5. Wavefront Correcting Technology

Wavefront correction has been performed by different techniques, depending on the source of aberrations, the field of application, and the instrumentation available. The correctors fall within two broad categories: (1) piston segmented devices [e.g., piston-tip-tilt, liquid crystal spatial light modulators (LC-SLM) and segmented mirrors] and (2) continuous surface mirrors (e.g., including deformable mirrors, membrane micro-mirrors, and bimorphs). The correction methods range from phase conjugation and computer-generated holograms to deformable mirrors, which nowadays are the most popular devices for adaptive optics.

Wavefront phase errors can be corrected by introducing an optical path difference in the beam by either varying the refractive index of the phase corrector (refractive devices) or by introducing a variable geometrical path difference (reflective devices i.e., deformable mirrors). The most common refractive devices use liquid crystals, the refractive index of which can be electrically controlled. Liquid crystal (LC) molecules are elongated and are polarised such that intermolecular forces between the crystals keep them relatively aligned. The basic form of a LC device consists of a layer of LC sandwiched between two pieces of optical quality glass. The orientation of the LCs is fixed by cutting microscopic grooves on the inner surfaces of the glass plates; the LCs line up in the direction of the grooves. Transparent electrodes are deposited on the glass surfaces, and they may be as small as 10 μm. LC devices can therefore provide many thousands of correction elements. These devices offer piston-like correction since there is practically no continuity requirement for the refractive index between pixels. They come in different varieties: (1) ferroelectric devices can produce phase changes of either 0 or pi radians and can operate at high frequencies; (2) nematic devices can provide continuous phase changes but are slower than ferroelectric devices. The first use of LC displays (LCDs) for dynamic ocular wavefront correction was by Prieto et al.[55]. More recently, ocular wavefront correction has been demonstrated using Liquid Crystal on Silicon devices (LCoS) [56]. In this device the LC is deposited on an array of silicon pixels and operated in reflective mode. The voltage applied to the pixels controls the refractive index, and the advantage is that higher speeds can be obtained. LC devices require the use of linearly polarised light [56]; Kong et al.[57], however, recently described an open loop ophthalmic AO system in which the uncorrected polarisation component is used by the wavefront sensor. A limitation of LC devices is the relatively limited dynamic range when using the device to correct ocular aberrations.

Deformable mirrors (DM) consist of a reflective faceplate acted on by a set of actuators. The faceplate can be continuous or segmented. While it is easier to manufacture segmented mirrors with a very large number of actuators, they have the disadvantage that the gaps between segments introduce greater spurious effects in the image (due to diffraction) than continuous mirrors. Many different types of actuators have been used and most of them have been applied to ocular AO systems [58]. The most common types of actuators are piezoelectric, electrostatic or magnetic.

In piezoelectric materials, an applied electric field gives rise to a change in shape. The most commonly used material is lead zirconate titanate (PZT). These mirrors were originally developed for use in astronomical AO [59] and were used in the first ophthalmic AO system [20]. They can be made to feature quite a large stroke, a linear actuation-to-voltage response, and low amounts of hysteresis. The typical size of a PZT actuator is 25 mm, so deformable mirrors using these actuators tend to be relatively large. Bimorph mirrors consist of two bonded piezoelectric ceramic wafers that are oppositely polarised parallel to their axis [60]. An array of electrodes is deposited between the wafers; applying a voltage to an electrode results in one wafer expanding locally and laterally while the other wafer contracts inducing a spherical bending. These mirrors are a natural choice for AO systems using a curvature wavefront sensor. However they can also be used with Shack-Hartmann (or any other) wavefront sensors, and were used in this way in an ocular AO system [61].

Electrostatic actuators are usually used in membrane-type mirrors or micromirrors [62]. Membrane mirrors consist of a reflective membrane which is deformed by means of electrostatic forces due to an array of electrodes placed a small distance behind the membrane. The local membrane curvature is proportional to the square of the signal voltage. The influence function of the actuators, i.e., the mirror shape when a single actuator has a voltage applied, is broader than those of other mirrors. They are very suitable for low-order correction, and the introduction of commercial models made low-cost adaptive optics possible for the first time. The stroke is limited by the fact that the actuators operate in ‘pull-only’ fashion in the usual configuration. Bonora and Poletto [63] introduced a ‘push-pull’ version having a transparent electrode in front of the mirror in order to extend the stroke. In another interesting development, Bonora et al.[64] proposed a “photocontrolled deformable mirror” (PCDM) in which a LCD is used to generate a light distribution on a photoconductive layer placed behind a membrane mirror. The control is therefore by light, and can be very high order or reduced to the order required. Electrostatic actuators are also applied in micromirrors (MEMS). In MEMS the electrodes do not act directly on the membrane, but rather on an intermediate membrane [65]. The mirror is attached to this membrane through posts, and the result is to localise the actuator influence functions. This can therefore provide higher order correction. Currently, there are MEMS by Boston Micromachines (Cambridge, MA, USA) with 32, 140 and 1020 actuators and the actuator size ranges from 300 to 500 μm and the corresponding stroke is from 1.5 to 5.5 μm or by IRIS AO, Inc. (Berkeley, CA, USA), with 111 to 489 actuators with inscribed apertures from 3.5 to 7.7 mm respectively and stroke from 5 to 8 μm.

Magnetic mirrors usually use voice coils to act on small magnets attached to the rear of a membrane mirror. These devices are therefore controlled by current rather than voltage. The main advantage is that a large stroke can be achieved, much larger than for other devices. A 52-Element device (Imagine Eyes, Orsay, France) was demonstrated in an ophthalmic AO system by Fernandez et al.[66] and more recently by Lombardo et al.[67]. The temporal response of this kind of mirror can be an issue, but it can be taken into account in the control system [68]. The ALPAO company (Montbonnot St. Martin, France) manufactures different versions of magnetic mirror having 37 to 277 actuators with actuator spacing of 1.5 or 2.5 mm and overall stroke up to 60 μm. They claim settling times of order 1 ms for their “hi-speed” range.

A novel magnetic fluid mirror is receiving attention [69]. In this device the surface of a magnetic fluid is coated with a reflective film and acted on by coils placed under the fluid volume. The deformation depends on the square of the magnetic field, but can be linearised by the addition of a strong, uniform magnetic field. The stroke can be large, and the response can be made fast by using high-viscosity ferro-fluids. However, these liquid mirrors must conserve volume which means that superposition of influence functions is not possible. This and the fact that they can evaporate are the main disadvantages of liquid mirrors. A liquid mirror which is electrostatically deformed has also been demonstrated recently [70].

The performance of wavefront correctors depends on a number of parameters, including the number and configuration of the actuators, the stroke, temporal response, linearity, hysteresis etc. Devaney et al.[71] compared eight different commercially available mirrors for correcting both ocular and atmospheric wave aberration. The sample included piezoelectric, membrane, bimorph and magnetic mirrors. Influence functions of all the mirrors were measured using interferometry. Wavefronts were simulated to have statistics corresponding to either ocular or atmospheric aberrations, with the correction achieved for each mirror determined by least-squares fitting the influence functions of each mirror to the wavefront. The number of mirror modes corrected and the size of the optical pupil projected on the actuator geometry were optimized for each device. In general, it was found that better correction can be obtained when there is a ring of actuators just outside the pupil. The optimal number of modes to correct depends on the mirror stroke and geometry. It was found that the mirrors with higher stroke (the magnetic and bimorph devices) should provide the best performance in terms of residual root-mean-square (RMS) wavefront error or Strehl ratio.