Chinese Optics, Volume. 18, Issue 3, 704(2025)
Analysis of multi-factor influences of tilt-to-length coupling noise in a test mass interferometer
Fig. 1. Schematic diagram of the simulated optical bench for the test mass interferometer
Fig. 2. Schematic illustration of positional factors. (a) The offset between the measurement and reference beam; (b) the piston effect; (c) the test mass shift and rotation
Fig. 3. Schematic diagram of the experimental setup. Components included: acousto-optical modulator (AOM), polarizing beam splitter (PBS), half wave plate (
Fig. 5. Histograms of LPS with LPF and AP definitions in 10,000 simulations
Fig. 6. Visualization of the main effect index (S1) for the LPF definition
Fig. 7. Visualization of the total effect index (ST) for the AP definition
Table 1. The type, position, and orientation of each component in the simulated optical bench used to analyze TTL coupling
View tableView in ArticleTable 1. The type, position, and orientation of each component in the simulated optical bench used to analyze TTL coupling
Label Component Name Center coordinate cm Normal Vector Laser Laser (0,0,0) (1,0,0) BS Beam splitter (25,0,0) (−1,0,0) M Mirror (25,50,0) (0,−1,0) TM Test mass (50,0,0) (1,0,0) QPD Quadrant photodiode (25,-25,0) (0,1,0)
Table 2. Physical parameters list
View tableView in ArticleTable 2. Physical parameters list
Parameter description Value Reference beam waist 0.5 mm Distance from reference beam waist 0 Reference beam frequency 2.8195 ×108 MHz +120 MHzMeasurement beam waist 0.5 mm Distance from measurement beam waist 0 mm Measurement beam frequency 2.8195 ×108 MHz +120 MHz+1.6 MHz QPD radius 1 cm QPD slit size 50 µm
Table 3. Comparison of rotation angle (µrad) and relative error (%)
View tableView in ArticleTable 3. Comparison of rotation angle (µrad) and relative error (%)
Rotation angle (µrad) Relative error (%) 100 3.78 200 2.84 300 3.69 400 2.24
Table 4. Parameter space for multiple factor analysis
View tableView in ArticleTable 4. Parameter space for multiple factor analysis
Factors Parameter Range Positional Beam offset (0 μm, 100 μm) Piston effect (lateral) (0 mm, 1 mm) Piston effect (longitudinal) (0 mm, 1 mm) Test mass lateral shift (0 μm, 100 μm) Test mass longitudinal shift (0 μm, 100 μm) Rotation angle (0 μrad, 100 μrad) Beam parameter Measurement beam waist (0.5mm, 1 mm) The distance from the waist of the measurement beam (0 mm, 50 mm) Detector parameter QPD slit (0 μm, 100 μm)
Table 5. Maximum (absolute value) and minimum (absolute value) of the LPS with both LPF and AP in 10,000 simulations
View tableView in ArticleTable 5. Maximum (absolute value) and minimum (absolute value) of the LPS with both LPF and AP in 10,000 simulations
Signal definition Maximum Minimum LPF 9.6939 ×105 pm6.4400 pmAP 9.1285 ×105 pm14.7801 pm
Table 6. Main effect index
S 1 and total effect indexS T for different parameters (LPF definition)View tableView in ArticleTable 6. Main effect index
S 1 and total effect indexS T for different parameters (LPF definition)Factors Parameter S1 ST Positional Beam offset 0.00037 0.00023 Piston effect (lateral) 0.01516 0.21815 Piston effect (longitudinal) 8.8911 ×10−75.3478 ×10−9Test mass lateral shift − 0.00096 0.00217 Test mass longitudinal shift − 1.0968 ×10−75.9016 ×10-11Rotation angle 0.75350 0.99122 Beam parameter Measurement beam waist 0.00081 0.00240 Distance from the measurement beam’s waist 5.8822 ×10−63.1740 ×10−7Detector parameter QPD slit 0.00017 0.00028
Table 7. Main effect index
S 1 and total effect indexS T for different parameters (AP definition)View tableView in ArticleTable 7. Main effect index
S 1 and total effect indexS T for different parameters (AP definition)Factors Parameter S1 ST Positional Beam offset 0.00093 0.00047 Piston effect (lateral) 0.01409 0.21586 Piston effect (longitudinal) 1.6607 ×10−65.29173 ×10−9Test mass lateral shift - 0.00117 0.00214 Test mass longitudinal shift − 1.6703 ×10−77.6198 ×10-11Rotation angle 0.75988 0.99156 Beam parameter Measurement beam waist 0.00085 0.00039 Distance from the measurement beam’s waist 2.1826 ×10−65.2593 ×10−8Detector parameter QPD slit 0.00073 0.00035
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Meng-yuan ZHAO, Jia SHEN, Xiao-dong PENG, Xiao-shan MA, Zhen YANG, He-shan LIU, Xin MENG, Jia-feng ZHANG. Analysis of multi-factor influences of tilt-to-length coupling noise in a test mass interferometer[J]. Chinese Optics, 2025, 18(3): 704
Category: Special Column on Space-based Gravitational Wave Detection
Received: Sep. 26, 2024
Accepted: Dec. 10, 2024
Published Online: Jun. 16, 2025
The Author Email: Xiao-shan MA (maxiaoshan@iet.cn)
