Apparent wavefront aberration of a Gaussian source in a Hartmann wavefront sensor with focus error

We examined the effect of a Gaussian pupil-plane irradiance profile on the wave-front aberration reported by a Hartmann wave-front sensor with focus error when observing a collimated point source. It was found that even when a planar wave-front is incident upon the Hartmann sensor pupil, centroid deflections are registered in the detector plane due only to the non-uniformity of the Gaussian irradiance profile. As a result, the reconstructed wave-front may contain large focus and spherical aberration terms. The magnitude of the apparent aberrations depends upon the amount of focus error and the width of the Gaussian profile. Results are presented for a model system, indicating aberration terms in excess of (lambda) /3 or equivalent Strehl ratio less than 0.5 for certain configurations.