Approximate model for the coupling of far-field wavefront errors and jitter in space-based gravitational wave laser...

Area of Science:

• Astrophysics
• Optical Engineering
• Gravitational Wave Detection

Background:

• Space-based gravitational wave observatories (e.g., LISA, Taiji, TianQin) require sub-picometer displacement sensitivity.
• Far-field wavefront errors (WFE) and laser pointing jitter are significant noise sources impacting measurement precision.

Purpose of the Study:

• To develop a comprehensive noise model for space-based laser interferometry.
• To analyze the impact of transmitted WFE, static pointing angle, and laser beam jitter on measurement sensitivity.

Main Methods:

• Utilized Nijboer-Zernike diffraction theory to derive an approximate expression for far-field WFE.
• Developed a noise model incorporating transmitted WFE, static pointing angle, and laser beam jitter.
• Investigated the effect of Zernike aberrations on far-field WFE.

Main Results:

• Derived a physically interpretable and computationally efficient approximate expression for far-field WFE.
• Identified that correcting $Z_3^{\pm 1}$ aberrations via beam tilt can worsen far-field WFE.
• The proposed model allows for system simulations and evaluation of tilt-to-length (TTL) noise.

Conclusions:

• Active suppression of $Z_3^{\pm 1}$ aberrations is necessary for optimal performance.
• The developed noise model provides theoretical insights for optimizing laser link design in gravitational wave missions.