Sensitivity of a refractive beam reshaper to figure error

When a pair of aspheric lenses is used to transform the transverse intensity profile of a laser beam, a deviation of the actual lens surfaces from their ideal shape causes the output beam to deviate in intensity and phase from the intended profile. In this paper, geometrical optics and the paraxial approximation are applied to derive simple expressions for the effect of small errors in the slope and curvature of the lens surfaces on the output intensity profile produced by a refractive beam reshaper. The results are applied to a Gaussian-to-flattop reshaper, which has been described in detail in previous publications, and provide insight into the tolerances required of the optics. For example, if the output intensity is required to be within 5% of the design value, then the tolerance on the lens curvature at the optic axis is less than 2%.