Four ways a fisheye maps angle to radius
A rectilinear lens puts a ray at r = f·tan θ, and past about 120° that number runs away. The four classical fisheye designs each choose a different function of θ, and this plots them together against a curve fitted to a real lens.
Try this
Push θ towards 90° and watch the rectilinear curve leave the plot while the equidistant one walks up in a straight line. That divergence is why a fisheye needs its own model.
Where this lab comes from
Fisheye Models: When Correcting the Lens Stops WorkingLesson 4 of the Image Formation unit. The pinhole model puts a ray at f·tan θ, which runs to infinity at 90 degrees, and past about 120 degrees of field the stretch toward the edges makes it impractical. Fitted to the same 15 photographs of one fisheye lens, pinhole plus Brown-Conrady reaches 7.326 px RMS and Kannala-Brandt reaches 0.644 px. At 80 degrees the first model predicts a radius of -35,572 px, a sign flip; the second predicts 458.8 px, which is on the sensor.
More in cameras and geometry
- Focus, aperture and depth of field — Move the subject and watch the focus plane and the blur follow.
- The scene, and what the camera sees — Orbit a 3-D scene on the left; the pinhole view updates on the right.
- Straight lines that bow — Brown–Conrady radial and tangential terms on a pixel grid.