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Journals >Chinese Optics Letters >Volume 18 >Issue 2 >Page 020604 > Article

Chinese Optics Letters
Vol. 18, Issue 2, 020604 (2020)

Analysis of detection error for spot position in fiber nutation model

Xueqiang Zhao^1、2、3, Yunpeng Zhang^1、2, Minjie Huang³, Peipei Hou¹, Ren Zhu³, Jianfeng Sun^1、2, Xia Hou^2、3、*, and Weibiao Chen^1、2、**

Author Affiliations

¹Key Laboratory of Space Laser Communication and Detection Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

²Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

³Laboratory of Space Laser Engineering, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

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DOI: 10.3788/COL202018.020604 Cite this Article Set citation alerts

Xueqiang Zhao, Yunpeng Zhang, Minjie Huang, Peipei Hou, Ren Zhu, Jianfeng Sun, Xia Hou, Weibiao Chen. Analysis of detection error for spot position in fiber nutation model[J]. Chinese Optics Letters, 2020, 18(2): 020604 Copy Citation Text

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Abstract

The influences of nutation trail accuracy, simplification of coupling model, spot position jitter, and power variation of incident light on the detection error are analyzed theoretically. Under the condition of satisfying the requirements, the nutation radius is less than 1.13 μm, the accuracy of the nutation trail is less than 0.04 μm, and the detection range is [?5 μm, +5 μm]. The nutation frequency is 160 times spot position jitter frequency and 100 times intensity jitter frequency of incident light. The analysis is of great significance for determining nutation radius and frequency in the tracking system based on fiber nutation.

Keywords

detection error fiber nutation tracking system

{\begin{cases} ρ_{x} = \frac{ω_{0}^{2}}{4 r} \ln [\frac{P (n T)}{P (n T + T / 2)}], \\ ρ_{y} = \frac{ω_{0}^{2}}{4 r} \ln [\frac{P (n T + T / 4)}{P (n T + 3 T / 4)}] . \end{cases}

(1)

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η (ρ) = η_{\max} \exp (- \frac{ρ^{2}}{ω_{0}^{2}}),

(2)

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η (r) = η_{\max} \exp (- \frac{r^{2}}{ω_{0}^{2}}) .

(3)

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κ (r) = \frac{η (0) - η (r)}{η (0)} .

(4)

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r \leq ω_{0} [\ln (\frac{1}{1 - κ_{m}})]^{1 / 2} .

(5)

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η {(ρ)}_{real} = \frac{{8 | \int_{ϵ}^{1} β \exp (- β^{2} r^{' 2}) J_{0} (2 \frac{β ρ r^{'}}{ω_{0}}) r^{'} d r^{'} |}^{2}}{1 - ϵ^{2}},

(6)

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ρ_{real} = \frac{ω_{0}^{2}}{4 r} \ln [\frac{η {(ρ + r)}_{real}}{η {(ρ - r)}_{real}}] .

(7)

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P_{d} (r) = \frac{1}{\sqrt{2 π} σ} \exp [- \frac{{(r - \bar{r})}^{2}}{2 σ^{2}}] .

(8)

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{\begin{cases} P (n T) = P_{in} η_{\max} \exp [- \frac{{(ρ_{x} - \bar{r} - 3 σ)}^{2}}{ω_{0}^{2}}], \\ P (n T + T / 2) = P_{in} η_{\max} \exp [- \frac{{(ρ_{x} + \bar{r} + 3 σ)}^{2}}{ω_{0}^{2}}] . \end{cases}

(9)

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Δ_{t} = \frac{3 ρ_{x} σ}{\bar{r}} .

(10)

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σ < \frac{1}{30} \bar{r} .

(11)

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\vec{s (t)} = \sum_{k = 1}^{n} \vec{A_{k}} \cos (2 π f_{k} t + φ_{k}),

(12)

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s {(t)}_{x} = \sum_{k = 1}^{n} | \vec{A_{k}} | \cos (θ_{k}) \cos (2 π f_{k} t + φ_{k}),

(13)

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s {(t)}_{x} = | \vec{A_{H}} | \cos (θ_{H}) \cos (2 π f_{H} t + φ_{H}) .

(14)

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v_{\max} = 2 π f_{H} A_{H},

(15)

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Δ s = v_{\max} \cdot \frac{1}{2 f_{n}} = \frac{π A_{H} f_{H}}{f_{n}},

(16)

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{\begin{cases} P (n T) = P_{in} η_{\max} \exp [- \frac{{(ρ_{x} - r)}^{2}}{ω_{0}^{2}}], \\ P (n T + T / 2) = P_{in} η_{\max} \exp [- \frac{{(ρ_{x} + r \pm Δ s)}^{2}}{ω_{0}^{2}}] . \end{cases}

(17)

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ρ_{x}^{J} = [{(ρ_{x} + r \pm \frac{π A_{H} f_{H}}{f_{n}})}^{2} - {(ρ_{x} - r)}^{2}] / 4 r,

(18)

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{\begin{cases} Δ_{J +} = \frac{π^{2} A_{H}^{2}}{4 r α^{2}} + \frac{ρ_{x} π A_{H}}{2 r α} + \frac{π A_{H}}{2 α}, \\ Δ_{J -} = \frac{π^{2} A_{H}^{2}}{4 r α^{2}} - \frac{ρ_{x} π A_{H}}{2 r α} - \frac{π A_{H}}{2 α}, \end{cases}

(19)

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P {(t)}_{in} = \frac{P_{\max}}{2} [1 + L (θ_{A})] + \frac{P_{\max}}{2} [1 - L (θ_{A})] \sin (4 π f_{A} t + φ_{ape}),

(20)

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{\begin{cases} P (n T) = P {(n T)}_{in} η (n T), \\ P (n T + T / 2) = P {(n T + T / 2)}_{in} η (n T + T / 2) . \end{cases}

(21)

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Δ_{tm} = \frac{ω_{0}^{2}}{4 r} \ln [\frac{P {(n T)}_{in}}{P {(n T + T / 2)}_{in}}] .

(22)

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Δ_{tm} = \frac{ω_{0}^{2}}{4 r} \ln {\frac{[1 + L (θ_{A})] + [1 - L (θ_{A})] \sin (4 π f_{A} t)}{[1 + L (θ_{A})] + [1 - L (θ_{A})] \sin (4 π f_{A} t + \frac{2 π}{β})}},

(23)

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References (13)

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Xueqiang Zhao, Yunpeng Zhang, Minjie Huang, Peipei Hou, Ren Zhu, Jianfeng Sun, Xia Hou, Weibiao Chen. Analysis of detection error for spot position in fiber nutation model[J]. Chinese Optics Letters, 2020, 18(2): 020604

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