http://arxiv.org/abs/2301.00814
Inspired by the combinatorial algebraic approach proposed by Dhurandhar et al., we propose two novel classes of second-generation time-delay interferometry (TDI) solution as well as their further generalization. The primary strategy of the algorithm is to enumerate specific types of residual laser frequency noise associated with second-order commutators in products of time-displacement operators. The derivations are based on analyzing the delay time residual when expanded in time derivatives of the armlengths order by order. It is observed that the solutions obtained by such a scheme are primarily captured by the geometric TDI approach and therefore possess an intuitive interpretation. Nonetheless, the fully-symmetric Sagnac and Sagnac-inspired combinations inherit the properties from the original algebraic approach, and subsequently lie outside of the scope of geometric TDI. Moreover, at its lowest order, the solution is furnished by commutator of rather compact form. Besides the original Michelson-type solution, we elaborate on other types of solutions such as the Monitor, Beacon, Relay, Sagnac, fully-symmetric Sagnac, and Sagnac-inspired ones. The average response functions, residual noise power spectral density, and sensitivity curves are evaluated for the obtained solutions. Also, the relations between the present scheme and other existing algorithms are discussed.
W. Qian, P. Wang, Z. Wu, et. al.
Wed, 4 Jan 23
25/43
Comments: 21 pages, 3 figures