Performance requirements

Both the specification for the optical path delay (OPD) and the angular jitter are described using a noise shape function, as shown Equation 1.

The requirements for OPD and angular jitter, defined in terms of amplitude spectral density (ASD), are multiplied with this noise shape function. It is designed such that the requirements are relieved below 2.8 mHz, and constant above this frequency. The requirements only apply within the LISA measurement band width, which is defined to be between 0.03 mHz and 1 Hz.

Table 1 shows the requirements for OPD and angular jitter.

Table 1:

Performance requirements for the PAAM.

Environmental requirements

Several additional requirements make the design of the PAAM quite challenging. First of all, due to the sensitivity of the measurement set-up on the Optical Bench, no magnetic materials are allowed. This rules out the use of any electromagnetic actuators or bearings. Second, due to the strict requirements on stray light, no contamination of the Optical Bench is allowed. Any outgassing materials, as well as mechanisms containing moveable parts with frictional contacts are not allowed. Third, the mechanism will have to survive launch loads of 25 g RMS, without the use of a launch locking mechanism.

3.1

Optical design

The optical concept for the PAAM is a mirror rotating around an axis in the mirror plane. This concept is chosen over alternatives due to its low transmission losses and low complexity. The mirror is coated for the wavelength of 1064 nm and for the incoming angle of 45 °. The reflectivity is specified as more than 99.9 %, and its flatness is better than 12 nm RMS over its entire diameter of 19.05 mm.

The Optical Path Delay (OPD) has been identified as the most critical requirement. If the laser beam and the reflecting surface are perfectly aligned with the rotation axis (Gimbal mount), the OPD due to rotation is theoretically zero. Figure 3 schematically shows the optical path delay due to a rotation of the mirror, when the beam and surface are not perfectly aligned.

Figure 3:

Schematic representation of the influence of alignment and jitter parameters of the mirror on the optical path delay of the incoming laser beam.

From Figure 3 it can be seen that the OPD equals the distance BB'-BB”. For small angles, this can be approximated by BD. The sensitivity of the distance BD, and hence the OPD, to the most relevant parameters is listed in Table 2. These parameters are the angular jitter, caused by rotation of the mirror around the optical axis in combination with an alignment offset, the longitudinal jitter, caused by piston sensitivity and angular jitter, and the rotation axis longitudinal jitter, caused by parasitical actuation forces through the Haberland hinge. Other misalignments of the optical axis and cross-couplings were shown to have negligible contribution to the Optical Path Delay.

Table 2:

Sensitivity of the OPD to relevant parameters:

3.2

Mechanical design

The rotation of the mirror is guided by a so-called Haberland hinge, a monolithical elastic cross hinge. Due to the limitations on magnetic materials and contamination, magnetic, hydrostatic or contact bearings were not allowed. The axis of rotation of the Haberland hinge is aligned with the mirror surface.

The material of choice is Ti₆Al₄V, due to its high allowable stress and high dimensional stability. The mechanical design is shown in Figure 2. The entire mechanism, excluding the functional components, is wire-eroded in a single fixture configuration, such that micrometer production tolerances are achieved.

A compact elastic transmission between the actuator and mirror allows actuation of the mirror angle without introducing parasitic forces. The elastic transmission also enables the inclusion of a second, independent actuator, such that the mechanism is redundant. The required mechanical stroke of ± 412 μrad can be actuated with an actuator stroke of 20 μm, with minimal hysteresis effects.

To minimize OPD due to temperature variations, the thermal center of the Ti₆Al₄V structure is placed in line with the axis of mirror rotation. This:

A finite-element model analysis (FEM) of the Haberland hinge was used to predict the longitudinal jitter, caused by the coupling between angular jitter and piston sensitivity. Production tolerances of ± 2 μm were included, which was justified by the accuracy and symmetry of the applied wire erosion process to manufacture the monolithical mechanism. Figure 4 shows the calculated piston movement of the mirror rotation axis under different actuation angles. The derivative of this curve is the piston sensitivity to angular jitter, which is 2.1 fm/nrad at the maximum angle. With the requirement of 8 , the predicted longitudinal jitter becomes 0.017 , which is significantly below the allocated budget of 0.28 .

Figure 4:

The piston movement of the axis of rotation under different actuation angles. By taking the derivative of the fitted polynomial, the piston sensitivity can be determined for different angles.

3.3

Electrical design

For the actuation, two piezo stacks (PPA20M) of Cedrat Technologies are used. For the stroke of 20 μm, and with the limitations on magnetic materials, a piezo stack is the most appropriate actuator. The stacks are driven with a high voltage piezo amplifier (Cedrat Technologies LA75B), which produces voltages between -20 and + 150 V.

Because of piezo hysteresis and discharge behaviour, a closed loop system is required to meet the requirement for angular jitter in the entire range. The controller acting between the sensor and piezo actuator can have a low bandwidth, because only disturbances within the LISA measurement band width have to be suppressed.

The sensor consists of an active target capacitive sensor system, which measures the displacement of the far end of the mirror. The tilting of the mirror is less than 0.5 mrad, which has only a small influence on the capacitive sensor signal. A one-time calibration ensures that the sensor signal is representative of the mirror angle with high enough accuracy.

The active target system is preferred over a passive target system for the following reason: in a passive target system, the cable capacitance is in parallel to the capacitance to be measured, and is typically a few orders higher. This makes it very sensitive to low frequency environmental changes which dramatically influence the cable capacitance. In an active target system, the target is connected to a virtual ground, which draws the current from the cable capacitance. This way, the system will be much less sensitive to environmental changes.

The capacitive probe is a standard Lion Precision probe, whereas the active target consists of an isolating BK7 plate, coated with a layer of gold. The active target, located on the moving part, is connected to the sensor cable by two thin copper wires, which add negligible parasitic stiffness to the Haberland Hinge.

The capacitance-to-digital (CDC) electronics were chosen to be an electronics board developed by Velista, especially for extreme requirements on low frequency noise. Typically, capacitive sensor electronics introduce 1/f type noise in the amplification, but the charge-integration configuration and precision electrical components chosen for the CDC board reduced this effect maximally².

4.1

Test description

Two requirements of the PAAM are critical and need to be tested: the OPD and the angular jitter. Both are measured at three different static angles within the range of the mechanism. The LISA measurement band width determines the length of each performance measurement: the lowest frequency to be measured is 0.03 mHz. With several repetitions of this period to obtain a proper spectral estimate, the measurement time per angle is approximately 48 hours.

To measure the OPD, the PAAM has to be aligned accurately in the resonance cavity. To achieve this, a modulation sine wave is used as a set point on the mechanism, which will follow this signal by rotation of the mirror. Through the amplitude of the sine wave, the misalignment of the axis of rotation with respect to the incoming beam can be estimated.

To measure the angular jitter, the PAAM is deliberately placed at an alignment offset. A modulation sine wave is used as a set point for the PAAM. Through the amplitude of the sine wave, the coupling of angular jitter to OPD can be estimated. A long measurement of OPD will then provide an indirect measurement of the angular jitter of the PAAM.

4.2

Test performance results

The results of the performance measurements of OPD and angular jitter are shown in Figure 6. For all angles, the performance of the mechanism is exactly according to the requirements. The peak visible at 50 mHz is the modulation sine wave which is used for alignment in the OPD measurements, and coupling estimation in the angular jitter measurements.

Figure 6:

Left:Amplitude Spectral Density of the OPD measurements on the PAAM. For all angles, the result meets the requirements. The peak at 50 mHz is introduced for alignment in the cavity. Right: Amplitude Spectral Density of the angular jitter measurements on the PAAM. The PAAM is deliberately placed at and alignment offset, to make the angular jitter dominant in the OPD measurement. For all angles, the result meets the requirements. The peak at 50 mHz is introduced to estimate the coupling of angular jitter to OPD.