Unwanted astigmatism in lenses with a concentric variation in sagittal power

A concentric variation in sagittal power, Fs, with zonal radius, y, has been used in some designs of varifocal and aphakic spectacle lenses. It is shown theoretically, using a paraxial approximation, that a gradient dFs/dy in sagittal power leads to the introduction of an amount y.dFs/dy of unwanted astigmatism. The validity of this result is illustrated experimentally.