Arm Locking for the Laser Interferometer Space Antenna

The Laser Interferometer Space Antenna mission is a planned gravitational wave detector consisting of three spacecraft in heliocentric orbit. Laser interferometry is used to measure distance fluctuations between test masses aboard each spacecraft to the picometer level over a 5 million kilometer separation. Laser frequency fluctuations must be suppressed in order to meet the measurement requirements. Arm-locking, a technique that uses the constellation of spacecraft as a frequency reference, is a proposed method for stabilizing the laser frequency. We consider the problem of arm-locking using classical optimal control theory and find that our designs satisfy the LISA requirements. INTRODUCTION The Laser Interferometer Space Antenna (LISA) is a space-based gravitational wave detector under joint development by NASA and ESA [1-3]. The goal is to measure gravitational waves, ripples in the curvature of space-time produced by astrophysical events such as black hole collisions. Gravitational waves produce an oscillating tidal strain in space, the effect of which is to modulate the distance between a set of separated inertial masses. The amplitude of the oscillations is proportional to the nominal distance between the masses. Therefore the wave ‟ s amplitudes are characterized by the strain, or ratio of change in length to nominal length. For astrophysical sources of interest to LISA, typical strain amplitudes are 10-21 and have Fourier frequencies between 10-4 Hz and 10-1 Hz. The LISA instrument consists of a triangular constellation of three spacecraft in heliocentric orbit at 1AU, trailing approximately 20 degrees behind Earth. Each arm in the constellation is nominally 5 million km long and varies by as much as one percent with an annual period. Laser interferometry is used to monitor distance fluctuations between freely floating masses that are contained within the spacecraft at each end of the arm and are isolated from external disturbances using the technique of drag-free control [4,5]. A measurement resolution of approximately 10 pm (1 pm = 10-12 m) is required for the interferometric measurement. LISA interferometry utilizes coherent optical transponders in order to compensate for the large diffraction losses caused by the immense distances between the spacecraft. A schematic representation of the LISA interferometer (restricted to two arms) is shown in Figure 1. Each of the three spacecraft, labeled „A ‟ , ‟ B ‟ , ‟ C ‟ , contain two instrumental payloads labeled „ A1 ‟ , „ A2 ‟ , „ B 1 ‟ , etc. These payloads consist of laser, an optical bench, and a phase measurement system. The phase-measurement system measures the phase difference between the local laser and the laser on the adjacent bench as well as the phase difference between the local laser and the received beam from the far spacecraft. These measurements are manipulated and combined to generate signals that suppress laser phase noise while retaining the gravitational wave signals. For example, consider the laser associated with payload A1 on spacecraft A as the „ master ‟ laser. The back-link fiber measurement is used to measure the phase difference between lasers A2 and A1. By adjusting the phase of laser A2 to track that of laser A1 (a phase-locked loop), the two beams traveling to the distant spacecraft behave as if they originated from the same laser. Similarly, lasers B1 and C1 track the incoming beam from the spacecraft A. With all of these loops in operation, the two remaining phase measurements on spacecraft A produce the following signals: Where is the phase of the master laser and is the round-trip light travel time between spacecraft A and j. https://ntrs.nasa.gov/search.jsp?R=20090027712 2018-03-29T05:42:35+00:00Z