The right pinhole diameter is worked out from the depth of the box using Rayleigh's formula, d = 1.9 × square root of (f × 0.00055 mm), and lies between 0.2 and 0.8 mm for common boxes: the deeper the box, the larger the pinhole needs to be. The pinhole diameter is the only optical setting on a pinhole camera, and it is what separates a readable image from a grey mush. Everything comes down to a few tenths of a millimetre, where a conventional camera would have a lens.
A pinhole camera has no lens and lets light in through a single opening, whose role is recapped in the guide to getting started with pinhole photography: this hole does the focusing and acts as the aperture at the same time. Its size therefore becomes the central parameter, and setting it means striking a balance between sharpness and brightness.
Why the pinhole diameter decides sharpness
Two opposing phenomena compete for the image, and the right diameter is the one that settles the contest.
A wide pinhole lets in plenty of light, so exposures are shorter, but each point of the scene is projected onto the paper as a spot larger than the pinhole itself. The image gains brightness and loses sharpness, because these spots overlap one another.
A very narrow pinhole projects finer spots and tightens the drawing, up to a threshold. Below that threshold, the light starts to diffract: passing through a tiny opening, it spreads out instead of travelling straight, and the image becomes blurred again.
Between the pinhole that is too wide and spreads the light, and the pinhole that is too small and diffracts it, there is a diameter at which the image is as sharp as it can be. That optimum is what practice looks for, and what a formula describes.
The diameter depends on the focal length
The optimum is not an absolute value, because it depends on the depth of the box, in other words the distance between the pinhole and the paper, which is the pinhole camera's focal length.
The logic is simple: the deeper the box, the larger the optimal pinhole, and the flatter the box, the smaller the pinhole must be. Light travels further in a deep box, its spots have time to spread, and a slightly wider pinhole compensates for that.
That is why the same pinhole does not suit every box. An opening that is perfect for a flat box will be too small for a deep box, where it will diffract, and the image will lose its crispness.
The formula for the optimum diameter
Opticians have put this trade-off into an equation. The optimal diameter d depends on the focal length f and on the wavelength of light, written lambda, according to a relationship of the form:
d = k × square root of (f × lambda)
The constant k is about 1.9 in the most widely used formulation, that of Lord Rayleigh, and the wavelength is taken towards the middle of the visible spectrum, at around 0.00055 mm. Above all, remember the logic of the calculation: the diameter grows with the square root of the focal length, so slowly. Doubling the depth of the box only widens the pinhole by a factor of about 1.4, not two.
In practice, for the usual beginner's boxes, this formula puts the optimum in a range of 0.2 to 0.8 mm. A flat box falls towards the bottom of the range, a deep box towards the top, and most home-made pinhole cameras sit somewhere in the middle.
For a box 10 cm deep, which means a focal length of 100 mm, the calculation gives about 0.45 mm.
Recognising a pinhole that is too large or too small
Knowing the optimum mainly helps you read your failures. In workshops, two images come up often, and each one gives away a badly sized pinhole.
A soft, bright photo, where the outlines bleed without it being camera shake, generally signals a pinhole too large for the box. Conversely, a dark and oddly softened image, which needed very long exposures, points to a pinhole too small, below the diffraction threshold. The logic of this deterioration ties in with that of the failed photo, where you learn to trace a defect back to its cause.
Straying from the optimum is tolerable within a comfortable margin, and a pinhole slightly off the calculation still gives good images. It is a clear drift that shows.
Making a clean pinhole matters as much as its size
The ideal theoretical size is no use if the pinhole is messy, and this is where practice catches up with the calculation. An ideal but roughly made opening in the metal gives a less sharp image than a pinhole slightly off size but perfectly round.
An irregular edge scatters light haphazardly, exactly like a pinhole that is too wide, and ruins the crispness the right diameter was supposed to give. To pierce a pinhole that is nice and even, lay the aluminium on a soft surface, turn a fine sewing needle while pressing gently, without pushing straight through in one go, then sand off the burr with very fine sandpaper.
Measuring the pinhole diameter
The most straightforward way is to scan the pierced plate at high resolution, next to a graduated ruler scanned under the same conditions. You then count the pixels of the pinhole and those of one millimetre on the ruler, and the ratio gives the diameter. A graduated magnifying loupe also gives a good order of magnitude. Failing that, the diameter of the needle you used, measured at the part that went through, serves as a first estimate.
The diameter governs the exposure and the paper
The diameter is never set on its own, because it controls the light coming in, and therefore the exposure time. A smaller pinhole darkens the image and lengthens the wait: the pinhole calculator gives the exposure time that matches your pinhole. To calculate it by hand, divide the distance between the pinhole and the paper by the diameter to get the pinhole's f-number, then multiply the reference time at f/16 by the square of the ratio between this f-number and 16.
A more than proportional increase
This increase is not even proportional, because beyond a few minutes the paper loses sensitivity as the exposure goes on, a phenomenon called the Schwarzschild effect. Reducing the pinhole can therefore push the exposure from around ten seconds to several minutes, or even an hour, far more than the simple ratio of areas would lead you to expect.
With a ready-to-use kit, this work is already done: the Sténoflex comes with a pinhole sized for its box depth and matched to its paper. This pinhole measures 0.26 mm in theory, 47 mm from the back, or about f/180. The optics remain fascinating to understand, but you can make good images without calculating anything yourself.
The pinhole diameter is the point where the optics of the pinhole camera come together: a single number that decides light and sharpness, which you learn to feel as much as to calculate.
Éric Marais — Photographer, author of two books on pinhole photography (published by Pearson) and creator of the Sténoflex. He has run introductory workshops in pinhole photography and analogue developing from the very beginning.