eLISA: a Demonstration of TDI. This applet shows the response of the LISA array to impulsive, plane gravitational waves incoming from random directions. Click-drag the mouse to rotate the coordinate system and emphasize the LISA-GW interaction. To view this applet you need a fairly recent browser with Java enabled, and a fairly fast computer.

The bluish moving plane represents the GW impulse, with the cross at the center representing the polarization tensor of the wave, and the long line representing the direction of propagation. The red beams between the spacecraft show (on a perpendicular axis) the frequency shifts of the emitted and received laser beams, as due to impacting GW; the basic Doppler observables y_ij (shown in the grey rectangles) are frequency differences between the incoming and the local reference laser. The GW pulses are normalize so that the geometrical factor 1+k.n is always approximately the same. Last, the larger rectangle at the bottom shows the TDI X combination being assembled from delayed copies of the y_ij: X is completely assembled only in the lighter region of the rectangle. The y_ij time series enter X at the time marked by the dim blue and red lines, with respectively a plus and a minus sign.

This applet is still in beta version, so I don't guarantee signs and factors of two for all quantities plotted. Please let me know if you have any idea or suggestion to improve this demonstration, and to make it graphically more pleasing.