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# keithwms

#### Grain, tonality, format size and all that

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by , 06-01-2008 at 01:29 PM (3325 Views)
How much is grain per detail (and tonal smoothness) a function of format size?

First, the film grain per area is a constant of format size. This is important.

We can estimate grain increase per one stop increase in required film sensitivity as ~2x. In other words, if you shoot a film at ISO 200 then there will be ~2x more grain per detail than the same shot at ISO 100.

Obviously this is a very rough approximation and a rather pessimistic one at that. There are many different kinds of film grain, many different developers and developing procedures... and there is no reason to expect a linear relationship which will certainly fail at ISO extremes. Still, this ballpark estimate seems reasonable because detail per grain is ultimately nothing more than a signal to noise ratio, and if we shoot at ISO 200, we do so because the signal is 2x weaker than it would be if we could take the shot at ISO 100. The development process is basically an amplification process, so I think it's reasonable to say that 2x weaker signal corresponds to ~2x weaker overall signal to noise ratio. Again this is just a ballpark estimate! Of course it will fail at ISO extremes an for certain films and developers etc.

Alright... if you buy that a one stop increase in ISO means 2x as much grain per detail, then you see right away that a jump in format size which roughly quadruples the film area will give the same detail per grain as a one stop reduction in film sensitivity.

Let us list the format sizes and the approximate frame areas; I will define the letters A,B,C, etc. to denote roughly quadruple area format jumps:

35mm: 24x36 mm = 863 mm^2 = "A"
645: 56×41.5 mm = 2324 mm^2 = 2.7*A
67: 56×70 mm = 3920 mm^2 = 4.5*A = B
4x5: ~12903 mm^2 = 3.29*B = C
5x7: ~22580 mm^2
8x10: ~51612 mm^2 = 4*C

So here is my simple conclusion. The following exposures will yield roughly the same detail per grain:

Equivalent detail per grain:
35mm @ ISO 400
=6x7 @ ISO 800
=4x5 @ ISO 1600
=8x10 @ ISO 3200

35mm @ ISO 50
=6x7 @ ISO 100
=4x5 @ ISO 200
=8x10 @ ISO 400

Do you believe it? Obviously this is very rough approximation based on many assumptions.
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P.S. upon further reflection, I do believe that the factor of 2x above is a bit too pessimistic, it might be closer to sqrt(2)=1.4x due to photon counting statistics.
I think your factors are way off mark. From experience APX25 in a 6x9 back was equivalent to 5x4 APX100, and 400 ISO 5x4 is ahead of any 35mm film, even of 25 ISO.

Ian
Ian, actually, what you describe agrees surprisingly well with what I said.

Obviously my factors are going to work better when the formats are closer together and the two film speeds that you are comparing are in the middle ISO range, say 100 to 800 or so.

Moreover, as I said in the blog, "a linear relationship .. will certainly fail at ISO extremes." APX 25 is an ISO extreme... what 4x5" 400 speed APX film can we even compare it to, fairly?? So we wind up comparing it to hp5+, tmax, delta 400, etc. Then it's all apples and oranges.

Anyway, that said, let's see just how "way off mark" my estimates are. Atcually I don't think it's so bad as you imply:

APX25 ->APX100 = 2 stop increase
6x9 -> 4x5 = 1 format jump
so my simple theory is off by maybe 1 stop? Pretty good, no?

As for 400 speed 5x4 being well ahead of any 35mm film, sure but again I don't think I am that far off at all, considering the size of the jump. The ratio of the area of 5x4 and 35mm films is roughly fifteen. That is huge. So that implies something like 4-stop difference on the ISO scale, i.e. ISO 400 4x5 = approximately ISO 25 in 35mm format. Again that is placing the 35mm film right on the ragged edge of what is technically possible. Realistically, to get the very best out of the ISO 25 films in 35mm format requires some special development. So, some nonlinearity doesn't surprise me at all.

Anyway.. like I said.. simple theory based on one simple assertion about amplification of noise, just to give some ballpark ideas! The idea was to give people an idea of what a format jump really does for them, in terms of detail per grain.

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