A.

INTRODUCTION

Due to time delay in the interferometer arms, the direction of transmitted light changes. To solve this problem, a picometer stable Point-Ahead Angle Mechanism (PAAM) was designed, realized and successfully tested. The PAAM concept is based on a rotatable mirror. The critical requirements are the contribution to the optical path length (less than 1.4 pm / rt Hz) and the angular jitter (less than 8 nrad / rt Hz). Extreme dimensional stability is achieved by manufacturing a monolithical Haberland hinge mechanism out of Ti₆Al₄V, through high precision wire erosion. Extreme thermal stability is realized by placing the thermal center on the surface of the mirror. Because of piezo actuator noise and leakage, the PAAM has to be controlled in closed-loop. To meet the requirements in the low frequencies, an active target capacitance-to-digital converter is used. Interferometric measurements with a triangular resonant cavity in vacuum proved that the PAAM meets the requirements.

Due to the evolution of the orbit during its trip around the sun, the laser beam angles have to be corrected for constantly. Not only the in-plane angles are affected, but also the so-called point-ahead angles, which correct for the offset caused by the time delay of the travelling light. The Point-Ahead Angle Mechanism (PAAM) is designed to perform the task of correcting the point-ahead angle.

The PAAM is developed and tested by TNO Science & Industry, with the help of the Albert-Einstein-Institute in Hannover. As an Elegant Bread-Board (EBB), it has successfully gone through all performance and environmental testing and is ready to be integrated in a functional breadboard of the Optical Bench for a LISA spacecraft.

B.

Driving requirements for the PAAM

The PAAM is required to steer the incoming laser beam through a range of ± 824 μrad, while contributing minimally to the optical path delay (OPD) and contributing minimally to the angular jitter of the laser beam angle. During operation, the mechanism will follow an annual trajectory that runs through the entire range twice.

1)

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.

Performance requirements
Description	Requirement	Unit
Optical Path Delay	1.4 · n(f)
Angular jitter	16 · n(f)

Table 2:

Sensitivity of the OPD to relevant parameters

C.

Point-Ahead Angle Mechanism design description

The PAAM consists of a mirror on a flexible rotational hinge, which can be actuated individually by either one of two piezo stacks. The angle is measured by a capacitive sensor. The system operates in closed loop. The overall design is shown in Top, and its realization is shown in Bottom. In the paragraphs below, the optical, mechanical and electrical design is described in detail.

D.

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, the OPD due to rotation is theoretically zero. Figure 2 schematically shows the optical path delay due to a rotation of the mirror, when the beam and surface are not perfectly aligned.

From Figure 2 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 Error! Reference source not found. 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.

E.

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 are not favored. 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 1. The entire mechanism, excluding the functional components, is wire-eroded in a single fixture configuration; such that optimal production tolerances are achieved.

Figure 1.

Top: CAD design of the Point-Ahead Angle Mechanism as designed by TNO Optomechatronics, including all its components. Bottom: Realization of the Point-Ahead Angle Mechanism. The mirrors can be actuated by one of two Piezo-stacks. The mirror is mounted with a bonded iso static mount design for details see [6].

Figure 2:

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

Figure 3:

Top: Meshed FEM model of the Haberland hinge, actuated to an extreme angle. Outcome of the FEM analysis is the longitudinal and lateral jitter of the axis of rotation. Production tolerances of ± 10 μm are taken into account. Bottom: 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.

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 is achieved by strategic placement of isostatic interfaces to the optical bench.

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 ± 10 μm were included, which was justified by the accuracy and symmetry of the applied wire erosion process to manufacture the monolithical mechanism.

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 ± 10 μm were included, which was justified by the accuracy and symmetry of the applied wire erosion process to manufacture the monolithical mechanism.

F.

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 (see Figure 4). 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.

Figure 4:

Schematic illustration of the active target capacitive sensor. The sensor measures the displacement of the tip of the mirror. The tilting of the mirror is taken into account by one-time calibration.

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 converter (CDC) electronics were chosen to be a custom electronics board, 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 maximally.

G.

Sensor noise testing

Due to the closed loop operation of the PAAM and the low frequency performance requirements, the most critical noise source in the loop is the capacitive sensor. To test the performance of the CDC board in combination with the active target capacitance, a test set-up was designed to measure the noise. A stable reference capacitance was placed in a temperature (± 1 K) and humidity controlled environment, while the CDC board was kept in a normal laboratory environment.

The resulting contribution of the electrical noise to the angular jitter in terms of amplitude spectral density is shown in Figure 5, calculated from the measurement using a simple model of the plant and a controller with a band width of approximately 10 Hz. In worst case, the capacitive sensor noise is low enough to achieve the required performance. Especially the low magnitude of 1/f type noise is a remarkable performance achievement for a displacement sensor. Noise measurements of other electrical components in the control loop resulted in noise levels that were much lower than the capacitive sensor noise within the band width of interest. It is therefore justified to consider the noise level of the capacitive sensor as a total performance prediction.

Figure 5:

Performance prediction of the angular jitter, based on capacitive noise measurements under controlled environmental conditions. A dynamical model of the PAAM and the controller is included. The predicted performance is below specification.

H.

Environmental testing

The specification for the launch loads is 25 g RMS. This random vibration load is applied to the Elegant Bread Board realization of the PAAM. The spectrum containing 25 g RMS was notched because of a lower Q-factor of the mechanism. In three translational degrees of freedom, an effective spectrum of approximately 20 g RMS was applied by a shaker. The response, measured with tri-axial accelerometers, showed no significant shift of resonance frequencies. After testing, visual inspection of the mechanism showed no degradation.

I.

Performance testing

The performance of the Elegant Bread Board realization of the PAAM was measured with the help of the Albert Einstein Institute in Hannover, because of their experience with measuring picometer stabilities and the availability of an existing measurement facility². For details on the Performance measurement setup see [2].

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:

Top: 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. Bottom: 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.

Figure 7:

The chosen Fiber Switching Unit Concept.

Figure 8:

The random vibration levels according to the ECSS

Figure 9:

The shock levels

Figure 10.

Top. Schematic sketches of the working principle of a linear piezo inertia actuator. (Picture courtesy of Attocube) Bottom: A cross section of the piezo inertia actuator in its housing. The labyrinth seal together with the potentiometer are implemented in the FSUA. The aim of the labyrinth seal is to keep possible debris generated in the actuator contact or potentiometer away from the optics. The aim of the potentiometer is to detect the wave plate orientation. The two rotating parts are preloaded on the drak green rotation stage with limited stroke with a defined preload.

Figure 11:

Wobble measurement of the first model of the FSUA after the life test. Wobble is still well within specified +/- 500 micro radians over 45 degrees of actuation.

Figure 12:

Top: The FSUA with integrated angular measurement system. Bottom: a photo of one of the sliding contact surfaces after the life test no signification degradation of the surface.

Figure 13:

Picture of the piezo-stepper test set-up, to measure the errors during constant velocity motion, introduced by stepping.

J.

Conclusion

With the design, realization and testing of the PAAM, TNO Optomechatronics has demonstrated that a scanning mechanism with picometer stability and under extreme environmental conditions is achievable. Performance test measurements have shown that it is compliant with the challenging requirements for optical path delay and angular jitter.

The analysis, as well as the measurement results, shows that application of a Haberland hinge in a monolithical structure enables rotation with negligible parasitical motion in terms of OPD. The thermal design of the structure showed to be sufficient to guarantee the thermal stability.

The angular jitter measurements have shown that an active target capacitive sensor system meets the extreme requirements on low frequency noise.

The Elegant Bread Board of the PAAM, as used in the performance testing, will be included in a bread board model of the LISA Optical Bench in the near future.

A.

Introduction

The Fiber Switching Unit Actuator is part of the Fiber Switching Unit as shown in the figure below. The aim of the FSU is to allow the optical bench to switch between two separate laser sources, one a redundant backup for the other. The lasers, and fiber feeds to the optical bench should be separate to give the maximum possible levels of failure robustness.

The aim of the Fiber Switching Unit Actuator is to hold and rotate the half wave plate of the FSU.

B.

FSUA requirements

To switch between two separate laser sources a rotation of 45 degrees of a half wave plate is mandatory. The main functionalities of the FSUA are:

The following requirements were considered to be design driving:

C.

FSUA design

D.

FSUA performance and environmental verification

On the first model of the FSUA Vibration tests, Thermal cycling tests and a life test is performed, in between all tests steps the wobble performance of the mechanism is determined, see figure above for the results.

E.

Conclusion

With the design, realization and testing of the FSUA, TNO Optomechatronics in cooperation with Attocube AG has demonstrated that in very limited available space it is possible to actuated a wave plate with a wobble less then +/− 75 micro radians, leading to a beam jitter of less ten +/−75 nm. It is also shown that the mechanism will survive the launch and thermal vacuum loads. The life test performed inside and outside vacuum shows no measurable degradation in performance of the FSUA.

Two mechanisms have been build and tested, ready to soon be integrated on the LISA/NGO optical bench EBB [3,4]

A.

Introduction

Due to seasonal orbit evolution effects on the relative positions of the three spacecraft, the outgoing laser beam angles have to be corrected with a stroke of ±2.5°. Critically important are the contribution to the optical path length, which has to be lower than 3 pm / √Hz, and the angular jitter, which has to be lower than 1 nrad / √Hz, both while the IFPM is scanning with a low constant velocity. Another driving requirement is the redundancy.

B.

Actuator performance testing

As with the PAAM, the mechanical concept is based on a mirror bonded to a monolithic structure, which allows rotation of the mirror by two elastic Haberland hinges. The axis of rotation is located in the plane of the mirror, thereby minimizing the coupling between angular jitter and optical path length.

As electromagnetic actuation is not allowed on the optical bench, the number of actuation options is reduced strongly. Electrostatic actuation is ruled out because of the holding and actuation force requirements. Piezo-stacks are ruled out because of the large stroke requirement. Other concepts, such as thermal or hydraulic actuation, are ruled out because of stability, heritage and resolution problems.

The most suitable actuator principle is a piezo-stepper, which has an unlimited stroke, but also a very fine resolution because of the analog mode option. This actuator is tested in a dedicated test set-up, in which the jitter during stepping is optimized and measured. The test set-up design, as shown in the figure above, features two opposing steppers with each 4 legs, pressed together by an elastic pre-stress configuration. Between the legs of the two steppers, a walking rod is pushed forward. The rod is attached to a large stroke elastic linear guidance, of which the displacement can be measured by a differential interferometer (Renishaw DI).

Four high voltage amplifiers, one for each stepping phase, are controlled by a dSpace system that uses feedback from the interferometer. The shape of the voltage signals determining the stepping phases, is optimized to enable constant velocity motion with very low disturbances. The optimized voltage shapes are based on [7]. By using an asymmetric waveform, in which the contact part of the stepping motion is significantly longer than the non-contact part, the contact parts of each leg tip overlaps, and the velocity does not drop to zero anymore. This way, a more continuous velocity can be achieved.

Measurements of the angular jitter during 0.5 nm/s (science mode) and 20 μm/s (beam acquisition mode) motion are performed. To make sure steps are performed during the measurement, a measurement time of 10000 seconds is used.

Figure 14 Top shows the tracking error of the piezo-stepper set-up in the time domain, while Figure 14 Bottom shows the spectrum, as compared to the requirement.

Figure 14:

Top: Time domain result of the tracking error of the piezostepper set-up during 10000 seconds of 0.5 nm/s motion. Bottom: Amplitude spectral density of the tracking error of the piezostepper set-up, during 10000 seconds of 0.5 nm/s motion.

The peak to peak tracking error is within ±5 nm. In the frequency domain, the low frequency noise is above the specification for angular jitter in science mode (corrected for the rotation arm). Above 5 Hz, there are some sharp peaks above the specification for angular jitter in science mode.

The tracking error during beam acquisition mode is also measured. Figure 15 Top shows the tracking error during 10 and 20 μm/s motion. The peak to peak error is approximately ±40 nm. Figure 15 Bottom shows the integration of the amplitude spectral density, showing the rms of the tracking error in beam acquisition mode. Below 500 Hz, the total contribution to the error is out of spec, but below 10 Hz the angular jitter is within 6 nm RMS.

Figure 15:

Top: Time domain result of the tracking error of the piezostepper set-up during 30 seconds of 10 and 20 μm/s motion. Bottom: Cumulative Spectral Density of the tracking error of the piezostepper set-up during 30 seconds of 10 and 20 μm/s motion.

As can be concluded from the test results, not all performance requirements are achieved. However, the performance is very close to the requirement, and with small adjustments to the design of the actuator configuration, we believe the angular jitter requirements can be fulfilled.

C.

IFPM design

With the knowledge from the piezostepper set-up, and additional requirements on the launch loads and redundancy, the piezostepper is integrated in the IFPM steering mirror concept. A CAD picture of the design is shown in Figure 16.

Figure 16:

CAD picture of the IFPM beam steering mirror design, including redundant piezo steppers.

Some properties of the mechanism: