Statistical Properties of Wavefront and Image Field of Misaligned Segmented Optical Systems

Yongfeng Zhang; Hao Xian

doi:10.3788/AOS201939.1111004

Acta Optica Sinica, Volume. 39, Issue 11, 1111004(2019)

Statistical Properties of Wavefront and Image Field of Misaligned Segmented Optical Systems

Yongfeng Zhang^1,2,3 and Hao Xian^1,2、*

Author Affiliations

¹Key Laboratory of Adaptive Optics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China

²Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China

³University of Chinese Academy of Sciences, Beijing 100049, China

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Figures & Tables(8)

Fig. 1. Typical structure of segmented mirror

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Fig. 2. Comparison between frequency density function (shown as scattered points) and theoretical PDF (shown as solid line) of Φˉpiston. (a) For different ring number of segmented mirror, when σ_piston

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Fig. 3. Comparison between frequency density function (shown as scattered points) and theoretical PDF (shown as solid line) of σΦpiston2. (a) For differen

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Fig. 4. Comparison between frequency density function (shown as scattered points) and theoretical PDF (shown as solid line) of σΦt2. (a) For different rin

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Fig. 5. Quantities listed in Table 1 as functions of segmented mirror number N and standard deviation σ_piston (or σ_t). (a) Standard deviation of Φˉpiston

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Fig. 6. Strehl ratio of piston error as a function of standard deviation σ_piston and segmented mirror number N. (a) N=331; (b) σ_piston=0.1 μm

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Fig. 7. Strehl ratio of tip/tilt error as a function of standard deviation σ_t

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Table 1. PDF, average value, and standard deviation for random variables $\overset{ˉ}{Φ}$
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Table 1. PDF, average value, and standard deviation for random variables $\overset{ˉ}{Φ}$
Random variable PDF Average Standard deviation
${\bar{Φ}}_{piston}$ N $(0, \frac{4 σ_{piston}^{2}}{N})$ 0 $\frac{2}{\sqrt[]{N}} σ_{piston}^{2}$
$σ_{Φ_{piston}}^{2}$ Γ $(\frac{N - 1}{2}, \frac{8 σ_{piston}^{2}}{N})$ $\frac{4 (N - 1)}{N} σ_{piston}^{2}$ $\frac{4 \sqrt[]{2 (N - 1)}}{N} σ_{piston}^{2}$
$σ_{Φ_{t}}^{2}$ Γ $(N, \frac{5}{3 N} s^{2} σ_{t}^{2})$ $\frac{5}{3}$ s² $σ_{t}^{2}$ $\frac{5}{3 \sqrt[]{N}}$ s² $σ_{t}^{2}$

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Yongfeng Zhang, Hao Xian. Statistical Properties of Wavefront and Image Field of Misaligned Segmented Optical Systems[J]. Acta Optica Sinica, 2019, 39(11): 1111004

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Paper Information

Category: Imaging Systems

Received: Jun. 14, 2019

Accepted: Jul. 29, 2019

Published Online: Nov. 6, 2019

The Author Email: Xian Hao (xianhao@ioe.ac.cn)

DOI:10.3788/AOS201939.1111004

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. PDF, average value, and standard deviation for random variables ΦˉRandom variablePDFAverageStandard deviationΦ¯pistonN0,4σpiston2N02Nσpiston2σΦpiston2ΓN-12,8σpiston2N4(N-1)Nσpiston242(N-1)Nσpiston2σΦt2ΓN,53Ns2σt253s2σt253Ns2σt2