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

		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 2. Amplitude of stray light

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Table 2. Amplitude of stray light

	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 3. Phase noise induced by stray light

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Table 3. Phase noise induced by stray light

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

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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

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