Mathematical Formula For Acros B&W Film Reciprocity

[Flauvius]

What is the mathematical formula to determine reciprocity for Fuji Acros b&w sheet film?

Flauvius

[Leigh]

It has no significant reciprocity law failure.

Per the datasheet (readily available online), there is no correction required out to 120 seconds, and
only 1/2 stop required out to 1000 seconds.

Acros is the only 4x5 film I shoot, and I've gone through a couple thousand sheets.

It's impossible to blow the highlights.
You look at the exposure curve and the upper end is a straight line.

99052 Click on image for a larger version.

- Leigh

[Nathan Potter]

I've always thought that the physical principles behind film reciprocity seem devilishly hard to understand and as Leigh has concluded I think the complexity of the process is too multi-variant to define by a reasonable formula for any film. Thus I know of no simplistic formula that could be useful to a casual user. The reported reciprocity of any film is determined experimentally by the manufacturer and in fact generalizes the exposure vs density over the visible spectrum.

At first cut one would suppose that the reciprocity of any film is a function of only the dose of exposure (time X intensity), in physics terms: watts/square meter X time. But right off, the reciprocity of a film is not linear with the product of dose but changes with intensity variation and time variation.

That is only the start. Most B&W films use dye couplers to enhance performance and these act as a third variable affecting reciprocity in a nonlinear way. Next actual reciprocity is a significant function of the photon energy wherein a single Xray photon, for example, is sufficient to form a latent image by exciting up to hundreds of electrons per Xray photon. On the other hand a near IR photon may be insufficient to free but a single electron in the halide emulsion. It's all about the particle energy in eV (electron volts).

Lastly reciprocity is a function of the temperature of the emulsion which microscopically traces to a change in the liberated electron mobility and mean free path in the halide emulsion.

All in all it's too much of a mess to put in a neat universal package that could be applied consistently across a plethora of different film types. Just rely on data from the manufacturer or take the time to do your own tests under the simplified conditions that you expect to use.

If you can lay your hands on a copy "The Theory of the Photographic Process" by Mees and James is quite informative.

Nate Potter, Austin TX.