Add optika.zernikes and ZernikeSag

[jacobdparker]

Summary

Stacked on #171 (will retarget to main once it merges; the branches are independent in content).

• optika.zernikes: Noll-indexed, RMS-normalized Zernike polynomials (noll(), zernike()) and their analytic gradients (zernike_gradient()), matching the convention of :cite:t:Noll1976 (reference added to refs.bib). The gradient uses an origin-safe series for R_n^m(rho)/rho, so it is exact at the center of the pupil.
• optika.sags.ZernikeSag: a sag profile that perturbs a base sag with a sum of Zernike polynomials, for modeling measured or analytic figure error. Element i of coefficients is the Noll-j = i + 1 coefficient over the disk of the given radius. The analytic normal() combines the base gradient with the Zernike gradients; the ray intercept falls back to the inherited numeric solver.

Because the figure error perturbs the surface, the same object is seen consistently by both the geometric raytrace and (in an upcoming PR) the physical-optics propagation - a single source of truth for tolerancing.

Tests

• noll() against the published index table; closed forms for j = 1, 2, 3, 4, 11.
• Monte-Carlo orthonormality of the basis over the unit disk.
• Gradients vs central differences.
• ZernikeSag through the standard AbstractTestAbstractSag battery, plus a geometric check that Noll Z4 shifts the focus of a paraboloid by the analytic amount.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.37%. Comparing base (9479771) to head (8455e8d).

Additional details and impacted files

@@                        Coverage Diff                        @@
##           fix/polygonal-aperture-bounds     #172      +/-   ##
=================================================================
+ Coverage                          99.35%   99.37%   +0.02%     
=================================================================
  Files                                116      120       +4     
  Lines                               6024     6248     +224     
=================================================================
+ Hits                                5985     6209     +224     
  Misses                                39       39              

Flag	Coverage Δ
unittests	99.37% <100.00%> (+0.02%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[roytsmart]

Kinda unfortunate this is called sag as well, if you refer to it, it has stutter: sag.sag. Is there a better word like base or sag_base or something that captures it without using the exact same word?

[jacobdparker]

Good call — renamed the attribute to base, so it now reads sag.base. Done in 8455e8d.

[roytsmart]

I don't see any difference between the two curves in this plot.

[jacobdparker]

You're right, and it was a real bug in the example: the perturbation is coma (Noll index 8), which varies as cos(phi) and is therefore identically zero along the y axis — exactly the slice the plot used, so the curves landed on top of each other. Switched the slice to vary along x, where the coma term is nonzero (~2.8 mm peak difference). Fixed in 8455e8d.

[roytsmart]

I feel like position should be first, is it standard for this function to put j first?

[jacobdparker]

Agreed — there's no strong convention for j-first, and putting position first matches the other field-evaluation functions. Flipped both zernike() and zernike_gradient() to (position, j) and updated the call sites. Done in 8455e8d.