This paper discusses how to design refractive optical elements to form a specified irradiance distribution on a curvilinear surface when a compact light source is used. The calculation is based on representing the surface of the element in terms of the distribution of the eikonal of the light field in an adjacent plane. The eikonal is defined in the form of a polynomial. The design of the refractive surface is based on gradient minimization of an error functional representing the difference of the calculated and specified irradiances of the field. An analytical expression is obtained for the gradient of the error functional. Refractive elements are designed for the formation of a rectangular irradiance distribution on flat and cylindrical surfaces.
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