Wavefront Aberrations

Zernike polynomial decomposition of optical aberrations — pupil function and PSF visualization

Wavefront error W(ρ,θ)
Pupil function |P|
PSF (point spread fn)

Zernike Terms

Wavefront Quality

RMS wavefront (λ)
Peak-to-valley (λ)
Strehl ratio
Maréchal critn

Zernike Polynomials

W(ρ,θ) = Σ aₙₘ Zₙₘ(ρ,θ)

Z₂₀ = 2ρ²−1 (defocus)
Z₂±₂ = ρ²cos/sin2θ (astig)
Z₃±₁ = (3ρ²−2)ρcos/sinθ (coma)
Z₄₀ = 6ρ⁴−6ρ²+1 (spher)

Maréchal: Strehl≈exp(−(2πW_rms)²)
Rayleigh λ/4 criterion: |W|≤λ/4