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We present the results from a laboratory multiconjugate adaptive optics experiment. The experiment is differentiated from other published work in that it has a programmable deterministic turbulence generator and an output science camera. The turbulence was generated using a dual layer turbulence emulator, and then corrected using an AO system with 2 wavefront correctors and a Shack-Hartman wavefront sensor, which processed information from five artificial guide stars. We report our results and also describe some of the problems.
©2004 Optical Society of America
1. Introduction
Multiconjugate adaptive optics (MCAO) is concerned with extending the field of view of conventional astronomical adaptive optics (AO) systems. All current AO systems use a single correcting element; usually a deformable mirror; to correct for the total effect of the atmospheric phase aberrations. Thus wavefronts from the guide star; either natural, or a laser; are well corrected, and the performance of adaptive correction degrades as the off-axis angle increases. This effect, known as angular anisoplanatism, limits the corrected field of view of an AO system to about 10 to 30 arcseconds at infrared wavelengths, and less at visible wavelengths. MCAO promises to increase the field of view, by assuming that the atmospheric turbulence can be stratified into a number of layers, and by then placing a wavefront corrector conjugate to each of these layers.
There are currently two schools of thought on how to implement MCAO [1]. The first is an extension of conventional AO, and is known as “classical” or “tomographic” MCAO [2–5]. The second is known as “layer-oriented” MCAO [6]. In a classical system, there is essentially one wavefront sensor per guide star, although in reality these can be different parts of the same wavefront sensor, and in the layer oriented approach there is one wavefront sensor per atmospheric layer. The relative merits of both approaches are currently a topic of debate, but neither of the systems has yet been implemented, on a telescope. Ragazzoni showed that the principle of tomographic wavefront sensing is possible [7]. There are two planned telescope systems, e.g. ESO’s MAD (MCAO demonstrator), the Gemini South MCAO system and two existing systems dedicated to solar observations, e.g the Dunn Solar Telescope tomographic system [8,9] and the Vacuum Tower Telescope layer oriented system [10, 11]. Our goal is to gain practical experience of MCAO, and hence our work can be considered to lie in between the large number of computer simulations performed and the ambitious on-sky experiments mentioned above. Other laboratory MCAO work has been published by Lund Observatory, Sweden [12] and the University of Victoria, Canada [13,14]. The latter group have not yet published closed loop results (to the best of our knowledge), and the Lund Group’s work does not include a programmable deterministic turbulence emulator, nor does their experiment contain the equivalent of an output science camera (the resultant PSFs are obtained by transforming the measured wavefronts). However, their experiment has the potential advantage of being able to increase the number of layers in the turbulence generation section.
Fig. 1. Dual conjugate AO system optical layout. LC is for the modal liquid crystal wavefront correctors, OAP is for off-axis parabola, SLM is for spatial light modulators based on ferroelectric liquid crystal, and WFS is for Shack-Hartman wavefront sensor.
In this paper we describe a closed loop laboratory system based on classical MCAO, which has the main purposes: (1) to experimentally demonstrate the principle of MCAO; (2) to provide valuable experience in the problems associated with constructing a MCAO system (3) to experimentally investigate multiconjugate non-common path errors; (4) to experimentally investigate problems and solutions associated with laser guide star (LGS) spot elongations; and finally (5) to compare star and layer oriented MCAO. We describe here our first closed loop results, answer some questions associated with points (1) to (3), and discuss the lessons learnt so far.
2. Experimental description
The first part of our system is a dual conjugate turbulence emulator, which is used to produce quantifiable aberrations in two different optical planes. The active elements are two ferroelectric liquid crystal (LC) spatial light modulators, each of which has 256×256 pixels on a 5×5mm substrate, which are placed in a holographic configuration so that accurate, high-speed analogue phase control can be produced. The general technique was proposed by Neil et al. [15] and the extension to dual conjugate system has previously been described in [16,17]. The light source is a HeNe laser, which is split into five light beams using a microlens array, in order to emulate five guide stars arranged in a square with one at the centre as shown on Fig. 2 (left). The turbulence emulator can either simulate evolving atmospheric turbulence, or classical Zernike modes for system testing.
Light from the turbulence emulator then propagates to the MCAO system. This system models an 8m-class telescopes with the lower turbulent layer at the telescope pupil and the upper turbulent layer at an altitude ranging between 3 and 8 km. Due to the small size of the turbulence emulator optics and to the fact that angles scale as the ratio of the aperture sizes, we could not reproduce the telescope off-axis angle. Instead we model the performances of 8m-class telescopes by assuming that the turbulence is at very high altitude and the results are normalized to the isoplanatic angle. In that case the maximum guide star separation we are able to simulate corresponds to 2 arcminutes in the near IR. Figure 2 (top) shows the laboratory setup and the system components are described in Table 1 below.
Table 1. Summary of the components of the MCAO system.
The light propagating onto the wavefront sensor consists of five beams, from the five guide stars, and if these were incident directly onto the lenslet, the off-axis focal spots were found to be significantly aberrated, which made centroid motion detection difficult. Therefore the five beams were incident onto five tilted mirrors before the lenslet array, which ensured that all the beams were incident on-axis. The camera, a QImaging Retiga [20], was large enough to incorporate all five spot patterns. The wavefront sensor uses a square Shack-Hartmann array, based on a 132×132 lenslet array with 188 microns pitch and 8 millimetres focal length (AOA 188-8.0-S)[19]. The plate scale is 3.6 waves per subaperture with 8-pixel sampling and there are 6 subapertures across the pupil diameter for each guide star.
The open loop system bandwidth was limited to 0.5–1Hz for the following reasons; (1) the wavefront correctors can not operate at atmospheric bandwidths although closed-loop atmospheric correction using dual frequency liquid crystals has been demonstrated [22]; (2) the slow rate dramatically reduced the cost and complexity of the system; and (3) since our turbulence can be “played back” on the turbulence generator at any speed, the system can be made to represent a system working at full speed. Also, in this experiment we were not interested in investigating the temporal performance of the system.
The least square control loop software was written in the Python language and hosted on a PC. Commands to the wavefront corrector were then sent to the controller, based on an FPGA system, and described further in Ref. [18].
The optical setup, shown in Fig. 1, was designed to represent an 8m telescope operating in the near infrared. The wavefront correctors are conjugated to the ground and to the 3–8km atmospheric layers. They are arranged in the order of occurrence of aberrations in the atmosphere i.e. there are no relay optics to reverse the natural telescope imaging. The light hits the upper wavefront corrector first as in, for example, the proposed Gemini MCAO system. It has been shown by Flicker [23] that this sequence of correction is not optimum and can result in propagation of amplitude fluctuations that leads to non negligible residual phase errors at visible wavelengths and for large air masses. In our case, we do not anticipate such an effect as a constraint.
Fig. 3. (Left) Pupil footprints for the upper layer and ground layer conjugated LC correctors assuming a maximum guide star separation of 2 arcminutes and 5km altitude for the upper turbulence layer. (Right) LC’s-WFS geometry. There are 6×6 subapertures across the pupil, which corresponds to 5×5 LC’s actuators.
Two off axis parabolas (F/13, f=1000mm) were used to collimate the beam on the LC correctors. The pupils project on to 70% of the LC’s diameter leading to 5×5 active actuators on an hexagonal grid on the ground conjugated corrector sampled by 6×6 WFS subapertures as shown on Fig. 3. Both modal LC correctors are polarization dependant and needed to be aligned accordingly. This resulted in a π/6 rotation between the LC’s and led to the overall geometry shown on Fig. 3 (right). The alignment of the wavefront sensor to the wavefront correctors was achieved by using the LC’s actuator print through and was refined by minimizing the response wavefront variance of the actuators.
For the experiment the seeing ranges from 0.3 to 1 arcseconds which corresponds to D/r0 between 5 and 30 in the near infrared and to 4”<Θ0<20” for the anisoplanatic angle, Θ0. For a turbulence layer at 5 km the maximum guide star off axis angle is 2” corresponding to a pupil shift of D/5 as shown in Fig. 3 (left).
3. System calibration
The poke responses of the modal LC’s were calibrated as a function of the frequency of the driving voltage. We selected a frequency of operation of 2900 Hz in order to achieve an influence function FWHM equal to half the interactuator spacing. In these conditions, the full poke amplitude range is 5.5 waves for driving signals ranging from 0 to 10 V peak to peak. We produced an average voltage amplitude function to compensate for the non-linearity of the phase-voltage response.
Fig. 4. Results of reducing static internal optical aberrations (without any induced turbulence) using an image quality metric and a simple algorithm based on optimizing the images quality metric. The left hand column shows the uncorrected image for each of the 5 guide stars (central star is in the middle). The center column shows how the image quality metric changed with iteration number. The ordinate shows iteration number and the coordinate is the image metric. The right hand column shows the image after correction.
The influence function variation between the actuators is around 10–20%. There are also two waves (peak to valley) of static defocus built in the LCs that was mostly compensated by the optical relay. In order to remove the remaining static optical aberrations including the non-common path aberrations, we used a simplex algorithm based on optimizing an image quality metric calculated from the science camera outputs. The metric, M, was given by,
where Ii,j is the intensity of the (i,j)th pixel. This metric was adapted to multiconjugate mode by adding the metrics from the individual stars, and the results of this optimization are shown on Fig. 4. The four peripheral stars all show improvement, including a peak intensity rise of a factor three. This method is a classical way of correcting non-common path errors and we are still investigating whether this is an optimum way to correct multiconjugate non-common path errors.
The control algorithm is based on the zonal reconstruction approach, i.e., the interaction matrix as shown on Fig. 5 was built by measuring the wavefront using a standard weighted centroiding algorithm for a sequential set of actuator pokes and a matrix inversion was performed using singular value decomposition. About ten to twenty “invisible” modes or modes associated with small eigenvalues such as piston where filtered out in the mirror basis as well as tip-tilt in order to generate the reconstruction matrix. In this particular case waffle modes are not a constraint because the geometry is different from the regular Fried geometry.
4. Static aberrations closed loop results
We initially performed several tests with the system in order to evaluate the amount of coupling between the two correctors. As an initial system test individual actuators in the wavefront correctors were poked, 2.5 waves in amplitude, in order to test if the system would correctly determine which of the wavefront correctors was being actuated and hence whether it could self-correct. Figure 6 shows that the accuracy of the correction is 5% of the input amplitude, i.e. 1/5 WFS pixel. There is a maximum of 5% crosstalk on the lower wavefront corrector actuators but no signal was incorrectly sent to the upper wavefront corrector. We can also see an improvement in the images, but this effect is small since only one actuator poke generates relatively small aberration and the results tend to be masked by optical aberrations which were not first corrected for.
Fig. 5. Dual corrector and five guide stars interaction matrix built by measuring the centroid motion for a sequential set of actuator pokes. The matrix inversion was performed using singular value decomposition. The matrix is broken down into 5×2 subarrays, corresponding to the 5 guide stars (indicated by the filled circles above) and the 2 wavefront correctors. The color scale has is in units of Shack Hartmann spot displacement (pixels).
We also tested the compensation of Zernike modes such as defocus and astigmatism, with amplitude up to five waves. Both aberrations where successfully corrected to 5% of the input amplitude accuracy in MCAO mode when introduced in either the upper or the lower atmospheric layer. Note that the corrector conjugated to the turbulence layer where the aberration was introduced achieved most of the correction independently. There is only a maximum correction coupling between the two correctors of 5%.
5. Emulated turbulence closed loop results
In order to emulate real MCAO telescope correction we also generated time evolving phase screens corresponding to Kolmogorov turbulence. Separate phase screens were produced for the lower and upper turbulence layer, which were temporally and spatially uncorrelated and had different values of r0. The tilt was removed from all the turbulence files and this mode was filtered out in the LC’s control algorithm. We measured the wavefront using four or five guide stars on a square grid, as shown on Fig. 3, separated diagonally by 2 arcminutes. The wavefront sensor SNR ranges from 15 to 30 for the five guide stars and photon and readout noise contributed to about the same level.
Fig. 6. Single contact pokes recovery on lower (right) and upper (left) LC’s. The left hand figure shows the magnitude of the signals being sent to each actuator in the LC versus time (increasing time is in the downward direction) when closing the loop. The two columns represent the lower LC and upper LC vectors. Any arbitrary pokes are self-corrected with minimal cross coupling between actuators and correctors. The quality of the corresponding images also so improves with time as shown on the right side of each graph, although just poking one actuator to begin with does not seriously degrade the image. It can be seen that (at the top of the figure) all the actuator signals are zero apart from the one which is poked. The system self-recovers although some crosstalk into other channels can be seen.
A comparison of a single conjugate AO and MCAO closed loop results using the wavefront sensor data is shown in Fig. 7. In single conjugate mode, the star, which is used for wavefront sensing, is well corrected whereas the others are actually further aberrated. In the dual conjugate mode all the stars are corrected and the degree of correction is fairly uniform as expected from the symmetrical star geometry. Clearly from these results we can see that the system is displaying MCAO behavior, however the magnitude of the correction is relatively small. For comparison, the number for the sum of the spot motions for a flat wavefront is close to zero, and therefore we have not yet demonstrated a clear improvement in the spot quality.
6. Conclusions and lessons learnt
We have demonstrated a closed loop MCAO laboratory system. We have demonstrated that the system can self-correct mirror pokes, correct Zernike modes, and show correction of Kolmogorov turbulence. However we have yet to demonstrate good quality improvements on the science camera. The reasons for this are two-fold:
1. Our standard least squares control method assumes linearity, whereas in practice the influence function on one of the LC actuators depends on its neighbors. This non-linearity needs to be accounted for. One could argue that this is a function only of this type of LC, and is not representative of deformable mirrors in general.
2. Any improvements in image quality are very easily masked by static aberrations in the system. Even though we can quite easily correct the image from one guide star using simplexing, it is difficult to correct all the stars simultaneously.
The work in progress concerns developing and improving the control algorithms and refining the control matrix filtering to optimize stability of the loop. Improvements also need to be made on the static aberrations before the full system utility can be realized. Our initial general conclusions from working with the system are that (1) the multiconjugate nature of the control system has been reasonably easy to implement and (2) the problem with MCAO has been in ensuring high optical quality within the system. The problem with AO in general is that perversely it generally places very strict optical tolerances on the system design. With single conjugate AO, one only needs to worry about a very narrow field of view, but with a larger FOV the problems become compounded.
Fig. 7. Closed loop results using the full MCAO system. The data (coordinate) consists of the sum of the spot displacements for each of the guide stars (represented in various colors) from the wavefront sensor as a measure of the degree of correction. The ordinate represents the iteration number in closed loop. The plots show the results achieved in single conjugate mode (left), and in dual conjugate mode (right). The turbulence had a strength of D/r0=16 on the upper layer only. The orange curve is for the central guide star, which was used for guiding in single conjugate mode. It can be seen that in this star is partially corrected whilst the spot motion for the other stars actually increases. In dual conjugate mode (right) the spot displacement for all the stars decreases.
Acknowledgments
This work was supported by the UK Particle Physics and Astronomy Research Council. The modal wavefront correctors were designed and constructed by Alexander Naumov (Physical Optics Corporation, USA), Svetlana Kotova and her team (Samara State University, Russia), Igor Guralnik and his team (P.N. Lebedev Institute, Samara Branch, Russia) and Mikail Loktev and Gleb Vdovin (Delft University of Technology, The Netherlands).
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