Camera Iris

What is modelled

The leaves of an iris rotate about pivots and their straight edges move together to a regular polygon whose apothem falls as the blades turn. The area of that polygon sets the light passing through, and the equivalent circle sets the f-number. A small opening also spreads light by diffraction, and the polygon leaves a star-shaped pattern with one spike per edge direction.

Equations

• Polygon area A = n a2 tan(π/n) with apothem a = a0 cos β, equivalent diameter D = 2 √(A/π) and N = f / D.
• One stop: A → A/2 and N → √2 N.
• Airy disc diameter 2.44 λ N, first zero of J1(x) = 3.8317.
• Hyperfocal H = f2/(N c) + f, limits s(H − f)/(H + s − 2f) and s(H − f)/(H − s), blur b = f2 |u − s| / (N u (s − f)).
• Diffraction pattern: squared modulus of the 2D Fourier transform of the opening mask.

Checks run in the page

• Polygon corners and the shoelace area against the closed form.
• One stop halves the area and multiplies N by the square root of two.
• The Airy zero from the integral form of J1.
• The thin-lens blur circle at both depth-of-field limits equals the chosen limit.

Honest simplifications

The blade motion is a single cosine law instead of the real pivot linkage, the lens is a thin lens, the wavelength is a single green value, the diffraction pattern comes from a 64 point mask and the vignetting and aberrations of a real lens are ignored.

• Press Stopped down and see the Airy disc grow beyond two pixels in the second plot.
• Press Five blades and compare the spikes of the pattern with the nine-blade pattern.
• Press Landscape, far subject and read how wide the sharp zone becomes.