﻿ 大口径拼接镜平移误差对其成像质量影响研究 Study on the Influence of Translation Error of Large Aperture Stitching Mirror on Its Imaging Quality

Optoelectronics
Vol. 09  No. 01 ( 2019 ), Article ID: 29445 , 6 pages
10.12677/OE.2019.91009

Study on the Influence of Translation Error of Large Aperture Stitching Mirror on Its Imaging Quality

Xuewei Chen

School of Science, Changchun University of Technology, Changchun Jilin

Received: Mar. 6th, 2019; accepted: Mar. 19th, 2019; published: Mar. 27th, 2019

ABSTRACT

As one of the development trends of larger aperture astronomical telescopes, the common phase errors among the sub-mirrors of the mosaic mirror have a great impact on the image quality of the mosaic mirror. In this paper, the effect of piston error, one of common phase errors, on image quality of stitching mirror is analyzed theoretically, and the effect of translation error on point spread function of stitching mirror system under different wavelengths is simulated and analyzed.

Keywords:Piston Error, Point Spread Function, Space Telescope, Co-Phasing

1. 引言

2. 平移误差对拼接镜成像质量影响理论分析

Figure 1. Structure of segmented telescope

$U\left(x,y\right)=A\left(x,y\right)\left[circ\frac{x-\frac{B}{2}}{\frac{D}{2}}\ast {\text{e}}^{i{\varphi }_{1}}+circ\frac{x+\frac{B}{2}}{\frac{D}{2}}\ast {\text{e}}^{i{\varphi }_{2}}\right]$ (1)

$A\left(x,y\right)=\left\{\begin{array}{ll}1,\hfill & 子孔内径\hfill \\ 0,\hfill & 子孔径外\hfill \end{array}$ (2)

$\Delta \varphi ={\varphi }_{2}-{\varphi }_{1}=\frac{2\pi }{\lambda }p$ (3)

$PSF\left(u,v,\lambda \right)={|FT\left[U\left(x,y\right)\right]|}^{2}=2\frac{{D}^{2}/2{J}_{1}^{2}\left(\pi D\sqrt{{u}^{2}+{v}^{2}}\right)}{{u}^{2}+{v}^{2}}$ (4)

$PSF\left(x,y,\lambda \right)=2\frac{{D}^{2}/2{f}^{2}{\lambda }^{2}{J}_{1}{}^{2}\left(\pi D/\lambda f\sqrt{{x}^{2}+{y}^{2}}\right)}{{x}^{2}+{y}^{2}}\left[1+\mathrm{cos}\left(\frac{2\pi p}{\lambda }-\frac{2\pi B}{\lambda f}x\right)\right]$ (5)

$PS{F}_{t}\left(u,v,\lambda \right)={\sum }_{k=1}^{n}\frac{PSF\left(u,v,{\lambda }_{k}\right)\Delta \lambda }{n}$ (6)

3. 平移误差对拼接镜成像质量影响仿真分析

(a) (b)

Figure 2. Simulated double pupil structure. (a) Hexagon structure of; (b) Segmented telescope with mask segmented telescope

(a) (b)

Figure 3. PSF and far field facula at piston error equals 0

(a) (b)

Figure 4. PSF and far field facula at piston error equals λ/16

(a) (b)

Figure 5. PSF and far field facula at piston error equals λ/8

(a) (b)

Figure 6. PSF and far field facula at piston error equals λ/4

(a) (b)

Figure 7. PSF and far field facula at piston error equals λ/2

4. 结论

Study on the Influence of Translation Error of Large Aperture Stitching Mirror on Its Imaging Quality[J]. 光电子, 2019, 09(01): 56-61. https://doi.org/10.12677/OE.2019.91009

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