Piston Error Extraction from Dual-Wavelength Interference Patterns Using Phase Retrieval Technique

Xiaoyang Li,Bincheng Li,Xu Yang,Hao Xian,Shengqian Wang

doi:10.3390/photonics9020111

Abstract

As next-generation large-aperture telescopes, synthetic aperture is a promising method for realizing high resolution observations. Co-phasing the misaligned segmented aperture is an important procedure for high-resolution observations with segmented telescopes. In this paper, a piston error detection method is proposed based on two interference patterns. Two interference patterns are generated by using a lens placed across two adjacent pupils in the exit pupil plane at two wavelengths and a method based on phase retrieval technique is proposed to extract the piston error from the two interference patterns. The introduction of dual-wavelength in the scheme overcomes the 2π ambiguities problem and expands the piston error detection range. Meanwhile, the proposed piston error extraction method based on phase retrieval technique allows high precision measurement of the piston error and is robust to offset lens. Various simulations are demonstrated and the feasibility of the proposed piston error detection method is validated.

Highlights

Astronomical space observations require optical imaging systems with apertures large enough to meet the demands of high resolution
The phase retrieval (PR) technique is used to extract piston errors from two interference patterns [18,19], which are generated by lens placed across two adjacent pupils in the exit pupil plane at two wavelengths
We propose a dual-wavelength piston error detection where I(u, v) is ameftuhnodc.tTiwono inotefrftewrenocevpaarttiearnbslmese:asOurnedeatistwtohweavpeilsentogtnhs earreruosred(pfo)r painstodn tehrroer other the wavelengthx.trTachtioenr,ewfohirceh,caIn(bue,evxp)recsasend abseforlleowwsr. itten as I(p, λ)

Summary

Introduction

Astronomical space observations require optical imaging systems with apertures large enough to meet the demands of high resolution. The piston error of adjacent sub-apertures can be extracted from measured interference patterns. The phase retrieval (PR) technique is used to extract piston errors from two interference patterns [18,19], which are generated by lens placed across two adjacent pupils in the exit pupil plane at two wavelengths. The mathematical model of the optical system is used to generate a series of interference patterns used as a template in both the narrowband and broadband methods. The proposed dual-wavelength piston error extraction method in this paper is described in detail. The analysis is performed for an optical system with three segments, as shown, since the increase in the number of mirror elements introduces no principal changes into the piston error extraction process.

Piston Error Extraction Method

Simulation

Conclusions