Full vibration isolator system and schematic that show the different stages of preisolation and the multipendulum stage with a test mass at the bottom of the chain.
First stage horizontal and vertical preisolation. The preisolator combines two ultralow frequency stages: (a) the horizontal inverse pendulum and (b) the vertical LaCoste linkage. The concept of the antispring for flexure spring constant cancellation is shown.
The Roberts linkage. (a) shows a one-dimensional diagram of a Roberts linkage with a suspended load from point , which stays in the same plane for variations in the position of and . (b) shows a diagram of the cube shaped design used in the AIGO suspension.
The multistage pendulum including three intermediate masses showing the rigid section, rocker mass, eddy current damping, and Euler springs for vertical isolation. At the bottom of the chain the control mass stage provides sensing and control for a test mass suspended with niobium flexures.
Diagram of one self-damped pendulum stage. Magnets that generate eddy currents on copper plates create the viscous damping for a high moment of inertia rocker mass.
Schematic of the intermediate mass showing the Euler spring vertical stage and the attachment to the rocker mass (Ref. 33).
Intermediate mass showing the integration of the high moment of inertia rocker mass with the Euler spring vertical stage. The intermediate mass has a hollow tube in the center to allow for the suspension wire to go through all the stages. The figure also shows the -shaped frame that hold the copper plates on top of the rocker mass. Attached to the rocker mass are the magnets that create the damping through eddy current generation on the copper plates (Ref. 23).
Control mass stage with test mass suspended. Actuation arms holding permanent magnets are attached to the control mass. From the control mass a suspension cage is attached and a test mass is suspended by four niobium ribbons.
The picture shows the ETM during the assembly of the second suspension system. A 2 in. mirror is mounted in a stainless steel support that gives the test mass the same size of a “real” test mass. At the back of the ETM we can see the electrostatic board.
ITM mechanical transfer function. The top graph shows the horizontal transfer function measured at the control mass level using the shadow sensor for sensing. The driving signal was injected at the magnetic actuator mounted on the inverse pendulum. The lower graph shows the vertical transfer function. The source was injected at the LaCoste stage and measured at the control mass stage vertical shadow sensors.
FFT measurement of the inverse pendulum stage. The figure shows the main inverse pendulum peak around 70 mHz followed by the coupling of the LaCoste vertical mode. Above 10 Hz we notice the internal modes of the supporting frame with slightly different frequencies in both directions.
FFT measurement of the LaCoste stage superimposed over one of the inverse pendulum axis measurements. The vertical axis measurement shows the LaCoste stage frequency followed by the Euler spring frequencies. Since the LaCoste stage is measured against the inverse pendulum and not directly attached to the rigid frame there is very little coupling of the high frequency modes.
FFT measurement of the Roberts linkage preisolation stage. We notice the coupling of the horizontal inverse pendulum frequencies and the LaCoste vertical mode. These are followed by the main Roberts linkage peak at 280 mHz. The peak around 660 mHz corresponds to the main pendulum mode followed by the main Euler spring mode at 2.5 Hz. Since the Roberts linkage stage in measured against the inverse pendulum there are no high frequency modes from the rigid frame.
The figure show both FFT measurements for horizontal and vertical axis of the control mass stage. We notice the low frequency rotation mode of the long pendulum below the 70 mHz peak of the inverse pendulum. This is followed by the LaCoste vertical and the Roberts linkage horizontal modes and the main niobium flexures yaw mode at 1.75 Hz. The vertical measurements show the Euler spring modes; above 10 Hz both axes show some of the supporting frame internal modes.
Diagram that shows the laser control system. A signal generator is used to generate the 10 MHz sideband used for cavity locking. PM corresponds to a phase modulator and FI a faraday isolator. The diagram does not include the optical components necessary to steer and mode-match the beam into the main cavity.
The semitheoretical transfer function is a combination of the measurements of the electronics in the control loop and the optical cavity theoretical frequency response and the PZT frequency response.
Comparison between the semitheoretical curve and an average of a few measurements of the loop frequency response at high frequency.
Measurement of the frequency response of the laser PZT signal. The top (blue) line shows the cavity frequency response and the bottom (red) line the laser noise. We notice that above 1 Hz the main contribution to the cavity displacement frequency response comes mainly from the laser noise.
Residual motion of the East arm cavity derived from the frequency response measurements. A residual motion of can be seen at 1 Hz, which is reduced to just below 3.3 Hz.
(a) Measurement of the frequency response of the laser PZT signal. (b) The green curve shows a matched model of the vibration isolator. (c) The red curve shows the improved vibration isolator without a local control system. (d) The purple curve shows the improved vibration isolator with a local control system.
Pitch and yaw angular residual motion for the ITM. The dotted lines show the angular residual motion for the control mass when controlled only with the shadow sensor. The continuous line shows the angular residual motion using the optical lever control loop.
The power inside the cavity is represented in a histogram over a period of 2 h. Note that the -axis is of arbitrary unit: the voltage of the photodetector measuring transmitted light.
Parameters for the 72 m cavity.
Cavity parameters that can be derived from our measurements. Here corresponds to the round trip optical path length, the optical frequency, the speed of light in vacuum, and corresponds to the measured characteristic decay time of the intensity defined as .
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