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!
The first thing to realize when making a pinhole is that the hole will need to be a lot smaller than the diameter of most sewing pins, more akin to the size of an acupuncture needle, typically 0.1 - 0.5mm.
You might think that the pinhole should be as tiny as possible as this will create the sharpest image. Theoretically, this is true up to a point, but light has certain properties of a wave (think ripples on a pond) which cause it to spread out when the wave reaches a narrow gap. This property is known as diffraction, and it is the bluriness caused by this which sets a lower limit for the useable size of the pinhole.
The table opposite gives pinhole diameters and resultant aperture f/number for typical camera sizes & is a good practical reference for general use. If using a light meter set to f/16, multiply the exposure reading by the figure in the f/16 comp(x) column.
The value of c = 1.56 has been arrived at by various theoretical means: photographic pioneer Lord Rayleigh used a value of 1.9, though anything between 1.2 - 2.0 is ok. The optimum pinhole size also depends on the scale of the object being photographed on the film itself. For very close-up photos, the pinhole size should be reduced by about 20%. What this means in practice is that there's an acceptable, and quite wide, margin of error. The actual size isn't critical, though it helps to get it within about 30% of the intended value. It's more important to know what size you've ended up with, as this affects the f/number and hence the exposure time.
Remember that all of these figures are based on achieving the sharpest image. But don't lose track of the fact that you're making a pinhole camera. If maximum sharpness really is required, why not just go out and buy the latest digital SLR...?
pinhole materials & what to do
The pinhole should be made in a material which is thin, opaque and soft enough to be pierced easily. Aluminium sheet is ideal and is generally available at your corner shop in a form which comes with free beer! Save the beer for later, as you need a clear head for this bit. Cut out a small piece from a flat part of the can (avoiding embossed logos, etc) & hold it on a hard surface. Using an ordinary sewing needle held firmly in a pair of pliers, pierce the centre of the aluminium while rotating the sheet beneath it. This is much easier than holding the aluminium still & twisting the needle. All that's required is to pierce the material. Don't go too deep. Then, flip over the sheet and gently sand away the back of the hole using a piece of 1000 grade wet & dry paper. Sand just enough to remove the burr, blow out the dust, then the pinhole can be checked.
getting it the correct size
To inspect your work, a microscope with graticule is ideal, but if such a tool isn't to hand, a computer scanner will do almost as well. The scan should be made in "film scanning" mode, with backlight on, at maximum resolution. (BUT most flatbed scanners are limited to a maximum optical resolution of about 2000 pixels per inch (ppi / dpi), even if they claim to offer far more. So use no higher that the 2400 dpi/ppi setting.) When zoomed in, the pixellation of the image can be used to measure the pinhole diameter. At 2400 pixels per inch, one pixel = 0.0106mm. If you're using Photoshop or similar, you can use the circular marquee tool to select the pinhole, and let it do the counting for you.
You'll probably need to sand some more, and even prick the hole again with the needle to get it as circular as possible. (If the hole goes over-size, mark it with the measured diameter & save for another day & another pinhole camera project.) A useful method of cleaning out the hole is to use a short length of wire of the correct diameter. Of course you'll need to be able to measure this (or read the size from the cable reel). 0.2mm diameter is a very common size for individual strands of flexible wire.
For wide angle cameras, the thickness of the material can affect the performance at the edges of the frame. Beer can* is usually about 0.1mm thick, and a slightly thinner variant is the foil used in take-away food containers. It's a bit more fiddly to work with, but otherwise is ideal. The 0.2mm pinhole above was made from the base of a 0.05mm foil food tray. Kitchen foil, though thinner still, is far too fragile to be worked.
* If you've not read Robert Pirsig's Zen and the art of motorcycle maintenance, read it NOW. Then the absolute suitability of this everyday material for the purpose will be confirmed.
Pinholes in aluminium foil.
L: 0.35mm dia in "beer can", R: 0.20mm dia in "takeaway tray".
Scan of the hole at 2400ppi in Photoshop.
The marquee is 19 pixels diameter, so that's 19 x 0.0106 = 0.20mm. (which agrees with the microscope view!) This is a raw scan with no attempt made to reduce flare in the scanner.
Count just the brightest pixels to measure the hole diameter.
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
... 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!
All contents © Martin Winfield, 2011