Cooke triplet · f = 100 mm · ±10° · designed in this page
Triplet — three pieces of glass, six radii, one descent.
Three conditions fix the powers by a 3×3 solve . Everything after that is
shape, and shape is what damped least squares buys — ten thousand rays a step, each one
refracted by Snell's law through six spherical surfaces, until the blur stops shrinking.
1 Elevation · true scale, both axes
What is computed. Every ray is traced in 3D: intersected with each sphere in closed
form, refracted by the vector form of Snell's law, no paraxial shortcut anywhere. The starting
powers come from a 3×3 linear solve — total power Σφ = 1/f , achromatism
Σφ/V = 0 , and a symmetry choice φ₁ = φ₃ .
Petzval curvature is then not a choice but a consequence, and it is printed as one.
What is approximated. Dispersion is a two-term Cauchy fit pinned to each catalogue
glass's nd and Vd : exact at
those two numbers by construction, so partial dispersion — and the secondary spectrum that follows
from it — is indicative, not catalogue-accurate. Nothing here diffracts; the Airy circle on plate 2
is drawn only to mark where ray optics stops being the right model. No vignetting, no coatings, no
tolerances. The three line colours are hand-set — this page computes optics, not colour.
The honest part. Damped least squares finds the nearest minimum and no other. Press
survey : 64 starting forms, each run down to its own lens, land anywhere
between 5 and 270 µm of blur — and only two of the 64 arrive somewhere worth building. The descent
is arithmetic; the seed is a decision. (Those dots trace a coarser pupil to fit 64 descents into
15 seconds, so they sit a few tenths of a micron off the white curve.)
S solve · R seed · V survey ·
←→ focus · L split λ