How to Use the Pinhole Optics Calculator

How to Use the Pinhole Optics Calculator

Pick a can and paper, then read the best pinhole size, f-number, trail width and field of view before you pierce the hole.

Open the Pinhole Optics Calculator

Sun safety: never look at the Sun directly, through the pinhole, or through a camera viewfinder, binoculars or a telescope. A solargraph can is safe because nobody looks through it: you mount it, walk away, and open it later in dim light. Aim it by its shadow, not by eye. Any lens pointed at the Sun needs a certified solar filter over the front, and eclipse glasses are for bare eyes only, never behind optics. Supervise children at all times.

What this tool answers

How big should the hole in my can be, how dim is the camera, how wide is the Sun's trail, and how much sky does the paper cover? The tool models one design: an upright can with the pinhole in the middle of the side wall and photographic paper curled around the inside wall. The theory is in Pinhole Optics.

What you see on the screen

Under the amber Sun safety note, the left column holds the inputs: Container and Paper dropdowns, then Focal length (f), Pinhole diameter (∂) and Wall thickness (w), all in millimetres. Below them are the Use optimal diameter (X mm for 2R) button, an amber reminder that preset sizes are nominal, and an Open full simulator link. The right column is the Optics card: eleven readouts and a coloured note about your hole size. A 3D cutaway of the can sits underneath; drag it to turn it. On a phone everything stacks in one column.

Step by step

1. Open the Pinhole Optics Calculator.
2. Choose your Container: two Monster cans, three Milo tins or a 330 ml soda can.
3. Choose your Paper: Ilford Multigrade RC 5×7", Ilford 5×7" (5" wrap), or Half-letter strip.
4. Check Focal length (f): choosing a container fills it with the slant distance from the pinhole to the centre of the can's base (85 mm for the default Monster can).
5. Set Wall thickness (w): 0 mm for a hole in thin foil, or the metal thickness if you pierce the can wall itself (presets: 0.1 mm for drink cans, 0.25 mm for tins).
6. Press Use optimal diameter to copy the suggested hole size into Pinhole diameter (∂), or type the size of the needle you own.
7. Adjust until the note under the readouts is green and no amber warning shows.
8. Press Open full simulator to see where the Sun's trails land.

The steps above on the real calculator: choose the can and paper, read the f-number and the best hole, use it, then try a 500 g Guyana Milo tin.

How to read the results

• Slant f (pinhole→base) and Effective f: the focal length you entered, and that minus half the wall thickness.
• Preview scale (2R): the can's inside diameter, the distance light travels to the paper on the far wall.
• f-number: f divided by hole diameter (f/177 with the defaults). It measures how dim the camera is, not depth of field, which is almost unlimited for any pinhole.
• Optimal pinhole (slant) and Optimal pinhole (2R): Rayleigh's best hole, 1.9 × √(λ × f) with λ = 550 nm (green light), for the slant distance and for the can's inside diameter. The button and the size note use the 2R value (0.361 mm for the default Monster can).
• Trail width (preview): the larger of the Sun's image and the blur, in mm.
• Sun disk (2R preview): the Sun's image, 2R × 0.53° (0.61 mm with the defaults).
• Capture width and Capture height: how far the paper reaches left-right and up-down from the centre (±77° and ±44° with the defaults).
• Vignetting limit: θ_vig = atan(∂/w). A thick wall acts like a short tunnel and cuts off light from the sides. Foil (0 mm) gives 90°.

The calculator's presets and optics for your can and paper, with a top-down cutaway of where the paper and the wall's cut-off fall.

The note under the readouts compares your hole with the 2R optimum:

• Green, "close to optimal": between 0.6 and 1.5 times the optimum.
• Amber, "soft (geometry-limited)": more than 1.5 times the optimum.
• Amber, "Dim and diffraction-limited": less than 0.6 times the optimum. A smaller hole is not sharper, because diffraction spreads the light.

Blur against hole size: the hole's own blur, diffraction, and Rayleigh's sharpest hole between them.

You swap a hole at the optimum for one half its size. What happens to the Sun's trail?

• Sharper and just as bright
• Sharper but dimmer
• Dimmer and softer: diffraction spreads the light (the right answer)
• No change

Below the optimum the trail gets dimmer and softer, because diffraction blurs a smaller hole more, not less.

A second amber warning, Thick-wall vignetting, appears when the vignetting limit is smaller than the capture width. Pressing Use optimal diameter with the defaults triggers it: a 0.361 mm hole in a 0.1 mm wall gives 75°, less than the 77° the paper covers. Use foil (0 mm) or sand the wall thin around the hole.

A 0.361 mm hole pierced in a 0.1 mm can wall: why do the paper's side edges fade?

• The paper is too short
• The wall acts like a short tunnel and cuts off light beyond about 75° (the right answer)
• The hole is too big
• Humidity in the can

The vignetting limit is atan(hole ÷ wall) = atan(0.361 ÷ 0.1), about 75°, less than the 77° the paper covers. Foil, or a wall sanded thin, opens it up.

In the 3D cutaway, the cyan line is f, the gold "blur" label is the trail width, the green ring is the optimal hole, and dashed amber lines mark the vignetting limit when the wall is thicker than 0 mm. Hide labels hides the labels.

What it does not do

• It models only an upright can with curled paper, not a flat-back box.
• You cannot type a can diameter. The 2R values, the button and the note follow the Container preset, even if you change Focal length (f). The simulator has an Inner radius box for a measured can.
• It does not aim the can or draw Sun trails. The Solar Pinhole Camera does.
• It gives no exposure time. Pinhole Daytime Exposure turns focal depth and hole size into a full-sun exposure at ISO 100.
• It has no save or export. Take a screenshot.

Using it from Guyana

The 500 g Milo tin preset for Guyana and the Caribbean is the large round tin common here, nominally 12 cm wide and 18 cm tall. Its wider body raises the 2R optimum to about 0.49 mm, close to a #10 sewing needle, but the default 5×7" paper then covers less sky (±43° by ±28°). For sealing a can against rainy-season humidity, see Solargraphy.

Common mistakes

• Trusting the preset size. Measure your can with calipers.
• A torn or oval hole. The numbers assume a clean round one, so check it under a magnifier.
• A tiny hole for sharpness. Below the optimum the trail gets dimmer and softer.
• A thick, burred wall around the hole. The paper's edges fade.
• Measuring in inches. The tool works in millimetres only.

Related

• Get an aim for your site and exposure dates from the Solargraph Install Planner.
• See the Sun's altitude and direction at each hour of today with Sun Path Today, Hour by Hour.
• Simulate the paper with the Solar Pinhole Camera (guide).