Using the deformable mirror as a spatial filter: application to circular beams

Adaptive optics correction of a wave front by a deformable mirror that acts as a lossless spatial filter is studied. The decomposition of the wave front into Zernike polynomials provides a means for deriving the rms error of a corrected wave front in analytic form. The spatial filter is given in a functional form related to deformable mirror characteristics. A step filter approximation is derived and the conditions where the approximation holds are examined. An example is provided to demonstrate the utility of the spatial filtering concept for adaptive optics systems analysis.