Robert Q. Fugate
Starfire Optical Range, USAF Phillips Laboratory, 3550 Aberdeen Ave, SE, Kirtland AFB, NM 87117-5776, 505-846-4712 ext. 314, fax 505-846-2213, email email@example.com
Mankind is on the brink of a revolution in ground-based optical and near infrared astronomy. The revolution is giant telescopes and adaptive optics. Astronomers are building and operating telescopes having light collecting apertures of 8-10 meters in diameter. These telescopes will have enormous light gathering power enabling astronomers to probe the depths of the universe with tools never before available. However, because of the atmosphere they will have the resolution of an 8-inch telescope. It is the diffraction-limited resolution of the Hubble Space Telescope that has made possible its new scientific discoveries and spectacular, mind-boggling images. The dozen new telescopes of the 21st century will be able to collect light nearly 20 times faster than HST, but they will achieve no more resolution than that obtained by a backyard astronomer. To paraphrase the old real- estate slogan, the three most important things about a telescope for doing important new science are (1) resolution, (2) resolution, and (3) resolution. Adaptive optics has the potential to significantly increase the resolution of large ground based telescopes. Figure 1 illustrates the point with three hydrogen alpha (634 nm) images of the Trapezium in the Orion nebula.
Figure 1. Three images of the Trapezium in the Orion Nebula. All images made through a hydrogen-alpha wavelength filter (653.3 nm) to emphasize ionized hydrogen. Top image: 1.5m SOR telescope no adaptive optics. Middle image: Hubble Space Telescope (courtsey C. R. O'Dell, Rice University). Bottom image: 1.5-m SOR telescope compensated with Rayleigh beacon adaptive optics. Note the incredible increase in resolution obtained with the HST over the uncompensated image and the improvement over the top image made with adaptive optics.
Over 40 years ago, the astronomer Horace Babcock  proposed the concept of adaptive optics. The basic idea is quite simpleinsert a wavefront corrector between the output of the telescope and the science camera which alters the phase of the optical wavefront to exactly cancel out the aberrations induced by the atmosphere. The wave-front corrector must be dynamic since the atmosphere is in constant motion and the resulting turbulence induces aberrations that change tens or even hundreds of times per second. The most mature technology for wavefront correction is the deformable mirroran electro-mechanical device that physically deforms a thin face sheet of glass ±2 µm by pushing and pulling on its surface with an array of small piston-like actuators. 
There are two other key components of an adaptive optics systema wavefront sensor and a beacona source of light outside the atmosphere that generates light bright enough for the wavefront sensor to measure. The wavefront sensor estimates the residual phase error at those points in the wavefront corresponding to the locations of the actuators in the deformable mirror. Bright stars make perfect beacons, but, as we shall see, lasers are needed to generate artificial beacons.
In adaptive optics systems, the deformable mirror is part of a closed loop servo. The motion of the actuators is controlled by the wavefront sensor which samples part of the light going to the science camera and determines the residual phase error after the wavefront reflects off the surface of the deformable mirror. The wavefront sensor and an electronic processor estimate the current phase of the wavefront at points corresponding to the locations of the actuators in the deformable mirror. If the phase is not zero with respect to a reference plane wave, the difference represents an error signal, some fraction of which is applied to the corresponding actuator. In a typical adaptive optics system used for astronomy, the closed loop bandwidth of the higher-order loop may be of the order of 100 Hz.
In typical ground based telescope implementations, the deformable mirror is not used to correct full aperture tilt (that component of wavefront distortion which causes the centroid of the focal plane image to jitter about). Full aperture tilt is normally compensated with a fast steering mirrora flat mirror that can be rapidly tilted in two orthogonal axes. This arrangement avoids using up the dynamic range of the deformable mirror. Some astronomical telescopes use the secondary mirror as a fast steering mirror to remove turbulence induced full aperture tilt. The ultimate combination is to make the secondary mirror a deformable mirror and rapidly tilt the entire mirror to correct full aperture tilt. This arrangement greatly improves the optical efficiency of the entire telescope/adaptive optics system.
A significant problem in using adaptive optics for astronomy is the lack of enough bright stars to serve as beacons for the wavefront sensor. Stars between 5th and 15th magnitude are required, depending on the science camera imaging wavelength, degree of compensation, strength of the turbulence, observatory seeing conditions, and viewing angle above the horizon. The problem is, even if we could use 15th magnitude stars for all observations, we could only correct less than 1 percent of the sky with adaptive optics. This limited sky coverage is caused by a property of the atmosphere known as anisoplanatism. If we measure (and correct with the adaptive optics) the distortion in the direction toward one star, we find that at any instant the distortion will be different when measured in some other direction at a slightly different angle through the atmosphere to a different star. So the compensation performed by the adaptive optics along the line of sight to the beacon star will provide less than perfect correction for stars in other directions. The size of the patch of sky where the correction will be very good (near the performance limits of an adaptive optics system) is only a few arc seconds in diameter in the visible part of the spectrum. As a consequence of anisoplanatism, we need to have bright stars spaced every few arc seconds throughout the sky. Unfortunately, even though there are millions of stars brighter than 15th magnitude, the sky is a very big place and an arc second is a small angular distancethere simply aren't enough bright stars for adaptive optics to work at maximum performance over the entire sky (there are on average only about 1000 stars per square degree brighter than 15th magnitude).
We can increase the sky coverage of a ground based imaging telescope with an adaptive optics system by creating artificial stars with lasers. A laser focused in the atmosphere backscatters light creating a small spot that serves as a beacon for the wavefront sensor. At this time, two scattering mechanisms seem practical. One is Rayleigh scattering from oxygen and nitrogen molecules in the lower atmosphere (at ranges up to 15 km from the telescope). Beacons generated by Rayleigh scattering have been demonstrated on our 1.5 m telescope at the Starfire Optical Range; the compensated image in Fig. 1 was made using a Rayleigh beacon.
The other mechanism is resonant scattering from sodium atoms in the mesosphere (created from meteor ablation) between 85 and 95 km above the earth's surface. Figure 2 is a simplified diagram of an ideal sodium layer laser beacon adaptive optics system installed on a large telescope. In this concept, the secondary mirror of the telescope serves three functionsfocusing the light from the primary onto the science camera, correcting phase aberrations by deforming the surface of the secondary (the secondary becomes the deformable mirror), and by correcting image jitter by rapid tip-tilt motion of the entire secondary/deformable mirror structure. Not all required technologies have been demonstrated to implement a system like this but they are under development and the layout shown in Figure 2 is useful for discussion of the concepts.
Figure 2. Diagram showing conceptual arrangement of laser beacon adaptive optics on a large telescope. A: scientific camera, B: dichroic aperture sharing element reflecting 589 nm wavelength radiation from the sodium beacon F, C: wavefront sensor, reconstructor and deformable mirror controller, D: deformable secondary mirror mounted on a fast 2 axis gimbal for higher-order wavefront correction and full aperture tilt control, E: sodium frequency laser for exciting mesospheric sodium, F: mesospheric sodium beacon created 90 km above the earth's surface radiating into 4 pi steradians, G: the mesospheric layer of sodium atoms ranging from ~85-95 km altitude, H: the turbulent atmosphere extending from the surface to ~20 km altitude, I: light rays from stars at infinity, J: light rays from the sodium laser beacon (note that they overlap only at low altitudes).
By studying Fig. 2, it is easy to see that if the beacon altitude is too low, the rays from the beacon will not completely sample the highest altitude turbulence (about 20 km). In fact, the strength of the turbulence at height h is weighted by a factor (1-h/H) for a laser beacon at altitude H. This means turbulence at the height of the beacon is not counted at all. The light from the laser beacon illuminates the aperture of the telescope with a cone of light while light from the stars illuminate the aperture with a cylinder of light (compare the solid and dotted lines in Fig. 2). This cone effect is one limitation of using a laser beaconbecause of its finite altitude, it will never perfectly measure all the turbulence. We can calculate in detail how well a beacon for a given aperture size, beacon altitude, and turbulence strength will work. These analyses indicate that we must use beacons at 90 km altitude. In some cases even that altitude is insufficient for imaging at short wavelengths.
Another, perhaps even bigger, limitation of laser beacons is that they provide no information about full aperture tilt induced by the atmosphere. The basic problem is that we have no way to measure where the beacon is with respect to the optical axis of the telescope. To first order the motion of the beacon as viewed by the telescope is canceled out by the two way propagation path. Light comes back to the telescope through nearly the same atmosphere that it travels through going up to the mesosphere, canceling out the apparent motion of the beacon. An image of the beacon made with the full aperture of the telescope appears stationary, whereas the image of a star (which passes through the atmosphere only once) is jittering. Clearly we cannot use any information from the laser beacon to compensate for the image motion of the star. What this means is that we must find a star in the field that is bright enough for full aperture tilt measurements. Fortunately, we use the entire aperture for this measurement, not smaller subapertures as in the case of the wavefront sensor. As a result, we can use much fainter stars (of the order of 20th magnitude and stellar density statistics predict that we can still get full sky coverage at this magnitude). We must still be concerned about anisoplanatism, but in this case it is only the tilt component that is important. Additional discussion regarding the limitations and performance predictions of laser beacon adaptive optics can be found in the references.[3-6]
We would like to arrive at a set of requirements for the laser to be used to excite mesospheric sodium and generate beacons suitable for our adaptive optics system. This is a problem with a lot of variables and a lot of interesting physics and engineering. We start from the signal requirements of the wavefront sensor and consider two imaging applications, near infrared astronomy and imaging of low earth orbiting satellites. I have added the satellite imaging application since it puts significant stress on the laser requirements so that laser designers are aware of this application as well. The performance of the adaptive optics system can be predicted by analyzing the major sources of error. These include fitting error, servo lag, measurement noise and anisoplanatic effects. Fitting error arises from the fact that we have a finite number of actuators and can't perfectly fit the surface of the deformable mirror to the distorted wavefront, especially at high spatial frequencies. Servo lag arises because we have a finite bandwidth in the control system and we are always catching up with the real time changes in the atmosphere but never quite get there. Measurement noise in the wavefront sensor arises from noise in the detector and from shot noise in the signal. Anisoplanatism errors arise due to using beacon sources that are not the object being imaged or sensing wavelengths considerably different than the imaging wavelength. All these sources of error are interrelated and one usually tries to design a system that more or less distributes the error equally amongst them. There isn't space in this short article to go into the details of the trade spaces that are possible. However, I have summarized a set of requirements resulting from one such trade study in Table 1 for the two imaging applications of interest.
|Parameter||Infrared Astronomy||Visible satellite imaging (3.5m SOR telescope)|
|Wavefront sensor subaperture size||35 cm square||11.7 cm square|
|Wavefront sensor integration time per measurement||2.5 ms||1.0 ms|
|Total wavefront sensor efficiency||50% (Cassegrain system)||15% (Coude room system)|
|Mesospheric sodium spot size||0.5 arcsec||1.0 arcsec|
|Detected signal per subaperture per measurement||150 photodetected electrons||150 photodetected electrons|
|Wavefront sensor measurement noise per pixel||10 electrons||10 electrons|
|Required signal from mesospheric sodium beacon at the ground||0.1 photons/cm2/ms||7.8 photons/cm2/ms|
Table 1. Requirements for laser beacon adaptive optics imaging systems.
Table 1 shows there is a large range of signal requirements for these two applications. We need to develop the connection between the signal level requirements of 0.1 and 7.8 photons/cm2/ms in terms of laser parameters such as spectral and temporal formats, beam quality and power. In order to understand how the requirements in Table 1 translate to laser parameters we need to look at the properties of mesospheric sodium and the interaction of laser radiation with atomic sodium in that environment.
Laser excitation of mesospheric sodium is a complex subject. However, the problem is a very interesting and important one and has attracted many excellent researchers. Table 2 summarizes the principle properties of mesospheric sodium. Additional details can be found in the literature.
|Column density||5x109 cm-2|
|Absorption profile||3 GHz Doppler broadened|
|Radiative lifetime||16 nanoseconds|
|Saturation intensity||6.3 mW/cm2, 10 MHz linewidth|
5 W/cm2, full absorption spectrum
Table 2. Properties of mesospheric sodium.
There are several important properties of mesospheric sodium in terms of laser excitation and generating laser beacons. We are interested in excitation of the D2 line of the sodium atom. Interactions between the one 3s valence electron and the nuclear magnetic field produce hyperfine splitting of the ground state of 1.77 GHz. The excited states are also split into 4 levels resulting in a total of 24 magnetic substates. The quantum selection rules allowed for these states make optical pumping by circularly polarized light possible, creating, in effect, a two state atom with a strong transition giving a substantial increase in signal return over non optically pumped populations. The absorption profile is inhomogeneously Doppler broadened to a full width at half maximum of approximately 3 GHz. The saturation intensity is fairly low (a few W/cm2 for the full spectrum), requiring careful design of the temporal and spectral waveforms of the laser. Laser-atom interactions for laser pulse widths of the order of the natural radiative lifetime of 16 ns or less (e.g. mode locked pulse trains) require analysis by solution of the Bloch equations. Two level rate equations are adequate for pulses long compared with 16 ns.
It is instructive to determine a sort of theoretically maximum limit on the number of photons we can expect for efficiently exciting the sodium layer. If we consider a cylindrical column of laser radiation that subtends either 0.5 or 1.0 arcsec (roughly 22 and 44 cm in diameter at the mesosphere respectively), we can ask the question: How much signal would these beacons generate at the ground if 1/4 of the atoms (the number at the saturation intensity) were continuously excited? The answer is 24 and 96 photons/cm2/ms respectively for a beacon directly overhead and 9 and 36 photons/cm2/ms 30 degrees above the horizon. These numbers far exceed the requirements shown in Table 1 of 0.1 and 7.8 photons/cm2/ms. So there is hope that, with the right laser, these requirements can be met.
Based on the rather incomplete and inadequate discussions above, we move on to discuss laser candidates suitable for generating sodium beacons for the two applications under consideration in this article. These fall into one of two categories: dye lasers and solid-state lasers. Dye lasers are a natural since they can be tuned onto the sodium D2 line resonance. However, a several watt CW dye laser will barely produce the required 0.1 photon/cm2/ms flux at the telescope for infrared astronomy. Several commercial and custom CW dye lasers have been deployed at telescopes and successfully used to obtain data and operate adaptive optics systems at various levels. Most agree that getting much more power than 3 watts from a narrow line CW dye laser and maintaining high beam quality is not likely.
The most significant development in high beam quality pulsed dye lasers for this application is the work at Lawrence Livermore National Laboratory. They have built a 15 watt average power 11 kHz pulse rate 100 ns pulse width laser and installed it on the 3-m Shane telescope at Lick Observatory. They have measured 0.25 photons/cm2/ms photon returns with this system and are currently integrating it with a Cassegrain mounted adaptive optics system. The dye master oscillator, preamplifier and amplifier are pumped with three 40 watt frequency doubled Nd:YAG lasers through large multimode fibers. The YAG lasers and the dye master oscillator are located off the telescope gimbal in a remote, environmentally controlled area. Only the dye preamp and amplifier are located on the telescope. This laser could be scaled to large average powers (200 W is not unreasonable) by adding more dye amplifiers and more Nd:YAG pump lasers. However, at 200W average power, 150 ns pulse length and 30 KHz pulse rate, the saturation intensity of 5 W/cm2 is reached (a loss of a factor of 2 in signal from an unsaturated condition) at a beam diameter of approximately one meter (> 2 arcsec) which affects performance of the adaptive optics system (an extended beacon source requires more power). For beam diameters of 1 arcsec (the requirement listed in Table 1), a laser with this pulse format will be in strong saturation. It is important to determine whether or not there are other laser options with more suitable pulse formats that minimize saturation.
There are a two basic approaches to using solid-state lasers to generate sodium laser beacons. These are (1) summing the two lines of Nd:YAG in a non-linear crystal and (2) Raman shifting or optical parametric oscillator generation of 1178 nm radiation and then frequency doubling to 589 nm. There are various implementations of these approaches but they basically reduce to one of these two principles.
Sum frequency generation of 589 nm is a fortuitous accident of nature in that the two strong gain lines of Nd:YAG (1064 and 1319 nm) are nearly perfect for generation of 589 nm radiation. Practical lasers using this principle were first built and demonstrated in field experiments by Tom Jeys at MIT/LL. The YAG lasers were initially flash lamp pumped but recently they have developed a diode laser pumped device that has been installed on the 3.5-m ARC telescope in southern NM. This laser has a 400 pulse per second train of 150 µs long macro pulses each containing a 100 MHz train of mode locked micro pulses each 700 ps wide. The natural spectral width of the micro pulses covers the Doppler broadened absorption profile. Recent analytical calculations by Peter Milonni at Los Alamos National Laboratory show that this laser pulse format is very resistant to saturation and returns more signal per watt of average power than high rep-rate Q-switched (<100 ns PW) formats.
An interesting variant of the sum frequency laser has been demonstrated in principle at Phillips Laboratory. It consists of an intracavity OPO and a KTP sum-frequency crystal. The resonator is pumped by a single 1064 nm Nd:YAG laser, the OPO generates 1319 nm and 589 nm is generated as the sum frequency and out coupled from the resonator. Ideal materials for operation of the OPO remain an issue to scale this configuration to high power.
There are several approaches that perform wavelength shifting to 1178 and frequency doubling to 589. The first device to produce light at 589 nm was a Raman shifted Alexandrite laser built by Light Age. The pulse format for this laser was 20 pps at 80 ns pulse width. The fundamental frequency of Alexandrite has also been used to generate light for pumping mesospheric potassium at 769 nm.
Recently, Bob Byer at Stanford suggested Raman shifting the 1064 nm line of Nd:YAG to 1178 nm with calcium tungstate and then frequency doubling to 589 nm. The desired center frequency of the D2 line does not occur at the peak of the Raman gain profile but exact on frequency operation can be obtained. This has been demonstrated in lab experiments at TRW by Eric Cheung et. al using an intra-cavity doubler. The pulse train consisted of 70 µs macro pulses containing a train of 134 MHz mode-locked micro pulses. They claim good beam quality and high efficiency. This arrangement is forgiving since the Raman process requires no phase matching and the doubler was non-critically phase matched LBO. The authors claim this approach is scaleable to ~100 watts of average power at 589 nm.
Another group lead by Dick Powell at the University of Arizona is working on configurational tuned Nd:YGAG which is intracavity Raman shifted by calcium tungstate and frequency doubled to 589 nm. The concept here is to get more efficient Raman conversion by shifting the pump frequency slightly. Initial experiments to demonstrate the concept are underway.
There is an urgent need for efficient, high beam quality lasers suitable for creating mesospheric sodium beacons for adaptive optics. Lasers useful for infrared astronomy need average powers of 10 watts and for visible wavelength satellite imaging 50-200 watts, depending on other properties of the laser. The laser should not preclude emitting circularly polarized light, have tenth wave beam quality, efficiently excite the Doppler broadened 3 GHz absorption profile, have angular jitter of the order of a fraction of the diffraction limited beam divergence, and have a temporal pulse train that does not saturate mesospheric sodium. In the ideal case these lasers should be mountable directly on the telescope, operate without loss in specifications over a wide range of temperatures, be efficient with easily removed waste heat, and be reliable with minimal service. Other than that most any old laser will do! The laser beacon adaptive optics community is interested in what the solid state laser community has to offer for this application.
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(c) Copyright 1996, The Institute of Electrical and Electronics Engineers, Inc.
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