[alt-photo] Ultra Long Exposure Reciprocity Failure?

[Francesco Fragomeni]

Hi all,

I've been trying to figure something out with this for a while now and my
guess is that the only real answer is testing but I'm hoping that someone
here might be able to offer some mathematical insight that I haven't
thought of or seen elsewhere. I am interested in making some ultra long
exposures and I am looking for a way to approach calculating the rate of
change in reciprocity failure as the exposures get longer. I understand
that reciprocity failure is not linear but logically there should be a way
to mathematically work out the rate of change of the failure over the
increase in exposure. I'm probably wrong about that otherwise someone would
probably have solved for it by now but alas I'll still put the question out
there.

A few broad questions:

I understand that with Solargraphy, exposures can be made on paper (rather
then film) for extraordinary long periods of time and reciprocity is not an
issue partly because paper does not have the same reciprocity failure
characteristic as film and also because in Solargraphy the latent image is
actually burned into the emulsion in positive (I believe). For an image to
be made in this way, must the sun actually be present in the frame and can
these ultra long exposures be made with the sun out of the composition? I'm
unsure of whether or not the intensity of the sun plays some role in the
etching of the image in the paper. To me, it makes sense that these types
of images can be made with or without the sun in the scene as they seem to
simply be the result of gross overexposure which effectively prints out on
the paper. Can someone confirm this or correct me if I am incorrect?

In reference to ultra-long exposures on film, a good example is the work of
Michael Wesley. I think his work was done on film. This is the basis for my
wondering how one can make ultra long exposures into months or years using
a material with a reciprocity failure characteristic like film has. Perhaps
at such long exposures film behaves like paper and prints out and
reciprocity is no longer an issue to be concerned with. Somehow I don't
think thats the case but I suppose its a possibility. Can anyone shed light
on this?

In the end, I'm primarily concerned with learning if there is a way, an
equation perhaps, that can be used to determine the rate of change in
reciprocity failure over the increase in exposure time. There must be a way!

Any insight from you big brains would be very helpful!

Thank you!

-Francesco Fragomeni
www.francescofragomeni.com