Combining low cost with high speed, dual-frequency liquid-crystal wavefront correctors widen the range of applications for adaptive optics.
Michael H. Anderson
Adaptive optics is a maturing science and has proven its usefulness in numerous laboratory and field demonstrations. Currently, its leading application is imaging through the atmosphere for satellite monitoring and for astronomy. The high cost of traditional wavefront-correction systems has limited this technology to well-funded research labs. New advances in liquid-crystal spatial light modulators (SLMs) promise to make this technology affordable and open up new applications.
Traditional adaptive-optics systems for astronomical imaging command astronomical prices. These systems use expensive deformable mirrors with hundreds of piezo-actuated elements priced as high as $2000 per actuator. While the performance of these systems is excellent, their high price impedes the development of industrial and medical applications. In contrast to deformable mirrors, the cost per actuator of liquid-crystal SLMs decreases as the number of actuators increases.1 Lower-cost wavefront sensors are already available from many manufacturers. Liquid-crystal SLMs together with available wavefront sensors could provide economical wavefront-correction systems.
The core of an adaptive-optics system consists of a wavefront sensor and a wavefront corrector. The Shack-Hartmann sensor is the most common method of wavefront sensing. In such a sensor, light from a point source located in the field of view of the image is imaged through an array of microlenses. The local wavefront tilt over each lenslet imposes a displacement of the focal spot away from the optical axis, from which an error signal can be calculated. In a closed-loop system the wavefront corrector drives the error signal to zero.
FIGURE 1. Full-cycle response time of a test cell filled with dual-frequency liquid crystal illustrates its speed. The upper trace is the transmission of the cell through crossed polarizers at 633 nm. The lower trace is the driving waveform. The figure shows three full waves of stroke (at 633 nm) in a cycle time of about 3.75 ms. The amplitude of the driving waveform is 100 Vrms. A standard nematic liquid crystal would require several hundred milliseconds to complete a cycle of this magnitude.
Atmospheric adaptive-optics systems must operate with closed-loop bandwidths of at least 50 Hz when the seeing conditions are good.1 Recent developments have resulted in a significant advance in the temporal response of nematic liquid crystals, making them a viable technology for wavefront correction.
Improvements in temporal response
Nematic liquid-crystal optics are formed by forcing the rod-shaped molecules to align in a common direction within a thin film bound by glass substrates. The liquid-crystal layer is typically several to tens of microns thick. The molecules can be rotated out of the plane of the optic by applying an electric field orthogonal to the layer via transparent conducting electrodes. Although the temporal response of the molecule to an applied field can be submillisecond for typical electric fields, the relaxation time is slower because the acting nearest neighbor and Van der Waals forces are weak. Hence the temporal response is dominated by a slow relaxation time.
Dual-frequency liquid crystals have been considered by the display industry.2,3 However, they are unsuitable for displays because of complicated drive signals and temperature sensitivity. For precision optics these are not significant disadvantages; devices can be temperature stabilized, and a higher degree of electronic complexity is tolerable.
Dual-frequency liquid crystals are characterized by an electrical polarizability that becomes stronger along the short axis of the molecule when the frequency of the applied field crosses a threshold value. Typically, this value is several kilohertz. Consequently, the molecules of dual-frequency liquid crystals can be driven both perpendicular and parallel to the plane of the optic by switching the frequency of the driving field. Weak restoring forces become unimportant.
FIGURE 2. Pixels in a dual-frequency liquid-crystal SLM made by Meadowlark Optics are laid out in a hexagonal array (top). This SLM was incorporated into a full adaptive-optic system tested at the Air Force Research Laboratory in Albuquerque, NM. Preliminary benchtop tests were performed on a collimated light source aberrated with a local heat source and a fan. Without adaptive correction, the image was degraded due to air turbulence (bottom left). With correction, aberrations were reduced (bottom right). The Strehl ratio improved from 8% to 34% with adaptive correction and a closed loop of 20-Hz bandwidth. A 50-Hz closed-loop bandwidth is possible with improvements in the frame download time.
A dual-frequency liquid crystal can be cycled at high speed (see Fig. 1). The time rate of change for the dual-frequency material remains relatively constant in time. In contrast, a standard nematic liquid crystal requires hundreds of milliseconds to complete the three-wave cycle. High-speed operation of dual-frequency liquid crystals requires strong driving fields. If the timing of the field duration is not controlled accurately, the optical phase delay (OPD) will not be driven past the desired value. In fact, under high driving fields, the field determines the time rate of change of the OPD. The standard driving techniques for nematic liquid crystals use the driving field to control the steady-state value of the OPD. This difference has significant consequences for the design of the feedback loop.
Meadowlark Optics has designed and built a liquid-crystal SLM using dual-frequency liquid crystals for a wavefront correction system at the Air Force Research Laboratory (Albuquerque, NM). The temperature-controlled optical head is patterned to form 127 hexagonal pixels 1 mm in size (see Fig. 2).
In astronomical imaging, light loss is of paramount concern, necessitating a polarization-insensitive wavefront corrector. Both transmissive and reflective liquid-crystal SLMs can be made polarization independent. The reflective design was chosen because it offers advantages for dual-frequency addressing.
Polarization-insensitive transmissive designs use two liquid-crystal layers with orthogonal molecular alignment, with each layer operating on an orthogonal polarization component. Unfortunately, this requires the use of twice the number of control lines. Additionally, in the dual-frequency driving scheme, errors in the OPD of a pixel accumulate in the manner of a random walk unless the OPD is under direct feedback control. A dual-layer transmissive design requires a wavefront sensor for each polarization component, increasing the complexity of the system.
The reflective design uses a true zero-order quarter-wave retarder placed between the liquid-crystal layer and a reflector.4 The quarter-wave layer in double pass acts as a half-wave retarder and rotates each polarization component of the outgoing wave by 90°. Hence, the extraordinary ray and the ordinary ray are interchanged and the device becomes polarization independent. The number of leads is half that required for the transmissive design, and each polarization component is treated identically. Kelly and Love showed that a true zero-order quarter-wave layer provided acceptable performance over typical observing bandwidths.5 A polymer retarder is the only suitable quarter-wave material due to its ability to be manufactured as a thin, true-zero-order quarter-wave retarder. A true-zero-order retarder also offers the advantage of a significantly improved field of view.
Nonastronomical applications of adaptive optics frequently require higher amplitudes of aberration correction. There is a relationship between the number of pixels and the amplitude of aberration that can be corrected. For near-diffraction-limited performance, there should be at least six pixels per wave of stroke. For example, a hexagonal array with 1-mm pixels and a 12-pixel span across the diameter can safely correct two waves of tilt. The correctable amplitude drops for higher-order aberrations.
Routing leads under reflective pixels on a multilayered glass backplane allows devices with 400-2000 direct-drive pixels. This structure allows the use of dual-frequency liquid crystals with their more-complicated drive scheme. Applications include point-to-point laser communications through turbulent media such as moving aircraft or between buildings. Other applications work in reverse where light must be delivered to a target. Laser welding through a plume of hot gases and endoscopic laser surgery are two such examples.
Slower applications could be based on a reflective silicon backplane with 64,000 pixels and higher. An excellent example of such an application is imaging of the human retina. When the iris is dilated during retinal examinations, aberrations of the lens and cornea predominate. Recently, a system operating with a deformable mirror has obtained spectacular images of individual photoreceptors.6,7 Reasonably priced retinal imaging systems should find use in early diagnosis of retinal disease. Interestingly, the subjects looking back out through the system report exceptional visual clarity. This suggests the ability to fabricate corrective lenses that compensate for aberrations beyond astigmatism.
As affordable adaptive-optics systems move out of the laboratory and real-life demonstrations of their utility become more common, a host of new applications will emerge. No longer will only expensive telescopes and government-funded optical systems be wearing state-of-the-art spectacles.
- G. D. Love, Appl. Opt. 36(7), 1517 (1 March,1997); see also "Adaptive Wavefront Shaping with Liquid Crystals," Optics & Photonics News, Oct. 1995.
- H. K. Bucher, R. T. Klingbiel, and J. P. VanMeter, Appl. Phys. Lett. 25, 186 (1974).
- M. Schadt, Mol. Cryst. Liq. Cryst. 89, 77 (1982).
- G. D. Love, Appl. Opt. 32, 2222 (1993).
- Thu-Lan Kelly and G. D. Love, Appl. Opt. 38(10), 1986 (1 April, 1999).
- J. Liang and D. R. Williams, J. Opt. Soc. Am. A 14, 2873 (1997).
- J. Liang, D. R. Williams, and D. Miller, J. Opt. Soc. Am. A 14, 2884 (1997)
MICHAEL H. ANDERSON is vice president of research and development at Meadowlark Optics, POB 1000, 5964 Iris Pkwy., Frederick, CO 80530; e-mail: firstname.lastname@example.org.