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Micro-machined membrane deformable mirrors (MMDMs) are being evaluated for their suitability as wavefront correctors at cryogenic temperatures. Presented here are experimental results for the change in the initial mirror figure of 37-channel MMDMs from OKO Technologies upon cooling to T=78K. The changes in the influence functions are also explored. Of the sample of 3 mirrors tested, one was found to have sufficiently small initial static aberrations to be useful as a wavefront corrector at this temperature. The influence functions at T=78K were found to be similar in shape to both those at room temperature and theoretical predictions of the MMDMs surface shape. The magnitude of the surface deflection at T=78K was reduced by around 20% compared with room temperature values.
©2001 Optical Society of America
1 Introduction
The need for cryogenic active or adaptive optics (AO) systems is driven by two main astronomical applications: satellite observations and ground-based IR observations. In the former case, satellites may be actively or passively cooled to cryogenic temperatures, while in the latter case, IR emissions from an ambient temperature AO system limit the depth of the observations. In order to reduce cooling times, and overall cost, a cryogenic AO system must be small. For this reason, among others, 37-channel electrostatic Micro-machined Membrane Deformable Mirrors (MMDMs) of 15mm diameter from OKO Technologies [1], have been evaluated for their suitability for cryogenic wavefront correction. We present the preliminary results for the change in the static properties of three such mirrors upon cooling to T=78K. These mirrors were designed for operation at room temperature, and have not been optimised for cryogenic temperatures. Of the three mirrors that have been characterised; one is an older design (Mirror A) which has an inter-actuator spacing of 1.75mm and the other two mirrors (Mirrors B and C) are of a more recent design with an inter-actuator spacing of 1.25mm. The results obtained for the mirrors’ static aberrations were for unpowered mirrors, and show that one of the sample of three mirrors performed substantially better than the other two. This difference is presumed to be due to variations in the manufacturing process. The static aberrations introduced by the cooling process are sufficiently small for the better mirror that a substantial fraction of the mirror’s dynamic range is still available for wavefront correction.
2 Micro-Machined Deformable Mirrors
The mirrors tested have been developed by OKO Technologies [1] for room-temperature wavefront correction. These 37-channel devices have been demonstrated to be suitable for adaptive optics at room temperatures [2, 3]. The mirrors themselves are constructed by coating a silicon wafer with silicon nitride on both sides. A mask is then cut into one of the nitride layers, before the silicon wafer is etched away through this mask. This leaves an aperture through to a silicon nitride membrane. This wafer is then mounted above a printed circuit board with the actuator pattern already installed (Figure 1a). Finally, a layer of Aluminium is deposited onto the membrane (Figure 1b). When this layer of Aluminium is grounded, the shape can be controlled through electrostatic attraction by applying voltages to the actuators [4]. For IR applications, the Aluminium can be replaced with a layer of Gold. The maximum central displacement for the mirrors considered here is approximately 11µm(18λ for the Zygo interferometer used in the following measurements).
The principal advantage of MMDMs for cryogenic applications is their small size. This reduces the time required to cool the system and reduces the cost of the system. The largest single disadvantage of these MMDMs is their fragility; the membrane is less than 1µm thick. However, for operation at cryogenic temperatures, the mirror is enclosed in an evacuated cryostat eliminating the risk of the membrane being punctured. The mirrors themselves are low-cost devices ([5]).
3 Experimental Set-up
Significant aberrations were observed when the unpowered mirror in its socket was cooled to T=78K for both mirror designs. In order to isolate the effect intrinsic to the mirror from that due to its mounting in the socket, an extension pin was attached to one of the mirror pins, and this extension pin was then mounted into the socket (Figure 2). In this way, the mirror was effectively mounted at a single point so that no thermal stress could be transferred from the mounting to the mirror.
This enables the evaluation of the mirrors’ characteristics to be undertaken in a best-case environment. Any significant contribution to the aberrations due to the thermal stress from the socket and mount could, in principle, be removed by replacing the socket with an alternative design involving flying leads to restore the electrical connections. The measurements were taken by first cooling the mirror to T=78K in a small Oxford Instruments liquid nitrogen cryostat. Regular measurements of the mirror’s surface were then taken with a Zygo PTI interferometer (λ=633.9nm) as the mirror gradually warmed up to room temperature. Taking measurements while cooling the cryostat was impractical due to the severe turbulence introduced by liquid nitrogen vapours. The temperature within the cryostat was measured by simply measuring the voltage across a diode. Tests had previously been conducted to determine a suitable mounting point within the cryostat, where the temperature would be similar to that of the mirror, to calibrate the diode and to verify that the material from which the mount was constructed did not appreciably change the measured temperature. A further point to note is that the Zygo measures the surface of the membrane, not the returned wavefront. Hence, where the results show defocus, a collimated beam reflected from the mirror would actually be focussed. For the measurements of the mirrors influence functions, the mirror was mounted in a socket in the conventional manner, since the electrical connections provided by the socket were required.
4 Results
4.1 Seidel Aberrations
Plots are presented below of the variation of the major Seidel aberrations with the temperature of each mirror. The data are presented with the tip/tilt on the mirror having been subtracted in software. In addition, the diameter of the mirror that is analysed is about 90% of the diameter of the measured image. This is due to the Zygo’s limited handling of differaction effects from the edges of the membrane surface. The temperature is measured without any physical contact on the mirror surface (due to the risks of destroying the membrane). Experimentally, the error in the temperature measurements has been determined to be less than 5K, by measuring the recorded temperature within the dewar in a variety of locations and circumstances simultaneously. It should be noted that the current set-up prevents the mirror being at an equilibrium temperature between T=78K and room temperature; it is always either cooling down or warming up.
Since the mirror cannot be held at an equilibrium temperature other than at room temperature or T=78K, the absolute errors in the recorded aberrations have been taken to be constant with temperature, and the measured errors from the cold measurements have been applied to each data point. It is obvious from the plots (Figures 4, 5) that the scatter on the measurements is much greater for larger aberrations. This is not an effect of the low temperatures involved, as can be seen by examining the plot for Mirror A (Figure 3). Despite similar temperatures, the scatter is much smaller. Therefore, it is assumed that the Zygo interferometer becomes less accurate for large aberrations, that is, aberrations leading to a peak to valley displacement of the membrane surface greater than about 8λ. The peak-to-valley (P-V) values recorded incorporate higher order terms than the individual Seidel aberrations presented, and so are not a simple sum of the other presented aberrations.
The results for Mirror A (Figure 3) show that there is still some throw left in the mirror after correcting for the astigmatism. The amount of correction achievable after removing the static aberrations depends on the beam size, relative to the total diameter of the mirror. This is due to the fact that the mirror edge is fixed, and so no correction at all can be achieved at the edges. Hence, only a portion of the mirror surface is utilised, in typical applications for these devices. The available displacement at 50% radius from the centre of the membrane is approximately 14λ. It should be noted that, were it possible to remove the astigmatism, the mirror would scarcely be affected by the cooling process.
The results for Mirror B (Figure 4) show very different behaviour from the first mirror. Cooling this mirror results in a P-V mirror displacement of 9.78±0.09λ. The predominant contribution to this behaviour is again astigmatism. However, with this mirror, the other aberrations are also on a significant scale, particularly Coma and Defocus. These results clearly indicate that this MMDM possesses considerably greater aberrations at cryogenic temperatures than the first MMDM.
The results for the final mirror (Mirror C, Figure 5) are distinctly different from Mirror B and are even further from the Mirror A results. The P-V mirror displacement here is 10.14±0.06λ, which is only marginally greater than for the second mirror. However, the contributions from the various individual aberrations are different to those for Mirror B. In particular, both Spherical Aberration and Defocus are larger in magnitude.
4.2 Phase Maps
The change in the mirrors caused by cooling to T=78K can perhaps be best illustrated through the use of phase maps of the mirror’s surface. These maps have been false-coloured to indicate regions of constant phase. In each case, one image is presented from the cold measurements, at a temperature of T=78K, and one from the room temperature measurements. Note that the image rotations are not necessarily the same between the cold images and the warm images.
The images for the Mirror A (Figure 6) show the increase in astigmatism caused by cooling. Note that the false-colour map used has been scaled for a total P-V displacement of 10λ to better illustrate the maps for the new mirrors. Hence there is very little detail visible in the warm maps. The cold phase map here is presented before the edges of the image are cropped for analysis. Hence the jagged edge caused by diffraction effects is still visible, notably at the lower left hand corner. The warm image presented has had part of the edges cropped, but further cropping was necessary before analysis.
The phase maps for Mirror B (Figure 7) illustrate the scale of the effect on the MMDMs of cryogenic cooling. The void at the lower-left hand corner of this, and sub-sequent cold images for Mirror B, was due to the aberrations caused by cooling the mirror, and is not a measurement artefact of the Zygo. This was confirmed through the use of a beam-splitter and a screen at a similar optical path length from the mirror as the Zygo.
Both of the images presented for Mirror C (Figure 8) are shown before clipping, hence the jagged edges. This image clearly shows that the mirror surface is heavily deformed by the cooling process. The void at the lower left corner of this image is also genuine, and not a measurement artefact. This was confirmed in the same manner as for Mirror B.
4.3 Influence Functions
In order to measure the influence functions of each actuator of the mirrors they were replaced in their sockets and driven to 250V. One actuator is shown from each ring of actuators, numbered as per Figure 1.
The first set of influence functions (Figure 9) was obtained using the Zygo interferometer and Mirror B at room temperature. The initial mirror surface image has been subtracted in software from each image.
The second set of influence functions (Figure 10) being presented here were obtained with an identical set-up to the warm influence functions above, except with the mirror cooled to T=78K. Note that the area missing from the images is caused by the aberrations present in the mirror. Again, the initial mirror surface has been subtracted from each image.
The final influence functions (Figure 11) are a set of theoretical influence functions obtained using the “response” program from the OKO Tech website (http://www.okotech.com/archive/response.zip). They are presented for comparison with the measured experimental influence functions at room temperature and at T=78K. The colour maps for all of the influence function images have been scaled for each individual image to highlight the detail in the images.
For comparison purposes, cross-sections through these influence functions have been taken (Figure 12). The first set of comparisons (Figure 12a) examine the three sets of influence functions (Theoretical, Warm and Cold) on a per actuator basis. Each individual influence function has been normalised to 1, to clarify the similarity in the shapes of the influence functions. The second set of comparisons (Figure 12b) show the variations in the influence functions along a radius for each set of conditions. In this case, the influence functions have all been normalised relative to the central actuator in the warm results. Note that the throw of the mirror for a given voltage is 20% lower for the cold results than the warm results. This indicates that either larger control voltages would be required at lower temperatures to obtain the same stroke as at room temperature, or that the mirror stroke at T=78K is constrained to be less than that at room temperatures. Which hypothesis is valid will be tested by applying larger voltages to the mirror and determining the cryogenic maximum stroke. This has not been done to date for practical reasons.
Fig. 12. Cross sections through influence functions. Note that 12a is normalised for each actuator independently, while 12b normalised to central actuator for the warm data)
These experimental influence functions at room temperature and at T=78K show good agreement with the theoretical influence functions. This is a promising result, and clearly indicates the feasibility of using the MMDM as a wavefront corrector at cryogenic temperatures. It also raises the potential prospect of a mass-produced AO system at room temperatures using the theoretical influence functions in the control loop, removing the need for each system to be individually calibrated. It is also worth noting that the warm results are consistent with previously published results by Dayton et al [2]. These results indicate that, if the static aberrations of the mirror can be overcome, MMDMs should prove to be suitable for cryogenic AO.
5 Discussion
The preceding results clearly show that each mirror is unique and that one of the mirrors tested (Mirror A) is superior at cryogenic temperatures to the other mirrors (Mirrors B and C). This result is not unexpected; there are enough variables in the mirror construction that the characteristics for each mirror can be expected to vary. Mirror A is of the older design, while Mirrors B and C are of a more recent design. Since the only difference between the design of the two mirrors is the actuator pad pattern, and the results were taken without powering the mirrors (indeed, without electrical connections to the mirrors), the change in mirror design is not believed to be significant. The presumption is that the different experimental results are due to variations in the mirror construction, rather than due to design differences. Mirror A is from a different manufacturing batch to Mirrors B and C. Thus selection of mirrors from a production batch for their properties at cryogenic temperatures may be necessary. The cause of the initial static aberrations is believed to be due to coefficient of thermal expansion mismatch between the Aluminium layer and the Silicon Nitride layer. This may be reduced by using Gold instead of Aluminium, and may potentially be reduced further by the use of other alternative materials. It is also likely, should the demand for cryogenic applications be sufficient, that the mirror design could be optimised for operation at cryogenic temperatures and yield performance comparable to that achieved at room temperature by current devices. These optimisations would have to be performed as part of the MMDM construction process, and are beyond the scope of this paper.
6 Conclusions
Three MMDMs have been tested for the extent of their static aberrations upon cooling to T=78K. The first mirror was of a different design to the other two, with the only difference in the designs being the size of the inter-actuator spacing. The static aberrations for the old mirror design increased upon cooling, but to a considerably lesser degree than for the new design. Differences in the designs of the mirrors are unlikely to be responsible for the marked differences between the results for the two designs. The most likely cause for the differences in the results between mirrors are slight variations inherent in the manufacturing process. Since the mirrors tested were not specifically designed for cryogenic applications, but still demonstrated reasonable functionality, development of special packaging for cryogenic applications should result in a functionality level similar to the existing room temperature devices.
The influence function results are encouraging, indicating a good agreement between warm and cold influence functions, and also a good agreement with the theoretical influence functions. Further tests are being conducted to study the dynamic response of these mirrors.
References and links
1. http://www.okotech.com/
2. D. Dayton, S. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne, S. Rogers, M. Vaidyanathan, and M. Shilko, “Laboratory and field demonstration of a low cost membrane mirror adaptive optics system,” Optics Communications , 176, 339–345, 2000 [CrossRef]
3. C. Paterson, I. Munro, and J.C. Dainty, “A low cost adaptive optics system using a membrane mirror,” Optics Express , 6, 175–185, 2000. http://www.opticsexpress.org/oearchive/source/20597.htm [CrossRef] [PubMed]
4. G. Vdovin, P.M. Sarro, and S. Middelhoek, “Technology and applications of micromachined adaptive mirrors,” Journal of Micromechanics and Microengineering , 9, R8–R19, 1999 [CrossRef]
