Film granularity - technical

[alanrockwood]

I have a question about film granularity as a function of density.

By granularity I mean the standard deviation of the density of a series of measurements using a circular region of film that is 0.048mm in diameter. The film would be uniformly exposed. The results are multiplied by 1000. At a density of 1 a fine grain film like T-Max 400 has a a granularity of 10.

In general, granularity for conventional black and white film increases with density. My question is "how much?" I realize that this would depend on the film type and developer conditions, but there must be some kind of "ball park" figures. For example, if we assume that the granularity is a linear function of density, then would a slope of the log exposure vs. density curve typically be about 0.5? If so then it would mean that film with a granularity of 10 at a density of 1 would have a granularity of 15 at a density of 2. If the slope was 2 then the granularity at a density of 2 would be 2.

I have searched in vain for information that is quantitative for popular film types.

What think ye on the matter?

Note added later: where I said "slope of the log exposure vs. density curve" I should have said "slope of the granularity vs. log exposure curve".

 

[Europan]

A rather academic question. I assume it to be non-linear, asymptotic with increasing density because you have more silver wool developed and packed together in those areas up to a maximum. Looking at the silver perpendicularly to the film surface seems to be an abstract approach to me. It has been found that reproduction of the taking lens geometry at projection, the use of the taking lens itself in projection, yields a different image quality with finest-grain emulsions. The silver must not be developed out into fuzzy patterns but rather stay as compact and tight as possible. So with popular film types as you say or high-speed films as I say the function in question most probably gets an empiric answer.

 

[bernard_L]

A rather academic question

+1
Even if you knew the answer, how would that change your approach to taking pictures or making prints?

Or, if you are seriously interested, why don't you S**N a film exposed through a step wedge (providing various density values) and compute the granularity. Scanning at, say, 2500dpi provides an effective aperture of 0.01mm (provided 2500dpi is honest and not interpolated). Import the D*****L image into a suitable software (matlab, scilab, octave, python...), generate in software rows of 0.05mm apertures, compute rms, and woaaalà.

 

[Alan Johnson]

Granularity as a function of density is discussed, with references, on p 528 of The Theory of The Photographic Process by Mees & James 3rd ed.
It is not necessarily the same for all materials, The Selwyn Granularity in theory is proportional to the square root of the density.
There are later modifications mentioned.

 

[ic-racer]

Granularity is proportional to the cube root of the density.