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Aperture and lens
The f-number N is focal length divided by pupil diameter. Light scales as 1/N2, the Airy disc as 2.44 lambda N, and depth of field grows with N.
Model checks
The science
What is modelled
A twelve-blade iris: a cam ring moves each blade pivot so the polygonal opening changes size. The cam link geometry and the measured clear-pupil table are those of the 3D page; the optical consequences are added here with standard formulas.
Equations
- Blade rotation from the cam link:
rho = a cos d + sqrt(L2 - a2 sin2 d),theta = atan2(rho sin d, rho cos d - a). - Exposure
~ 1/N2; one stop is a factor sqrt(2) in N. - Airy disc diameter
2.44 lambda N(first zero of the Bessel function J1). - Hyperfocal distance
H = f2/(N c) + fwith near and far limits around the focus distance.
Checks run in the page
- The cam link keeps its design length.
- Two stops give a quarter of the light.
- The Airy coefficient from a numerical J1 zero.
- Depth-of-field limits against an independent thin-lens blur calculation.
Honest simplifications
A polygon with fixed twelve sides, nominal f-numbers calibrated to the measured pupil rather than derived from blade geometry, a single wavelength of 550 nm, thin-lens depth of field with a fixed circle of confusion and no aberrations or vignetting.
What to try
- Press Wide open f/2, then Stopped down f/16 and watch the light and the Airy disc.
- Press Landscape f/11 to see the focus range reach infinity.
- Raise the pixel pitch to see when the image stops being diffraction-limited.