We present here results using two novel adaptive optic elements, an electro-static membrane mirror, and a dual frequency nematic liquid crystal. These devices have the advantage of low cost, low power consumption, and compact size. Possible applications of the devices are astronomical adaptive optics, laser beam control, laser cavity mode control, and real time holography. Field experiments were performed on the Air Force Research Laboratory, Directed Energy Directorate’s 3.67 meter AMOS telescope on Maui, Hawaii.
© 2002 Optical Society of America
Adaptive optics (AO) systems have been in operation for roughly 30 years. As the field matures increased numbers of possible applications are being discovered however their practical implementation has been greatly limited by the high cost, high power consumption, and size of traditional adaptive optics systems. Some of these applications are small portable astronomical AO systems, laser beam control, ophthalmology imaging, and laser communication systems.
Recently significant advances have been made in the development of micro-machined electro-mechanical systems (MEMS) based adaptive optics elements. In particular electrostatic membrane mirrors , and nematic liquid crystal based devices . These devices are small, light, consume low power, and have a cost that is an order of magnitude less than traditional adaptive optics. In addition the compute power of small inexpensive Pentium based computer systems has increased dramatically eliminating the need for custom real-time processing hardware to implement the control algorithms. The MEMS based AO systems cost is on the order of hundreds of dollars per actuator as opposed to thousands of dollars per actuator typical cost of conventional systems.
In this paper we present a proof-of-concept demonstration of these two devices for imaging bright low earth orbit (LEO) solar illuminated satellites through atmospheric turbulence, performed on the Air Force Research Laboratory, Directed Energy Directorate’s 3.67 meter AEOS telescope on Haleakala Maui. The aperture was stopped done to 1.12 meters in order to match the number of actuators and dynamic range of the devices. High-resolution satellite imagery, aided by adaptive optics, is of interest both for military and commercial applications, as well as amateur observations. At present such imagery can only be obtained at a handful of fixed sites. With the advent of small low cost adaptive optics we envision a much larger network of fixed and mobile ship or truck based military, commercial, and amateur observing stations.
In a previous experiment the membrane mirror was demonstrated against bright stars using a 1 meter telescope . Closed loop Strehl ratios of about .1 were obtained. As will be shown the refined membrane mirror system, described here, produces considerably better results. Several groups have demonstrated a liquid crystal device for adaptive optics in the laboratory and over short paths of atmospheric turbulence [4–15], however we believe that this is the first time a dual frequency liquid crystal AO system has been successfully operated with any type of observation on an astronomical telescope. To our knowledge, this is the first demonstration of either device to improve images of LEO satellites.
2. Electro-static membrane mirror
Typical micro-machined membrane mirrors consist of a silicon chip mounted over a printed circuit board holder. The chip contains a silicon nitride membrane, which is coated with aluminum to form a mirror. An array of electrodes is etched onto the printed circuit board under the membrane. When an electrode is energized, an electrostatic force is produced on the portion of the membrane above the electrode, causing the mirror surface to deform. A schematic of such a device is shown in Fig. 1.
The electrode pattern for the OKO Technologies 37 actuator device  is shown in Fig. 2. The electrodes are arranged in a hexagonal pattern. The diameter of the membrane is 15 mm, with the membrane fixed to the edges of a circular aperture. The center-to-center spacing of the electrodes is 1.75 mm. This gives the center-to-center separation of the two end electrodes, along a radial, as 10.5 mm, or 70% of the full 15 mm aperture. Since the membrane is fixed along the edges of its circular aperture, it cannot be controlled to an arbitrary shape near the edge. Thus we only control its shape over the central 70% of the membrane, which lies above the electrode array.
Figure 2 also shows the arrangement of the Shack-Hartmann lenslets used in our wave-front sensor, with respect to the membrane mirror electrodes. A square array Shack-Hartmann wave-front sensor was used rather than a hexagonal because the square geometry matched that of the pupil plane detector array. The lenslet array consisted of 600 μm width lenslets in a square array, with 72 mm focal lengths.
The wave-front sensor camera was a 64×64 pixel Lincoln Laboratory 12 bit camera capable of running up to 1300 frames per second. We ran it with an exposure time of 1.0 milli-second. This allowed for an open loop bandwidth of up to 1 kHz for the wave-front control system.
The focal plane camera used to record open and closed loop focal plane data was a 256×256 12-bit Dalsa camera model CA-2048M-014J. It was run with between 10 and 25 milli-second exposures. Short exposure images were collected to allow the possibility of implementing subsequent post-processing algorithms to further improve image quality.
Imaging Technology frame grabbers were used with both cameras. Two twenty-channel D/A converters were used to drive the high voltage amplifiers that control the electro-static actuators of the mirror. A fast photographic enlarger lens was used to re-image the Shack-Hartmann spots onto the wave-front sensor detector array.
In previous papers [3,16] we described analysis of the OKO mirror and open and closed loop control for disturbance generation, and aberration correction. The equation for a stretched membrane over a circular aperture with fixed edges was solved using an approach from Claflin and Bareket . From this solution we were able to generate theoretical influence functions. Using the influence functions, and matrix inversion techniques we developed a multi-input multi-output (MIMO) control law to control the mirror using measurements from the wave-front sensor. The closed loop response was tested against static and dynamic aberrations, and a 3 dB closed loop bandwidth of 80 Hz was measured using a 500 MHz Pentium computer to implement the control algorithm. The bandwidth was primarily limited by the time required to read out the wave-front sensor detector array and make the control calculations.
3. Dual frequency liquid crystal device
The use of nematic liquid crystal devices for wave-front shaping and control has been investigated for some time [4–15,18–24]. One of the first engineering studies for the use of the device in astronomical AO systems was performed by Bonaccini, Grusa, Esposito, et. al. [19,20]. The main technological push behind the devices has been for the display industry, which has invested a large amount of money in developing materials, techniques, and hardware that can be modified for optical wave-front control applications. The main drawbacks in these materials are polarization dependence and low temporal bandwidth. Using a polarization rotator and a dual frequency material these two problems can be solved [19–22].
Liquid crystal is a material that has both properties of liquid and a crystal. It is a uniaxial birefringent material with two axes having a fast (or ordinary) dielectric constant ε0 and index n0, and a slow (or extraordinary) crystal axis having dielectric constant εe and index ne. As illustrated in Fig. 3, the phase of light with polarization oriented in the direction of the slow axis will be retarded with respect to that with polarization along the fast axis.
An interesting property of the nematic liquid crystal is that when an alternating electric field is produced across the material the crystal axis will rotate so as to align itself with the field, reducing the phase retardance introduce by the slow axis. This action happens very quickly. When the field is removed the material slowly relaxes back to its original position. When the crystal axis (slow axis) rotates, it is no longer perpendicular to the direction of light propagation. In this way the strength of the alternating electric field can be used to modulate the phase retardance of the polarization along the slow axis according to the following two equations:
In order to both reduce and increase the phase retardance rapidly, a dual frequency material is used. In this material the dielectric anisotropy, Δε=εe-εo, changes sign above a certain frequency of the applied electric field. At low frequencies the crystal axis rotates to align itself parallel to the field, but at high frequencies the axis rapidly rotates to align perpendicular to the field. Thus the slow axis can be rapidly rotated in both directions to rapidly increase or decrease the phase retardance by changing the frequency of the applied electric field.
Several experiments have been performed in order to understand the behavior of the liquid crystal material . The experiments were then used to validate a theoretical model [11,18] for the static and dynamic response based on approximate solutions to the Erickson-Leslie equation [18,23]:
which relates the crystal axis rotation θ to the applied electric field E. The terms K11, K33, α2, α3, γ1 and I are parameters of the liquid crystal, which was LC-1001 from Niopik laboratories in Moscow, Russia. The model was then used in the design of our control algorithm.
Figure 4 shows a diagram of a multi-segment device produced by Meadowlark optics using the dual frequency liquid crystal material. The arrangement of the Shack-Hartmann lenslets in the wave-front sensor are shown overlaid on the liquid crystal segments. The diagram shows that there is a geometric mismatch between the liquid crystal segments and the wave-front sensor lenslets. This mismatch is aggravated by the fact that wave-front sensor measures tilts, while the device is piston only. In fact some of the actuators are unobservable. To over come this problem we use a spatial filtering approach, which is outlined in the references [10,24].
We have successfully implemented this device in a MIMO closed loop feedback control system correct for turbulence induced phase aberrations. Figure 5 shows a block diagram of the control algorithm. An integral (or for digital systems a summation) controller is one of the most common and straightforward approaches to feedback control. The measured error signals are fed into an integrator the output of which is used to drive the device under control. However the integral controller by itself does not take advantage of the dual frequency effect.
The underlying idea of incorporating a dual frequency pulse control with the integral control in order to increase bandwidth comes from Dorezyuk, Naumov, and Shmal’gauzen . At each time step a pulse is generated to rapidly slew the phase retardance. A low frequency pulse is used to decrease the phase retardance, while a high frequency pulse increases the phase retardance. The pulse width is always 780 μsec long, which is the minimum pulse width we can generate using the drive electronics. A detailed study was performed as described in reference  to determine the response of the dual frequency material, to both high frequency and low frequency pulses. Based on this study a non-linear proportional only control algorithm was developed to generate the pulses. After the short pulse is generated a conventional integral controller is used to generate a low frequency sustaining voltage between pulses.
Both the proportional and integral gains must be set to a value that insures control system stability. We have found that the liquid crystal is extremely sensitive to temperature variations. Thus although we had a set of nominal gains, the exact settings were determined experimentally. While observing an unresolved object the gains were increased until the system just became unstable. Then the gains were reduced by 20 %.
Using only an integral controller with low frequency drive voltage we could obtain a 5 Hz closed loop bandwidth . Adding the dual frequency pulse control we increased the 3dB bandwidth to 40 Hz . This is still lower than that of the membrane mirror primarily due to limitations of the liquid crystal drive electronics. A detailed description of the control algorithm derivation, as well as laboratory results and measured disturbance rejection is given in the references [8–10].
An inherent limitation of a liquid crystal based AO system is the chromatic dispersion of the liquid crystal material. This limits the optical bandwidth to no more than several hundred nano-meters. Conventional astronomical AO systems, with reflective optics, often use a band in the visible to drive the wave-front sensor while the science camera works in the infrared, near 2.2 μm. The device described here could not work in such a situation, however our primary interest is low earth orbit solar illuminated satellites, which are often bright enough that we can divide the same near infra-red (NIR) optical band between the wave-front sensor and the focal plane camera.
4. Field System
The two devices were next repackaged to fit on a single breadboard as shown in Fig. 6. A pickoff mirror on a kinematic mount was used to direct the incoming beam to one or the other devices. Optical filters were place in the system to pass light from 700–950 nm. A 50/50 beam splitter cube was used to split the light between the wave-front sensor and the focal plane camera. The magnification was such that each lenslet in the Shack-Hartmann wave-front sensor had an effective diameter of 16 cm referenced to the telescope entrance pupil.
A separate tip-tilt mirror, shown in the lower center of Fig. 6, was used to off-load tip-tilt correction from the AO devices. This is particularly important with MEMS devices due to their limited dynamic range. A stop was placed at a pupil image of the telescope aperture so that only light from a 1.12 meter diameter segment was used. The segment was located off of the optical axis so that the central obscuration was not included in the segment and could not adversely affect the control algorithms.
The breadboard was mounted on a visiting experiment table in one the Coude rooms at the AEOS telescope as shown in Fig. 7.
4.1 Estimated Corrections
The compensated image Strehl ratio of an adaptive optics system can be estimated by ,
where σ2 is the residual wave-front variance over the pupil and to first order is made up of contributions from the fitting error, temporal bandwidth limitations, and wave-front sensor error,
The fitting error arises from the non-zero separation of the corrector actuators and can be given by:
where rs is the actuator spacing referenced to the telescope entrance pupil, and α is a factor related to the geometry of the adaptive device. The value of α is usually determined experimentally. Values of 1.26 for a piston only device such as the multi-segment liquid crystal and .4 for a smooth modal influence function have been reported .
The temporal error results from the limited temporal bandwidth of the control system and can be given by:
where fg is the Greenwood frequency and f3dB is the 3dB bandwidth of the AO control system.
The error associated with the Shack-Hartmann wave-front sensor is primarily due to the limitations on accuracy of centroid determination under each Shack-Hartmann sub-aperture lenslet. Assuming the target is unresolved by each lenslet, with the resulting spot near the center of a quad array of detectors, it can be given by :
where snr is the radiometric signal to noise ratio of the wave-front sensor detector.
We can use the previous set of equations to estimate expected performance of the AO system using the two devices. The following table gives the assumed parameters for observations of a bright star.
We were fortunate to have light winds for most of our experiment period. Typical turbulence parameters were r0 between 15 and 20 cm and Greenwood frequency between 30 and 40 Hz. at our optical band of 700–950 nm. Substituting all parameters into eqns. (4)–(8) gives the following estimates for Strehl ratios:
for the membrane mirror, and
for the liquid crystal device. The estimated liquid crystal Strehl is less than that of the membrane mirror because of the piston only nature of the device and the lower 3dB bandwidth.
4.2 Experimental Results
In this section we show experimental results from a series of open and closed loop measurements made on stars and extended objects, using the two devices. A series of data were first collected using the membrane mirror leg of the instrument shown in Fig. 6. The pick-off mirror was then rotated to operate the liquid crystal leg.
Figure 8 and 9 show open and closed loop images of bright stars using the membrane mirror and liquid crystal device respectively. These measurements were made in order to estimate system performance and compare to calculated estimates as just outlined. Approximately two seconds of data was averaged to form the long exposure images. The Strehl ratio was estimated by computing the ratio of the peak intensity in the images to what would be expected if the images were diffraction limited.
The closed loop Strehl ratio estimated from the membrane mirror data was .35 compared to a calculated value of .49, while for the liquid crystal device the closed loop estimate was .18 compared to a calculated value of .23. The discrepancies are most likely due to unaccounted for wave-front aberrations in the optics system.
We next consider observations of extended targets. The primary goal of these experiments was do demonstrate improved imagery of LEO satellites. We collected images of two well-known objects, Seasat using the membrane mirror, and the International Space Station (ISS) using the liquid crystal device.
It is well known that the performance of a Shack-Hartmann wave-front sensor degrades when the extended object is resolved by individual sensor lenslets. This degradation occurs for two reasons. First the error in the centroid estimates increases approximately proportional to the angular diameter of the resolved object . More importantly energy from the image formed by one lenslet can spill over into the image formed by adjacent lenslets causing cross talk in the centroid estimates.
The system magnifications were such that the diffraction limited angular resolution of each Shack-Hartmann lenslet was 5 μrad, while the field of view of the detector sub-array allocated to each lenslet was 30 μrad. Both targets were resolved by the wave-front sensor and we had spill over problems with the ISS, which was much larger than 30 μrad. However in both cases the wave-front sensor locked onto bright unresolved glints from the target. These glints are apparent near the center of Fig. 10b and 11b. Thus even though the targets were large, the wave-front sensor behaved almost as if they were unresolved.
The movie associated with Fig. 10 b) begins with open loop images and proceeds as the membrane mirror control loop is closed. In the movie associated with Fig. 11 b) the SLM control loop is initially closed. During the last 20% of the movie, the control loop is opened and closed several times.
In summary we have demonstrated adaptive optic systems based around two novel adaptive optic devices: an electro-static membrane mirror and multi-segment dual frequency liquid crystal device. Past work has concentrated on laboratory measurement. Experiments described in this paper were performed using the devices in conjunction with the Air Force Research Laboratory, Directed Energy Directorate’s AOES telescope in Maui, Hawaii, both with bright stars and LEO sunlit satellites observed in terminator. We believe that this is the first time either device has been used with LEO observations and the first time a dual frequency liquid crystal device has been demonstrated with any type of observation on an astronomical telescope. The advantages of these devices over conventional adaptive devices are lower cost, smaller size, and decreased power consumption.
The system described here was meant to demonstrate the devices for this specific application. System modification would be required, particularly with the liquid crystal device, to use the devices for general astronomical applications.
The closed loop 3dB bandwidth of the membrane mirror device was about 80 Hz, while that of the liquid crystal was about 40 Hz. During this proof of concept experiment we were fortunate to have moderate winds, so the Greenwood frequency was often below 40 Hz with r0 in excess of 15 cm. Performance calculations were compared to observations of bright stars. These indicate that there is some room for improvement particularly with the membrane mirror.
Due to the limited number of actuators we only used a 1.12 meter diameter segment of the AEOS 3.67 meter aperture. Even so we were still in the low order correction regime for most atmospheric conditions. For this reason we collected short exposure focal plane images to allow the possibility of improvement via post-processing algorithms.
The performance of a Shack-Hartman wave-front sensor degrades as extended objects are resolved by the lenslets of the sensor. In this case the sensor will tend to lock onto a high-resolution feature on the target. In the case of the two targets shown the sensor locked onto bright glints.
The membrane mirror is very straightforward to control, however there are practical limitations to the number of actuators which may be implemented in the device. The dual frequency liquid crystal device is much more complicated to control and provides piston-only correction, however it has the potential of fabrication with large numbers of elements.
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