Figure 4. The measured fundamental Fourier mode of the tangent angle and its derivative, the curvature, illustrate that two boundary conditions are satisfied.

(A) Snapshots of the measured fundamental Fourier mode of the tangent angle $\psi (s,t)=\tilde{\psi }\left(s\right)e^{i\omega t}+{\tilde{\psi }}^{*}\left(s\right)e^{-i\omega t}$at successive times with interval Δt=4 ms for a beat pattern satisfying the clamped head condition. (B) Same representation of the curvature, ∂_sψ (s,t). The arrows point to the base (A) and tip (B) of the axoneme and indicate the expected boundary conditions (zero tangent at the base and zero curvature at the tip). The estimated error of the tangent angle is less than 10⁻² rad. The estimated error of the curvature is 10⁻² rad∕μm, or approximately 5% of the maximum value. Note that the last experimental data point is approximately 2 μm before the actual end of the flagellum.