Abstract: A method for changing a shape of a surface of an optical element by particle irradiation includes: modelling the problem of determining a resulting change of the surface shape of the optical element from a control variable; determining a predefinition for the control variable of the particle irradiation from a predefined desired change of a surface shape of the optical element by ascertaining an extremum of a merit function; and radiating particles onto the surface of the optical element with a locally resolved effect distribution corresponding to the determined predefinition for the control variable, for the purpose of producing local surface changes at the surface of the optical element. Ascertaining the extremum corresponds to the solution of an Euler equation. The Euler equation defines an integral operator. The eigenvalues of the integral operator are determined, and the predefinition is a linear combination of a finite number of eigenfunctions of the integral operator.

Abstract: A method for changing a shape of a surface of an optical element by particle irradiation includes: modelling the problem of determining a resulting change of the surface shape of the optical element from a control variable; determining a predefinition for the control variable of the particle irradiation from a predefined desired change of a surface shape of the optical element by ascertaining an extremum of a merit function; and radiating particles onto the surface of the optical element with a locally resolved effect distribution corresponding to the determined predefinition for the control variable, for the purpose of producing local surface changes at the surface of the optical element. Ascertaining the extremum corresponds to the solution of an Euler equation. The Euler equation defines an integral operator. The eigenvalues of the integral operator are determined, and the predefinition is a linear combination of a finite number of eigenfunctions of the integral operator.