Method for generating a mathematical model for positioning individual mirrors of a facet mirror in an optical system

A method for an optical system, the optical system comprising:

• a facet mirror with individual mirrors,
• actuators which are configured to position the individual mirrors in accordance with manipulated variables (SG),
• sensors which are configured to capture sensor actual positions (SI) of the individual mirrors,
• an adjustment unit which is configured to provide intended positions (SP) of the individual mirrors, and
• a controller unit which is configured to provide the manipulated variables (SG) in accordance with the provided intended positions (SP) and the captured sensor actual positions (SI), and
• the method comprising:
• a) providing the intended positions (SP) of the individual mirrors with the adjustment unit,
• b) capturing measurement actual positions (MI) of the individual mirrors) with a measuring device,
• c) generating a mathematical model (MM) for positioning the individual mirrors in accordance with the captured measurement actual positions (MI) and the intended positions (SP),
• wherein a difference (EA) between a respective measurement actual position (MI) and a respective intended position (SP) is formed in said step c) and the mathematical model (MM) is generated in accordance with the difference (EA) formed, and
• d) positioning the individual mirrors of the facet mirror in accordance with the mathematical model (MM).