Multi-zonal computer-generated holograms for high-precision optical adjustment purposes: part I: sensitivity and optical performance.

Multi-Zonal computer generated holograms (MZ-CGHs) in combination with interferometric wavefront measurements are perfectly suited as optical adjustment tools - especially if the demands on the alignment accuracy are very high. After reviewing the basic idea for alignment with MZ-CGHs, we derive the analytic relation between the interferometrically observed tilt and power values and the associated lens placement errors, including estimates of the applied approximations. This analysis yields the parameters determining the principle sensitivity of the method. Subsequently, the achievable accuracy of large 6″ MZ-CGHs in practical application is tested with a series of different optical measurements which confirm the technical feasibility. The productive use of the technique will be presented in part II of the paper for different examples in the framework of the Euclid space telescope.