Status of the eLISA on table (LOT) electro-optical simulator for space based, long arms interferometers

Abstract

We report on the progress in the realization of an electronic / optical simulator for space based, long arm interferometry and its application to the eLISA mission. The goal of this work is to generate realistic optics and electronics signals, especially simulating realistic propagation delays. The first measurements to characterize the simulator are also presented. With the present configuration, noise reduction factors of 5×10⁷ for optical beat notes and 10⁹ for RF beat notes have been achieved using the Time Delay Interferometry algorithm. The principle of the experiment has been validated and further work is ongoing to identify the residual noise sources and optimize the apparatus.

Appendices

Appendix A: development of time delay interferometry equations

The combination of the recorded signals results in the following equations:

$$\begin{array}{@{}rcl@{}} s_{TT;1} &=& s_{OS;1} + \frac{s_{TO;1}+s_{Ref;1}}{2} + D_{2^{\prime}1} \frac{s_{TS;2^{\prime}}}{2} \\ &=& D_{2^{\prime}1} \eta_{L;2^{\prime}} - \eta_{L;1} + g_{w;2^{\prime}1} + \delta_{TM;1} + D_{2^{\prime}1} \delta_{TM;2^{\prime}} \\&&+ o_{TS;1} + D_{2^{\prime}1} o_{S;2^{\prime}1} \end{array} $$

(8a)

$$\begin{array}{@{}rcl@{}} s_{TT;1^{\prime}} &=& s_{OS;1^{\prime}} + \frac{s_{TO;1^{\prime}}+s_{Ref;1^{\prime}}}{2} + D_{31^{\prime}} \frac{s_{TS;3}}{2} \\ &=& D_{31^{\prime}} \eta_{L;3} - \eta_{L;1^{\prime}} + g_{w;31^{\prime}} + \delta_{TM;1^{\prime}} +D_{31^{\prime}} \delta_{TM;3} \\&&+ o_{TS;1^{\prime}} + D_{31^{\prime}} o_{S;31^{\prime}} \end{array} $$

(8b)

$$\begin{array}{@{}rcl@{}} s_{TT;2^{\prime}} &=& s_{OS;2^{\prime}} + \frac{s_{TO;2^{\prime}}}{2} + D_{12^{\prime}} \frac{s_{TS;1}}{2} \\ &=&D_{12^{\prime}} \eta_{L;1} - \eta_{L;2^{\prime}} + g_{w;12^{\prime}} + \delta_{TM;2^{\prime}} + D_{12^{\prime}} \delta_{TM;1} \\&&+ o_{TS;2^{\prime}} + D_{12^{\prime}} o_{S;12^{\prime}} \end{array} $$

(8c)

$$\begin{array}{@{}rcl@{}} s_{TT;3} &=& s_{OS;3} + \frac{s_{TO;3}}{2} + D_{1^{\prime}3} \frac{s_{TS;1^{\prime}}}{2} \\ &=& D_{1^{\prime}3} \eta_{L;1^{\prime}} - \eta_{L;3} + g_{w;1^{\prime}3} + \delta_{TM;3} + D_{1^{\prime}3} \delta_{TM;1^{\prime}} \\&&+ o_{TS;3} + D_{1^{\prime}3} o_{S;1^{\prime}3} \end{array} $$

(8d)

Also, the back-link fiber being reciprocal [9], which means that the added noise from 1 to 1’ is identical to the noise added when propagating from 1’ to 1: $\eta _{B;1} = \eta _{B;1^{\prime }}$,the differential noise between laser 1 and 1’ can be deduced from s _{R e f;1} and $s_{Ref;1^{\prime }}$:

$$ \frac{s_{Ref;1} - s_{Ref;1^{\prime}}}{2} = \eta_{L;1} - \eta_{L;1^{\prime}} + \frac{o_{Ref;1}-o_{Ref;1^{\prime}}}{2} $$

(9)

Practically, the laser frequencies will not be let freely running but will be phase locked on a master, frequency stabilized source (e.g. Laser 1). From the previous equations, assuming perfect correction, this phase locking means that:

$$\begin{array}{@{}rcl@{}} s_{Ref;1} &=& 0 \Rightarrow \eta_{L;1^{\prime}} = \eta_{L_{1}} - \eta_{B;1} + o_{Ref;1} \end{array} $$

(10a)

$$\begin{array}{@{}rcl@{}} s_{OS;2^{\prime}} &=& 0 \Rightarrow \eta_{L;2^{\prime}} = D_{12^{\prime}} \eta_{L;1} + g_{w;12^{\prime}} - D_{12^{\prime}} \delta_{OB;1} - \delta_{OB;2^{\prime}} \\&&+ D_{12^{\prime}} o_{S;12^{\prime}} + o_{OS;2^{\prime}} \end{array} $$

(10b)

$$\begin{array}{@{}rcl@{}} s_{OS;3} &=& 0 \Rightarrow \eta_{L;3} = D_{1^{\prime}3} \eta_{L;1^{\prime}} + g_{w;1^{\prime}3} - D_{1^{\prime}3} \delta_{OB;1^{\prime}} - \delta_{OB;3} \\&&+ D_{1^{\prime}3} o_{S;1^{\prime}3} + o_{OS;3} \end{array} $$

(10c)

Assuming that δ _{O B;q} =0 and η _B;q =0 (these noises can be subtracted using s _{T O;q} and s _{R e f;q} signals) and neglecting both test mass and other local noises (δ _{T M} =o _{x x;q} =0), this configuration is effectively equivalent to a transponder, where the phase noises of the incoming beams on S/C 2 and 3 are transferred on the beams sent back to S/C 1.

Appendix B: phasemeter reference measurement

The ASD of data recorded on channel 1 and the ASD of the difference between channel 1 and 2 are represented on Fig. 14.

Fig. 14

Reference level of phasemeter noise

The ASD of raw values and differences between other channels give very similar results. These results show that the raw data are slightly above the eLISA requirements for the phase measurement noise, while the differential measurement between two channels is marginally compatible with the requirement. The difference between the two curves are due to a relatively strong common mode between the channels, whose origin is unclear for the moment, but could be due, e.g. to a residual phase jitter between the reference signal (at 72.001 MHz in this experiment) and the synthesized 2.001 MHz signal.