A.

Mirror Flattening

The prefabricated piezo discs have a poor surface quality of mainly astigmatic shape. Conventional grinding and lapping mitigates the initial deformation to a certain degree. Moreover, due to the large stroke of the mirror and the low order of the initial deformation, the mirror is able to fully compensate for its unpowered deformation without impairing its dynamic range significantly. The actively flattened surfaces of DM-1 to DM-3 are shown in Fig. 3. Despite the low amplitude print-through effect caused by the electrode pattern, the current mirror generation enables surface fidelities exceeding Strehl ratios of 0.95. This was made possible by continually improving the bonding processes, which are currently further refined. Note that the surface of DM-1 was measured with a Shack-Hartman wave-front sensor (SHS), which could not resolve the fine structures of the print-through properly.

Fig. 3

Actively flattened mirror surfaces of DM-1,-2 and -3. DM-1 was measured with a Shack-Hartmann wave-front sensor, DM-2 and DM-3 were measured interferometrically

B.

Zernike Amplitudes and Fidelities

The surface figures of the Zernike modes Z₁ to Z₁₂ have been applied to the deformable mirrors in closed-loop operation to determine the maximum possible amplitudes. The loop operation started at amplitudes of 0.5 μm for every Zernike mode. The amplitude was raised in steps of 0.5 μm until one of the following criteria arose:

The comparison of measured and numerically calculated maximum Zernike amplitudes is shown in Fig. 4 for DM-2 and DM-3. The measured amplitudes correspond well with the numerically calculated Zernike amplitudes, the stroke even exceeds the requirements from the statement of work. In defocus mode (Z₃), a stroke of 45 μm was achieved (30 μm required), the trefoil modes (Z_9,10) were reproduced with a stroke of 15 μm (5 μm required).

Fig. 4

Measured Zernike amplitudes along with the calculated Zernike amplitudes for DM-2 and DM-3

Note that the discrepancy between calculated and measured maximum amplitudes of DM-3 originates from exceeding the dynamic range of the utilized Shack-Hartmann wave-front sensor for certain Zernike modes and is not a miscalculation. Fig. 5 shows interferograms of certain low order Zernike modes at high stroke.

Fig. 5

Interferograms of certain low-order Zernike modes (from left to right: Z₄, Z₈, Z₁₀, Z₁₁), reproduced with high stroke

B.

Control Bandwidth

The mirror was driven in open loop operation at varying loop frequencies. The results for loop bandwidths ranging from 1 Hz to a maximum of 123 Hz are shown in Fig 6. As can be seen, the maximum achieved amplitudes of the respective Zernike modes exhibit a significant drop between 57 Hz and 100 Hz. This can be understood in terms of the mirror’s response to a step-like voltage signal. The response is influenced by piezoelectric creep, and by the limited power that the high voltage driver can deliver. This results in a finite electrical loading time of each actuator. Typical settling times range between 10 ms and 100 ms, the exact value depending on the input voltage. The combination of creep and actuator loading allows sensibly driving the mirror with frequencies up to approximately 50 Hz.

Fig. 6

Zernike amplitudes in open-loop operation at varying control loop bandwidths

A.

Performance in thermal vacuum

The deformable mirror DM-1 was subjected to thermal cycling in a vacuum chamber at EADS Astrium. Measurements of the mirror surface at different temperatures between 100 K and 300 K were conducted with a high resolution Shack-Hartmann wave-front sensor (116 x 116 lenslets), located in front of the vacuum chamber. A schematic view along with a photograph of the experimental setup is shown in Fig. 7. Performance measurements were conducted at thermal equilibrium. The surface figures of the Zernike modes Z₁ to Z₁₀ have been applied to the deformable mirrors in closed-loop operation to determine the maximum possible amplitudes in the same fashion as described in the previous section.

Fig. 7

Left: Schematic of the thermal vacuum performance verification test setup. Right: Deformable mirror in the open chamber. The red dots indicate the positions of temperature sensors in proximity of the mirror.

Fig. 8 shows the maximum Zernike amplitudes at varying ambient temperatures, as well as after 8 temperature cycles between 100 K and 300 K. The drop in amplitude at lower temperatures is due to the decrease of the piezoelectric coefficient, which decreases with approximately 0.4% per Kelvin [5]. The achieved Zernike amplitudes after cycling are similar to those before cycling, no degradation could be observed. Note that due to an issue with the high-voltage driver electronics, the performance measurements shown in Fig. 8 were conducted with only half the maximum allowed voltage the mirror could be driven with. We have also conducted performance measurements after thermal cycling between -10°C and 40°C, with no degradation observed either.

Fig. 8

Maximum achieved relative Zernike amplitudes of DM-1 in thermal vacuum at different temperatures, and after completion of 8 thermal cycles between 100 K and 300 K

B.

Vibration tests

The deformable mirror DM-1 was submitted to sinusoidal and random vibration tests at EADS Astrium. The designated test levels are given in table 1, the test setup is shown in Fig. 9. Each test step was preceded and followed by a low-level 0.5 g sweep to determine the system’s resonance frequencies.

Table 1

– Vibration Test Levels

Fig. 9

Vibration test setup and positioning of the vibration and control accelerometers

Fig. 9 shows the deformable mirror DM-1 attached to the adapter cube of the shaker system. Two accelerometers (control sensors 1 and 2) act as feedback sensors for the shaker system, another two accelerometers (vibration sensor 1 and 2) record the response of the deformable mirror. The vibration sensors were attached to the mirror housing, rather than to the piezo disc, which is the most delicate part of the DM. The mechanical parts made of the steel-alloy Kovar mainly contribute to the final mirror weight of 1.8 kg. The deformable component, consisting of the piezo disc with steel segments and glass substrate weighs 35 g, which is less than 2 % of the total mass. Hence, the contribution from the light, delicate parts may be hard to detect by the acceleration sensors which were attached to the much heavier mirror housing. It is therefore conceivable that the response recorded by the vibration sensors is mainly governed by the response of the mechanical mirror parts rather than by the response of the piezo disc.

Fig. 10 shows the transfer functions from the three low-level sweeps recorded by the acceleration sensor 2, attached to the mirror housing in proximity of the piezo disc. One sweep was conducted prior to testing, one was conducted after the sine vibration test, and the last one after the random vibration test in out-of-plane (OOP) direction. As can be seen, the response shows a deviation around 1820 Hz after the random vibration test compared to the other two sweeps. This may indicate a corruption which occurred during the random vibration test.

Fig. 10

Transfer functions recorded by sensor 2 for the three low-g sweeps

After the low-level sweep following the random vibration test in OOP direction, the DM was detached from the shaker and visually inspected. The upper part of Fig. 11 shows an image of the front side of the DM directly after the vibration test. One can see fine debris clinging to the adhesive side of the Kapton protection tape. Disassemblement of the DM revealed that the piezo spiral arms broke off the central disc. FEM simulations yielded that the sites of fracture coincide with regions where the piezo disc exhibits the most stress when elongated. The results of the simulation along with the sites of fracture are shown in the lower part of Fig 11.

Fig. 11

Top: Debris stuck on the Kapton protection foil directly after the vibration test along with an image of the broken spiral arm structure Bottom: Numerically calculated van-Mises stress inside the piezo disc when elongated

To improve the resilience of the three-arm structure towards vibrations, we have designed two types of three-arm structure, referred to as the “spiral arm design” and the “bridge design”. The two designs are depicted in Fig. 12. In the bridge design, further mechanical stability is achieved by connecting the end of each spiral arm to the crosspiece of the neighbouring arm, thus creating a bridge-like structure.

Fig. 12

Spiral arm design (left), and bridge design (right)

Numerical calculations yielded a reduction of the van-Mises stress by a factor of 4 in the bridge design when applying load in arbitrary directions, the tip/tilt deformation is reduced by a factor 4 as well. The out-of-plane elongation under load is reduced by a full order of magnitude. The first two mirrors feature the spiral arm design, DM-3 and DM-4 were made in the bridge design. Vibration tests of the mirrors with bridge design are imminent.

C.

Irradiation tests

The deformable mirror DM-2 was subjected to gamma irradiation at ESTEC’s Co60-facility. A total dose of 50 krad (Si) at a dose rate of 1 krad/h was applied at atmospheric pressure and room temperature.

Prior and after irradiation, the mirrors performance was tested by applying a voltage of 100 V to every actuator and measuring the response. No degradation of the actuator response was observed.

Proton irradiation tests are imminent.