty. If I find it I'll post it.

Well also in theory if you don't compensate for reciprocity failure in exposure you can push the highlights with a longer development like any normal film you've under exposed... But you will get an image that's higher in contrast and lower in shadow detail.

That's basic photography though...

[Taija71A]

I'm ressurecting this discussion from a different angle, I think. What about adjustments for developing after doing long exposures with these films, is there a formula for working this out? I did read somewhere once, can't quote it verbatim though, that if you double the time, halve the development, or triple the time, one third the development, which sounds more like the KISS theory than a mathematical standard.



Makes no sense, if you adjust properly for reciprocity you develop as normal....

____

Hi Colin! Is this the Table... That you were perhaps referring to?

_________________________


... from Ansel Adams: The Negative (The Ansel Adams Photography Series / Book 2).

Chapter 3 (Exposure).


Table 1 (Correction for the Reciprocity Effect).

If indicated exposure time is (in seconds):

1
10
100

Use this development change:

-10%
-20%
-30%

_________________________


The above cited chart from AA is of course... Nothing more than a 'Basic' guide (*Depending upon the respective B&W Film that you are using).

But, it all does makes perfect sense (when you think about it) and examine the 'Shape'... Of some various Film Characteristic Curves.
--

Best regards,

-Tim.
_________

[Colin D]

That is sort of along the lines I was thinking actually. I did try a 30% development reduction for HP5 on a 6 min exposure with reasonable results which led me to believe there was some merit in the idea but the exact maths I wasn't sure about.
Well if AA was a promoter of this process it must have some merit.

Cheers

[Taija71A]

____

Good stuff Colin! :)
Glad to be of some assistance to you...

Cheers!
_________

[StoneNYC]

That is sort of along the lines I was thinking actually. I did try a 30% development reduction for HP5 on a 6 min exposure with reasonable results which led me to believe there was some merit in the idea but the exact maths I wasn't sure about.
Well if AA was a promoter of this process it must have some merit.

Cheers

Remember he was using an emulsion that doesn't exist anymore.

I highly doubt this would work for Acros100 and certainly not TMY-2 as it's highly affected by over and under development. But that's just a guess.

[Taija71A]

... I highly doubt this would work for Acros100 and certainly not TMY-2 as it's highly affected by over and under development. But that's just a guess.


Wrong Guess. It is 'Under Development' -- That we are speaking about here!




Use this Development change:

-10%
-20%
-30%


Would you care to try again? :D

[kintatsu]

There was a simple one, I think it was on darkroomagic.com, that showed a couple films and then a column for conventional films. I've used that with success, it even shows the approximate effects on contrast, as in N+x. I think it was Ralph Lambrecht's site. The site is no longer, it would appear.

[ImSoNegative]

I found a great formula that works everytime, not sure if anyone else has posted it yet but here goes: 1.7 multiplied by metered time
plus .12 multiplied by metered time squared= corrected time, this formula works like a charm for me

[gbogatko]

How does one post excel spreadsheets (.xsl files). I have a S.S. that was based on some formula that I read about on APUG. It gives me good results.

George

[Boinzo]

As StoneNYC says - forget it. Just get my App! :-)

I wish this discussion had been around when I started developing Reciprocity Timer 3 years ago.

This is the formula my app uses for Delta 100 and for HP5+

e = (0.51 * (m^1.62)) + m

where e is actual exposure and m is measured.
This is based on the Gainer/Bond Method as outlined in the article linked in the first page.
This yields times very close to Ilford's official charts.