Adaptive Optics

Acronym: AO

Definition: a class of techniques where wavefront distortions are actively compensated

More general term: optics

German: adaptive Optik

Categories: general optics, methods

Author: Dr. Rüdiger Paschotta

How to cite the article; suggest additional literature

URL: https://www.rp-photonics.com/adaptive_optics.html

Adaptive optics is a technological solution to a fundamental problem in optical science: the distortion (aberration) of wavefronts. These are typically caused by random inhomogeneities (spatial variations) in optical systems or in the atmosphere; in the latter case, the distortions can also be time-dependent because of movement of air (turbulence). Adaptive optics seeks to rectify that problem by correcting these distortions, often in real-time. Such techniques are applied in advanced imaging methods to provide clearer, sharper images, obtaining the native resolution of the instrument, as is limited e.g. by diffraction). Also, there are some other application areas, e.g. where optimum beam focusing is required.

The development and implementation of adaptive optics involve a complex interplay of physics, engineering, and computational algorithms. This multidisciplinary technology relies on advances in fields like optics, control systems, signal processing, and more. It is a dynamic and vibrant field that continues to advance and find new applications.

The Principle of Adaptive Optics

Adaptive optics operates on the principle of measuring wavefront distortions and compensating for these distortions to deliver a corrected optical wavefront. While the optical setups using that principle can differ in many respects, a system typically contains the following key components:

• a wavefront sensor,
• a wavefront correction device, and
• a control system, forming the drive signals of the correction device from the wavefront sensor readings.

These components may be combined into an open-loop or closed-loop control system. Here, an open loop means that the sensor detects the uncorrected wavefronts, i.e., cannot “see” how well the correction works. A closed loop means that the sensor detects the corrected wavefronts, thus having the chance to eventually achieve near-perfect compensation despite adverse aspects such as, for example, a possible nonlinearity of the phase corrector system. However, one then needs to take care that dynamic instabilities are avoided. Often, one then applies an integrating control system, exhibiting a response function which decreases substantially with increasing frequency.

Note also that there are also sensorless imaging systems, i.e., not requiring a wavefront sensor. Here, the required wavefront correction is obtained by varying the effects of the correction device (with some set of settings) on the obtained images themselves – using some preexisting knowledge of the image, e.g. that it should contain well localized features.

The mentioned components are explained in the following.

1. Wavefront Sensors

Wavefront sensors are devices that measure the shape of an optical wavefront. The most commonly used type of wavefront sensor in adaptive optics systems is the Shack–Hartmann wavefront sensor. This sensor consists of an array of microlenses which focus the incoming light onto a detector plane (a focal plane array). Each microlens creates a focal spot on the detector, and the local wavefront direction can be inferred from the position of such a spot, i.e., from the deviation of its position from the nominal position.

Other types of wavefront sensors, in particular pyramid wavefront sensors, are also used in certain applications. Pyramid sensors offer advantages in terms of sensitivity and dynamic range, making them suitable for challenging applications with strong wavefront distortion.

A vital detail is the number of sensor elements, limiting the number of degrees of freedom. Obviously, that number must at least be the number of aberration modes to be corrected (see below), and is often actually chosen even a few times higher than that.

2. Wavefront Corrector

A central component of an adaptive optics system is the wavefront correction device, which physically alters the optical wavefront to counteract the measured distortions. It is essentially a phase modulator with some spatial resolution – a spatial light modulator.

The most common type of wavefront corrector is the deformable mirror (Figure 2). Typically, such a mirror has a substantial number of actuators which can deform the surfaces in various ways such that a wide range of wavefront distortions can be neutralized. Deformable mirrors used in adaptive optics systems come in various forms, including continuous-faceplate deformable mirrors, segmented mirrors, and micro-electromechanical system (MEMS) mirrors. Each of these types has its specific advantages and limitations, and the choice of deformable mirror depends on the specific requirements of the application.

The phase excursions for the reflected light are directly related to spatial movements according to <$\delta \varphi = 2 \: k \: \delta z = (4\pi / \lambda) \: \delta z$> (where the factor 2 results from the double pass of light). The included wavelength dependence is ideal if the aberrations are caused by refractive index variations with no wavelength dependence – which is at least a reasonable approximation, for example, in the case of atmospheric turbulence. A hypothetical spatial light modulator producing wavelength-independent phase changes would be substantially less suitable for various applications.

Another variant are deformable phase plates which can be operated in transmission rather than in reflection. They contain a deformable membrane above a liquid, allowing one to modulate the optical path length in the liquid:

There are also liquid crystal spatial light modulators (LCSLM), which are based on liquid crystal modulator technology as otherwise often used in displays. Note, however, that in this case the wavelength dependence of achieved phase changes may be disturbing, and that such modulators normally operate with polarized light. On the other hand, they offer high spatial resolution, and some of them operate in transmission rather than reflection, which may be advantageous. However, many modulators are based on liquid crystal on silicon (LCOS) technology, which is also reflective.

For application in an AO system, various details of the correction device need to be considered. In particular:

• Normally, each actuator of a deformable mirror primarily controls the height elevation of the mirror surface in its immediate surroundings, but also has some effect on the surface shape further away. Similar phenomena can occur to some extent in other kinds of correction devices.
• The achievable optical phase changes must be large enough. (Some applications require particularly large phase excursions.)
• For high-precision correction, one may need to carefully characterize the detailed response of each input channel, as e.g. different actuators of a deformable mirror may have different effects due to random variations of imperfections caused by mechanical coupling. It may be required even to regularly apply a certain calibration procedure, effectively measuring the influence functions of all correction channels.
• For high-speed correction, not only the limited actuator bandwidth needs to be considered, but also the complete frequency-dependent amplitude and phase response.
• Of course, the effects of a correction device strongly depend on where exactly it is placed in an optical system. See below for further explanations.

3. Control Systems

The control system in an adaptive optics setup is responsible for generating the control signals for the correction device based on the wavefront measurements obtained by the wavefront sensor. Ideally, it should provide accurate compensation while fully exploiting the offered speed of the correction device. For various reasons, that task is not trivial:

• One needs to somehow map some number of sensor readings to some number of actuators (e.g., in a deformable mirror), taking account the known effect of each actuator. This is often far from a simple one-to-one mapping, since the actuators may only have somewhat different responses but also affect overlapping regions of the wavefronts. A large control matrix (which may be sparse, depending on the situation) is needed.
• For fully exploiting the bandwidth of the correction device, one should also achieve the optimum temporal shape of the correction signals, considering the full frequency-dependent amplitude and phase response. (Note that the bandwidth limitations of the wavefront sensor are normally much less relevant.)
• In cases where the limits of the travel range of actuators may occasionally be reached, one may need to optimize the behavior of the control system for such situations. Also, one should properly deal with other possible kinds of nonlinearities.

For these reasons, the design of a control system often involves the use of sophisticated algorithms and the use of high-speed signal processors to achieve rapid and accurate correction of wavefront distortions. Modern digital technology provides powerful components for such systems, which can also be fine-tuned during operation, such as to reach e.g. maximum control speed and accuracy in a closed-loop system while avoiding any dynamic instabilities.

There are various common control algorithms used in adaptive optics systems, including integrator-based controllers, adaptive filters, and model-based controllers. The choice of control algorithm depends on the specific requirements of the application, such as the degree of wavefront distortion, the desired correction speed, and the constraints of the correction device.

Some Technical Details

Characterization of Optical Aberrations

A simple measure for the strength of aberrations is the r.m.s. (root-mean-square) deviation of optical path length. That normally needs to be compensated to level well below <$\lambda / 10$>.

In some cases, the peak-to-value aberrations are given, which are more directly linked to the required travel range (dynamical range) of a wavefront corrector, although they are in a way less representative than the r.m.s. deviation.

Such single quantities carry very little information; they do not tell anything about the spatial shape, how fast spatially the aberrations vary, etc. Therefore, more sophisticated ways have been developed to specify how strong aberrations a system has, which need to be compensated. The most common form is a decomposition into aberration modes based on Zernike polynomials. Here, the wavefront distortion is characterized by a function <$W(\rho, \varphi)$> which specifies the deviation of optical path length as a function of the radial coordinate <$\rho$> (normalized to the pupil radius) and the azimuthal angle <$\varphi$>. That is then considered as a linear superposition of Zernike polynomials <$Z_n^m(\rho, \varphi)$> with amplitude coefficients <$a_n^m$>:

$$W(\rho, \varphi) = \sum_{n = 0}^{\infty} \sum_{m = -n}^{+n} a_n^m \: Z_n^m(\rho, \varphi)$$

Different terms in that equation correspond to different types (“modes”) of aberrations like piston, tilt, defocus, astigmatism or coma, as explained in the article on optical aberrations.

In adaptive optics, one may design a system such that it directly deals with Zernike modes (modal control), compensating those up to some maximum order. Alternatively, one may use the Zernike model of aberrations only for analysis, but not directly in the mentioned sense – for example, working based on spatial zones of the modulator (zonal control). Of course, that decision has a profound impact on the signal processing.

High-end applications, e.g. in astronomical telescopes, sometimes need hundreds or even thousands of Zernike terms to be compensated – which, of course, requires wavefront sensors and correctors with such large numbers of channels. Still, the r.m.s. deviations may be moderate, e.g. limited to a few microns. In retinal imaging, one deals with an order of magnitude stronger corrections, but requiring only a moderate number of Zernike terms (e.g. a couple of dozens of terms).

Correction Requirements

The requirements for wavefront correction can vary substantially between different application cases. The following aspects need to be considered:

• The required wavefront accuracy. This is normally of the order of <$\lambda / 10$>, although smaller values may still give somewhat better performance (with diminishing returns).
• The number of aberration modes (e.g., Zernike modes) is related to the required number of sensor elements and actuators of the wavefront corrector. With a large number of modes, one can compensate for even rather complicated kinds of distortions. A high number is normally required for a large telescope, for example.
• The required control bandwidth is another important parameter. While in some cases (microscopy) the aberrations may have hardly any time dependence, a control bandwidth of at least a couple of Hertz is required in ophthalmology, while telescopes benefit from a larger bandwidth of e.g. 50 Hz. Realized with an integrating control system, for example, that may require an update rate of the order of 1 kHz.

Placement of Wavefront Sensor and Correction Device

The following considerations are required essentially because optical distortions are not simply preserved along the optical path in the system, but rather evolve in a complicated way. In particular, phase distortions are eventually converted to intensity variations in the image plane – exactly the problem to be addressed with AO.

Typically, an adaptive optical system contains a single wavefront sensor and a single wavefront corrector; this is called single-conjugate adaptive optics (SCAO). The correct placement of those in the optical system is critical for reaching good performance; this can be understood based on Fourier optics. Generally, one will try to position both the wavefront sensor and the wavefront corrector in planes which are conjugate to that where the aberrations are largely generated because that gives the best chances to properly compensate for them. For a telescope, for example, one often (but not always) uses pupil-conjugate planes since atmospheric propagation largely generates phase changes in that plane, which result in intensity changes in the image plane (thus distorting the image). Trying to compensate for this with a phase modulator in the image plane could obviously not work. However, one also sometimes uses a deformable secondary mirror, which is unfortunately not in a pupil-conjugate plane.

In principle, even better performance can be achieved with multiconjugate adaptive optics (MCAO) (see e.g. Ref. [8]), which essentially means using wavefront sensors (and correctors) in at least two different planes which are not mutually conjugate. That way, one can better compensate for aberrations coming from different places – for example, from atmospheric turbulence in a wider range of directions and also from imperfect components of an imaging system. However, that approach will, of course, substantially increase system complexity and cost, and is therefore rarely used.

Applications of Adaptive Optics

The potentials of adaptive optics are utilized in a wide range of fields, each with its unique challenges and requirements. Some of those are discussed in the following.

Astronomy

Already well before the year 2000, large ground-based astronomical telescopes have reached a performance which was no longer diffraction-limited but became severely limited by the turbulent nature of the Earth's atmosphere. In other words, it was substantially worse than theoretically possible for a large telescope if there were no atmospheric distortions. That is the case even for telescopes placed on high mountains in regions with rather favorable atmospheric conditions. The main problem is refractive index variations based on temperature inhomogeneities, which affect the density of air, and these effects are strongest for telescopes operating at short wavelengths of light. The problem is further compounded by turbulence, letting the optical distortions vary rapidly.

One way to overcome that barrier was the development of large space-based telescopes, such as the Hubble Telescope and the James Webb Space Telescope. However, for various reasons, it remained highly desirable to also solve that problem by somehow greatly reducing the effects of atmospheric distortions in ground-based telescopes. For example, such telescopes can have substantially larger mirrors than space-based telescopes, and can be gradually optimized as they are far better accessible during operation.

Adaptive optics has become the key solution for the explained problem [1], and is now applied at many observatories.

One of the challenges in high-quality image correction is the accurate measurement of time-dependent wavefront distortions. A basic principle is the utilization of distant stars as virtual point sources, delivering rather precisely plane wavefronts before reaching our atmosphere, which distorts them. For accurate wavefront correction, such a guide star must be (a) sufficiently close to the observation direction (so that the corresponding isoplanatic patch contains the objects of interest) and (b) sufficiently bright for precise wavefront measurements. As such a star is not always available for an observation, one may use an artificial guide star generated by sending a suitable laser beam into the sky (→ laser guide stars). One possibility is to realize a sodium beacon, where the laser beam's wavelength is precisely tuned to an absorption resonance of sodium atoms at 589.2 nm (as occur at around 90 km altitude in the atmosphere), which then emit fluorescence light. There are also Rayleigh beacons where one uses Rayleigh scattering of light from a pulsed laser, typically at a shorter wavelength, e.g. in the green spectral region. Laser guide stars very much improved the possible coverage of the sky, although they are not ideal, mostly due to the cone effect.

Various kinds of wavefront correctors have been optimized specifically for application in astronomical telescopes [6]. Although large telescopes are often equipped with active optics based on a multi-segment primary telescope mirror, the related positioning control is normally far too slow to be used for adaptive optics; therefore, an additional fast wavefront corrector with a large number of actuators (hundreds or even thousands) and high speed is required.

Traditional AO systems with a single laser guide star can only correct for distortions over a small region of the sky. However, multi-conjugate adaptive optics (MCAO) systems have been developed which use multiple guide stars and deformable mirrors to correct for distortions over a wider area, enabling the study of larger astronomical regions.

Some prominent examples of large observatories using adaptive optics technology:

• The Keck Observatory on Mauna Kea (an active volcano) in Hawaii with its twin 10-meter telescopes has been among the first to be equipped with adaptive optics systems since 1999. These have been regularly upgraded to improve their performance [3].
• The 5.1-meter Hale Telescope at the Palomar Observatory in California was also one of the first telescopes to be equipped with an adaptive optics system, and also has been regularly upgraded.
• The 8.2-m Subaru Telescope, located at Mauna Kea, Hawaii, has an AO system based on a wavefront sensor with 36 photon-counting avalanche photodiode modules and a bimorph wavefront correcting deformable mirror with 36 driving electrodes. The system has been in service since 2002.
• The Large Binocular Telescope (LBT), located in Arizona, USA, features an innovative AO system that includes an adaptive secondary mirror with 672 actuators and a high-order pyramid wavefront sensor. This system has achieved performances never seen before on large ground-based optical telescopes, with images showing a contrast as high as 10^-4.
• The Gemini South Telescope in Cerro Pachón, Chile has a multi-conjugate adaptive optics system (GeMS) and was the first sodium-based multi-Laser Guide Star (LGS) adaptive optics system. It uses five laser guide stars and two deformable mirrors. The system has been in regular operation since 2011, producing images close to the diffraction limit in the near infrared [8, 9].
• The Very Large Telescope (VLT) in Chile, operated by the European Southern Observatory (ESO), has been equipped with adaptive optics systems for many of its instruments. These systems have allowed the VLT to produce some of the sharpest images of the night sky.
• The Giant Magellan Telescope (GMT) uses a set of seven 8.4-m mirrors and is under construction at the Las Campanas Observatory in Chile. The goal is to reach an image resolution surpassing that of the Hubble Space Telescope. Adaptive optics will be based on a deformable secondary mirror containing over 7000 voice coil actuators, and use different techniques (including six laser guide stars), depending on the observed objects.

Given the importance and the high cost of the overall astronomical installations, substantial investments were done to implement that technology with high precision. Using highly advanced AO technology, all these observatories now provide far better images of galaxies, planets and other celestial bodies than previous telescopes; the final limit of diffraction-limited resolution of large telescopes has been approached much more closely in that way. This has facilitated the detailed study of a wide range of astronomical phenomena. For instance, AO has enabled astronomers to examine the surfaces of planets in our solar system, observe the formation of stars in distant galaxies, and study the supermassive black hole at the center of our galaxy, the Milky Way.

Vision Science and Ophthalmology

In ophthalmology, it is often required to record accurate high-resolution images of the retina, the light-sensitive organ in the eye. For example, that can help to improve the diagnosis and treatment of a range of retinal diseases, such as retinal detachment, glaucoma, diabetic retinopathy, age-related macular degeneration or retinitis pigmentosa. Further, high image resolution (allowing the imaging on the level of cells) is important for fundamental vision research; for example, it helped to precisely identify the different types of photoreceptors.

Similar to astronomy, one faces the problem of (also somewhat time-dependent) image aberrations, but in this case primarily caused by the cornea and the eye's lens. Of course, such aberrations also limit the eye's vision, but here we focus on the challenge of diagnosis. Again, one employs adaptive optics to obtain significant improvements in the quality of retinal images by compensating for such aberrations. AO retinal imaging can reveal pathological changes in the retina at an early stage, allowing for early intervention and improving patient outcomes. Besides, the measurements quickly and reliably determine the details of required prescription glasses.

Quite different methods of adaptive optics in-vivo retinal imaging have been developed:

• Various methods are based on a wavefront sensor and a correction device, integrated into some kind of imaging system:
  • Flood illumination implies that images are taken with a flash of incoherent light and imaging of the retina with some camera. This is done immediately after compensating wavefront errors, using an additional infrared laser source. A non-ideal aspect is that aberrations measured at one (infrared) wavelength do not allow perfect compensation at other (visible) wavelengths used for imaging.
  • In scanning laser ophthalmoscopy (SLO), one uses a laser source both for aberration measurement and imaging with a raster scan. The principle of confocal scanning microscopes is employed to obtain substantial longitudinal resolution and suppress effects of light scattered outside the plane of interest.
  • Optical coherence tomography (OCT) is another option [10], using a spatially coherent light but temporally incoherent source, e.g. a lower-power wavelength-swept laser or a superluminescent source. While the longitudinal resolution of OCT is inherently excellent, the transverse resolution can also be improved significantly using AO. In any case, a low-power beam (often in the near infrared) is sent through the eye's pupil, and light returning from the retina is analyzed. Note that the retinal details are not apparent within the pupil plane, where the wavefront measurement and correction is done. Therefore, it is possible to use the same beam for wavefront analysis and imaging. The pupil is usually dilated to reduce image blurring by diffraction. That would normally increase the detrimental effects of aberrations of the eye, but those can be largely compensated with AO.
• Sensorless AO takes a different approach, not requiring a wavefront sensor. Instead, it iteratively adjusts the correction device such as to optimize certain sharpness metrics from the obtained images. Sensorless AO can be simpler and less expensive than traditional AO. However, the iterative process is substantially slower than wavefront sensing. Also, the image quality metrics may not always guide the system towards the optimal correction; it depends substantially on details of the object
• Computational AO is a newer method that leverages computational techniques to correct wavefront aberrations. Instead of using hardware such as wavefront sensors and deformable mirrors, computational AO uses algorithms to computationally correct the aberrations in the retinal images. One approach involves capturing a series of images with different defocus settings (a method called “computational optical sectioning”) and then computationally combining them to create a high-resolution image. Requiring less optical hardware, computational AO can be a cost-effective method that simplifies the imaging setup, but it can be computationally intensive and may not achieve the same resolution as traditional AO.

In addition to retinal imaging, AO has also been applied in the field of refractive surgery, such as Laser-Assisted In Situ Keratomileusis (LASIK), and other vision correction methods. These procedures aim to reshape the cornea to correct refractive errors such as myopia (nearsightedness), hyperopia (farsightedness), and astigmatism. AO systems can be used to measure the patient's wavefront aberration with high precision before surgery, helping to guide the reshaping of the cornea. After surgery, AO can be used to evaluate the effectiveness of the procedure and identify any residual aberrations.

Furthermore, AO has been used in research to study further details of the optics of the eye, providing insights into how different structures of the eye contribute to overall visual acuity. For example, AO has been used to investigate the effect of the eye's tear film on visual quality, to study the impact of age and disease on the optical properties of the cornea and lens, and to identify photoreceptors and their defects for patients with limited color vision.

Microscopy

Microscopy is one of the areas where a significant part of the image imperfections can be caused by aberrations – either in the optical system or in the samples themselves. The latter becomes relevant for microscopy techniques where images are taken at some (often variable) depth inside a sample – for example, in confocal scanning microscopes and in two-photon excitation fluorescence microscopes. There are quite different technical variants of adaptive optics tailored to specific use cases, involving both relatively traditional methods of microscopy and advanced techniques such as confocal scanning microscopy and fluorescence microscopy.

Due to the difficulty of measuring the required wavefront corrections, sensorless techniques are often used, although it generally depends on the imaged objects how well such methods work. A helpful aspect is that the aberrations in microscopy samples are usually hardly time-dependent, allowing sensorless methods to work.

Free-space Optical Communications and Directed Energy

Adaptive optics has important applications in systems where laser beams need to be sent through the atmosphere and atmospheric distortions have detrimental effects. Some examples:

• Free-space optical communications over long distances can benefit from adaptive optics. In the simplest case, only the direction of a laser beam is stabilized, but more sophisticated beam optimization can also be employed. However, cost constraints often make it difficult to apply advanced techniques.

• Particular challenges are met in the defense sector, e.g. where adaptive optics is used in directed-energy weapons systems to deliver high-energy laser beams with minimal distortions over long distances. The ability to focus a high-energy beam onto a small target area is crucial for the effectiveness of these systems, and adaptive optics may play a key role in achieving this. While it may be impractical to sufficiently accurately measure the wavefront distortions caused on the long path to a distant target, one may only compensate for distortions with an origin within the used laser system – for example, from time-dependent thermal lensing in the power amplifier. Another challenge is related to the high beam intensities; a number of optimizations is required to achieve the required power handling. For example, one may place a deformable mirror in an expanded part of the laser beam before passing the final optical amplifier.

Challenges and Future Directions

Despite the significant advancements and broad adoption of adaptive optics in many years, there remain various challenges to be addressed. Some examples:

• Magnitude of compensated distortions: One of the key challenges is the correction of large phase aberrations, particularly in applications such as microscopy, where the sample itself introduces significant distortion. Improving the dynamic range of wavefront correctors while preserving other important qualities is an area of ongoing research.
• Integration: Many optical systems were not originally designed with adaptive optics in mind, and retrofitting these systems with adaptive optics can be difficult and expensive. The more compact wavefront sensors and wavefront correctors are, the better are the chances to integrate them into various devices.
• Usability: The operation of adaptive optics systems requires specialized training and expertise, which can be a barrier to widespread adoption. Efforts to develop user-friendly adaptive optics systems with automated operation are crucial to expanding the reach of this technology.
• Cost: The cost of adaptive optics equipment, particularly deformable mirrors and high-speed wavefront sensors, can be prohibitive. Developing lower-cost techniques could greatly expand the possible areas of application.

Continued research and development in this field should lead to more effective and economically viable adaptive optics systems. Further advances in wavefront sensors, wavefront correctors, but also concerning optical setups and control strategies can be expected.

See also: deformable mirrors, wavefronts, telescopes, laser guide stars