Cryogenic wavefront correction using membrane deformable mirrors

Cryogenic wavefront correction using

membrane deformable mirrors

H. M. Dyson, R. M. Sharples, N. A. Dipper

Astronomical Instrumentation Group, Department of Physics,University of Durham, South Road, Durham, DH1 3LE, UK

[email protected]

G. V. Vdovin

Electronic Instrumentation, Technical University of Delft,Mekelweg 4, 2628 CD Delft, The Netherlands

Abstract: Micro-machined membrane deformable mirrors (MMDMs)are being evaluated for their suitability as wavefront correctors at cryo-genic temperatures. Presented here are experimental results for thechange in the initial mirror figure of 37-channel MMDMs from OKOTechnologies upon cooling to T=78K. The changes in the influencefunctions are also explored. Of the sample of 3 mirrors tested, one wasfound to have sufficiently small initial static aberrations to be useful asa wavefront corrector at this temperature. The influence functions atT=78K were found to be similar in shape to both those at room tem-perature and theoretical predictions of the MMDMs surface shape. Themagnitude of the surface deflection at T=78K was reduced by around20% compared with room temperature values.c© 2001 Optical Society of AmericaOCIS codes: 220.1000 Aberration Compensation; 010.1080 Adaptive Optics

References and links1. http://www.okotech.com/

2. D. Dayton, S. Restaino, J. Gonglewski, J. Gallegos, S. McDermott, S. Browne,S. Rogers, M. Vaidyanathan, M. Shilko, “Laboratory and field demonstration of alow cost membrane mirror adaptive optics system,” Optics Communications, 176,339-345, 2000

3. C. Paterson, I. Munro, J.C. Dainty, “A low cost adaptive optics sys-tem using a membrane mirror,” Optics Express, 6, 175-185, 2000.http://www.opticsexpress.org/oearchive/source/20597.htm

4. G. Vdovin, P.M. Sarro, S. Middelhoek, “Technology and applications of microma-chined adaptive mirrors,” Journal of Micromechanics and Microengineering, 9, R8-R19, 1999

5. http://www.okotech.com/pricelist/index.html

1 Introduction

The need for cryogenic active or adaptive optics (AO) systems is driven by two mainastronomical applications: satellite observations and ground-based IR observations. Inthe former case, satellites may be actively or passively cooled to cryogenic tempera-tures, while in the latter case, IR emissions from an ambient temperature AO systemlimit 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 elec-trostatic Micro-machined Membrane Deformable Mirrors (MMDMs) of 15mm diame-ter from OKO Technologies [1], have been evaluated for their suitability for cryogenic

(C) 2001 OSA 1 January 2001 / Vol. 8, No. 1 / OPTICS EXPRESS 17#29573 - $15.00 US Received November 29, 2000; Revised December 21, 2000

http://www.okotech.com/

http://www.opticsexpress.org/oearchive/source/20597.htm

http://www.okotech.com/pricelist/index.html

wavefront correction. We present the preliminary results for the change in the staticproperties of three such mirrors upon cooling to T=78K. These mirrors were designedfor operation at room temperature, and have not been optimised for cryogenic tempera-tures. Of the three mirrors that have been characterised; one is an older design (MirrorA) which has an inter-actuator spacing of 1.75mm and the other two mirrors (MirrorsB and C) are of a more recent design with an inter-actuator spacing of 1.25mm. The re-sults obtained for the mirrors’ static aberrations were for unpowered mirrors, and showthat one of the sample of three mirrors performed substantially better than the othertwo. 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 thebetter mirror that a substantial fraction of the mirror’s dynamic range is still availablefor wavefront correction.

2 Micro-Machined Deformable Mirrors

The mirrors tested have been developed by OKO Technologies [1] for room-temperaturewavefront correction. These 37-channel devices have been demonstrated to be suitablefor adaptive optics at room temperatures [2, 3]. The mirrors themselves are constructedby coating a silicon wafer with silicon nitride on both sides. A mask is then cut intoone of the nitride layers, before the silicon wafer is etched away through this mask. Thisleaves an aperture through to a silicon nitride membrane. This wafer is then mountedabove 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 thislayer of Aluminium is grounded, the shape can be controlled through electrostatic at-traction by applying voltages to the actuators [4]. For IR applications, the Aluminiumcan be replaced with a layer of Gold. The maximum central displacement for the mirrorsconsidered here is approximately 11µm(≈ 18λ for the Zygo interferometer used in thefollowing measurements).

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Fig. 1. Micro-Machined Deformable Mirror

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 isless than 1µm thick. However, for operation at cryogenic temperatures, the mirror isenclosed 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 wascooled to T=78K for both mirror designs. In order to isolate the effect intrinsic to themirror from that due to its mounting in the socket, an extension pin was attached to oneof 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 thermalstress could be transferred from the mounting to the mirror.

Fig. 2. Demonstration of single-pin mirror mounting

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 thermalstress from the socket and mount could, in principle, be removed by replacing the socketwith 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 Ox-ford Instruments liquid nitrogen cryostat. Regular measurements of the mirror’s surfacewere then taken with a Zygo PTI interferometer (λ=633.9nm) as the mirror graduallywarmed up to room temperature. Taking measurements while cooling the cryostat wasimpractical due to the severe turbulence introduced by liquid nitrogen vapours. Thetemperature within the cryostat was measured by simply measuring the voltage acrossa diode. Tests had previously been conducted to determine a suitable mounting pointwithin the cryostat, where the temperature would be similar to that of the mirror, tocalibrate the diode and to verify that the material from which the mount was con-structed did not appreciably change the measured temperature. A further point to noteis 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 mirrorwould actually be focussed. For the measurements of the mirrors influence functions,the mirror was mounted in a socket in the conventional manner, since the electricalconnections 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 thetemperature of each mirror. The data are presented with the tip/tilt on the mirror havingbeen subtracted in software. In addition, the diameter of the mirror that is analysed isabout 90% of the diameter of the measured image. This is due to the Zygo’s limitedhandling of diffraction effects from the edges of the membrane surface. The temperatureis measured without any physical contact on the mirror surface (due to the risks of


destroying the membrane). Experimentally, the error in the temperature measurementshas been determined to be less than 5K, by measuring the recorded temperature withinthe dewar in a variety of locations and circumstances simultaneously. It should be notedthat the current set-up prevents the mirror being at an equilibrium temperature betweenT=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 roomtemperature or T=78K, the absolute errors in the recorded aberrations have been takento be constant with temperature, and the measured errors from the cold measurementshave been applied to each data point. It is obvious from the plots (Figures 4, 5) thatthe scatter on the measurements is much greater for larger aberrations. This is not aneffect of the low temperatures involved, as can be seen by examining the plot for MirrorA (Figure 3). Despite similar temperatures, the scatter is much smaller. Therefore, it isassumed that the Zygo interferometer becomes less accurate for large aberrations, thatis, aberrations leading to a peak to valley displacement of the membrane surface greaterthan about 8λ. The peak-to-valley (P-V) values recorded incorporate higher order termsthan the individual Seidel aberrations presented, and so are not a simple sum of theother presented aberrations.

Fig. 3. Variation of Zygo-measured aberrations with temperature for MMDM A

The results for Mirror A (Figure 3) show that there is still some throw left in themirror after correcting for the astigmatism. The amount of correction achievable afterremoving the static aberrations depends on the beam size, relative to the total diameterof the mirror. This is due to the fact that the mirror edge is fixed, and so no correction atall can be achieved at the edges. Hence, only a portion of the mirror surface is utilised, intypical applications for these devices. The available displacement at 50% radius from thecentre of the membrane is approximately 14λ. It should be noted that, were it possibleto 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 firstmirror. Cooling this mirror results in a P-V mirror displacement of 9.78 ± 0.09λ. Thepredominant contribution to this behaviour is again astigmatism. However, with thismirror, the other aberrations are also on a significant scale, particularly Coma andDefocus. These results clearly indicate that this MMDM possesses considerably greateraberrations at cryogenic temperatures than the first MMDM.


Fig. 4. Variation of Zygo-measured aberrations with temperature for MMDM B

The results for the final mirror (Mirror C, Figure 5) are distinctly different fromMirror B and are even further from the Mirror A results. The P-V mirror displacementhere is 10.14±0.06 λ, which is only marginally greater than for the second mirror. How-ever, the contributions from the various individual aberrations are different to those forMirror B. In particular, both Spherical Aberration and Defocus are larger in magnitude.

Fig. 5. Variation of Zygo-measured aberrations with temperature for MMDM C

4.2 Phase Maps

The change in the mirrors caused by cooling to T=78K can perhaps be best illustratedthrough 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 presentedfrom the cold measurements, at a temperature of T=78K, and one from the roomtemperature measurements. Note that the image rotations are not necessarily the samebetween the cold images and the warm images.


The images for the Mirror A (Figure 6) show the increase in astigmatism caused bycooling. Note that the false-colour map used has been scaled for a total P-V displacementof 10λ to better illustrate the maps for the new mirrors. Hence there is very little detailvisible in the warm maps. The cold phase map here is presented before the edges of theimage are cropped for analysis. Hence the jagged edge caused by diffraction effects isstill visible, notably at the lower left hand corner. The warm image presented has hadpart of the edges cropped, but further cropping was necessary before analysis.

(a) Cold (b) Warm

Fig. 6. Mirror A

The phase maps for Mirror B (Figure 7) illustrate the scale of the effect on theMMDMs 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 themirror, and is not a measurement artefact of the Zygo. This was confirmed through theuse of a beam-splitter and a screen at a similar optical path length from the mirror asthe Zygo.

(a) Cold (b) Warm

Fig. 7. Mirror B

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 heavilydeformed by the cooling process. The void at the lower left corner of this image is alsogenuine, and not a measurement artefact. This was confirmed in the same manner asfor Mirror B.


(a) Cold (b) Warm

Fig. 8. Mirror C

4.3 Influence Functions

In order to measure the influence functions of each actuator of the mirrors they werereplaced in their sockets and driven to 250V. One actuator is shown from each ring ofactuators, numbered as per Figure 1.

The first set of influence functions (Figure 9) was obtained using the Zygo interfer-ometer and Mirror B at room temperature. The initial mirror surface image has beensubtracted in software from each image.

(a) Actuator 1 (b) Actuator 2 (c) Actuator 8 (d) Actuator 20

Fig. 9. Room temperature influence function phase maps

The second set of influence functions (Figure 10) being presented here were obtainedwith an identical set-up to the warm influence functions above, except with the mirrorcooled to T=78K. Note that the area missing from the images is caused by the aberra-tions present in the mirror. Again, the initial mirror surface has been subtracted fromeach image.



Fig. 10. Cold influence function phase maps

The final influence functions (Figure 11) are a set of theoretical influence functionsobtained using the “response” program from the OKO Tech website(http://www.okotech.com/archive/response.zip). They are presented for comparisonwith 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 indi-vidual image to highlight the detail in the images.


Fig. 11. Theoretical influence function phase maps

For comparison purposes, cross-sections through these influence functions have beentaken (Figure 12). The first set of comparisons (Figure 12a) examine the three setsof influence functions (Theoretical, Warm and Cold) on a per actuator basis. Eachindividual influence function has been normalised to 1, to clarify the similarity in theshapes of the influence functions. The second set of comparisons (Figure 12b) show thevariations in the influence functions along a radius for each set of conditions. In thiscase, the influence functions have all been normalised relative to the central actuatorin the warm results. Note that the throw of the mirror for a given voltage is 20% lowerfor the cold results than the warm results. This indicates that either larger controlvoltages would be required at lower temperatures to obtain the same stroke as at roomtemperature, or that the mirror stroke at T=78K is constrained to be less than that atroom temperatures. Which hypothesis is valid will be tested by applying larger voltagesto the mirror and determining the cryogenic maximum stroke. This has not been doneto date for practical reasons.


http://www.okotech.com/archive/response.zip

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These experimental influence functions at room temperature and at T=78K showgood agreement with the theoretical influence functions. This is a promising result,and clearly indicates the feasibility of using the MMDM as a wavefront corrector atcryogenic temperatures. It also raises the potential prospect of a mass-produced AOsystem at room temperatures using the theoretical influence functions in the controlloop, removing the need for each system to be individually calibrated. It is also worthnoting that the warm results are consistent with previously published results by Daytonet al [2]. These results indicate that, if the static aberrations of the mirror can beovercome, 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 mirrorstested (Mirror A) is superior at cryogenic temperatures to the other mirrors (MirrorsB 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. MirrorA is of the older design, while Mirrors B and C are of a more recent design. Sincethe 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 electricalconnections 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 themirror construction, rather than due to design differences. Mirror A is from a differentmanufacturing batch to Mirrors B and C. Thus selection of mirrors from a productionbatch for their properties at cryogenic temperatures may be necessary. The cause ofthe initial static aberrations is believed to be due to coefficient of thermal expansionmismatch between the Aluminium layer and the Silicon Nitride layer. This may bereduced by using Gold instead of Aluminium, and may potentially be reduced furtherby the use of other alternative materials. It is also likely, should the demand for cryogenicapplications be sufficient, that the mirror design could be optimised for operation atcryogenic temperatures and yield performance comparable to that achieved at roomtemperature by current devices. These optimisations would have to be performed aspart 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 coolingto T=78K. The first mirror was of a different design to the other two, with the onlydifference in the designs being the size of the inter-actuator spacing. The static aber-rations for the old mirror design increased upon cooling, but to a considerably lesserdegree than for the new design. Differences in the designs of the mirrors are unlikely tobe responsible for the marked differences between the results for the two designs. Themost likely cause for the differences in the results between mirrors are slight variationsinherent in the manufacturing process. Since the mirrors tested were not specificallydesigned for cryogenic applications, but still demonstrated reasonable functionality, de-velopment of special packaging for cryogenic applications should result in a functionalitylevel similar to the existing room temperature devices.

The influence function results are encouraging, indicating a good agreement betweenwarm and cold influence functions, and also a good agreement with the theoreticalinfluence functions. Further tests are being conducted to study the dynamic responseof these mirrors.


Cryogenic wavefront correction using membrane deformable mirrors

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