An engineer characterising a deformable-mirror test bed measures an rms wavefront…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging

What an Instrument Can See, Ch Aberrations: the phase written on the pupil

Problem

An engineer characterising a deformable-mirror test bed measures an rms wavefront error σW=0.35\sigma_W = 0.35 waves at λ=550 nm\lambda = 550\,\mathrm{nm} over the clear pupil, after removing piston, tilt and defocus. Applying the Maréchal approximation, the engineer writes: S≈e−(2πσW)2=e−(2π×0.35)2=e−4.84=0.0079,S \approx e^{-(2\pi\sigma_W)^2} = e^{-(2\pi\times0.35)^2} = e^{-4.84} = 0.0079, and reports: "the mirror gives a Strehl ratio of about 0.008, so it is essentially unusable." ((a)) Check the arithmetic in the quoted line. ((b)) Find the error in the reasoning, and state, with a numerical check against the stated validity range of the Maréchal approximation, why the reported value of 0.008 cannot be trusted as the actual Strehl ratio.

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