1. INTRODUCTION

Progress in astrophysical research is strongly linked to increasing telescope apertures on the ground and in space. With the 6.5 m mirror diameter of NASA’s James Webb Space Telescope (JWST), a great step forward in sensitivity and resolution has now become reality. Envisioning larger apertures or space telescope arrays, the weight and cost of such a facility would be enormous if one just scales the known technologies. Studies are now being done to find successors for the JWST with larger apertures and better wavefront quality in the shorter wavebands [1]. The technology foreseen relies on segmented mirror primaries, building on the heritage of JWST. Regarding the known timescales or costs, one can expect that any scaled versions may come with decades of building and significant costs. Envisioning a space-based facility of a significantly larger aperture or a final dream of a space telescope array, seems to be difficult in such a framework as it might overstretch the weight, volume or cost envelopes. When we imagine the construction of an extremely large aperture in space, or even the building blocks of a space-based telescope array for interferometrical combination, four obvious key elements play a role:

Reducing the areal weight of the primary mirror by a large factor will require working with very thin structures when building the primary mirror, which unavoidably requires adaptive technologies to keep it in shape. In this article, we propose the utilization of very large thin parabolic pre-shaped polymer membrane mirrors, adaptively kept in shape to maintain the best optical performance. Since the polymeric membranes are highly flexible, it is possible to roll them up into tubes to make them fit into a launch vehicle. Enabling technologies are the production of thin membranes exhibiting the shape of an optical surface for the primary mirror, and a technology to shape that surface by adaptive optics methods. Fig. 1 shows the enhancement of sensitivity that can be gained by a large optical space telescope over current facilities.

 

Fig. 1. Limiting flux density of various telescopes expressed in janskys, assuming a point source at $10\sigma$ detection in ${10^4}\;{\rm{s}}$. The upcoming facilities JWST and The Extremely Large Telescope (ELT) in northern Chile will be groundbreaking compared to 10 m class telescopes and HST. The data points from JWST, the Hubble Space Telescope (HST), the Gemini Observatory (with telescopes in Chile and Hawaii), the Spitzer Space Telescope, and Stratospheric Observatory for Infrared Astronomy (SOFIA) are taken from [2]. Overplotting the anticipated sensitivity of a 20 m sized space telescope shows that more than an order of magnitude can be gained. ST 20 (1) shows the case of a 20 m aperture with 220 K warm surfaces, and 20 m (2) shows the case of a 120 K telescope. Both observing at 45° to the solar system plain. 20 m (3) shows a 120 K telescope observing at the minimum zodiacal light background direction. The ELT MICADO takes high-resolution images of the universe at near-IR wavelengths.

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As a proof of concept, we have developed a process to grow such membranes on a paraboloid formed by a rotating liquid in a vacuum chemical vapor deposition process. In our test chamber, we have successfully deposited prototypes up to 30 cm in diameter of reasonable optical quality and that are deformable by radiative adaptive methods. The size of the prototypes was only limited by the vacuum chamber, and we think that mirror diameters could be formed spanning many meters. The process described here has the potential to create mirrors for extremely large telescopes or other missions at much lower cost than conventional methods.

While we have focused on the astrophysical application here, the methods described may be used in other areas. The growth of thin polymer mirrors and the described adaptive shaping has the potential to lead to low-cost adaptive mirrors, exhibiting a huge amount of actuators.

2. LIQUID PARABOLIC MOLD

The fabrication of either shape memory membranes or other pre-shaped membranes has, until now, largely required a high-quality solid mandrel to provide the precision shape for polymeric films. Envisioning extremely large diameters well above 10 m, a monolithic mandrel structure would not really be possible since the cost of the mold would be as high as that of the ground-based primary for a very large telescope.

Instead, it is well known that a rotating liquid forms a surface with a parabolic shape, and that could serve the purpose. This property has been used to form primaries of zenith pointing telescopes, as described by Borra et al. [3] and Sica et al. [4], or recently by Kumar et al. [5]. The possibility to use a rotating liquid to supply the shape for a polymeric membrane for display purposes has been published already by Ninomiya [6] and a patent application was filed by Carreras et al. [7]. Those publications propose to pour a suitable polymer onto the rotating liquid surface, cure it in place, and apply an optical reflective stress coating on top.

The early results [6], using an epoxy resin on liquid, resulted in meter-sized mirrors suitable for display purposes. In contrast, it is much harder to achieve the optical quality necessary for an astronomical telescope. When pouring the polymer onto the supporting rotating liquid it is difficult to generate uniform membranes because of two main issues: The flow of the viscous polymer on the supporting liquid takes a long time to average out to optical precision, and shrinkage occurs during curing.

Nevertheless, the simplicity of a rotating liquid surface forming an optically perfect parabolic surface is so compelling that we have explored further methods to use it. The key relations have been known for a long time. See, for example, Turkington [8] for the combined rotation and border effects, and the work of Rayleigh [9] for the capillary wall tension effects. As such, we just noted the relation between the rotational speed and the focal length $f$ as

A. Thin Polymer Film on Liquid Deposition

While forming a mathematically perfect paraboloid when rotating the liquid, major disturbances can arise from air turbulence above the moving liquid, dust particles, or vibrations. Assuming a 20 m F#1 rotating liquid, according to Eq. (1) the border velocity amounts to $\approx\! 10\;{\rm{m}}/{\rm{s}}$, which is enough to create heavily disturbing winds. To make use of the high-quality liquid mandrel, we have been looking into possibilities to overcome those effects. For similar reasons, Borra et al. [10] proposed to use the absence of an atmosphere and deposit metals as reflective layers on a rotating liquid surface, forming a telescope on the moon. This proposal includes one condition we believe is mandatory to generate high-quality films on the liquid: a reasonably good vacuum. In the search for a process that allows a deposition of high-quality polymer films on a rotating liquid, we have identified eight items:

After a search of the vacuum deposition processes, we found that many of the conditions above are fulfilled by the deposition of Parylene films. Poly(para-xylylene), known as Parylene coatings, can be deposited at room temperature by chemical vapor deposition and are widely used for many applications, including microelectronics, biotechnology, the coating of implants, or microelectromechanical (MEMS) devices. Parylene films are deposited conformal and pinhole free inside a deposition chamber. The coatings are chemically resistant to solvents, are biocompatible and exhibit excellent barrier properties for nearly any liquids or gases. Parylene thin films have been used for aerospace and space applications and can withstand high radiation and a wide temperature range from cryogenic to $\approx\! {200^ \circ}{\rm C}$, depending on the type. Many publications exist on the deposition process and the coatings applications. A textbook style overview was published by Fortin and Lu [11]. While a low or zero thermal coefficient of expansion (CTE) for an optical system is usually desired, being less sensitive to radiation environment changes, we propose to regard this property not as a drawback; on the contrary, we make use of it as outlined in Section 4.2 for adaptively shaping the surface. Parylene (c-type) exhibits a CTE of 35 ppm/K, which is less than many polymers.

The possibility to deposit Parylene onto liquids, and its use in a variety of applications such as varifocal lenses or micromachining applications, has been discovered, and a patent was filed by Keppner and Benkhaira [12]. In Charmet et al. [13], several applications of this process are discussed. Among others, liquid drops encapsulated by a Parylene film may serve as lenses. Charmet et al. [13] has shown a detailed analysis of the deposition process and the resulting morphology of the polymer film.

B. Parylene Deposition Chamber

To test the deposition of relatively thick films on liquids that serve my purpose, we set up a custom deposition chamber. The schematics of the reactor are very similar to many typical Parylene coating systems, and follow the method developed by Gorham [14]. The dimer in a boat can be loaded into an evaporator chamber via a quick lock door. There, the dimer is evaporated at temperatures between 120°C to 150°C. The thermal cleavage of the dimer takes place in a pyrolyzer at $\approx\! {700^ \circ}{\rm{C}}$. The connections, transfer, and door are heated to elevated temperatures to avoid condensation of the dimer or early excess deposition before the coating chamber. The pressure in the system is mainly set by the evaporation rate, which depends on the temperature and dimer load in the evaporation chamber. Pressure in the chamber is measured with a Pirani gauge and a heated Baratron absolute capacitance manometer. In the early experiments, a roughing pump in conjunction with a liquid nitrogen trap was used, supplying a minimum process base pressure of $\approx\! 2 \cdot {10^{- 3}}\;{\rm{mbar}}$. In later tests, we added a turbo molecular pump in the chain, which creates a cleaner environment inside the chamber. The whole setup was located on a vibration isolated table, and could be surrounded by an air-conditioned enclosure. A sketch of the chamber, including the rotational table, is shown in Fig. 2.

 

Fig. 2. Schematics of the coating reactor with the rotating table and the liquid on top. The evaporator is loaded with a boat of Parylene dimer powder. During the coating process it is heated to $\approx\! {130^ \circ}{\rm C}$, evaporating the dimer at a satisfactory rate. The dimer molecules are then cracked into monomers when passing the pyrolyser, being heated to $\approx\! {694^ \circ}{\rm C}$. Entering the reactor via the “showering” distribution tube, the polymerization takes place on all surfaces, including the parabolic liquid surfaces. The rotation table is supported by a ball bearing and driven by a speed controlled external motor. Vacuum is maintained with a turbo molecular pump backed by a scroll pump and protected by a liquid nitrogen trap.

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C. Liquids

For this study we investigated a series of liquids in terms of their suitability as a liquid mandrel. We looked for room temperature low vapor pressure candidates that show high viscosity and density and can be dissolved in standard solvents. Several classes of liquids were identified that feature low vapor pressure at room temperature: ionic liquids, liquid polymers, paraffinic hydrocarbons, and polyphenyl ethers (PPEs). Searching for low vapor pressure liquids started with liquids used for diffusion pumps in high vacuum applications. Among those, we looked at paraffinic hydrocarbons, mainly due to their solubility in nonpolar alkane solvents, which is available in the laboratory. Hydrocarbon pump oils, a mixture of higher alkanes, are usually refined from crude oil through dewaxing, solvent extraction, and further purified through vacuum distillation. LVO 500, a white oil from Leybold without additives and a probe FC 2068 white oil from Fauth were used. Other diffusion pump oils composed of silicon oils might be considered in further studies because they possess even lower vapor pressures.

Developed for high temperature lubrication, polyphenylene ethers (PPEs) are a class of liquids that are interesting for this deposition process. What makes PPEs suitable are their extremely low vapor pressure, very high viscosity at room temperature, high density, and a very high surface tension. Additionally, the liquid does not wet steel and aluminum, and thus does not migrate away and creep into unwanted locations. We have been testing a five-ring PPE Santovac 5 (Santolubes Manufacturing LLC) in diffusion pumps down to ${10^{- 10}}\; {\rm hPa}$.

Polyethylene glycol (PEG) is a long-chained polymer of ethylene oxide. Depending on its molecular weight, a PEG is liquid up to ${M_{\text{mol}}} \approx\! 600$, exhibiting a low vapor pressure. PEGs can be dissolved in water and alcohols, are nontoxic and widely used in medicine and other areas. PEGs exhibit higher vapor pressures than the diffusion pump liquids listed above but are still suitable for the Parylene process. In terms of both costs and the convenience of handling, those liquids are advantageous.

Ionic liquids are composed of ions and can exhibit very low vapor pressures due to the strong ionic bonds. Depending on the composition of the anion and kation pairs, the properties of ionic liquids can in some sense be “designed” to match the application in mind. A test kit supplied by IoLiTec Liquids Technologies for my application has been setup to contain liquids with low pressure, high viscosity, and densities. The huge combination of possibilities using ionic liquids offers the option to tailor the liquid exactly to a specific set of needs.

D. Film Properties Grown on the Liquids

For the basic film formation tests, we have placed a set of Petri dishes filled with a small amount of each of the liquids inside the reactor. To facilitate handling of the grown films later on, a simple silicone ring was placed in the liquid, so that half of the ring was immerged. The upper half was coated by the Parylene and hence connected to the film grown on the liquid. This set of 10 liquids was treated in a single process inside the coating reactor. After evacuation and degassing, the Parylene coating process with 30 g dimer was applied (Parylene c-type, Plasma Parylene Systems GmbH).

In general, a transparent Parylene film grew on all the liquids being tested. To evaluate the properties, the film held by the ring was cut out of the dish, and thoroughly washed by the matching solvent. The grown films were inspected visually, with a microscope and an interferometer. The thickness of the film was measured by a spectral reflection method and with a probe (Heidenhain). Because the films were grown in the reactor with a simple deposition geometry, as discussed in Section 2.5, the thickness can depend slightly on the substrate location inside the chamber. The two hydrocarbon test samples were clearly thicker than the other samples, with a matching higher opacity and surface roughness.

The surface properties were checked by measuring the total integrated scatter (TIS), by photometrically detecting an incident, and transmitting and reflecting a laser beam in a variety of wavelengths. By relating the TIS to surface roughness [15], the rms surface quality can be estimated with this method. Because it is not possible to distinguish between the front and back surfaces of the transparent film in this setup, the values reported in Table 1 distribute the scattering equally onto both surfaces, giving an indication of the smoothness of the film growth on the liquid. Charmet et al. [13] and Binh-Khiem et al. [16] reported that the side facing the liquid shows many more irregularities when viewed in SEM images. We recognized that the side facing the liquid is more hydrophilic than the vacuum facing side, which appears very smooth and hydrophobic with a high water contact angle, and so we expected that side to be of higher surface quality. Figure 3 graphically shows the measured surface roughness from the TIS measurements. From those data, it is possible to conclude that the films on the hydrocarbon oils show the highest roughness, which matches the enhanced thickness values, and roughness is likely due to a more porous growth on the surface of the liquid. The films grown on the five-ring PPE and the ionic liquid IL-0018 are the clear frontrunners in terms of surface smoothness. Looking at the liquid properties and the resultant surface roughness we concluded that a high liquid density and high viscosity are most important here. This can be understood because the film growth will most likely start with islands of connected polymers. The less those can sink into the liquid before the film is uniformly closed, the smaller the roughness will be. While the achieved surface roughness is already in a range that is suitable for optical use, one can tune the deposition process even further to achieve smoother faces. As reported by Reichel et al. [17], one option is to apply an Argon buffer gas, which suppresses the volume polymerization for an improved surface quality.

Table 1. Properties of the Grown Films

View Table

 

Fig. 3. Estimated surface roughness (rms) of the membrane samples, derived with photometric scatter measurements. The measurements have been taken with four laser wavelengths at 635, 520, 488, and 405 nm. The numbers relate to the liquid number from Table 1. Number 11 is the result from an uncoated microscopy slide. The films grown on the PPE and IL0018 show results close to a glass surface.

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E. Uniformity of the Growth Process

We investigated the spatial uniformity of the deposition process in the laboratory chamber with a variety of inlet and outlet arrangements. The goal was to find a geometry that would deposit the film uniformly on a rotating surface at the bottom of the chamber. As such, we placed a flat stainless steel tray where the rotating surface would later be put. The 380 mm diameter tray was filled with a small amount of PEG 400, forming a smooth and flat surface. Figure 4 shows the four chamber geometries under test: a) a simple deflector plate at the inlet with a straight pumping outlet and b) the inlet of the monomer flow is directed toward one side of the liquid, while the outlet toward the vacuum pump is distributed under the liquid. A very homogenous coating can be reached by creating a “shower like” inlet and an outlet under the substrate [11]. In that respect we have tested two “shower” geometries shown in Figs. 4(c) and 4(d).

 

Fig. 4. Thickness variations of the 380 mm diameter films grown in various coating chamber settings. A sample tray covered with PEG400 was always placed on the bottom of the 400 mm diameter vacuum chamber. The inlet and outlet of the chamber was modified, as sketched in the figure. The left inset shows a top view schematic, while the right inset shows a side view. (a) The monomer flow from the inlet tube was covered with a simple squared baffle plate approximately 3 cm inside the chamber and the outlet toward the cold trap is a simple outflow flange above the surface of the liquid. (b) In this variation, the inlet was stopped down so that the flow is directed directly toward the liquid surface on the inlet side, and the outlet has been covered so that the pump sucks are distributed below the liquid surface. (c) The inlet tube lets the monomer flow into a distribution tube, extending the full diameter of the chamber. It contains many holes on the bottom toward the liquid surface, “showering” the molecules downward. The outlet is as in (b). (d) A shorter distribution tube is used, preparing for the center of the chamber to be free for a PVD unit. As the next steps awaiting a rotating target we expected that a slightly one-sided coating could even lead to a more uniform result, since the middle of the chamber is not enhanced.

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Loading the evaporator with 100 g of Parylene, we successfully coated the liquid in each case with a film with a 50 µm thickness. After cutting the films out of the tray and washing the liquid off, the thickness of the film was mapped with the spectral reflection method. The results are shown in Fig. 5. The simple deflector with an open pumping flange resulted in the largest pressure differences in the chamber and therefore in the largest thickness variation. Figure 5(b) shows how a directed flow toward a distinct location can create a local enhancement of the film thickness. An arrangement like that could be used as a tool to actively control the film thickness locally, combined with an in-situ measurement of the deposited polymer amount. Excluding the outermost area, where the deposition on the liquid competes with the tray walls, both showering geometries showed less than a 2% variation over the surface. From this measurement with a static liquid we can calculated the uniformity that one can expect with a rotating liquid, by rotationally averaging the data. With the shower-type geometries, we expected to reach below a 0.2% thickness variation, with that only occurring radially.

 

Fig. 5. Thickness variations of the 380 mm diameter films grown in the various coating chamber settings. A sample tray covered with PEG400 was always placed on the bottom of the 400 mm diameter vacuum chamber. The inlet and outlet of the chamber was modified, as shown in Fig. 4. The numbers given for the color scale refer to the relative thickness variation, $\delta t/t$ of the $\approx\! 50\,\,\unicode{x00B5}{\rm m}$ thick membranes.

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3. PROTOTYPE PARABOLIC MEMBRANE

A. Growth of a Paraboloid Membrane on Liquid

Motivated by the successful growth of large uniform membranes with satisfactory thickness, we built up a driven rotation stage inside the coating reactor to generate a parabolic liquid surface. We have set up an aluminum plate, having milled a parabolic cavity with 300 mm diameter in its surface, such that the liquid forms a uniform 2–3 mm thick film on the surface upon rotation with appropriate speed. This quite thin liquid film, in conjunction with the high viscosity of the fluids used, helps to make the setup vibration insensitive. The table was supported by a precise ball bearing and a rotational vacuum feedthrough. An external motor with controlled speed drives the assembly at constant rotational velocity. A sketch of the setup is shown in Fig. 2. We grew membranes successfully by loading up to 100 g dimer amount per coating, resulting in a polymer growth of up to 60 µm thickness per run. Repeating this coating process several times resulted in membranes that were 140 µm and 210 µm thick. In the future in a more automated setup run without human supervision, it will be possible to grow any thickness in a single run without breaking the vacuum. Nevertheless we could show here that an interruption of the process followed by a continuation of the coating is possible. After finishing the polymer membrane, the rotation of the table was stopped, and the table was transferred into a high vacuum coating chamber where a layer of $\approx\! 75\;{\rm{nm}}$ aluminum was evaporated onto the front surface. During this coating process, the membrane was still kept on the liquid, buffering the heat load during coating. With this process, several parabolas were grown successfully on PEG400 and PPE liquids spinning at 0.3715 Hz to form a F#3 surface.

B. Border Effects During Growth

Once the first 30 cm membrane mirrors were grown and tested, we realized that only the innermost area was parabolic, while the borders showed a high surface gradient that was not accessible for the Shack–Hartmann measurement. In the first 140 µm membranes this unusable border was 10 cm wide, leaving a central 100 mm border. Previously, Ninomiya [6] also reported that a 100 mm border was unusable after curing. While the liquid naturally forms a steep gradient surface at the contact with the boundary due to its tension, this effects decays over 20–30 mm. That size scale can be calculated by the formulas given by Turkington [8] or measured as we have done by placing the corresponding solid–liquid contact under an interferometer. To understand what is happening at the borders while the film is forming on the liquid we placed a laser on a stage above the reactor that allowed the measurement of the local surface gradient during the growth process. Because the beam is reflected through the transparent top, the location of the spot at the position of the optical axis gives a measure of the local surface gradient. Figure 6 shows some of the measurements taken with this setup. The liquid surface without Parylene on top follows the expected parabolic shape perfectly, with a steep gradient from the surface tension starting 20 mm from the boundary. With the first Parylene film formation we observe that the steep surface gradient close to the boundary decreases, while further away the gradient increases, while in the central area we observed a decrease in the focal length during this process. We think that we observed a simple surface tension effect here, due to the interface change at the border from liquid–solid–vacuum to liquid–solid–solid upon film formation. At the moment when a solid film forms at the location of the steep concave liquid-border contact, the liquid is pulled up at the contact area and toward the arriving solid film. Since it is pulled upward toward the borders, the liquid in the central area is pulling the surface down and toward a shorter focal length. The experimental results, when we filled slightly more liquid, so that the shape of the border meniscus was less steep, supported this view. In this case, the border gradient changed less than before during the growth and the resultant membrane was usable over the central 200 mm. While this border effect may not be critical when generating meter-sized membranes, we may prefer that the liquid does not move at all during the growth process. As such we have filled for the next growth as much liquid to the point where the meniscus tension shape at the border just disappeared. Growing a membrane on this liquid surface we measured zero change in local surface gradient within the accuracy of the laser probe. This membrane replicated the focal length as given by the rotating liquid and is optically measurable over a 250 mm diameter. Tiny defects from the surface tension at the imperfections at the edge of the border were visible and preventing the usage over the full 300 mm diameter. This might be optimized if needed with diamond turning, polishing, or coating the edge accordingly.

 

Fig. 6. Left panel shows the measurement schematic setup to probe the surface gradient in situ during the Parylene deposition. A laser beam parallel to the optical axis is reflected from the surface and its focus position on the axis is recorded. Numerically integrating the gradients and subtracting the ideal parabola results in the differential surface sag shown in the right-hand panel. The dashed line denotes the liquid surface with the border tension calculated from [8]. The red line shows the surface of the first 140 µm membrane grown, which is pulled up $\approx\! 0.5\,\,{\rm{mm}}$ at the borders, while the inner area is pulled down correspondingly. Since we measured the gradient of the surface, the z offset assumes that the volume pulled up must equal the volume pulled down in the center. Filling a bit more liquid resulted in the blue curve. The pulling up at the borders was reduced to $\approx\! 200\,\,\unicode{x00B5}{\rm m}$, leaving the membrane closer to the original liquid shape. The green curve shows the case with the amount of liquid increased, such that the meniscus at the border vanishes. Within the accuracy of the measurement, no pulling effect is present anymore.

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C. Optical Testing

After coating the membrane with aluminum, cutting it off the table and washing away the liquid, the surface was ready for optical testing. We set up an optical test tower, as sketched in Fig. 7, consisting of a single mode fiber source at 532 nm located at the radius of the surface under test. The back reflected beam was split off and analyzed with a commercial Shack–Hartmann sensor (Optocraft GmbH) with a large dynamic range. A fold mirror was added in between to accommodate for the limited space available above the optics bench. Figure 8 shows the surface measured wavefront from two of the membrane mirrors, just passively resting on an aluminum ring: a 210 µm thick membrane over the central 200 mm, and a 200 µm thick membrane over the central 250 mm of the aperture. The raw wavefront always shows the inherent spherical aberration from the paraboloid being tested at its radius. Subtracting tip, tilt, focus, and the spherical term, the membranes showed a $\approx\! 0.8\;\unicode{x00B5}{\rm m}$ rms surface over 200 mm diameter. Smaller patches of 50 mm diameter show rms surface deviations of 120 nm. As can be seen, especially in the lower panel in Fig. 8, the thin optics easily picks up deformations at the border and is easily deformed by temperature effects in the laboratory environment as well as bending under gravity. With the prototype membranes being good enough to be optically measured by a Shack–Hartmann sensor, a feedback to an adaptive shaping system is possible.

 

Fig. 7. Three photographs from the first membrane being readied for an optical measurement. (l–r): Freshly aluminized membrane in the coating chamber, washing the membrane mirror while it is fixed to a clothesline after released from the liquid, and the membrane residing in the optical test setup for investigation of the optical shape.

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Fig. 8. Surface deviation of two membranes. A 210 µm (top) and a 200 µm (bottom) thick membrane measured in reflection with a Shack–Hartmann sensor. The upper membrane could be tested over the inner 200 mm and the membrane shown in the lower panels over a 250 mm diameter. The membrane is just left to lie on its outer diameter border on a milled aluminum ring. In both cases, the optically measured raw surface is shown on the left. Subtracting tip, tilt, and the inherent spherical aberration results in the right panels with a typical surface rms of $0.8\;\unicode{x00B5}{\rm m}$ over a 200 mm diameter.

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4. PACKAGING, DEPLOYMENT, AND ACTIVE SHAPING

A. Packaging and Deployment

One main reason to develop the membrane mirrors described in this paper was to find a way to package extremely large telescopes compactly so they fit into available or planned launch vehicles, or to fit in a tube fixed to the side of a launch vehicle. With a very experimental approach we have simply tested how a 140 µm thick paraboloid-shaped membrane behaves when it is rolled up.

Two ways to roll up the membranes are shown in Fig. 9. We found that they can easily be rolled up from one side to the other, forming a tube with slightly convex walls, or rolled up from two sides forming two tubes, which may be advantageous upon deployment. While we have seen that the Parylene polymer is soft enough to not really harm the coating at the front surface upon contact, there might be a need for protection against direct contact when scaling the system to meter sizes.

 

Fig. 9. Two examples of how the membrane paraboloid can be rolled up for packaging, demonstrated with one of the early 30 cm prototypes. Rolls can be formed wrinkle free with this geometry, returning to the original shape upon release.

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Assuming that a large membrane might be rolled to form tubes with diameters of $\approx\! 1/10$ of the mirror aperture, a 15 m class telescope could already fit in the Ariane V long fairing. Two future launch systems, the NASA SLS Block 2 Cargo, or the Space X starship fairings would be able to carry even several 20 m class rolled membrane telescopes to space.

There may be many options to unfold the rolled membrane mirror so that its shape is restored. One would be to bond a triangular flexible membrane or mesh to the outer diameter of the parabola. This could be done when it is still located on the turntable, to make use of a well-defined border. The triangular sheet would be rolled with the parabola. Upon deployment can the three edges of the triangle can be pulled, restoring the original plane of the turntable’s outer diameter. Another way to add more control on the border locations would require more mounting points around the diameter, and adding an actuator that could change the pulling direction and hence the location of the border point. Although we will leave the packaging details and unfolding discussion for forthcoming publications because they require engineering at a level of detail beyond the scope of this article, a sketch of a possible folded and unfolded structure is given in Fig. 10.

 

Fig. 10. Sketch of one way to fold and unfold the telescope membrane, by bonding the primary mirror to a triangular membrane. Pulling the triangle at its edges into a plane restores the original shape.

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B. Radiation Power Controlled Shape

Because thin optics is easily deformed and the mirror will not return to an optically perfect shape when unrolled, there are two possibilities that can correct for errors:

For the latter case electrostatic solutions have been proposed by several authors [18,19]. While these solutions are a possibility, electrostatic control usually requires a backing structure and dealing with high voltages.

 

Fig. 11. Estimated local displacement of the mirror surface when applying a local temperature change dT. Three cases are shown, for three base temperatures of the surface: room temperature 293 K, a near earth case of 173 K, or a shielded L2 telescope with 40 K. The difference arises from the expectation that the CTE will decrease with temperature. The right panel shows the radiation power required to achieve a desired local displacement. Given the ${T^4}$ dependence of the radiation coupling, a low temperature mirror will require very low radiation power to be actively controlled.

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Following a discussion [20], we proposed to shape the mirror by applying a local thermal control that exploits the CTE of the material, making the full primary adaptive. Closely similar concepts have been developed for gravitational wave detectors, using ${{\rm CO}_2}$ lasers to imprint phase corrections on mirrors [21], or for the correction of UV objectives in semiconductor technologies [22]. Those technologies have shown control ability with sub-nm precision.

With the thin polymer membrane, we expected large displacements to occur at low irradiation power, due to the relatively large thermal expansion factor. As we started from a paraboloid curved surface, local heating resulted in an increase of the local curvature as the material expanded, and a local cooling led to a curvature decrease. In a simplified model, we can estimate the local displacement of the optical surface by using the change in the arc length over a locally heated patch that is caused by the thermal expansion of the material. Using this geometric model we arrived at the plots given in Fig. 11. These use the parameters of the prototype mirror, which has a 1.8 m radius, and a locally heated patch size 30 mm in diameter. While we do not yet have reliable data on the cryogenic CTE of Parylene, we estimated that it will decrease in a similar way to polymers such as epoxy resin [23]. Therefore, we assumed that the room temperature CTE of $35\,\,\unicode{x00B5}{\rm m}/{\rm m/K}$ (Parylene C-type) will decrease to 75% at 173 K and 38% at 40 K. The calculated displacement values for moderate local temperature changes are well within the several 10 µm range, as needed to cope with larger surface deformations. Additionally, we estimated the radiation power required to raise the temperature correspondingly, since it would set the power level needed for the radiator that controls the shape. The right hand panel in Fig. 11 shows the three curves for room temperature (293 K), near earth orbit (173 K) or L2 (40 K) levels of mirror temperature. At room temperature, mW levels of radiation are needed to achieve a local displacement of order 20 µm; this value, however, decreases to 0.3 mW at 173 K and is in the µW regime for a 40 K telescope. Scaling those values to a 10 m class telescope would require a total radiation source on the order of 100 W to be included in the system, when shaping the mirror at room temperature. This would decrease to a 30 W or even a 1 W level when going to the low temperature membranes in a space environment. On the other hand, this estimation for the total power needs may far exceed the real need, since not every small 30 mm diameter patch may need to be irradiated at this level. Instead, it depends strongly on the surface structure function of a large diameter membrane. In the space telescope application we would let the mirror cool down to the desired operating temperature (behind a suitable sun shield) and irradiate it over its diameter with a spatially controllable light source that is absorbed either in the polymer on the backside or the coating on the front side. For the backside illumination, Parylene offers several absorption bands in the IR for this purpose. By irradiating the front surface, a light source that is sufficiently absorbed in the metal layer can be used. Having a local intensity control over this light source results in a control over the deformation. If a stroke of order 30 µm must be controlled with a resolution at the nm level, roughly a 14-bit intensity control would be required. As such, the irradiating source could be an intensity-controlled laser scanning system, an LCD device, or a micromirror array. Apart from space qualification issues, LCD devices may not deliver the needed intensity resolution, but micromirror arrays or a scanning system are a viable choice.

As the basic principle of this radiative adaptive optics is so compelling, and because it adds basically no weight to the system and does not touch the sensitive membrane mirror, we decided to further evaluate this possibility. Since the first calculations have shown that even very small temperature changes can result in a large stroke, we tested the principle with the 30 cm 210 µm thick membrane mirror. We have tested both options: radiating small amounts of thermal radiation from a discrete backside array made of tungsten bulbs, and front illumination of the coated side with optical light, spatially controlled with a DLP.

When radiating $\approx\! 1.2\;{\rm{mW}}$ onto patches of $\approx\! 30\,\,{\rm{mm}}$ diameter from the backside we could achieved a 10 µm local stroke. This is lower than calculated, but since the test was not performed in a vacuum, a higher heat dissipation is quite reasonable. To assess how a control with more elements might appear, and how localized the deformation would be, we set up an array of radiators. Figure 12 shows the schematic setup and a photograph of the radiator array. Figure 13 shows how the surface deforms with an arrangement of 37 radiators placed behind the mirror over a 200 mm diameter area, when different combinations are activated. Each of the deformations appears distinct when the radiators are switched on, with the surface deformation relaxing nicely upon deactivation. With the absorption bands at 10 µm of Parylene the radiators behind the membrane need only to be warmed slightly above room temperature to be seen by the membrane.

 

Fig. 12. Schematic of the optical setup, with the array of radiators added below the membrane and a DLP beamer above. Two photographs are added on the right: The lower one shows the 37-radiator array, the other one a letter F pattern radiated with the DLP as can be seen in scattered light on the membrane mirror.

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Fig. 13. Deformation of the membrane mirror with radiating small amounts of energy onto the back surface. An arrangement of 37 radiators has been placed under the membrane mirror, nicely demonstrating the thermal adaptive optics principle with switching some of them on. For the measurements shown in the panels, the wavefront without actuating the radiators has been recorded and is subtracted. Here, the measured wavefront from the Shack–Hartmann sensor is shown, being positive (white) on the sensor, with the surface to add local curvature. Peak wavefront deformation within a 35 mm FWHM amounts to $\approx\! 20\,\,\unicode{x00B5}{\rm m}$ in the measurement shown here. The single radiator influence function is close to Gaussian and switching off returns the surface reliably to the original shape. The stripe patterns in the lower panels are taken without really tuning the radiators, leaving the individual radiator influence visible on purpose.

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Fig. 14. First attempt to correct for disturbances of the membrane by tuning the radiators. The upper left shows the wavefront as measured; right, with the spherical term subtracted. With the membrane residing passively on its aluminum ring above the radiator array the reflected wavefront accumulates a $\approx\! 10\,\,\unicode{x00B5}{\rm m}$ P-V distortion. The arrangement of radiators below the membrane is denoted on the lower left, with the circle indicating the 200 mm area that is visible in the wavefront measurements. When powering the radiators at a moderate level, the individual ones can be leveled, ironing out most of the wavefront distortion. The right panel shows the resulting wavefront. If the prominent dust defect is ignored, the membrane could be tuned to a remaining 75 nm RMS surface deviation.

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This array of radiators can be used to correct for surface distortions being picked up from the border mount or other sources. Figure 14 shows my first attempt to do so. We have used the 210 µm thick membrane and placed it on an aluminum ring above the radiator array, picking up significant deformation from its support. The reflected wavefront distortion over the measurable inner 20 cm showed a 10 µm P-V distortion. The radiator array with the distribution as shown in Fig. 14 is heating the membrane with an average level of 1.5 mW per radiator. Increasing or decreasing the level allows the local curvature to be changed in a positive or negative direction. By manually tuning individual radiators we deformed the membrane locally and with feedback from the wavefront sensor decreased the wavefront deformation to a 150 nm rms, from a corresponding 75 nm mirror surface deviation.

 

Fig. 15. Deformation of the membrane with the 250 mm usable aperture while illuminating it with the DLP beamer from the front side. In this setup, any pattern of radiation can be dialed in, deforming the surface accordingly. Here are just three exemplary examples: A letter F image, a cross, and two points and a bow. The upper panels show the file dialed into the DLP; the lower panel shows the reflected phase as measured with the Shack–Hartmann system. To accent the membrane reaction, the bias without radiation power has been subtracted here.

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Since in a telescope setup the backside of the primary may be obstructed by structures or instruments, it may be easier to illuminate the front side of the mirror. As such, we have tested this possibility by setting up a commercial DLP beamer to serve the purpose. Figure 12 shows the setup schematic. The beamer is located at the side of the mirror, illuminating the membrane from the top. The keystone shape and location of the beamer can be adjusted, providing a sharp and undistorted image at the membrane plane. With a bolometric sensor we measured the output power addressing the R, G, and B channels, or all together. Powering all channels equally at once we have measured a maximum power output of 1950 mW over a 1038 Pixel diameter circle. The ability to locally shape the membrane with this front illumination was demonstrated by displaying simple patterns as letters in the center of the mirror. We estimated the absorbed power contributing to the surface warming to be 4 mW in the letter images. Figure 15 shows the files we have dialed into the beamer output and the measured wavefront. The letters are imprinted on the phase, demonstrating the localized deformation of the membrane. For the moment, we considered this qualitative result encouragement to continue this route. The digital control over the local radiated power will enable an adaptive shape control with feedback from the wavefront sensor. With the extensive amount of content those next steps will bring, we have postponed a further detailed discussion of the radiative adaptive optics for future papers.

5. CONCLUSIONS

In this paper we have presented a concept for an extremely large space telescope primary, or other applications that require an adaptively shapable or rollable membrane mirror. We have filed a patent [24], and successfully experimentally investigated a predicating process to grow parabolic membranes on a rotating liquid by chemical vapor deposition, resulting in optical quality polymer membrane mirrors. The first prototype laboratory results are reported here, but we expect that the next steps to be explored are the behavior of large-scale membranes, the influence of border effects at that level, rolling and packing on meter scales, and their adaptive shaping. Once a facility has been built up that allows the growth of those large-sized membranes, many units can be produced at low cost within short timescales. Those mirrors can be rolled for packaging and launch, unfolded in orbit, and reach an areal weight well below $1\; {\rm{kg}}/{\rm m^2}$. With the proposed radiative controlled deformation, those thin mirrors can be tuned into the desired shape. Having such a building block on hand enables the cost-effective production of extremely large space telescopes or even arrays of such telescopes.