Random Vibration Testing of Microelectromechanical Deformable Mirrors for Space-based High-Contrast Imaging

For this study, we procured two 2040-actuator DMs from BMC with the characteristics specified in Table 1 and layout illustrated in Fig. 1. The DMs were manufactured on 1.1 mm thick substrates that is more than four times stiffer than the standard substrate. This thickness was optimized through a finite element analysis studying the stresses on the mirror caused by random vibrations using conservative RST coronagraph instrument flight acceptance specifications (see blue curve in Fig. 7). It brings about a higher resistance to bending stresses exerted by the thin films. This change also reduces the surface deformation of the unpowered DM and then increases the DM usable stroke for wavefront control after flattening. BMC developed custom tooling at the commercial MEMS foundry to work with the new substrate and process these thicker wafers.

Beside the substrate thickness, no step in the manufacturing process is different from usual BMC DMs. The procedure, illustrated in Fig. 2, was as follows:

1. (i)

   Silicon dioxide and a low stress silicon nitride layer were deposited on a single crystal silicon substrate to electrically insulate the conductive substrate from the MEMS devices (Fig. 2, step 1).

2. (ii)

   The first layer of polysilicon (referred to as Poly 0a) was then deposited, patterned, and etched to create actuator base electrodes and wire routing for the array (Fig. 2, step 2).

3. (iii)

   A low-temperature oxide (LTO) layer was deposited and polished using chemo-mechanical polishing techniques to flatten the layer. A second dielectric film, low-stress silicon nitride was then deposited (Fig. 2, step 3-4).

4. (iv)

   The LTO and silicon nitride layer was lithographically patterned and etched to provide a path for electrical connectivity between the wire traces, actuator electrodes, and grounded landing pads, which were produced in a subsequent polysilicon thin film (Poly 0b) deposition and patterning process (Fig. 2, steps 4).

5. (v)

   An array of actuator electrodes was fabricated (Fig. 2, step 5). Then, a thick sacrificial layer (Oxide 1) made up of phosphosilicate glass (PSG) and a thin barrier layer of LTO was deposited on the Poly 0b layer to create the actuator gap (Fig. 2, step 6). The stroke of the electrostatic actuators depends on its thickness.

6. (vi)

   The Oxide 1 film was patterned and etched once more to create the actuator anchor features (Fig. 2, step 7).

7. (vii)

   A second layer of polysilicon, Poly 1, was deposited, patterned, and etched to create actuator anchors and compliant actuator flexures with integrated hard stops (Fig. 2, step 8).

8. (viii)

   A second sacrificial layer, Oxide 2, was deposited and polished to remove print-through from the underlying films. The mirror attachment post features were then patterned and etched into the Oxide 2 film (Fig. 2, steps 9-11).

9. (ix)

   A final polysilicon layer, Poly 2, was then deposited, polished, and patterned (Fig. 2, step 12).

10. (x)

    Metal bond-pads were added to allow for wire-bonding of the device, and to allow the wafers to be diced into individual DM devices.

11. (xi)

    Finally, the sacrificial oxide layers were removed using a wet etch “release” process (Fig. 2, step 13).

Once the devices were received from the foundry, BMC inspected the DMs using visible and IR optical microscopy and interferometry to identify potential optical, electrical, and subsurface manufacturing defects. Using a custom probe station, each candidate die that passed this initial inspection was tested to determine actuator response. Their electro-mechanical and optical performance were then characterized, including responsiveness of each actuator, stroke limits, unpowered surface error, and actuator defects.

We selected two devices for this study, which we refer to as Device Under Test (DUT) 1 and 2. Their initial surface properties are summarized in Table 2. DUT 1 is a 100% functional unit that was coated with an evaporated thin film of aluminum at BMC’s facility. The purpose of DUT 1 is to confirm or reject the hypothesis that a fully functional 2K MEMS DM can survive a launch environment. On the other hand, DUT 2 had some unresponsive actuators. We kept its face sheet uncoated to allow for the post vibration infrared inspection of the DM surface to help understanding any failure mode. This DUT aimed to test the hypothesis that defects causing anomalous actuators can propagate to neighboring actuators during random vibrations[16].

For both DUTs, coated-dies were attached with adhesive to a ceramic package specifically designed for the 2K DMs (see in Fig. 3). The DM die and the ceramic package were electrically connected using gold wire-bonds applied with a high-precision automated tool at BMC’s facility. JPL also fabricated flex cables that were connected in the back of the new chip carrier through a pin-grid array (PGA) and terminated in 528-pin MEG-Array connectors (see Fig. 4).

The packaged DMs were tested using high-voltage drivers commercially available from BMC to characterize their electro-mechanical and optical performance. BMC’s electronics connect to the DM via the MEG-Array connectors.

Both DUT 1 and 2 underwent a battery of tests before and after exposure to random vibrations. The carrier, die, die bonds, PGA joints and carrier to test mount bonds were inspected in all phases. The actuator functionality and performance were tested using the steps outlined below. The MEG-Array connectors and receptacles are not envisioned as part of the flight system and are therefore not included in our analysis. The workflow of these experiments for both DUTs is illustrated in Fig. 5. Results of these tests are described in Sec. 4.

Before applying the face sheet coating to DUT 1, both DUTs were inspected at BMC using transmissive infrared microscopy. The system was automated to translate the DM and image many actuators in sequence. To achieve this, a MLS203 fast X-Y stage was installed on a BX51 Olympus microscope. The microscope was also equipped with a MFC1 Motorized Microscope focus controller to focus either on the wiring or on the mirror layer. The wiring layer was inspected on the entire die of dimension 32.8$\times$32.8 mm by steps of 400 $\mu$m (size of the actuator pitch) for a total of 6,224 images. The mirror layer inspection was restricted to the device area to image each actuator individually and 4,080 images were taken in a serpentine clockwise path. In total, 10,804 images were recorded per DM, to be compared before and after random vibe in case of failure. DUT 2 had three actuators with clearly visible defects just after fabrication (see the infrared image of an anomalous actuator in Fig. 14).

DUT 1 was then coated and both DMs were sent to the HCIT facility at JPL for testing. Functional testing was done using a Fizeau interferometer (Zygo Verifire). The DMs were placed inside of a plastic enclosure that was purged with a continuous flow of dry air to maintain a relative humidity of $<$30% during operation and to avoid any electrostatic discharge event[17]. The devices were connected through the MEG-Array connectors to a commercial 14-bit electronics provided by BMC for the 2K-DM to perform a battery of functional spatio-temporal tests. The input voltage was limited to 90 V.

The HCIT team developed a series of functionality tests aimed at highlighting defective actuators before and after random vibe that were sorted in several categories. A “pinned” actuator is fixed to its unpowered position and is easily noticeable when uniform voltage is applied to the DM. A “free-floating” actuator does not move through electric commands but remains free to move to follow the displacements of its neighbors. “Tied” actuators occur when more than one actuator respond to a command sent to a single actuator index. A “weak” actuator moves significantly less than its neighbors with the same command. Finally, an “anomalous” actuator can be any of the above categories or otherwise defective. The standard functionality test process consists of the routines described below. For each surface measurement recorded by the Zygo interferometer, the uncommanded surface was subtracted and piston, tip and tilt aberrations were removed from the data in post-processing.

The functionality test routines are as follows:

DUT 1 was also tested for high-contrast imaging purposes using the In-Air Coronagraph Testbed (IACT)[18] in the HCIT facility at JPL. The IACT optical layout is shown in Fig. 6. A 637 nm monochromatic light source was injected into the enclosed testbed through a single mode fiber to simulate a star. A charge 6 vector vortex coronagraph (VVC) was used to limit the sensitivity to low order wavefront aberrations due to air turbulence[19, 20, 21, 22].

The injected light was passed through a linear polarizer (LP) and a quarter wave plate (QWP) to circularly polarize the light source upstream of the focal plane mask (FPM). The LP had an extension ratio of $10^{5}$ and the QWP had a retardance of 0.24$\lambda$ at 637nm. The off-axis parabola (OAP) 1 then collimated the beam and reflected it toward a 18.48 mm pupil, immediately followed by DUT 1. There were 46.2 actuators across the beam at the DM. Similar to the functional test described above, DUT 1 was placed inside a plastic box with a continuous flow of dry air to reduce the humidity. To limit air turbulence, the flow was optimized to reach a relative humidity of 25% to meet the DM specification. A Fluke DewK thermo-hygrometer was inserted in the dry box to actively sense the humidity level through a software watchdog. The box had an opening on the front side to allow the beam to reflect off DM to the 1524 mm focal length OAP2 that focused the light on the VVC FPM. The FPM was fixed to a 3-axis mount. The diffracted light was then reflected on the 762 mm focal plane OAP3 and blocked by a Lyot Stop (LS) of diameter 7.5 mm on a 2-axis mount. Considering the magnification of the OAPs, the LS diameter was 81.2% of the pupil image.

A “D” shaped field stop (FS) of size 3-10$\lambda/D$ was added in the downstream conjugated focal plane. The purposed of the FS was to enhance the contrast in the final focal plane at the camera by minimizing stray light or photo-electrons inside the corrected regions adjacent to saturated regions. The FS was placed on a 3-axis mount to optimize focus and can be moved in and out for calibration purposes. The dark images that are later subtracted from the dark hole images were recorded by fully blocking the light at the FS plane.

After the FS, the beam is then collimated by OAP5 to pass through another set of QWP and LP that minimize the incoherent leakage caused by the imperfect retardance in the VVC FPM. The rotation angles of the QWP+LP were optimized by minimizing the signal on the science detector with the VVC FPM fully removed from the beam. Finally, the OAP6 directed the light to the science detector where the final image is formed. A neutral density filter wheel can be used for calibration purposes, for instance to prevent the over-exposure of the unocculted PSF used for calibration, and also has an optical lens to allow pupil imaging. The science camera Andor Neo sCMOS electrically cooled to -40 °C and the generated heat was removed with a water cooler. The camera was mounted on a single-axis stage to control the focus. The pixel pitch was 6.5 $\mu m$ and the resolution of the focal plane images is 24.7 pixels per $\lambda/D$.

Standard wavefront sensing and control (WS&C) algorithms and calibration procedures dedicated to high-contrast imaging were used to minimize the simulated stellar intensity at the detector plane and improve the raw contrast level (intensity of the attenuated starlight normalized by the maximum of the unocculted PSF)[23]. Phase retrieval algorithms based on both Gerchberg–Saxton formalism[24] and the fitting of low-order Zernike modes were used to flatten the DM and calibrate its response. At least three images close to the focal plane and three images close to the pupil plane were used to run the algorithm. After flattening the DM the Strehl ratio of the unocculted PSF was very close to 1.0. The VVC FPM and the LS were automatically centered on the beam iteratively through the acquisition of pupil images. Dark images and off-axis PSFs were then recorded and the FS is introduced in the beam to allow the desired off-axis dark hole region to pass through.

Wavefront sensing and wavefront control are performed respectively with pair-wise probing (PWP) and electric field conjugation (EFC)[25, 26] through FALCO software[27]. Both algorithms require a high-performance DM to achieve contrast levels of $\sim 10^{-8}$. The dark hole (DH) region where the stellar residuals are attenuated is defined by the FS aperture that goes from 3 to 10 $\lambda/D$. While the contrast improves in the DH, the exposure time on the science camera is increased from 100 s to 300 s to maintain a sufficient signal-to-noise ratio. The $\beta$-bumping technique[28] is regularly used to achieve the best possible coherent contrast in the dark hole region. The raw contrast in the dark hole is intricately linked to the DM performance. Performance testing results for DUT1 are presented in Sec. 4.1.

In previous work, we have demonstrated robustness of actuators that were surrounded by functional actuators under flight-like thermal cycles and vibrations as well as the compatibility of partially-functional 50$\times$50 MEMS DMs with vacuum environments[16]. This work expands the previous study since we specifically test the robustness of actuators at the vicinity of defective actuators as well as fully-functional 50x50 MEMS DMs.. The DMs and their respective mounts were shaken at JPL on a 10-inch cube shaker. The flex cable was fixed to the edge of the mount with a flex clamp while the other end of the flex was curled loosely and taped down onto the moving platform of the shaker to avoid any damage. Particle contamination and humidity were controlled during the test to ensure the DMs are not subject to alternative sources of electric degradation and failure[29], as suspected in previous studies[15]. The applied signal ranges between 20 Hz and 2000 Hz, which corresponds to typical frequency ranges for most launch vehicles. The temporal acceleration spectral density of the vibrations in each of the three spatial axes was between 0.01 g²/Hz and 0.4 g²/Hz and is shown in Fig. 7. The DMs therefore underwent 11.7 gRMS over all frequencies for 2 min per axis. This qualification test is conservative to any potential launch vehicles and surpasses the flight acceptance followed by the Roman Space Telescope Coronagraph Instrument specifications.

DUT1 is a 100% yield device intended to validate that a fully functioning MEMS DM passes random vibration testing. The criteria of success are visual inspection of the structure; the actuator responsiveness, stroke, and voltage-to-displacement gain; and the ability to create a dark hole at relevant contrast levels ($\sim 10^{-8}$). This section compares the results of functional and performance testing before and after random vibration at JPL.

Fig. 8 represents one of the 16 regular grids of actuators that were poked during the functional test of DUT1 before and after the random vibe test. The image resolution has been slightly decreased after vibe because we did not insure same Zygo zoom settings before and after random vibe test. Such a resolution remains acceptable for direct comparison with pre-vibe data since we have many more than the required 4 pixels per DM actuator. As in the 15 other grids, the behavior of the actuators was identical before and after random vibe regardless the applied voltage. No anomaly in the influence function shape nor displacement of the DM surface occurred. After DM flattening, the final shape was measured to be 3.41 nm RMS wavefront error before and 3.37 nm RMS after random vibe. Around the flat setting, the quadratic relationship between the surface displacement amplitude of each actuator and the applied voltage remains identical before and after vibe. All functional tests performed did not show any anomalies on DUT1 either before and after the DM was random vibed.

After functional testing, DUT1 was installed on IACT to test the DM performance in a coronagraph instrument. Figure 9 shows the normalized intensities in the science image before and after random vibe, and after a few dozen WS&C iterations. The mean contrast in the DH is $1.19\times 10^{-8}$ (before random vibe) and $9.53\times 10^{-9}$ (after random vibe) while the spatial standard deviation is equal to $1.42\times 10^{-8}$ and $1.28\times 10^{-8}$, respectively. The mean coherent contrast is equal to $3.80\times 10^{-9}$ before and $4.34\times 10^{-9}$ after with a respective standard deviation of $3.71\times 10^{-9}$ and $3.86\times 10^{-9}$. The small difference in coherent contrast is explained by a slightly higher internal turbulence on the testbed after random vibe. We also observe in Fig. 9 some horizontal artifacts that result from diffraction effects caused by a slight misalignment of the field stop in the z-direction. These highly localized effects did not impact convergence of the PW+EFC algorithm nor the computation of contrast performance. The decrease of flux after random vibe might induce an underestimation of the mean incoherent intensity leading to a slight overestimation of the contrast performance after random vibe.

Figure 10 overlays the radial profile of each total intensity image whose mean contrast is calculated in annulus of $\lambda/8D$. On one hand, both Fig. 9 and Fig. 10 emphasize that IACT performance are limited at low separations by an Airy pattern. This pattern is not sensed by PWP. This pattern is known to be an incoherent leakage due to manufacturing defects in the VVC FPM and in the LP and QWP[23]. This leakage could be further reduced by improving the retardance error in the QWP and extinction of the LP that are currently used. On the other hand, the coherent component in the DH was measured below $10^{-8}$ in both cases and its speckle intensity structure was modified at each iteration. We therefore attribute the remaining coherent component to the internal turbulence in IACT on timescales of a single WS&C iteration. This effect could be reduced on IACT by lowering the dry air-flow or by installing an additional WS&C system to specifically control low order spatial aberrations at higher temporal frequencies [30]. Nonetheless, from the results of both performance and functional test on DUT1, we can conclude that DUT1, a 100% functional 2K MEMS DM, survived random vibrations similar to a launch vehicle.

DUT2 had a few defective actuators and no metallic coating with the intention of testing the hypothesis that anomalous actuators can propagate to neighbors during rocket launch. DUT2 is not coated to allow IR inspection after random vibe. DUT2 also underwent the battery of functional tests described above, but was not used for performance testing.

In pre-vibe function testing, DUT2 was found to be $\sim 99.3$% functional (see in Fig. 11: it had three pinned actuators, two couples of tied actuators, and two couples and one triplet of weak and tied actuators (whose voltage to amplitude gain is divided by the number of associated actuators). One result of functional test is shown in Fig. 12 where the same grid of actuators was poked with respect to the grid in Fig. 8. The poke grid measurements show that DUT2 did not change behavior at actuator level. As an example, Fig. 13 shows the deflection for neighbors of one defective actuator (index 1283) while applying individual voltage of 0.025 BMC unit on top of a flat bias of 0.05 BMC unit. Their influence functions have been fitted with a Gaussian whose maximum amplitude is reported in this plot. Error bars are computed as the standard deviation of the measured amplitude for the 8 neighbors. Deflection of 1283 actuator’s neighbors remain identical before and after random vibration: failure did not propagate during rocket launch simulation. These results were confirmed by the remaining functional tests, described in Sec. 3.3.

Preliminary tests with post-vibe DUT2 presented new anomalous actuators with respect to pre-vibe, particularly tied characteristics. After further investigation, we realized these anomalies were due to poor connections at the MEG-Array connectors level rather than the DM. Indeed, the connectors were disconnected before the random vibe and then reconnected for the functional tests. This process is sensitive since the pins can be easily bent if the connectors are not carefully handled. The defective connectors were fixed either by disconnecting and then reconnecting the faulty MEG-Array connector or by replacing the connector savers if the initial reconnection appeared unsuccessful. The state of the MEG-Array connectors was carefully inspected throughout the whole process. Given the challenges faced by our team related to connectors, we advocate for the development of more robust high-density connector technology and more practical DM driver electronics[8].

We also imaged the initial defective actuators and their neighbors with the infrared microscope to confirm the DM was not affected by the simulated rocket launch. No changes to the anomalous actuators nor their neighbors were notice during the post-vibe infrared inspection. Figure 14 shows the infrared image of one tied actuator as well as the neighbor of another, focusing either on the wiring layer or on the mirror layer, before and after random vibe. The anomaly shown on the pinned actuator is apparent on both layers. The comparison of the images before and after random vibe shows that the damage has not propagated from the initial defect. The second set of images shows that none of the neighbor carrier, die, die bonds, PGA joints, nor actuators were affected by the random vibe test. From these results, we saw no evidence that anomalous actuators propagate to neighbors during random vibe.

This paper is the end product of the intermediary work presented in the SPIE Proceedings: Prada et al. 2021 (”Environmental testing of high-actuator-count MEMS deformable mirrors for space-based applications,” Proc. SPIE 11823, Techniques and Instrumentation for Detection of Exoplanets X, 118230M (1 September 2021); doi: 10.1117/12.2594263).