Analysis of offset error for segmented micro-structure optical element based on optical diffraction theory

Abstract

Micro-structure optical elements are gradually applied in modern optical system due to their characters such as light weight, replicating easily, high diffraction efficiency and many design variables. Fresnel lens is a typical micro-structure optical element. So in this paper we take Fresnel lens as base of research. Analytic solution to the Point Spread Function (PSF) of the segmented Fresnel lens is derived based on the theory of optical diffraction, and the mathematical simulation model is established. Then we take segmented Fresnel lens with 5 pieces of sub-mirror as an example. In order to analyze the influence of different offset errors on the system’s far-field image quality, we obtain the analytic solution to PSF of the system under the condition of different offset errors by using Fourier-transform. The result shows the translation error along XYZ axis and tilt error around XY axis will introduce phase errors which affect the imaging quality of system. The translation errors along XYZ axis constitute linear relationship with corresponding phase errors and the tilt errors around XY axis constitute trigonometric function relationship with corresponding phase errors. In addition, the standard deviations of translation errors along XY axis constitute quadratic nonlinear relationship with system’s Strehl ratio. Finally, the tolerances of different offset errors are obtained according to Strehl Criteria.