I've put together this page of useful info, formulae & figures for people who want to design their own pinhole cameras or who are just interested in photographic technicalities.   In most cases you won't need to use the formulae, & the tables of figures will give you everything necessary, though some knowledge of basic maths & preferably a scientific calculator will be needed to work things through!

## calculating the exposure

 OK. So you have the pinhole and know its diameter. If your camera & pinhole combination is one of those shown in the table at the top of the page, you can simply read the aperture f/number there. To calculate the f/number, simply divide the focal length by the pinhole (lens) diameter. E.g. for a 50mm camera, that's 50/0.26 = f/192. That's why the "f/number" is written that way. In a pinhole camera the focal length is always the distance between the pinhole and the film. (If the same pinhole is used in a different camera, eg 100mm, its f/number changes to become 100/0.26 = f/384 (which, in photographic terms, is 2 stops (2 squared) smaller because the same amount of light is spread over 4 times the area.) Knowing the f/number, you can put this into a handheld exposure meter & read off the required exposure in seconds for whatever film you are using. If the meter won't handle an aperture that tiny, the best option is to meter for f/16 and multiply the reading by a compensation value. For typical pinhole cameras, this is shown in the "f/16 comp" column of the table above. To calculate, it's simply the square of the pinhole f/number divided by the square of the reference f/number. So, for a pinhole of f/192, that's (192x192) / (16x16)= 144 times. E.g. If metering at f/16 gives 1/64second. The exposure for the pinhole is (1/64) x 144 = 2.25 seconds. No exposure meter? - The Sunny 16 Rule - If you don't have an exposure meter you can use what's known as the "sunny 16 rule" to get a fairly good approximation of the correct exposure at f/16. In full sunlight, with an aperture of f/16, you need an exposure of 1/(film ISO speed). Double this for hazy sunshine, x4 for overcast / light cloud, x8 for heavy cloud. E.g. for Delta 100, in light cloud that's 1/100 second x 4 = 1/25 second exposure. Now, just as you would if using an exposure meter, you can use the f/16 compensation given in the table at the top of the page to arrive at the correct exposure for your pinhole & camera combination.

## film & reciprocity law failure

Usually with photographic film & other light sensitive materials, we make the assumption that the exposure time is doubled for each halving of the light level. ie 1/2 light => 2/1 exposure. One figure is the reciprocal of the other, and the rule is known as the reciprocity law. It holds true most of the time from exposures of hundredths of a second to around a second or so - as used in most cameras.

With pinhole cameras, because the aperture is so small the exposure is correspondingly large, typically ranging from 1 second to many minutes or even hours. When exposure times exceed a few seconds, most films don't "see" as much light as they should do, and so the exposure time has to be lengthened to compensate for this. The compensation varies from film to film and the exact amount required is often not easy to determine. Sometimes manufacturers include details in their technical data sheets for the films, though this tends to be quite vague as the process by which the non-linearily occurs is still not fully understood.

The table on the right gives a guide to the compensation required for Ilford Delta 100 film which I use. It's a rough starting point for other black & white film types. There's a huge discrepancy at long exposure times, so it really is necessary to compensate if you want to see anything at all on your film! Most colour films don't follow this table too well & you end up with strange colour shifts, though the effect can be interesting... Trial & error is the order of the day. But if you want accurate colour, by far the best choice is Fuji Provia 100 colour transparency film which maintains its accuracy without requiring any compensation up to about 2 minutes! It requires E6 processing though, which most high-street labs no longer offer.

 Ilford Delta 100 long-exposure compensation measured exposure compensated exposure 1s 1s 2s 3s 4s 8s 8s 22s 16s 1m 32s 3m 65s 8m 2m 22m 4m 1h 8m 3h 16m 8h

## ... and finally

If you've got this far, you can now treat yourself to that glass of warm & rather flat beer which you poured earlier - remember? You're also probably wondering how to keep track of all of these figures when out in the field. Don't forget that you need only calculate once for your particular choice of pinhole, camera and film type, then simply print a table on a piece of paper, laminate it if you can & attach this to the pinhole camera itself.

The procedure out in the wilds is then simply: meter - look at table - count the exposure. Done!

Happy pinholing!

All contents © Martin Winfield, 2011