Liquid deformable mirrors are a young but promising technology. They offer engineers a lower-cost alternative to their solid counterparts as well as the ability to generate extremely large deformations.
A liquid mirror image.
Liquid mirrors have a major intrinsic advantage over solid optics. While the fundamental forces of nature conspire to deteriorate the surface qualities of solid mirrors, they confer the desired shape upon liquid mirrors, which follow equipotential surfaces.
Equipotential surfaces can be shaped by rotation to yield paraboloidal surfaces. Alternatively, magnetic fields can be applied to ferrofluids to generate surfaces with complex shapes. Thus, liquids do not require polishing or diamond-machining like solid surfaces do. Moreover, the support systems of liquid optics are also considerably simpler. Consequently, liquid optics are far less expensive than solid ones, and they are easier to maintain.
Of course, liquids are not perfect. Liquid surfaces are susceptible to winds, dirt and vibrations. In addition, they cannot be tilted and must remain horizontal. However, recent work has shown that, with the right setup and techniques, these limitations can be overcome.
Parabolic surfaces generated by rotating liquids
Mercury has been used to make inexpensive paraboloidal mirrors with excellent surface qualities. The technology is young but its performance is well-documented by laboratory tests. Engineers have constructed liquid-mercury zenith-pointing telescopes with diameters up to 6 m at very low costs.
The surface of a liquid held in a container that rotates in a gravitational field naturally takes the shape of a parabola; a common application of this type of mirror is as the primary mirror of a telescope. The focal length f of the mirror is related to the acceleration of gravity g and its angular velocity ω by
f = g/(2ω2).
To obtain focal lengths and diameters of practical interest, one must provide systems that allow rotational periods on the order of several seconds and linear velocities at the rims of the order of a few kilometers per hour. One needs a value of dw/w of the order of 10-6 to keep df below the diffraction limit for a 2-m diameter mirror. This can be easily achieved.
Interferometric tests of mercury liquid mirrors have demonstrated diffraction-limited performance. The figure on the right shows a typical measured wavefront for a 2.5-m diameter mirror in the testing tower at Laval University, along with the image of a point source observed at the center of curvature. The wavefront has a root- mean-square deviation of less than 33 nm, which is consistent with diffraction-limited performance.
The image shows a typical diffraction-limited image with diffraction rings. Because the wavefront and point-spread function (PSF) are observed at the mirror’s center of curvature, they are measured through null lenses that correct spherical aberration at the center of curvature of any parabolic mirror. Null lenses inevitably introduce wavefront aberrations. Seeing over the optical path of the testing tower also deteriorates the wavefront. Consequently, the mirror actually has an even better surface quality than what is shown in the figure. Observations of the PSF over many hours show few degradations.
Wavefront and point source.
The liquid container rests on a three-point mount that aligns the bearing axis of rotation parallel to the gravitational field of the Earth, necessarily within a fraction of one arcsecond. Current liquid mirrors use air bearings because they are convenient and because commercially available units have the required precision and low friction. The container must be sufficiently stiff to support the liquid, yet also as light as possible to limit the cost of the bearing. Because the mirror is only centrally supported, it can be susceptible to a bending instability. A small tilt would move liquid to one side, resulting in asymmetric loading that can run away if the system is not sufficiently rigid.
It is important to work with mercury layers thinner than 2 mm. This not only minimizes weight and therefore cost; it also helps dampen disturbances that can be induced by wind or vibrations. Although surface tensions do not allow layers thinner than 4 mm, simple techniques have been developed to work with layers of mercury thinner than 1 mm.
A word of caution: Mercury vapors can be harmful if inhaled over long periods of time. However, mercury evaporates slowly, and you can eliminate all danger by using proper ventilation. Furthermore, a transparent oxide skin will develop in a few hours and effectively decrease evaporation to undetectable levels. The surface of a mercury mirror is easily cleaned.
Liquid mirrors at work
Liquid mirror telescopes were originally developed for astronomy. However, although not optimized for astronomical observations, the NASA Orbital Debris Observatory was the first to operate a liquid mirror telescope (3-m diameter) for an extended period of time; it operated continuously for eight years and yielded published astronomical research. Its primary purpose was to observe space debris.
The Large Zenith Telescope (LZT) at the University of British Columbia uses the largest liquid mirror ever built. Its 6-m diameter is the third-largest optical telescope in North America. It is being used to carry out an astronomical survey. To simplify logistics and reduce cost, scientists have placed the instrument near Vancouver, Canada; unfortunately, the poor quality of the site has limited its data-collection ability.
Nonetheless, the LZT has shown that a large liquid mirror is relatively inexpensive to construct and operate, and it can produce high-quality astronomical data. Recently, the LZT used a sodium lidar to measure temporal variability of the Earth’s mesospheric sodium layer. The resulting data will aid with the design of the Thirty Meter Telescope adaptive optics system.
These liquid mirror telescopes were first-generation instruments and have been operated under non-ideal conditions. However, in 2010, the International Liquid Mirror Telescope (ILMT) collaboration will operate in a good astronomical site (Devasthal, Indi a) using a 4-m liquid mirror telescope that is optimized for astronomical observations. ILMT observations will be able to obtain faint-magnitude images, cover a substantial portion of the sky, and make an unprecedented number of nightly observations and total time of observation per object.
The University of Western Ontario has operated a lidar system for several years that uses a 2.7-m diameter liquid mirror to collect powerful lidar light that is reflected from air molecules. This allows measurements of air density, pressure, temperature and the composition of the atmosphere. Such data will be used to study global warming and aid in our ability to predict weather.
MELLF-coated ferrofluid: (Left) MELLF-coated ferrofluid without a magnetic field. (Right) The surface deformed by several millimeters by the magnetic field of a permanent magnet located under the container.
Liquids other than mercury
Although existing LM telescopes use mercury mirrors, lighter liquids can be used that require less expensive bearings and containers. Engineers have made and tested liquid mirrors that use eutectic alloys of gallium. Gallium has a relatively high melting temperature (30°C), but it can be reduced by adding appropriate metals—such as indium. Furthermore, gallium and its eutectic alloys supercool easily to a stable state.
Experiments have shown that these alloys remain liquid to minus 27° C. Astronomical observations have been carried out with a 1-m diameter gallium-indium alloy mirror to temperatures below 0° C. Although gallium oxidizes almost instantaneously, gallium oxide is transparent and protects the underlying metal from oxidization; however, if the liquid is stirred, as occurs during startup, a thick oxide crust will hopelessly degrade reflectivity and surface quality. In practice, a simple skimmer has been used to remove this crust.
Ferromagnetic deformable mirrors: (Left) Aberrated point spread function (PSF) (Right) PSF corrected by a 37-actuator FDM at the right. The corrected PSF has a Strehl ratio of 0.84.
Mirrors have been made by spreading metal liquid-like films (MELLFs), which are self-assembling reflective colloidal films, on the surface of a liquid. Their main advantages include low cost and, by virtue of the liquid’s viscosity, the ability to tilt a rotating mirror by tens of degrees. We have made and tested a 1-m diameter liquid mirror tilted at 1 degree.
In recent work, scientists have reported successfully coating an ionic liquid with silver. Ionic liquids do not evaporate in a vacuum, and some can remain liquid at very low temperatures. This type of liquid may be used in a liquid mirror telescope on the moon. An optical/infrared telescope with a 20- to 100-m aperture located on the moon would be able to observe objects 100 to 1,000 times fainter than the proposed next generation of space telescopes, thus furthering our understanding of the early universe.
Ferrofluidic deformable mirrors
Ferromagnetic liquids have been coated with MELLFs, resulting in surfaces that can be shaped by this application of magnetic fields; this generates reflecting surfaces with complicated shapes that can rapidly vary with time. Such versatile optical elements will have numerous scientific and technological applications. Their main advantages are that they are inexpensive and can produce very large deformations. They could be used to make cost-competitive ferromagnetic deformable mirrors (FDMs) with thousands of actuators capable of strokes ranging from nanometers to hundreds
The third figure on the right compares a MELLF-coated ferrofluid without a magnetic field to the same surface after it was deformed by several millimeters through the application of a magnetic field from a permanent magnet located under the container. The bottom figure shows an experimental result: An aberrated PSF is compared to a PSF corrected by a 37-actuator ferrofluidic deformable mirror. The corrected PSF has a Strehl ratio of 0.84. The 37-actuator FDM prototype used to obtain these data is shown in the figure above to the right without the ferrofluid container.
Liquid mirrors are a young but promising technology that has begun to deliver results. Very large rotating mercury liquid mirrors have been used in observatories. They have demonstrated their robustness, the low costs of construction, and ease of maintenance. Ferrofluidic deformable mirrors have been demonstrated in the laboratory and are rapidly progressing.
Ermanno F. Borra is a professor at Laval University in Canada.
References and Resources
>> International Liquid Mirror Telescope Homepage
>> The Liquid Mirror Laboratory Homepage
>> The Large Zenith Telescope Homepage
>> NASA Optical Debris Observatory Homepage
>> Purple Crow Lidar Liquid Mirror Telescope
>> Liquid Mirrors: Optical Shop Tests and Contributions to the Technology, Astrophys. J. 393, 829 (1992).
>> Optical Tests of a 2.5-m diameter Liquid Mirror II: Behavior under external Perturbations and Scattered Light Measurements, Appl. Optics 36(25), 6278 (1997).
>> Gallium liquid mirrors: Basic technology, optical-shop tests and observations, Publications of the Astronomical Society of the Pacific 109, 319 (1997).
>> Image Quality of Liquid-Mirror Telescopes Publications of the Astronomical Society of the Pacific 119, 456 (2007).
>> Metal films deposited on liquids and implications for the lunar liquid mirror telescope. Nature 447, 979 (2007).
>> Tiltable rotating liquid mirrors: a progress report, Astronomy & Astrophysics 479, 597 (2007).
>> Wavefront correction with a 37-actuator ferrofluid deformable mirror, Opt. Express 15, 18199 (2007).
>> A lunar infrared telescope to study the early universe, Astrophys. J. 680, 1582 (2008).
>> The International Liquid Mirror Telescope, Opt. Photon. News 20(4), 29 (2009).