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Home , Optics, Ray tracing (physics)

Anti- coating of large-format for sub-mm applications

Peter C. Hargrave Cardiff University, Department of & , 5 The Parade, Cardiff CF24 3AA, UK [email protected]

Giorgio Savini Department of Physics and Astronomy, University College London, Gower Street, London CF24 3AA, UK

ABSTRACT

We have recently developed a repeatable and reliable technique for anti-reflection coating large lenses, suitable for use at sub-mm . Small lenses have been coated using this technique, and are currently flying on-board Herschel- SPIRE and Planck-HFI. We have recently coated much larger, highly-curved lenses (up to 380 mm ) for the EBEX and Polarbear cosmic background (CMB) experiments. In this paper, we present details of the coating technique, experimental results of coated samples, and comparison of the results to theoretical predictions. We also present an indication of their technology readiness level (TRL) for future space applications such as B-Pol. Keywords: sub-mm, , anti-reflection, coating, , telescope

1. INTRODUCTION There is increasing need to employ refractive optical components in millimetre (mm) and submillimetre (sub-mm) optical systems. This is particularly true for experiments designed to detect the B-mode from the of the cosmic microwave background. In order to reach the sensitivity goals of such experiments, it is unlikely that a Gregorian reflector and feedhorn system alone, such as used on Planck [1], will have enough throughput. To achieve higher focal plane area utilization, the individual pixels must be smaller, leading to a higher edge taper. This problem has traditionally been addressed in mm and sub-mm systems by the use of a reflective cold Lyot stop, created with re- optics. Many of the new generation of focal plane detector array technologies also require a flat, telecentric field, also created with re-imaging optics. As throughput grows and f-number shrinks, re-imaging optics with reflectors becomes more difficult because of the limited amount of space for folded beams to clear obstructions. Cold lenses are the natural solution, but they come with a set of their own problems. Several experiments which employ cold re-imaging lenses coupled to a Gregorian telescope have already been deployed (ACT, SPT, GBT) or are nearing deployment (POLARBEAR and EBEX [2]). Additionally, the BICEP and BICEP2 [3] experiments employ solely refractive optics. However, these systems are still in the initial operational , and the full polarization performance has yet to be determined. Future CMB-polarization satellite missions have been proposed (EPICS, CMB-Pol, B-Pol) which make use of several refractive telescopes, each telescope optimised over a narrow frequency band. This optical configuration should provide low aberrations and polarization for a large focal plane and large field of view. Additionally, it should provide minimal beam imperfections, such as differential ellipticity, differential beam width and differential gain. But there are many uncertainties over the performance modelling of such systems. Reflections in optical systems cause loss and lead to systematic effects. For typical plastic lenses, reflections can be >10% at each surface. Reflections can be >30% for silicon substrates. Additionally, reflection from lenses causes polarized ghosting which must be reduced. These effects can be greatly reduced by the use of anti-reflection (AR) coatings. This paper describes a new technique for applying broadband mm and sub-mm anti-reflection coating layers to large, highly-curved lens substrates.

Millimeter, Submillimeter, and Far- Detectors and Instrumentation for Astronomy V, edited by Wayne S. Holland, Jonas Zmuidzinas, Proc. of SPIE Vol. 7741, 77410S © 2010 SPIE · CCC code: 0277-786X/10/$18 · doi: 10.1117/12.856919

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2. ANTI-REFLECTION COATING THEORY AND TECHNIQUES 2.1 Theory and design

For a slab of material of index of ns, without AR coatings the reflective loss is given by

2 »()1- ns ÿ R = … Ÿ (1) ()1+ ns ⁄

at each surface at incidence. For silicon (ns=3.4), R is 30%.

The application of anti-reflection coating on a flat slab of dielectric substrate, with a given index of refraction ns follows two very simple guidelines. The first is to ensure that a coating material with an optical index of refraction nc is

available, where nc = ns at the same frequency at which ns is measured. The second requirement is to make sure that it is possible to obtain, manufacture or engineer the thickness of the coating material such that its resulting thickness is one quarter of the required transmission within the material. These simple theoretical requirements don’t always translate as easily into the real world, where materials are available with a limited range of index of refraction, which limits choice of materials and application. Moreover, a number of secondary requirements, which do not concern optical design directly, need to be taken into account which are highly relevant to the success of the application. For instance, if the coated lens needs to be cooled, then thermal expansion coefficients of the substrate and coating should be matched as closely as possible if the system is to survive cryogenic cycling. The nature of anti-reflection coatings can be very different depending on the wavelength that the coating is optimised for. As in this work we are focussing on coatings for large optical elements to be used at sub-mm to mm wavelengths, we will discuss only issues relevant to such materials. Lens and coating material design considerations Design considerations when choosing the lens substrate and coating materials should include:- ñ Thermal conductivity of substrate material. If the lens component is of large diameter and is to be used cold, then radiative heating of the lens needs to be controlled by the use of thermal IR blocking filters. ñ Availability of suitable coating materials. The range of materials with a suitable to match a certain substrate material is limited. The choice may be further limited by the form and thermo-mechanical properties of that coating material. ñ Machineability of substrate material. ñ Intrinsic of the substrate material. ñ -induced birefringence caused by cooling to cryogenic . ñ Transmission losses in the substrate material. The waveband of the experiment obviously limits this choice. Typical material data for suitable materials for use in the mm and sub-mm range are shown in Table 1. It should be borne in mind that these material parameters will vary as a function of and as a function of frequency. More detailed material information can be found in Lamb (1996) [4]. Coating thickness and index Unlike optical and near infrared coatings, where deposition is obtained with layers which are deposited through evaporation or sputtering, the thickness required at these large wavelengths makes it more practical to employ layers of material that are available at thickness values close to the required quarter-wavelength in the material (few hundreds of microns). A suitable coating material must meet the requirements on refractive index for matching to the substrate, but also be flexible and ductile enough to allow it to be laminated to a curved substrate. The theoretical ideal value for the required thickness can not always be exactly coincident with the available values of coating material thickness, or can deviate slightly from the achieved thickness after application due to the bonding

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process. Similarly, the index of refraction is unlikely to be an exact match to the theoretically required value indicated above, or will have a wavelength dependence that will unlikely match the above relation at all wavelengths. For these reasons, modelling the efficiency of the anti-reflection coating becomes necessary, and a wavelength dependent code has been produced in order to predict the performance of the coating prior to its application. This allows for a tuned design of the coating in question, allowing us to choose in some cases slightly different thickness for the two sides of the lens when the exact required value happens to be in between two readily available values, or when the lens is required to work in a spectral range larger than a small interval around a given wavelength. Typically this is required when a band width >30% is desired. After the coating is applied, spectroscopic measurements of the optical element will allow the recovery of the exact optical parameters by comparing with variations on the original simulation. Spectroscopic measurements are straightforward for a flat slab, and can be done with a lens too providing that either a small at the centre is used, or that the comparison be made with an identical uncoated lens. Table 1. Dielectric properties of materials suitable for mm and sub-mm lenses and coatings. Material Index n Loss tangent (150GHz), tan d Silicon 3.42 2.2 x 10-4 3.07 / 3.40 2.3 / 1.2 x 10-4 TMM 10i 3.13 TMM 10 3.03 TMM 6 2.55 TMM 4 2.12 TMM 3 1.81 1.87 0.001 Cirlex® 1.84 0.008 Stycast 1266 1.68 0.023 HDPE 1.54 3 x 10-4 LDPE 1.51 3 x 10-4 Polypropylene 1.50 6.5 x 10-4 PTFE 1.44 3 x 10-4 Porous PTFE 1.2

Coating thermo- A serious design consideration for coating lenses to be used at cryogenic temperatures is that, as far as possible, the thermal expansion coefficients of the substrate material and coating material should be closely matched, if the system is to survive multiple thermal cycles. This should be considered very early on in the design stage, which may guide the choice of lens substrate material, and the overall optical design of the system Coating bonding Fundamental to any coating application is the bonding element, or glue. In some cases, the coating material itself will have adhesive properties, or will adhere to a surface with a given . For coatings applied as layered sheets, a more conventional approach is adopted, where the glue-like element is also of a well-defined index of refraction and of constant thickness. This glue layer is factored into the transmission line model calculation for the predicted performance.

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In the case of porous PTFE coatings on ultra-high molecular weight polyethylene (UHMW-PE), we use low density polyethylene (LDPE) layers of constant thickness of a few microns. The similarity in index of refraction of the glue layer produces very minor changes in the design or simulation. The melting point of the LDPE is sufficiently lower than the UHMW-PE to allow us to heat the assembly to melt only the glue layer, without melting the substrate. This process needs careful control, however. 2.2 Review of previous work The BiCEP experiment [3] used two high density polyethylene (HDPE) lenses and two poly-tetrafluouroethane (PTFE) thermal filters, all anti-reflection coated with single-layer porous PTFE membranes, using thermal lamination techniques. The lenses were coated by using a low density polyethylene (LDPE) “glue” layer, a few microns thick. The porous PTFE layer was pre-formed to the right shape, and the lamination to the lens substrate was performed using an aluminium press shaped to match the lens surfaces. For large lenses, this technique becomes awkward and costly. The Atacama Cosmology Telescope [5] used silicon lenses. These were coated using a machined piece of Cirlex® (Dupont) polyimide glued to the silicon surface with Stycast 1266 (Emerson & Cuming). Problems with de-lamination on cooling to cryogenic temperatures due to differential thermal contraction were overcome by the use of a thin layer of Lord Ap-134 adhesion promoter prior to the application of the Stycast. The resulting coated lens was subsequently found to endure multiple cryogenic cycles. However, due to the large mismatch in the coefficient of thermal expansion of the substrate and coating materials, this would be a difficult technology to fully space-qualify. Another promising material for anti-reflection coating silicon substrates is TMM, a Rogers Corporation product. TMM is commercially available as rigid sheets, in a range of dielectric constants. The Cardiff group has been developing a multi- layer coating for planar samples made from TMM and porous PTFE. Work is in progress at UC Berkeley to investigate applying TMM to curved surfaces by thermosetting it over a curved form. Simulated dielectric anti-reflection (SDAR) coatings consist of a layer of dielectric which has been perturbed by the removal of material to form sub-wavelength structure. The of these structures is chosen to tune the effective index of refraction of this layer to any value between the index of refraction of the substrate and that of a . SDAR coatings have been applied to several fielded systems (DASI, CAPMAP, SPT / APEX). This technique is naturally better suited to lower frequency systems, as feature size and available machining techniques become much more challenging at higher frequencies. One must also be very careful to use that minimize cross-polarization.

3. MODELLING AND SIMULATIONS OF COATED LENSES Although it is possible in principle to include coatings in physical -tracing packages, drastically increasing the number of polygons of the required global mesh by reducing the size of the necessary mesh, we prefer a more “classical” but adaptive method of predicting the global performance of a lens by performing a statistical average of the local performance of the coating, based on the arrival angle of a given set of rays. The easiest case of normal incidence on a plano-convex lens will see a set of rays with a given distribution impact the curved side of the lens, each ray with a given angle. With our first assumption being that we are designing the coating ultimately to reduce reflection , we can ignore ghost reflections when exiting the lens as they will be negligible and follow the path of the rays through the lens. Each ray will travel through the coating in two separate instances with given angles depending on their position with respect to the optical axis. This will produce a given efficiency of the anti-reflection application at that wavelength. With a known given distribution of rays we can then apply appropriate weights to the spectral transmissions and obtain the overall lens spectral efficiency (retaining the spectral information as a function of ray exit position or angle). Different input angles can then be easily input to predict how the coating efficiency will vary for off-axis rays and to what extent the coating will behave for different parts of the focal plane of the lens. The capability of performing the calculation separately for each ray based on the input position and incident angle of that ray is fundamental, as it allows complex, non-homogeneous coating forms to be accurately modelled. One of the expected potential defects of the anti-reflection coating due to its bonding procedure is an anisotropic thickness which is a result of stretching a planar sheet over a curved surface. Such a coating would have a thickness which varies radially. Modelling the effect of such a coating is straightforward, as the single ray module will allow us to model a coating thickness which is function of the lens-entry point. The natural subsequent step in this modelling that we plan to incorporate is to extract the coating efficiencies as a function of the input polarisation state. This requires a local change of the coordinate reference frame adopted at each

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interface and has not yet been implemented. This will be the next fundamental step, to model potential polarization artefacts introduced by the insertion of a lens with a homogeneous or inhomogeneous coating layer. We have coupled two well-proven techniques to provide an expected performance of these coated lenses. As the ray- tracing is performed the entering point and angle of the incoming rays is recorded and a separate transmission line module is applied to extract a of the actual transmission after local interference occurs at the air- coating-lens interface. This transmission is recorded and “associated” to the ray history which then proceeds through the nominal coating to the next interface (second side of the lens). As the same applies to each interface, at the exit from the lens a second transmission is obtained and is then multiplied to the original ray history to obtain the spectral content of that ray path. One of the main assumptions that the model relies on is the constant nature of the optical constants which would otherwise require a separate ray-tracing for different frequencies. This is not exclusive though of the fact that if this approach were preferred, a single frequency ray-tracing can be performed and the TL module will yield a which is obtained for a given frequency with the given material parameters involved (which now can also be frequency dependant). We show in Figure 1 the difference between three cases. The first being the nominal effect of an ideal coating when applied to a flat slab of the same material of the lens (this does not include the interferences generated by the slab itself since the curved surfaces will render the fronts spatially non coherent), the second will be the efficiency of the lens calculated by combining the interference patterns caused by the coating presence at each surface of the lens independently and integrating over the surface of the lens. Last we have also simulated as one possible case study, the effect on the overall lens transmission of a coating defect such as a inhomogeneous thickness (exaggerated in this case) of 50% of its nominal value at the centre of the lens with a linear decrease to the full nominal value at the edges of the lens which we speculate could be a predicted effect caused by excessive pressure.

Figure 1 Overall modeled spectral efficiency of a UHMW-PE lens with a porous PTFE coating on each side tuned for maximum transmission at 150 GHz. Black: Nominal transmission as modeled for a flat slab. Blue: Modified transmission by taking into account the different interference angles from a parallel plane wave incident on axis given a lens curvature radius/diameter ratio of 0.7. Red: Effective overall efficiency in the case of a stretched coating with half the nominal thickness at the centre.

The ray based interference allows in principle for different coating defects to be simulated and by retaining the information for each ray it is possible to also establish how this spectral efficiency will vary across the imaging plane of the lens. One of the fundamental assumptions underlying the model is that the curvature of the lens and the thickness of the coating are such that they do not allow the incident angle of the ray to change, within the multiple reflections of the coating , beyond the spread of angles within the point spread function of the telescope or instrument considered.

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4. THE PROCESS In this section, we present a method for AR coating large HDPE lenses with a matching layer of porous PTFE. The technique uses atmospheric pressure to press the coating and glue layer onto the lens substrate. A purpose-built vacuum chamber enables us to coat lenses up to 380 mm diameter, and the chamber is sealed by a ring-mounted silicon rubber membrane which acts as the coating press surface. This technique is fully scalable to larger lenses, limited only by material availability and appropriate tooling. In order to achieve good, uniform coatings, the coating material must first be mounted to a ring, to enable it to be stretched evenly over the curved lens surface, as shown in Figure 2. The substrate must be thoroughly cleaned and de- greased. The coating/glue layer is slowly stretched down over the lens substrate, glue-side down, as shown in Figure 3 and Figure 4.

Porous PTFE AR coating Silicon rubber vacuum seal HDPE lens & LDPE glue layer on on aluminium ring clamp Aluminium ring clamp

Figure 2 Typical lens, with coating/glue layer constrained by aluminium ring, and ring-mounted silicon rubber vacuum seal.

Silicon rubber

Porous PTFE

LDPE glue layer

Annular support for lens, on perforated base

Figure 3 Component arrangement prior to coating.

For a large lens, and/or a highly curved substrate, this pre-stretch stage is vital, and the coating layer may typically be left overnight to stretch over the substrate with weights applied around the peripheral ring.

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A crucial point is that the desired final coating thickness must take into account the amount of stretching. Therefore, when selecting the initial coating material thickness, one must account for the reduction in coated thickness by simply accounting for the change in surface area in going from a planar disc of material to the surface area of the coated lens.

To vacuum pump

Figure 4 Pre-vacuum stretch

Post-stretching, the silicon rubber layer is applied, the system sealed, and a vacuum is applied slowly to the system.

To vacuum pump

Figure 5 System under vacuum.

Once under vacuum, it is best to leave the system for a few hours to allow any contaminants to outgass. This process may be aided by gentle heating. Then heat is applied to the silicon rubber-sealed surface, by means of a hot-air gun, as indicated by Figure 6. This part of the process needs much care and attention, as it is very difficult to control. The goal is to uniformly heat the glue layer to ~130°C.

For an UHMW-HDPE lens substrate, the melting point is close to that of the LDPE glue layer. The beauty of this technique is that, for a large lens, only the top surface layer is heated to any significant temperature. The bulk of the lens remains cold. However, good process control is vital, and this is currently under development.

Care must be taken to ensure that, whilst applying the heat, that the heat has sufficient time to penetrate the silicon rubber and the A/R coating layer (both typically poor thermal conductors), sufficient to melt the glue layer, and bond

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with the lens substrate. Uniformity of heating is also vital. This process is currently aided by the use of a thermal infrared . Heat applied to this surface

To vacuum pump

Figure 6 Heat is applied to the top surface

Once satisfied that the entire lens surface has been uniformly heated to the correct temperature, the system is allowed to cool, and then bought back to atmospheric pressure. The lens is removed from the jig, and excess coating material is trimmed off with a blade.

5. RESULTS HDPE and polypropylene lenses have been successfully coated with porous PTFE for Polarbear, EBEX [2], Planck-HFI [1] and Herschel-SPIRE [6], the latter two having passed a space-qualification process. Quartz windows have also been coated with polypropylene using this process. Optical measurement and evaluation of the coated lenses at component level is difficult, and this is currently the subject of an ESA technology development study. There are indications of slight deviations from the pre-coating form of some of the EBEX lenses. These lenses are thin at their perimeter (few mm), and the deformation is the result of ~1-bar differential pressure applied during the coating process. We have achieved very good, uniform coatings over a range of substrate forms, including negatively curved surfaces (see Figure 8). When coating negative-curvature surfaces, air tends to get trapped in the void formed by the coating and silicon layer. If the coating is porous-PTFE, then the porosity helps, and the void empties over the course of a few hours.

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Figure 7: EBEX lenses, pre-delivery. Good Figure 8: Capability to coat negative- process repeatability and control curvature surfaces

Figure 9: 380 mm diameter lens for Figure 10: Another Polarbear lens Polarbear

Figure 11: Lens for Herschel-SPIRE Figure 12: Herschel-SPIRE flight-model spectrometer detector flight-spare array. spectrometer detector lens after coating. Fit-check prior to coating.

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6. DISCUSSION – PROBLEMS, UNCERTAINTIES & FURTHER WORK Coating uniformity As the lens coating material is stretched over the substrate, it is not currently known whether the final coating has an isotropic thickness over the whole surface. This is currently being evaluated by careful metrology, using a polished aluminium “lens” former, to ensure no uncertainties due to substrate deformation. The behaviour of the coating layer under different degrees of stretch will also be evaluated using FEA analysis. Real lenses will be tested in our antenna test range, and the results compared to models. Substrate deformation One has to bear in mind that this process involves applying a differential pressure of ~1-bar to the lens substrate. If the lens substrate has to be HDPE, then it should be of a sufficient thickness at the perimeter (for a certain diameter) to withstand this pressure. Heating the glue layer This is the least controlled area of the process at present, and success is down to the individual skill and care applied by the operator. The heating can be monitored by an infrared camera, but assumptions have to be made about the temperature of the actual glue layer itself (thickness & therefore thermal conductance of the coating layer must be considered). We are considering enhancing the jig with fixed heaters, to improve uniformity of heating, and the placement of in-situ thermometry. Substrate & coating choice If the optical design allows, it is better to employ polypropylene lens substrates, as the melting point is significantly different from that of the LDPE glue layer. This is not an issue with quartz or sapphire lens substrates, but the stretching of a polypropylene coating layer becomes more difficult (has to be achieved with gentle heating). Measurement & modelling It is very difficult to test the optical performance at component level, and this is currently the subject of an ESA technology development study. We will spectrally measure substrate and coating combinations for bi-planar samples, and coated and uncoated lenses in our antenna test range. We are developing and enhancing in-house code to model the optical and polarization performance of coated lenses, and will be working in collaboration with TICRA on the development and validation of a coated lens plug-in module for GRASP.

REFERENCES

[1] P. A. R. Ade et al. “Planck pre-launch status: the optical architecture of HFI.” A&A special issue (2010) [2] P. Oxley et al. “The EBEX experiment”, Proc. SPIE Int. Soc. Opt. Eng. 5543:320-331,2004 [3] R. W. Aikin et al. “Optical performance of the BICEP2 telescope at the South Pole” SPIE Astronomical telescopes & instrumentation [7741-31] (this volume) [4] Lamb, J. W., “Miscellaneous data on materials for millimetre and submillimetre optics”, Int. J. IRMMW, 17 (12), 1997-2034 (1996) [5] J. W. Fowler, M. D. Niemack, S. R. Dicker, A. M. Aboobaker, P. A. R. Ade, E. S. Battistelli, M. J. Devlin, R. P. Fisher, M. Halpern, P. C. Hargrave, A. D. Hincks, M. Kaul, J. Klein, J. M. Lau, M. Limon, T. A. Marriage, P. D. Mauskopf, L. Page, S. T. Staggs, D. S. Swetz, E. R. Switzer, R. J. Thornton, and C. E. Tucker, "Optical Design of the Atacama Cosmology Telescope and the Millimeter Bolometric Array Camera", Applied Optics 46, 3444-3454 (2007). [6] Matthew J. Griffin et al. “Herschel-SPIRE: design, in-flight performance and scientific capabilities” SPIE Astronomical telescopes & instrumentation [7731-39] (this volume)

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