Light from astronomical objects must travel through the earth’s turbulent atmosphere before it can be imaged by ground-based telescopes. To enable direct imaging at maximum theoretical angular resolution, advanced techniques such as those employed by the Robo-AO adaptive-optics system must be used.
The angular resolution of ground-based optical telescopes is limited by the degrading effects of the turbulent atmosphere. In the absence of an atmosphere, the angular resolution of a typical telescope is limited only by diffraction, i.e., the wavelength of interest, λ, divided by the size of its primary mirror’s aperture, D. For example, the Hubble Space Telescope (HST), with a 2.4-m primary mirror, has an angular resolution at visible wavelengths of ~0.04 arc seconds. The atmosphere is composed of air at slightly different temperatures, and therefore different indices of refraction, constantly mixing. Light waves are bent as they pass through the inhomogeneous atmosphere. When a telescope on the ground focuses these light waves, instantaneous images appear fragmented, changing as a function of time. As a result, long-exposure images acquired using ground-based telescopes – even telescopes with four times the diameter of HST – appear blurry and have an angular resolution of roughly 0.5 to 1.5 arc seconds at best.
Astronomical adaptive-optics systems compensate for the effects of atmospheric turbulence. First, the shape of the incoming non-planar wave is determined using measurements of a nearby bright star by a wavefront sensor. Next, an element in the optical system, such as a deformable mirror, is commanded to correct the shape of the incoming light wave. Additional corrections are made at a rate sufficient to keep up with the dynamically changing atmosphere through which the telescope looks, ultimately producing diffraction-limited images.
The fidelity of the wavefront sensor measurement is based upon how well the incoming light is spatially and temporally sampled1. Finer sampling requires brighter reference objects. While the brightest stars can serve as reference objects for imaging targets from several to tens of arc seconds away in the best conditions, most interesting astronomical targets do not have sufficiently bright stars nearby. One solution is to focus a high-power laser beam in the direction of the astronomical target to create an artificial reference of known shape, also known as a ‘laser guide star’. The Robo-AO laser adaptive optics system2,3 employs a 10-W ultraviolet laser focused at a distance of 10 km to generate a laser guide star. Wavefront sensor measurements of the laser guide star drive the adaptive optics correction resulting in diffraction-limited images that have an angular resolution of ~0.1 arc seconds on a 1.5-m telescope.
The impact of atmospheric turbulence on astronomical imaging was first recognized centuries ago by Christiaan Huygens4 and Isaac Newton5. The first conceptual adaptive optics designs to compensate for the effects of turbulence were published independently by Horace Babcock6 and Vladimir Linnik7 in the 1950s. The U.S. Department of Defense then funded the development of the first adaptive-optics systems in the 1970s for the purpose of imaging foreign satellites during the Cold War8. The civilian astronomical community made progress developing systems in the 1980s; however, after declassification of military research on adaptive optics in 1992 (ref. 9), there was an explosion in both the number and complexity of astronomical systems10.
The majority of the approximately twenty visible and infrared telescopes today with apertures greater than 5 meters are equipped with adaptive-optics systems (e.g. refs. 11-19). As telescopes become larger, and thus more capable at collecting light, there are greater gains in resolution and sensitivity when using adaptive optics. Unfortunately, large-telescope adaptive-optics systems are extremely complex and restricted in their operation to near-infrared wavelengths due to current technology; they require teams of support staff, often with large observing overheads, and access to these scarce and valuable resources is also limited.
At the other end of the size spectrum, there are well over one-hundred telescopes in the 1-3 meter class, but very few of these are fitted with adaptive optics. Correcting atmospheric turbulence, even at shorter visible wavelengths, becomes tractable with current technology on these smaller telescopes because they look through a much smaller volume of atmospheric turbulence (Figure 1). The total amount of turbulence-induced optical error scales almost proportionally with the telescope primary mirror diameter and inversely with the observing wavelength. The same adaptive-optics technology that is used with near-infrared light on the larger telescopes can be used with visible light on modest-sized telescopes. Additionally, many telescopes of this scale are either being retrofitted (e.g. ref. 20) or newly built with fully robotic, remote and/or autonomous capabilities (e.g. ref. 21), significantly increasing the cost-effectiveness of these facilities. If equipped with adaptive optics, these telescopes would offer a compelling platform to pursue many areas of astronomical science that are otherwise impractical or impossible with large telescope adaptive-optics systems22. Diffraction-limited targeted surveys of tens of thousands of targets23,24, long-term monitoring25,26, and rapid transient characterization in crowded fields27, are possible with adaptive optics on these modest apertures.
To explore this new discovery space, we have engineered and implemented a new economical adaptive-optics system for 1-3 meter class telescopes, Robo-AO (refs. 2,3; Figure 2). As with other laser adaptive-optics systems, Robo-AO comprises several main systems: the laser system; a set of electronics; and an instrument mounted at the telescope’s Cassegrain focus (behind the primary mirror; Figure 3) that houses a high-speed optical shutter, wavefront sensor, wavefront correctors, science instruments and calibration sources. The Robo-AO design depicted herein illustrates how a typical laser adaptive-optics system operates in practice.
The core of the Robo-AO laser system is a Q-switched 10-W ultraviolet laser mounted in an enclosed projector assembly on the side of the telescope. Starting with the laser itself, the laser projector then incorporates a redundant shutter, in addition to the laser’s internal shutter, for additional safety; a half-wave plate to adjust the angle of projected linear polarization; and an uplink tip-tilt mirror to both stabilize the apparent laser beam position on sky and to correct for telescope flexure. A bi-convex lens on an adjustable focus stage expands the laser beam to fill a 15 cm output aperture lens, which is optically conjugate to the tip-tilt mirror. The output lens focuses the laser light to a line-of-sight distance of 10 km. As the laser pulses (~35 ns long every 100 μs) propagate through the atmosphere away from the projector, a tiny fraction of the photons Rayleigh scatter off air molecules and return towards the telescope (Figure 2B). The returning scattered photons originate along the entire upward path of the laser, and would otherwise appear as a streak that would make the wavefront measurements inaccurate. Within the adaptive-optics instrument, a high-speed Pockels cell optical shutter28 is used to transmit laser light only returning from just a narrow slice of the atmosphere around the 10 km projector focus, resulting in the laser appearing as a spot. Switching of the Pockels cell is driven by the same master clock as the pulsed laser, with a delay to account for the round trip time of the laser pulse through the atmosphere. Ultimately, only about one in every trillion photons launched is detected by the wavefront sensor. Even so, this radiant flux is sufficient to operate the adaptive-optics system.
The ultraviolet laser has the additional benefit of being invisible to the human eye, primarily due to absorption in the cornea and lens29. As such, it is unable to flash-blind pilots and is considered a Class 1 laser system (i.e. incapable of producing damaging radiation levels during operation and exempt from any control measures30) for all possible exposures of persons in overflying aircraft, eliminating the need for human spotters located on site as normally required by the Federal Aviation Authority within the U.S.31. Unfortunately, the possibility for the laser to damage some satellites in low Earth orbit may exist. For this reason, it is recommended for both safety and liability concerns to coordinate laser activities with an appropriate agency (e.g. with U.S. Strategic Command (USSTRATCOM) within the U.S.32).
The wavefront sensor which measures the incoming laser light within the Robo-AO Cassegrain instrument is known as a Shack-Hartmann sensor33, and includes a lenslet array, optical relay and imaging sensor. The lenslet array is a refractive optical element, flat on one side, with a grid of square-shaped convex lenses on the other side. It is located at a position optically conjugate to the entrance pupil of the telescope. When the ‘return light’ from the laser passes through the lenslest array, images of the on-sky laser are created at the focus of each of the lenses in the array (Figure 4). This pattern of laser images is then optically relayed to a UV-optimized charge-coupled device (CCD) camera. The lateral x-y position of each image gives a measure of the local gradient or ‘slope’ of the light wave through each lens of the array. The signal-to-noise ratio of each position measurement with Robo-AO ranges from 6 to 10 depending on Zenith angle and seeing conditions (6.5 electrons of detector noise in each of four pixels with a signal ranging from 100 to 200 photoelectrons per image per measurement).
The overall shape of the light wave is then calculated by multiplying the measured slopes by a pre-computed wavefront reconstructor matrix. The reconstructor matrix is created by first making a model of the pupil geometry that is sub-divided by the lenslet array. Individual ortho-normal basis functions (in this case disk harmonic functions up to the 11th radial order, for a total of 75 functions; ref. 34) are realized over the model and a 2-D least-squares solution to the best-fit plane across each lens in the array is calculated. While this is an approximation to the average gradient, the difference is negligible in practice, with the benefit of easily handling the geometry of partially illuminated lenses at the edges of the projected pupil. An influence matrix is thus derived that converts unit amplitudes for each basis function with the slope offset for every lens. The reconstructor matrix is then created by taking the pseudo-inverse of the influence matrix using Singular Value Decomposition. Once the shape of the light wave is known in terms of coefficients of the basis set, a compensatory inverse shape can be commanded on the high-order wavefront corrector. The process of making a measurement, then applying a correction, and repeating this cycle over and over, is an example of an integral control-loop. Robo-AO executes its control-loop at a rate of 1.2 kHz, necessary to keep up with the dynamics of the atmosphere. A scale factor (also known as the gain of the integral control-loop) of less than 1, and typically close to 0.6, is applied to the correction signal to maintain the stability of the control-loop while still minimizing the residual error of corrected light.
The high-order wavefront corrector within Robo-AO is a micro-electro-mechanical-systems (MEMS) deformable mirror35. Robo-AO uses 120 actuators to adjust the illuminated surface of the mirror, sufficient in spatial resolution to accurately fit the calculated correcting shape. The actuators have a maximum surface deviation amplitude of 3.5 μm which corresponds to optical phase compensation of up to 7 μm. In typical atmospheric conditions at astronomical observatories, this compensation length is greater than 5 sigma of the amplitude of the turbulence induced optical error and therefore results in significant correction headroom. Furthermore, the deformable mirror can compensate for static optical errors arising from the instrument and telescope at the cost of reduced dynamic range.
One subtlety to using a laser as a probe of the atmosphere is its inability to measure astronomical image motion36. The returning laser light is viewed from roughly the same position from which it is projected and therefore should always appear in the same location on sky. Any overall tilt measured in the returning laser light wave by the wavefront sensor is dominated by mechanical pointing errors. The tilt signal is used to drive the laser system’s uplink tip-tilt mirror, thus keeping the Shack-Hartmann pattern centered on the wavefront sensor. Correcting astronomical image motion is handled separately with the science cameras as explained below.
Robo-AO uses four off-axis parabolic (OAP) mirrors to relay light from the telescope to the science cameras achromatically (Figure 3). The relay path includes a fast tip-tilt correcting mirror as well as an atmospheric dispersion corrector (ADC)37 comprised of a pair of rotating prisms. The ADC solves a particular issue related to observing objects through the atmosphere that are not directly overhead: the atmosphere acts as a prism and refracts light as a function of wavelength, with the overall effect becoming stronger as the telescope points lower in elevation, causing images – especially those that have been sharpened by adaptive optics correction – to appear elongated in the direction normal to the horizon. The ADC can add an opposite amount of dispersion to the incoming light, effectively negating the effect of the atmospheric prismatic dispersion (Figure 5). At the end of the OAP relay is a visible dichroic that reflects light of λ < 950 nm to an electron-multiplying charge-coupled device (EMCCD) camera while transmitting infrared light towards an infrared camera. The EMCCD camera has the ability to capture images with very low electronic (detector) noise38,39, at a frame rate which reduces the intra-exposure image motion to below the diffraction-limited angular resolution. By re-centering and stacking a series of these images, a long-exposure image can be synthesized with minimal noise penalty. The EMCCD camera can also be used to stabilize image motion on the infrared camera; measurements of the position of an imaged astronomical source can be used to continuously command the fast tip-tilt to re-point the image to a desired location. Ahead of each camera is a set of filter wheels with an appropriate set of astronomical filters.
An internal telescope and source simulator is integrated into the Robo-AO system as a calibration tool. It can simultaneously simulate the ultraviolet laser focus at 10 km and a blackbody source at infinity, matching the host telescope’s focal ratio and exit pupil position. The first fold mirror within Robo-AO directs all light from the telescope’s secondary mirror to the adaptive-optics system. The fold mirror is also mounted on a motorized stage which can be translated out of the way to reveal the internal telescope and source simulator.
While the Robo-AO system is intended to operate in a completely autonomous fashion, each of the many steps of an adaptive optics observation can be executed manually. This step-by-step procedure, along with a brief explanation, is detailed in the following section.
The method presented here describes the manual operation of the Robo-AO laser adaptive-optics system. In practice, Robo-AO operates in an automated fashion; the vast majority of procedures are controlled by a robotic sequencer which performs the same steps automatically.
The Robo-AO system has been engineered for straightforward replication at modest cost, with materials (~USD600K) and labor being a fraction of the cost of even a 1.5-m telescope. While there are roughly twenty optical telescopes around the world greater than 5 m in diameter, telescopes in the 1-3 m class number well over one-hundred and are projected as potential hosts for Robo-AO clones. In addition to the current system deployed at the 1.5-m P60 telescope, the first of hopefully many clones is being developed for the 2-m IGO telescope42 in Maharashtra, India, and a variant using bright stars instead of a laser for wavefront sensing is being commissioned at the 1-m telescope at Table Mountain, CA43. A revolution in diffraction-limited science may be at hand.
The authors have nothing to disclose.
The Robo-AO system is supported by collaborating partner institutions, the California Institute of Technology and the Inter-University Centre for Astronomy and Astrophysics, by the National Science Foundation under Grant Nos. AST-0906060 and AST-0960343, by a grant from the Mt. Cuba Astronomical Foundation and by a gift from Samuel Oschin.