Our desired output profile is a uniform distribution of maximum extent K from an input Gaussian of 1/e² width W. The input distribution has irradiance Pexp{-(2R²/W²)} and the output distribution is a step-function of irradiance H and maximum radial width K 

Now that we can calculate the output coordinate value S for every input coordinate X, we can use the REAY optimization operand to specify an array of input ray coordinates and their respective output target values in the merit function editor. In the REAY operands we will specify the normalized input coordinates and the corresponding targets at the image plane. Instead of inserting the operands manually, we will write a ZPL macro to automatically generate the merit function and optimize the lens.