Comparative study of detection modes for space-based gravitational wave observation

Jingui Wu; Xiaoyong Wang; Shaojun Bai; Kailan Wu; Zhongkai Guo; Yongchao Zheng; Yun Wang; Xuling Lin

doi:10.12086/oee.2024.230134

Journals >Opto-Electronic Engineering >Volume 51 >Issue 2 >Page 230134 > Article

Opto-Electronic Engineering
Vol. 51, Issue 2, 230134 (2024)

Comparative study of detection modes for space-based gravitational wave observation

Jingui Wu^1、2、3, Xiaoyong Wang¹, Shaojun Bai¹, Kailan Wu^1、3, Zhongkai Guo¹, Yongchao Zheng¹, Yun Wang¹, and Xuling Lin^1、3、*

Author Affiliations

¹Beijing Institute of Space Mechanics & Electricity, Beijing 100094, China

²School of Mathematical Science, Capital Normal University, Beijing 100048, China

³School of Physical Science and Technology, Lanzhou University, Lanzhou, Gansu 730000, China

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DOI: 10.12086/oee.2024.230134 Cite this Article

Jingui Wu, Xiaoyong Wang, Shaojun Bai, Kailan Wu, Zhongkai Guo, Yongchao Zheng, Yun Wang, Xuling Lin. Comparative study of detection modes for space-based gravitational wave observation[J]. Opto-Electronic Engineering, 2024, 51(2): 230134 Copy Citation Text

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Fig. 1. Optical path of detection scheme

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Fig. 2. Phasor presentation of interference signal

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Fig. 3. Extreme point shift

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Fig. 4. Relationship between 1f_RIN and G

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Fig. 5. Optical path of stray light

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Fig. 6. Relationship between suppression factor and G

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		单像元(对)加性噪声功率谱密度	四象限平均相位噪声幅值谱密度
散粒噪声	单探测器	$\frac{1}{4} q_{e} R_{pd} (P_{1} + P_{2})$	$\frac{\sqrt{2}}{2 ρ τ} \sqrt{\frac{q_{e} (P_{1} + P_{2})}{η_{12} R_{pd} P_{1} P_{2}}}$
散粒噪声	平衡模式	$\frac{1}{4} q_{e} R_{pd} (P_{1} + P_{2})$	$\frac{\sqrt{2}}{ρ τ (1 + G)} \sqrt{\frac{q_{e} (P_{1} + P_{2})}{η_{12} R_{pd} P_{1} P_{2}}}$
探测器噪声	单探测器	$S_{pd}$	$\frac{\sqrt{2}}{ρ τ R_{pd}} \sqrt{\frac{S_{pd}}{η_{12} P_{1} P_{2}}}$
探测器噪声	平衡模式	$2 S_{pd}$	$\frac{4}{ρ τ R_{pd} (1 + G)} \sqrt{\frac{S_{pd}}{η_{12} P_{1} P_{2}}}$
强度噪声1f_RIN	单探测器	$\frac{R_{pd}^{2}}{16} (ρ^{4} P_{1}^{2} + τ^{4} P_{2}^{2}) S_{r} (f)$	$\frac{\sqrt{S_{r} (f_{12})}}{\sqrt{2 η_{12}}} \sqrt{\frac{ρ^{2} P_{1}}{τ^{2} P_{2}} + \frac{τ^{2} P_{2}}{ρ^{2} P_{1}}}$
强度噪声1f_RIN	平衡模式	$\frac{R_{pd}^{2}}{64} [{(ρ^{2} - G τ^{2})}^{2} P_{1}^{2} + {(τ^{2} - G ρ^{2})}^{2} P_{2}^{2}] S_{r} (f)$	$\frac{\sqrt{S_{r} (f_{12})}}{\sqrt{2 η_{12} ρ τ (1 + G)}} \sqrt{{(ρ^{2} - G τ^{2})}^{2} \frac{P_{1}}{P_{2}} + {(τ^{2} - G ρ^{2})}^{2} \frac{P_{2}}{P_{1}}}$
强度噪声2f_RIN	单探测器	$\frac{R_{pd}^{2}}{32} η_{12} ρ^{2} τ^{2} P_{1} P_{2} S_{r} (f + f_{12})$	$\frac{\sqrt{S_{r} (2 f_{12})}}{2}$
强度噪声2f_RIN	平衡模式	$\frac{R_{pd}^{2} {(1 + G)}^{2}}{128} η_{12} ρ^{2} τ^{2} P_{1} P_{2} S_{r} (f + f_{12})$	$\frac{\sqrt{S_{r} (2 f_{12})}}{2}$

Table 1. Summarize of read out noise

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	本地干涉仪 $A_{1} \approx A_{2}$	科学干涉仪 $A_{1} ≫ A_{2}$
同频共路	$A_{11} ≪ A_{1}, A_{22} ≪ A_{2}$	$A_{11} ≪ A_{1}, A_{22} ≪ A_{2}$
异频共路	$A_{12} ≪ A_{1}, A_{21} ≪ A_{2}$	$A_{12} ≪ A_{1}, A_{21} \approx A_{2}$
同频异路	$A_{21} ≪ A_{1}, A_{12} ≪ A_{2}$	$A_{21} ≪ A_{1}, A_{12} ≪ A_{2}$
异频异路	$A_{22} ≪ A_{1}, A_{11} ≪ A_{2}$	$A_{22} ≪ A_{1}, A_{11} \approx A_{2}$
伪干涉信号相对幅值一阶小量	$\frac{A_{22}}{A_{2}}, \frac{A_{11}}{A_{1}}, \frac{A_{12}}{A_{2}}, \frac{A_{21}}{A_{1}}$	$\frac{A_{22}}{A_{2}}, \frac{A_{11}}{A_{1}}, \frac{A_{12}}{A_{2}}, \frac{A_{21}}{A_{1}}, \frac{A_{12}}{A_{1}} \frac{A_{21}}{A_{2}}$
伪干涉信号相对幅值二阶小量	$\frac{A_{11}}{A_{1}} \frac{A_{22}}{A_{2}}, \frac{A_{12}}{A_{1}} \frac{A_{21}}{A_{2}}, \frac{A_{11}}{A_{1}} \frac{A_{12}}{A_{2}}, \frac{A_{21}}{A_{1}} \frac{A_{22}}{A_{2}}$	$\frac{A_{11}}{A_{1}} \frac{A_{22}}{A_{2}}, \frac{A_{11}}{A_{1}} \frac{A_{12}}{A_{2}}, \frac{A_{21}}{A_{1}} \frac{A_{22}}{A_{2}}$

Table 2. Amplitude of stray light

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杂散光项	单探测器模式	平衡探测模式
$\frac{A_{22}}{A_{2}}$	$\frac{A_{22}}{A_{2}} \sin (φ_{22})$	$\frac{A_{22}}{A_{2}} \sin (φ_{22})$
$\frac{A_{11}}{A_{1}}$	$\frac{A_{11}}{A_{1}} \sin (- φ_{11})$	$\frac{A_{11}}{A_{1}} \sin (- φ_{11})$
$\frac{A_{12}}{A_{2}}$	$\frac{A_{12}}{A_{2}} \sin (φ_{12})$	$- \frac{(ρ^{2} - G τ^{2})}{ρ τ (1 + G)} \frac{A_{12}}{A_{2}} \sin (- φ_{12})$
$\frac{A_{21}}{A_{1}}$	$\frac{A_{21}}{A_{1}} \sin (- φ_{21})$	$- \frac{(τ^{2} - G ρ^{2})}{ρ τ (1 + G)} \frac{A_{21}}{A_{1}} \sin (φ_{21})$
$\frac{A_{12}}{A_{1}} \frac{A_{21}}{A_{2}}$	$\frac{A_{21}}{A_{1}} \frac{A_{12}}{A_{2}} \sin (φ_{12} - φ_{21})$	$\frac{A_{21}}{A_{1}} \frac{A_{12}}{A_{2}} \sin (φ_{12} - φ_{21})$
$\frac{A_{11}}{A_{1}} \frac{A_{22}}{A_{2}}$	$\frac{A_{11}}{A_{1}} \frac{A_{22}}{A_{2}} \sin (φ_{22} - φ_{11})$	$\frac{A_{11}}{A_{1}} \frac{A_{22}}{A_{2}} \sin (φ_{22} - φ_{11})$
$\frac{A_{11}}{A_{1}} \frac{A_{12}}{A_{2}}$	$\frac{A_{11}}{A_{1}} \frac{A_{12}}{A_{2}} \sin (φ_{12} - φ_{11})$	$- \frac{(ρ^{2} - G τ^{2})}{ρ τ (1 + G)} \frac{A_{11}}{A_{1}} \frac{A_{12}}{A_{2}} \sin (φ_{11} - φ_{12})$
$\frac{A_{21}}{A_{1}} \frac{A_{22}}{A_{2}}$	$\frac{A_{21}}{A_{1}} \frac{A_{22}}{A_{2}} \sin (φ_{22} - φ_{21})$	$- \frac{(τ^{2} - G ρ^{2})}{ρ τ (1 + G)} \frac{A_{21}}{A_{1}} \frac{A_{22}}{A_{2}} \sin (φ_{21} - φ_{22})$

Table 3. Phase noise induced by stray light

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