An image-based indirect wavefront aberration estimation which is noise optimal is presented. The minimum variance estimation is obtained by linearizing the focal plane intensity distribution in terms of the aberration parameters and a known set of derivatives of the point spread function. The technique was also made to work successfully for unknown extended sources by Fourier transforming the image to the frequency space. The results obtained from a computer simulation show excellent noise rejection. With a signal-to-noise ratio of 5, the wavefront correction is achieved down to 0.1 λ. In some cases, this method worked when the initial signal-to-noise ratio was less than one. Since the estimation is performed with a linear approximation, the dynamic range of operation was found to be limited to 0.35 RMS λ.
Gregory S. Um,
Brian F. Smithgall,
Carey L. O'Bryan,
"Minimum Variance Estimation Of Wavefront Aberration", Proc. SPIE 0351, Wavefront Sensing, (1 August 1983); doi: 10.1117/12.933917; https://doi.org/10.1117/12.933917