When a gravitational wave passes through the interferometer, the spacetime in the local area is altered. Depending on the source of the wave and its polarization, this results in an effective change in length of one or both of the cavities. The effective length change between the beams will cause the light currently in the cavity to become very slightly out of phase (antiphase) with the incoming light. The cavity will therefore periodically get very slightly out of coherence and the beams, which are tuned to destructively interfere at the detector, will have a very slight periodically varying detuning. This results in a measurable signal.
When a gravitational wave passes through the interferometer the spacetime in the local area is altered. Depending on the source of the wave and its polarization, this results in an effective change in length of one or both of the cavities The effective length change between the beams will cause the light currently in the cavity to become very slightly out of phase (antiphase) with the incoming light. The cavity will therefore periodically get very slightly out of coherence and the beams which are tuned to destructively interfere at the detector, will have a very slight periodically varying detuning. This results in a measurable signal.