Analytical design of refractive optical elements generating a prescribed two-dimensional intensity distribution

A new source-target mapping for the design of refractive optical elements generating prescribed $2\mathrm{D}$ intensity distributions is proposed. The calculation of the optical element is reduced to the solution of ordinary explicit differential equations. The simulation results presented demonstrate high performance of the proposed method. While generating uniform rectangular intensity distributions with angular dimensions varying from $80^{\circ}\times1^{\circ}$ to $40^{\circ}\times20^{\circ}$, the normalized root-mean-square deviations between the generated and required distributions do not exceed $15 \%$.