Coupling of a single-mode fiber with a deformable mirror in a space-based nulling interferometer

Abstract

This master thesis is dedicated to the study of single mode fibers as spatial filter in a space-based nulling interferometer. They are used to decrease the requirements on the wavefront quality that an adaptive system needs to achieve.

In order to do so, a mathematical model of the coupling efficiency of a single mode fiber placed at the focus of a telescope was developed. The model is based on the Gaussian approximation of the fundamental mode LP_01 that is propagated in the single mode fiber. Also, the model is based on the theory of Fourier optics in order to determine the electric field at the input of the fiber. The model allows to compute the coupling efficiency for any static aberrations. Also, the point spread functions of a circular pupil subjected to different aberrations are simulated thanks to the fast fourier transform algorithm.

The study is performed in the waveband [3-7] µm in order to develop a nulling interferometer for exoplanets detections. The diffraction limited performances of the system are analysed. After that, the effect of static aberrations on the coupling efficiency is analysed. Then, the simulation of typical aberrations encountered in space is performed. They represent non common path aberrations (NCPA).

The simulation of the model proves that the coupling efficiency drops from 81.45% (diffraction limited performance) to 30 % when 120 Zernike polynomials are used to represent NCPA. In order to get a RMS wavefront error below 0.1 rad a deformable mirror capable of reproducing the first 115 Zernike polynomials is needed.