On design of free-form refractive beam shapers, sensitivity to figure error, and convexity of lenses.

The problem of design of a two-lens optical system for reshaping the irradiance distribution of a laser beam in a prescribed manner is considered in the geometrical optics approximation. The presented design equations are derived in a rigorous manner and are applicable to free-form two-lens optical systems without any a priori symmetry assumptions on radiance profiles and beam cross sections. The obtained equations are applied to derive an equation defining sensitivity of the output radiation intensity to figure errors. This equation is applied to analyze sensitivity in several cases, including rotationally symmetric reshapers with nonrotationally symmetric figure error. The presented approach shows also that even in the general case two different designs are available for the same data. In one of these designs one lens is always concave or convex and the second is convex or concave, while in the second design the lenses may be neither convex nor concave. Since, in general, the surface lenses are aspherical, the availability of a design with convex/concave lenses is particularly important for fabrication.