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Adaptive Optics in Biology

Carl J Kempf

1 IntroductionObservations at the cellular level are driving the need for imaging systems that canperform at or beyond the resolution limits of many existing wide-field microscopesystems. Imaging in vivo is particularly useful for understanding basic biologicalprocesses, disease diagnosis, and drug development. Observed regions are frequently3D volumes and maintaining high resolution throughout the volume is a majorchallenge.

New technologies have enabled major advances in biological imaging in recentdecades. Ultrasound and magnetic resonance imaging are now routine clinicalprocedures. Impressive as these are for the ability to scan very deep into tissue, theirresolutions are typically no better than hundreds of microns. Optical microscopes ofvarious types still provide the highest levels of resolution. These commonly yieldstunning images with resolutions reaching sub-micron levels, enabling opticalmicroscopes to observe cellular and sub-cellular structures. However, the resultingimages are often degraded by optical aberrations occurring in the samples beingobserved. These arise from variations in refractive index within the biological tissueand the effects become more acute when peering deep into tissue.

A technology known as adaptive optics (AO) has the capability to counteract theundesired effects of optical aberrations. Originally developed for astronomy, thistechnology has taken hold in biological imaging over the past two decades. It is nowcommon in a few imaging modalities in research applications. Manufacturers ofadaptive-optics equipment have simultaneously adapted the size, ease of use, andprice of components to better fit biological imaging applications, thus enablingfurther application.

Within the broad field of biological imaging, my discussion in this ebook will beaimed at high-resolution optical imaging. This means, essentially, microscopes andophthalmoscopes. But even when restricting discussion to these instruments, thereremains a wide variation in design and operation that has important consequences

doi:10.1088/978-0-7503-1548-7ch1 1 ª IOP Publishing Ltd 2017

when applying adaptive optics. This work reviews the important classes of instru-ments and the corresponding challenges. It then moves on to key concepts andtechnologies in adaptive optics that guide a practitioner interested in weighingdesign options. Finally, results from representative systems are presented and futuredirections are discussed.

2 BackgroundImportance of in vivo imaging

Imaging live subjects, both human and animal, is a key tool for advancing medicalcare. A familiar example is clinical care of human patients—think of making adetailed observation of a patient’s retina to check for the onset of disease. An evenlarger application area involves imaging animal subjects—from fruit flies toprimates—in research settings. The mouse, in particular, receives a lot of attentionfor its use as a model organism for treating human diseases. Regardless of theorganism, however, the goal is to observe ongoing physiological process in as muchdetail as possible, as rapidly as possible, and with minimum distress or damage.Further, the imaging system must be able to repeat measurements on a periodic basisas consistently as possible. This is where a well-functioning adaptive-optics systemadds value. Ideally, such a system enables imaging at a level of resolution that wouldotherwise be impossible, at depths that would otherwise be unattainable, and withina time frame that is not detrimental to the subject.

Imaging deep into tissue and specimen-induced aberrations

Microscope builders trim out nearly all the aberration from the instrument itself togive nearly diffraction-limited imaging, which is the maximum possible under idealconditions. The specimen itself is therefore the main contributor of aberrations thatdegrade images. But since every specimen is unique, it is not possible to predict andcorrect these aberrations a priori. Moreover, aberrations accumulate when imagingdeeper into samples to obtain 3D volumetric images. Maintaining imaging reso-lutions at or near the micron level becomes very challenging. This problem is madeworse when looking deep into specimens: light absorbs and scatters a lot, leaving lessavailable to form an image. Depending on the tissue being observed, the wavelengthof light used, and the particular imaging modality, the depth limits vary signifi-cantly. Under favourable conditions, this maximum depth at which a useful imagecan be taken is currently limited to hundreds of microns. Adaptive optics cannotrestore the light that has been lost to absorption and scattering, but the techniquecan make the best possible use of what light is available—restoring contrast andsharpness to what would otherwise be a faint and fuzzy image.

To compound the challenge, aberrations within the sample can vary with timeand location. For in vivo measurements, this time variation could be due to naturalmovements or to biological processes. In ophthalmic imaging, for example, the eyeis seldom completely stationary. Good aberration correction requires correctingaberrations that can change at frequencies up to a few hertz. Even for ex vivoimaging, samples frequently dry out or undergo other changes that require some

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degree of tracking slowly time-varying events. Fortunately, the time scales are slowcompared to atmospheric corrections, so technology already exists that can operateat the requisite speeds. Spatial variations can present a different challenge. In opticalsystems that scan a beam at high frequencies, the scanning frequency is oftenkilohertz or tens of kilohertz—rates beyond which adaptive optics can keep up.These can be handled by doing local optimizations within an image and, withsufficiently fast electronics synchronized to the scanning, corrections determined bythe optimization process can be applied in an open-loop fashion during the scanning.

Diffraction limited imaging and the effect of aberrations

In any optical system, fundamental properties of light impose limits on how goodthe imaging can be. Any optical detector—even something as fundamental as oureyes—sees an image of the object being observed. This distinction between the imageand the underlying object is important; the image is never a perfect rendering of theobject. Exactly how well the image reveals the features present in the underlyingobject depends on the resolution of the system. Resolution is simply the ability todistinguish closely spaced objects. In a high-resolution image, closely spaced featuresin the object can be seen as distinct, separate features. In a lower resolution image,these blur together.

The limit to the resolving power of a system—i.e. the diffraction limit—isimposed by the wave nature of light. As the light passes through an optical system,constructive and destructive interference effects limit the sharpness of the image thatis formed. Consider a simple system in which a circular beam of coherent,monochromatic light enters a single ideal lens. At the focal length of the lens, thelight is concentrated down to a region of high irradiance. This region is not aninfinitely small point, however, as this would imply an infinitely high energy density.The reason why the light spreads goes back to how the light is collected by the lens.Rays of light at all points throughout the circular beam travel slightly differentdistances to reach the focal plane of the lens. These path differences lead to bothconstructive and destructive wave interference. Only along the centre axis of the lensdo the waves have a predominantly reinforcing effect, leading to the region of highirradiance that we think of as the focused spot of light. This region is therefore a 3Dshape that extends along the axis of the beam. The cross section through the regionof maximum intensity has a sharp, but not infinitely high, intensity peak. Known asthe ‘point spread function’ (PSF), this spreading of the light is key to understandingoptical systems.

The smaller and more sharply peaked the PSF, the higher the resolving power ofthe optical system. The factors governing shape of the PSF for this simple system arethe wavelength of light, the beam diameter, and the focal length of the ideal lens.This notion of diffraction-limited resolution applies directly to more complex opticalinstruments assembled out of multiple lenses and mirrors. In this case, the singleideal lens is replaced by series of real lenses and mirrors. Instrument manufacturersstrive to make this assembly of components function together as a near-perfectsystem that approaches the diffraction limited resolution. Even small deviations

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from perfection in the shape and placement of lenses in the assembly cause smalladditional variations in the optical path lengths known as aberrations. These, inturn, lead to a PSF for the overall system that spreads the light out over a largerregion of lower intensity, thus falling short of the diffraction limit. The result isimages that have more blurring and less resolution.

Figure 1 shows images of three point spread functions taken from an optical testbed. The image on the left is a relatively good PSF, largely free of aberrations. Theimage in the center shows the same PSF with a small amount of focus aberration.Note that the peak irradiance has dropped significantly and the light has spread outover a large area. Focus aberrations impart a bowl-shaped optical path lengthvariation that is symmetric about the optical axis and thus the spreading of light atthe PSF is symmetric around the optical axis. The figure at the right shows theoriginal PSF, this time corrupted by a small amount of coma error. Coma, unlikefocus, imparts aberrations that are not symmetric. Note that the peak irradiance hasdropped again, but the light has spread out in a more complicated pattern along thevertical direction in the image. Faint bands of slightly higher intensity are visiblebelow the bright region.

Wave-fronts and modal representations

Diffraction-limited performance, which instrument makers go to great lengths toachieve, is lost when the sample itself introduces aberrations. One well known issuein microscopy is the matching of the refractive index between the cover glass and thesample. If this index deviates from the anticipated value, it induces aberrations. Withcareful preparation, these can be reduced or avoided. The more challenging cases areaberrations induced by refractive-index variations within the sample. As thesevariations are inherent in the specimen, they cannot normally be altered, particularlyfor in vivo imaging where the goal is to observe with minimal intrusiveness.

One very useful way to understand and quantify effects of aberrations is toconsider the effect upon a wave-front. A wave-front simply represents how a cross

Figure 1. Point spread function (PSF) images. On the left is a well-formed PSF, largely free of aberrations. Thecentre image has a small amount of defocus aberration; note that the central core has spread evenly and peakintensity is lower. The right-hand image has a small amount of coma aberration; note that that intensityspreading is in the vertical direction.

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section of the beam propagates through space. For a beam that is neither convergingnor diverging and free of aberrations, the wave-front is simply a flat disk propagat-ing along the beam axis. When aberrations are present, these add variations in theoptical path length. These variations in the path length are represented by theretardation of portions of the wave-front, thus warping the otherwise flat disk. If afocus aberration is applied to an otherwise flat wave-front it becomes bowl-shaped.If astigmatism is applied to an otherwise flat wave-front, it becomes saddle-shaped.

Our eyes are a good example of an imperfect optical system. The cornea and lensof the eye work together to focus light on the retina at the back of the eye. Unlike theideal lens example above, these elements are seldom free from aberrations. Theseaberrations cause additional optical path-length changes over the wave-front. Interms of the point spread function, these path-length changes result in furtherspreading of the region of high irradiance. This, in turn, leads to blurred images. Wewear spectacles to apply the opposite aberrations to the light entering our eye. This‘pre-warps’ the light so that after it has passed through the lens and cornea, theaberrations cancel the pre-warping and thus restore the flat, error free wave-front.

Various methods exist to represent wave-fronts. One method that is widely usedin optics is ‘modal decomposition’. As in other fields of engineering, this involvesrepresenting a function as a collection of basis functions, with each one scaled by aweighting coefficient. This concept is usually introduced in engineering and physicsby showing how a square wave can be built up as a series of sine waves ofsuccessively higher frequencies. In the case of a wave-front, the goal is to represent ashape defined over a 2D circular domain. A modal basis set widely used in optics isthe Zernike polynomials. A description of these can be found in, for example, thetext by Born andWolf (see ‘Additional resources’). Figure 2 shows how a wave-frontwith aberration can be represented as a sum of modal basis functions.

Figure 2. Wave-front (top) generated by adding together three low-order basis functions from the set ofZernike polynomials.

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The shape of the wave-front strongly affects how easily aberrations can becorrected with adaptive optics. Ignoring, for the moment, how these wave-fronterrors vary in time, consider how they vary in space. Shapes that have fewercurvature reversals (such as bowl shapes and saddle shapes) are generally easier tocorrect. These are described as having a low ‘spatial frequency’. On the other hand,wave-fronts that are very wavy are said to have high spatial frequency. In additionto the shape, the size of the errors is significant. Any adaptive-optics system willultimately encounter limits in correcting wave-front errors as they become large inmagnitude or have high spatial frequencies.

Adaptive optics history and key concepts

Since the first telescopes were built, astronomers noticed that the quality of theimages they observed depended greatly upon the prevailing winds. We now knowthis is because light rays reaching the ground travel through regions of theatmosphere with varying density. As the density changes, so does the refractiveindex. These density changes are far from uniform and vary with time. In otherwords, ground-based telescopes face a set of rapidly changing aberrations. Thesenudged imaging performance away from the diffraction-limited-imaging that waspotentially available with the best telescopes under the best possible observationconditions.

In 1953 astronomer Horace Babcock proposed a clever solution, which includedthe main elements of any modern adaptive-optics system. First, light is made toreflect off a device that can rapidly impart optical path-length corrections atdifferent regions throughout the beam to flatten the wave-front and thus counteractthe effects of aberration. Second, the remaining wave-front errors are measured afterthe correction. Finally, a feedback control loop uses the measurement to continu-ously adjust the corrections applied to the wave-front. At the time this scheme wasfirst proposed, the requisite technology was in its infancy. The wave-front corrector,for example, was adapted from an entirely different application and the develop-ment of suitable technology progressed slowly at the outset.

Astronomers were not, however, the only people interested in looking up into thesky. Various defence-related agencies were also very keen to look at items passingoverhead, with the advent of orbiting satellites strongly stimulating this interest.Indeed, the technical challenges are very similar to those encountered when lookingat distant stars or planets. Unlike stars and planets, though, the items of interest todefence agencies may pass overhead rather quickly—and simply waiting for weatherconditions to improve was not an option. By the late 1960s and throughout the1970s, defence agencies began investing heavily in adaptive optics. With these largerbudgets, the development of adaptive-optics technology progressed rapidly and ahandful of pioneering systems with stunning levels of performance were built.

These systems heavily influenced the various systems that followed, even forapplications outside of atmospheric correction. In modern adaptive-optics systems,the device most commonly used to impart optical path length changes is a‘deformable mirror’ (DM). This device has a reflective surface that can be

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modulated rapidly by a computer. The key idea is simple—if the mirror takes on ashape that is an inverted version of the wave-front, then after the beam is reflectedoff the deformable mirror the optical path lengths will once again be uniform andthe effects of atmospheric aberrations will be cancelled. The sensing element inmodern adaptive-optics systems is a ‘wave-front sensor’, which is a speciallyconstructed camera that takes measurements that can be used to estimate the shapeof the wave-front. The feedback control system in modern adaptive-optics systems isalmost always implemented using some form of computer, with the processingpower determined largely by how fast the system needs to operate.

Figure 3 shows a simplified representation of a telescope equipped with adaptiveoptics. The aberrated wave-front entering the telescope is represented by a wavy lineand as the light proceeds through the telescope, it bounces off a deformable mirror.

Figure 3. Simplified astronomical telescope with adaptive optics. Note that the deformable mirror (DM) has ashape that is the inverse of the wave-front error, scaled so that reflection from the DM imparts optical path-length changes that exactly cancel the error.

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The mirror is, however, shaped to cancel optical path-length variations. So whenshaped correctly, the wave-front leaving the mirror becomes flat again. A portion ofthe beam directed to the camera used to record scientific images is split off andpassed to the wave-front sensor. Any residual aberrations present after correctionare detected and used to apply additional corrections to the DM.

By the late 1980s, the legacy of the defence spending was a fledgling industrybuilding deformable mirrors, making wave-front sensors, and supplying expertise inimplementing adaptive-optics systems. At first, these components were ill-suited tobiological imaging, being big, expensive and difficult to obtain. Nevertheless, by the1990s the situation had improved enough that adaptive optics began to be applied inophthalmic research. Some of the first instruments to demonstrate this weredeveloped at the University of Rochester in the 1990s, with the techniquesubsequently being adopted in various areas of microscopy.

The trend toward adoptive-optics application in life sciences is currently accel-erating. In vision science and ophthalmic care, adaptive optics is firmly establishedin high-end research systems. Microscopy has lagged ophthalmics, but is now arapidly growing application area. This trend is driven by growing demand for higherresolution images and supported by the availability of correctly sized and reasonablypriced components. Importantly, individuals with experience in developing andapplying adaptive optics are no longer cloistered within the defense community. Awealth of expertise has built up around the application of adaptive optics inbiological imaging. There is now a deep well of publications that validate thetechnology provide a basic roadmap for what is known to work effectively, with thetexts edited by Jason Porter and colleagues, as well as by Joel Kubby (see Additionalresources), being required reading for those serious about applying adaptive opticsin ophthalmics and microscopy, respectively.

3 Current directionsRequirements for adaptive optics in biological imaging

Capturing an exact set of requirements that an adaptive-optics system must meet inbiological imaging is difficult because there are so many different types of system. Afew general themes do, however, emerge.

First, the optical power levels are usually low. It might be tempting to apply highlevels of illumination in the quest for more returned light and thus a better image,but this approach has its limits, particularly because many samples are degraded ordamaged by exposure to light. The light may be toxic to the system underobservation and thus cumulative exposure must be limited. Light will also oftenhave a bleaching effect that makes structures harder to resolve as the cumulativeexposure increases. Finally, low optical power levels may be a matter of safety andcomfort for live human or animal subjects. The one exception is in laser surgery, inwhich case the adaptive-optic components need to stand up to average power levelsthat may be as high as a few watts. This usually requires specialized optical coatingsthan can stand the high peak intensity of a pulsed laser with very short pulses.

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Furthermore, the components may have to be actively cooled to ensure that opticalquality is not lost due to thermally induced deformations.

Second, optical aberrations in biological systems tend to change very slowly. Inspite of this, many biological imaging systems require fast update rates for thedeformable mirror or similar device used to modulate the wave-front. This is due tothe growing popularity of systems that sense the aberrations indirectly instead ofusing a wave-front sensor. These systems will be described in detail later in thisebook. A key property of these systems is that they are iterative and require tens oreven hundreds of shapes to be imparted to the wave-front in order to converge on ashape that best cancels the effects of aberrations. To do this quickly and limitcumulative exposure of the specimen, a deformable mirror with fast update rates isneeded.

Third, the wave-front correction often needs to be synchronized with cameras,scanners and other elements of the system. For example, a camera’s imageacquisition may need to be precisely timed to occur immediately after a wave-frontcorrection has been applied to minimize the overall time required for an iterativealgorithm.

Finally, no discussion of adaptive optics is ever complete without talking aboutwhat kind of deformable mirror or similar device is needed in order to apply optical-phase adjustments to the wave-front. These requirements vary in terms of the overallamplitude of the phase correction that is needed, the spatial fidelity (i.e. the level of‘waviness’) that must be achieved, and how quickly the device needs to respond. Thisreally depends upon the particular application and the nature of the aberrations tobe cancelled. In general, however, correcting aberrations in biological imaging is lessdemanding than correcting atmospheric turbulence in astronomy. Whereas astron-omers usually need thousands of points of actuation (for adequate spatial fidelity),those studying biological samples can make do with hundreds of points of actuation.And whereas astronomers need to be closing a control loop at kilohertz rates,biological imaging can usually perform well operating at tens of hertz. The overallamount of phase correction required depends on what it being observed—the mostdemanding cases are usually aberrations of the eye in which the requisite wave-frontcorrection can be on the order of 10 microns.

Importantly, the type of imaging system usually has a strong impact on the designof an adaptive-optics system. A few of the key types of instruments and relatedtechnologies are reviewed here as background before delving into more details ofadaptive-optics systems.

Wide-field microscopes

The wide-field microscope remains the fundamental high-resolution imaging systemin many labs. It involves illuminating a sample and then collecting light from itthrough adjustable levels of magnification. Illumination can be projected onto theback of the sample before collecting the transmitted light. Alternatively, illumina-tion can be directed onto the top of the sample before collecting the reflected light.One widely used variant is the fluorescence microscope. In such a system, the

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illumination excites fluorescent emission from the sample. The emission can comefrom naturally occurring proteins or, commonly, fluorescent dyes that bind tospecific sites within the specimen. Illumination is at a shorter wavelength (higherenergy) than the emission. The specificity of the binding and the light emission atparticular wavelengths make these systems particularly good at revealing biologicalstructures. The resolving power of wide-field systems has been extended through anumber of techniques, the most notable of which is ‘structured illumination’, wherethe illumination is intentionally patterned in a small number of different ways. Thesepatterns are successively applied to the sample and the images for each are recorded.These images are then computationally reconstructed to form an image at higherresolution would have been possible with a single image using ordinary illumination.Other extensions to resolution have been obtained by carefully structuring thestimulation of fluorescence (either in space or in time) and then capturing andreconstructing images—these systems form a long and growing list of acronyms suchas STED, PALM, and STORM.

These various wide-field systems share some attributes. First, they can be used togenerate 3D volumetric images by stepping the focal plane through the object underobservation, taking digital images at each step. These image stacks are thencomputationally combined into a 3D volume image.

One shortcoming in most wide-field applications is that any stray light that hasbeen reflected from or scattered off planes other than the current focal plane can turnup in the image, which leads to a loss of contrast. In volumetric imaging, the imagestaken deep into tissue are most strongly degraded by the effects of stray light fromother planes, with the light from the plane of interest becoming successively dimmerwhile the noise from back reflections from other layers grows. As a result, features ofinterest fade into the growing background noise. This problem is compounded byaberration effects that degrade the true signal returning from the layer of interest.Fluorescence techniques are popular because the wavelength separation betweenstimulation and emission allows back reflections to be filtered, but because thefluorescent light leaving the sample is still subject to aberration, higher levels ofimaging resolution can therefore be obtained by correcting these with adaptive optics.

Confocal and multi-photon microscopes

Confocal microscopes are so named because they block light returning from planesother than the focal plane reaching the detector. They do this thanks to a relaytelescope that is placed in the optical path, typically right before the detector that isused to capture the image. The telescope makes the light converge and then divergein an hour-glass shape, with a precisely sized pinhole carefully aligned to match thenarrowest point of the hour-glass shape. Only the light that is correctly focused willthen make it through the pinhole. Light from other focal planes follows an hour-glass shaped path, but the narrowest point will shift axially ahead of or behind thepinhole, thus blocking the vast majority of light from these out-of-focus planes.

Confocal systems are often implemented as scanning systems that sweep thefocused beam through a rectangular area in the specimen. Only a small amount of

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light is reflected back from the specimen, with the amount of returning light beingsometimes three or four orders of magnitude less than the illumination. A highlysensitive detector is therefore an essential part of a confocal-microscopy system.

Aberrations on both the inbound and outbound paths are important. Correctionon the inbound path makes sure that that stimulus is localized to a small spot, thusensuring the reflections emulate a point source within the sample. Light collectedfrom the outbound path is directly affected by aberrations on the way to thedetector. Fortunately, the path traversed by the light in both directions is the same,so if the aberrations detected on the outbound path can be correctly sensed andapplied, they will also correct the inbound beam. When scanning deep into tissue,these systems do lose some signal, but the returned images remain free from the straysignals that plague wide-field systems. Most high-resolution ophthalmoscopes areconfocal microscopes that have been optimized to look at the structures in the backof the eye.

Rejecting out-of-plane light in this way leads to wonderfully sharp images. Thedownside, however, is that such systems are technically complex. As well as needinga detector that is highly sensitive, the detector sampling must be synchronized withthe scanning mirrors. Confocal systems therefore need more electronic hardwareand software than other microscopes.

An alternative device is the two-photon microscope, which has received a lot ofattention in recent years. The name comes from the method of generating lightemission within the sample. The core idea is that if the illumination intensity can bevery highly concentrated in space and time, two photons will simultaneously excitefluorescence. Relative to single-photon excitation, the energy of this two-photonexcitation is doubled, which means that the emitted light will be at twice thefrequency of the excitation.

This wavelength distinction is very helpful. First, it provides the usual benefit offiltering out back reflections from the excitation. Second, this method allowsexcitation at longer wavelengths, which is very useful because longer-wavelengthlight scatters less when penetrating deep into tissue—and the opposite of whathappens with a standard fluorescence microscope. Furthermore, the emission riseswith the square of the incident irradiance, so very little emission occurs outside thefocal plane of the incident stimulus. Two-photon systems are therefore inherentlyconfocal.

When it comes to adaptive-optics correction, the inbound stimulus is most criticalin two-photon systems. This ensures that the irradiance reaches the high levelsneeded to strongly stimulate the two-photon emission. As with confocal systems,two-photon systems use scanning techniques and can step the focal plane in the axialdirection in order to generate 3D volumetric images.

Optical coherence tomography

Optical coherence tomography (OCT) systems use interferometry to reject scatteredlight when imaging deep into tissue. What happens is that after the light leaves thesource, it is split. Part of the light travels into the sample and is reflected back from

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various depths within the tissue. The rest of the light, meanwhile, travels down areference arm, reflects back and then re-combines with the other beam. But whereasan ordinary interferometer uses light with a very specific frequency, OCT systemsuse light sources that span a range of frequencies. When the light recombines, itcreates an interference pattern if the optical path-length of the light reflected fromthe sample matches the reference arm. Light reflected from other depths within thesample is then ignored. So by sweeping the position of the reflector in the referencearm, the depth into the sample from which reflections are considered can be swept inthe axial direction. The resulting interference pattern is then cast onto a photo-detector and the resulting signal is processed to recover the strength of theinterference pattern, thus giving the strength of the reflected signal from withinthe sample. By adding scanning in lateral directions, the OCT system can build up avolumetric image.

OCT systems can scan very deep into tissue, reaching depths of more than 1 mm.This penetrating ability is due to the relatively long wavelengths that can be used andthe ability to completely reject reflections from layers other than the one of interest.The resolution is lower than in most traditional forms of microscopy, but OCTsystems have nevertheless been widely applied in both clinical and research settingfor ophthalmic care. In the case of ophthalmics, adaptive optics has been success-fully applied to OCT systems to increase resolution.

Image post-processing and deconvolution

Computerized post-processing of digital images is now standard practice in imagingscience, with one technique—deconvolution—being so widely used that it deservesspecific mention. A number of different implementations have evolved in recent decadesand it is a method that works particularly well with adaptive optics. Deconvolutioncleverly recognizes that an image of an object is formed through an optical process thatcan be modelled and, to some degree, computationally reversed to obtain a higherquality representation of the object. This method re-assigns light forming the image tocounteract the blurring effect of the PSF. Deconvolution can be applied to 2D imagesor 3D volumes and is most commonly applied to wide-field images, as they are mostprone to the effects of out-of-focus light appearing in the image.

The name hints at the process. Image formation can be expressed as theconvolution of the system’s PSF with light coming from every point in the object.Deconvolution is the reversal of this process. If we can somehow come up with adigital representation of the object that, when convolved with the system PSF,results in a computed image that matches the image actually captured then we knowthat we have obtained a perfect representation of the underlying object.

This technique runs into practical limits. Because the PSF tends to blur the image,the high spatial-frequency components of the image are lost. The deconvolutionprocess seeks to restore these. The limiting factor is the noise that is invariablypresent in any image. Noise, typically a high-spatial frequency effect, eventuallybecomes amplified to the point that the deconvolution method can no longerimprove the estimation of the underlying object.

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Since the deconvolution process depends on a model of the PSF, inaccuracies andinconsistencies in this model further degrade the ability of deconvolution to improvean image. Depending upon the particular deconvolution software implementation inuse, the computational model of the PSF could be based on theory, measurement, oriteratively estimated during the deconvolution.

The net result is that deconvolution can restore some lost resolution, but cannever replace lost signal. Adaptive optics can complement deconvolution (or otherpost-processing techniques) by removing aberrations and restoring signal that wouldotherwise be indistinguishable from noise. Further, adaptive optics will sharpen thePSF and, importantly, make it more consistent, thus assisting the post-processing.

Adaptive optics technology: wave-front correctors

The heart of any adaptive-optics system is the device used to modify the wave-front.Recall from figure 3 that a DM was introduced to do this. There are a few othertechnologies that can be used, but most have shortcomings that limit widespread useand the only serious alternative to a DM is a spatial light modulator (SLM).

Most SLMs are based on liquid-crystal devices that contain lots of individualpixels, each of which retards the phase of the light by a small amount. Oneshortcoming of the SLM is that the retardation is usually less than one wavelength.So, to compensate for larger path length differences, which are common inbiological imaging, a ‘phase-stepping algorithm’ is required. This algorithm isapplied to pixels for which the desired amount of phase adjustment exceeds thecapabilities of the device. A computational adjustment by an integer number of fullwavelengths is applied so that the remaining correction to be applied at that pixelfalls within the capabilities of the device.

Another shortcoming with SLMs is that the phase retardation depends upon thewavelength, so they are best suited to monochromatic applications. These devicesare also sensitive to the polarization of the incident beam. Further, depending uponthe particular technology used, the devices can be optically lossy and thus inefficient.Finally, the response speeds can be slow. On the other hand, the key benefit of SLMsis the large number of actuation points—sometimes as many as thousands—at areasonable price. In systems where the light loss and polarization are not a concern(such as correcting the inbound illumination in a multi-photon microscope) the SLMcan be an attractive option.

The most widely used phase modulation device is the DM. These are exactly whatthey sound like—mirror surfaces that can be deformed rapidly under computercontrol. The advantages are that these are highly reflective, insensitive to polarization,do not require phase wrapping, and respond on millisecond or sub-millisecond timescales. These devices typically have tens to hundreds (and sometimes even thousands)of actuation points across the optical aperture. Early DMs developed for defense andastronomy used piezoelectric actuators that push and pull on an optical surface,typically a thin sheet of glass with an optical coating. Such devices were large withdiameters of a few hundred millimeters. This fits well with the very large primaryapertures in telescopes. On the other hand, this does not match well to the much

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smaller beam sizes common in biological imaging. Smaller, cheaper versions of theseDMs have been developed recently. These newer devices have diameters approachingthe 10 mm range and so are better suited to biological applications. The piezoelectricdevices have some hysteresis and require moderate-to-high amounts of transient drivecurrents. Both these factors add some difficulty to controlling the devices.

Other DMs use magnetic or electrostatic actuation. These systems are typicallytens of millimetres in diameter. The magnetic systems use a combination of magnetsand coils to push or pull on an optical surface, typically a polished metal membranewith an optical coating. The main distinction is that the magnetically actuatedmirrors can push or pull with a lot of force over a long distance, allowing the surfaceof the mirror to be moved further than with a piezoelectric or electrostatic system.However, the magnetic forces rely upon the continuous application of drivecurrents, so the thermal stability of the device can be a problem.

The last major class of DMs is electrostatically actuated devices built out ofsilicon using a microelectronic mechanical system (MEMS) process. The surfaceitself can be either a single, thin plate or sub-divided into segments. These devices areusually very small, with diameters of ten millimeters or less. This small size is verywell matched to beam diameters used in biomedical optics. The surface is supportedon an elastic (spring) structure and electrostatic forces are used to pull on the opticalsurface against the restoring force of the elastic structure. These DMs are free of thehysteresis associated with piezoelectric DMs, take very little power to operate, andavoid the thermal stability problems associated with magnetically actuated DMs.An example of a MEMS deformable mirror with a segmented surface is shown infigure 4. This device has an optical aperture of 3.5 mm and has 111 actuators driving37 hexagonal segments. Each segment can be actuated in a full three degrees of

Figure 4. Example of a 111 actuator, 37-segment deformable mirror with segments arranged in a tightlypacked hexagonal pattern with an inscribed diameter of 3.5 mm made with a MEMS process. (Image courtesyof Iris AO, Inc.)

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freedom: piston, tip and tilt. The segments can be addressed individually or as anentire array. Positioning repeatability is at the nanometer level. The segments arerelatively thick, an advantage for high power applications where high reflectivitydielectric coatings are required.

Adaptive optics technology: feedback alternatives

As introduced in figure 3, adaptive optics is simply a way of counteracting thedetrimental effects of optical aberrations by measuring the wave-front and feeding itback to the DM. This is not, however, the only way of implementing an adaptive-optics loop. An alternative is to omit the direct measurement of the wave-front. Thebest shape to put on the DM is then determined by making a series of trialadjustments to it and observing the effects upon the science image being acquired.This method is called an ‘indirect’ or ‘sensorless’ approach.

The two concepts are summarized in the highly simplified system shown infigure 5. The system is representative of a microscope in which light is directed into asample, with the figure depicting returned light emanating from a point within thesample. As the light leaves the specimen, it picks up aberrations, represented by anon-flat wave-front propagating out of the sample into the objective lens. Theoptical path is highly simplified, showing only those elements related to the adaptive-optics correction between the objective lens and the camera used to form thescientific image of interest.

The upper part of figure 5 represents a direct sensing method and the lower partshows an indirect method. In both cases, the shape applied to the surface of the DMis an inverse of the aberrations. Upon reflection, the added optical path lengthrestores a flat wave-front. As the wave-front propagates back through the system, iteventually arrives at the scientific imaging camera. In the upper part of the figure,note the presence of a dedicated wave-front sensor—this is the distinguishing featureof the sensor-based system.

Adaptive optics technology: direct wave-front sensing

Directly sensing the wave-front is standard practice in most adaptive-optics systemsused for astronomy. It is also commonly used in ophthalmic imaging. The chiefadvantage is speed, which is needed for keeping up with rapidly fluctuatingdisturbances.

The most popular device for direct wave-front sensing is the Shack–Hartmannsensor, which is simply a camera with a lenslet array mounted in front of the detector(see figure 6). The array divides the incoming beam into sub-regions, typically on arectangular or hexagonal pattern. Each sub-region has a small lenslet that focusesthe light to a spot on the camera detector. If the incoming wave-front is flat, the spotpattern on the camera is perfectly regular and the spots exactly coincide with thecenters of the lenslets. If, however, the wave-front is aberrated, the slope in a sub-region entering a lenslet shifts the location of the corresponding spot. The cameraimage is processed on a frame-by-frame basis and the spot shifts relative to the flatwave-front case are determined.

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Once the spot shifts are known, the incoming slopes at the sub-regions can becalculated. This is the first step in the process of reconstructing the incident wave-front. There are various methods involved in reconstruction, but the basic concept isshown in figure 7. One approach is to enforce continuity constraints at the sub-region boundaries and then tile together flat facets representing the wave-front in

Figure 5. A sensor-based (direct) approach is shown in the upper drawing. A sensorless (indirect) approach isshown in the lower drawing. The indirect approach involves less hardware and directs all the returned light tothe since camera, but is iterative and thus is better suited to slowly varying aberrations.

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each sub-region. The displacements and slopes in each sub-region are chosen to best-fit the slopes observed by the wave-front sensor. This is known as a zonal approach.Another option is to represent the aberration to be identified as a collection ofmodes. The weighting coefficients applied to each mode are chosen to best-fit first-derivatives of each mode to the slopes actually observed at the wave-front sensor.This is known as a modal approach. A fuller discussion of both approaches is offeredin the book by Hardy (see Additional resources).

Once the wave-front is reconstructed, the inverse of it is applied to the DM. Afactor of one-half is applied since the mirror operates in reflection, so the amount ofoptical phase correction is twice the DM displacement.

Although simple in concept, the control algorithm usually ends up being a lotmore complicated in practice, with extra features usually being needed to tuneperformance. Another consideration is how to handle cases where the spot quality ispoor, for example, if the spots are too dim, too bright, or corrupted by noise. Worsestill, the spots could become biased by unwanted reflections from within the opticalsystem or layers within the sample that are not at the optical plane of interest. Theperformance of the system depends upon ensuring the wave-front sensor, DM, andsource of the aberrations are optically conjugate to one another. Even small detailsare critical, such as ensuring the system is aligned properly or maintaining thecorrect algebraic sign and magnitude of the feedback in a system with multiplemirrors and relay telescopes. Getting these correct takes time and working out thereasons why is never immediately obvious, but failing to do so leaves you with asystem that does not work properly.

Beyond the difficulties in implementing a robust algorithm, there are opticaldownsides to the sensor-based approach. First, precious photons returning out of the

Figure 6. Shack–Hartmann wave-front sensor concept. The lenslets focus incoming light to a series of spots onthe camera detector. A non-flat wave-front will result in light entering lenslets that has local tilt causing a shiftin the location of the corresponding spot. This is detectable and can be used to compute the shape of the wave-front.

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sample need to be split off to run the wave-front sensor. Second, the wave-frontsensor simply responds to any incoming light. Since the inbound illumination beamis usually much stronger than the return, any stray ‘back reflections’ from within theoptical system or an out-of-focus plane within the sample itself add noise to wave-front sensor measurement. They can often be tracked down and eliminated, but it alladds to the effort required to get a system up and running. Third, the optical paths tothe science camera and the wave-front sensor are not identical, which gives rise tonon-common path errors. These errors can be tracked down and corrected byadding the proper offsets to the wave-front sensor, but again this means more effortto get a system up and running.

The bottom line is that the conceptual simplicity of the wave-front-sensor approachcan be overwhelmed by the actual effort required to get things running reliably in apractical situation. The enduring attraction, however, is the ability to applycorrections very quickly and thus cancel effects of rapidly fluctuating aberrations.

Figure 7. Direct wave-front measurement and reconstruction. The upper drawing shows how a wave-front isdivided into sub-apertures and the local slope at each sub aperture results in a spot-shift on the detector array.The middle drawing shows how the spot shifts are used to recover the local slopes (or, equivalently, normalvectors) at each sub aperture. The lower drawing shows the reconstructed wave-front.

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Adaptive optics technology: indirect wave-front sensing

An alternative approach is to skip the direct wave-front measurement and insteaduse the scientific image that is being acquired to determine the shape for the DM.This approach requires less complex hardware and is therefore cheaper.Importantly, precious photons do not need to be diverted away from the imagingcamera to run a wave-front sensor.

The indirect approach works by applying a series of trial shapes to the DM andmeasuring the effects upon the image. The trial shape that improves the image themost is kept and used as the initial condition for a successive set of trial shapes.The process continues until there is no further improvement in the image. Ideally,the DM has converged on the shape that is optimal in rejecting the disturbance—inother words an inverse of the wave-front error, with the usual factor of one-half toaccount for reflection.

There are, however, two downsides to the indirect approach. First, the algorithmsfor applying trial shapes, analyzing image ‘goodness’, and guiding the iterationtoward convergence can become very complex. Second, the iteration is timeconsuming. Convergence of a direct sensor-based approach requires only a handfulof steps. An indirect approach, on the other hand, may take tens or even hundreds ofiteration steps for convergence. Fortunately, aberrations encountered in biologicalsamples usually change very slowly. Nevertheless, the time for measurements shouldbe kept as short as possible for reasons outlined earlier. Two main questions arise inthe development of an indirect sensing algorithm. First, what is the best metric to useas a measure of quality in the image? And second, what sort of trial shapes should beapplied?

In selecting the image metric, it could be the contrast of some feature within someregion of the image, the brightness of some feature within the image, or simply themaximized brightness of the whole image. A good metric is one that, whenmaximized, ensures that the quality of the image is improved as much as possible.In practice, there may not be a way to know this with certainty. The best approach istherefore to start with a simple metric that is easy to compute. Because of theiterative nature of the solution, computational simplicity and speed are important.In a well-designed system, the camera will be able to run at full frame-rates withoutwaiting around for computations to complete.

In selecting the set of trial shapes to put on the DM, the considerations should beease of analysis and overall speed. Taking advantage of any a priori knowledgeabout the expected aberrations is always helpful. So while it is possible to put a largecollection of random shapes on the wave-front corrector and check for the bestresult, this would take a lot of time. Most algorithms therefore use some sort ofiterative technique to improve the image metric—often referred to as ‘hill-climbing’algorithms. The key idea is that shape of the DM evolves so that the changes in themetric are maximized at each step. In the hill-climbing analogy, the path of steepestascent is favored.

One very straightforward method is to represent the optimal shape for the DM asa series of modes with weighting coefficients that will be determined during the

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iteration. On a first full step of iteration, an initial best-guess of the ideal shape ismade. In the absence of any other knowledge, a guess of zero for all the coefficients(i.e. a flat DM) can be used. The response in the image is recorded and the metric iscalculated. The modes are then perturbed slightly on a one-by-one basis. Those notbeing perturbed are held at the current best guess. For each perturbation, the imageis acquired and the metric calculated. After going through all the modes, thecollection of image metric versus perturbation amplitude is evaluated for each mode.The value of the perturbation that maximizes the image metric is used to update thenew best-guess for that modal coefficient. After all the coefficients are updated, theresulting shape is now the new best-guess and the process repeats. The process endswhen the improvement diminishes to a sufficiently small interval. This process issummarized in the flowchart shown in figure 8.

A quantitative metric of image quality must be selected. For example, you couldchoose to maximize the total pixel intensity over the whole image, or even a sub-region in the image. This simple ‘light-in-a-bucket’ approach is a good startingpoint. If there is some a priori knowledge of what the image should look like, a moresophisticated metric can be applied. If there is structure within the sample that isknown and predictable, it can be used. For example, fluorescent beads are some-times added to samples and maximizing the peak of the return signal from a beadwill provide a correction that is optimized for that region of the image. If otherfeatures in the sample result in particularly bright lines or bands, maximizing thecontrast along a line or multiple lines crossing these features can also be used.

Whatever metric is used, the core idea is making an initial best-guess of a shape toput on the DM, adjusting it slightly with a series of trial shapes, sampling the result,and modifying the best-guess. Like any iterative approach, the aim is to drive thebest-guess towards an overall, optimal, best image. In many practical cases, thechallenge is to find an algorithm that is robust and converges rapidly.

Example application: indirect wave-front sensing

A simple case of low-order correction is used to illustrate how such an algorithmevolves over a few full steps of iteration. Figure 9 shows results from an optical testbench and graphically depicts how the image, the metric, and the DM shape evolveover five steps of iteration. The correction is provided by the DM shown in figure 4.The top row in figure 9 is the evolution of the PSF image, including someannotations (in blue) that show the cross-sectional shape. The second row is theimage metric, which is calculated by taking the integrated intensity squared of thecentral core of the PSF. The third row is a series of bar charts representing the modalweighting coefficients obtained as the best guess shape for the DM at the conclusionof each of the five steps of iteration. The ordering of the coefficients is astigmatism,focus, and oblique astigmatism. The bottom row is the corresponding shape appliedto the DM.

The aberration to be cancelled in figure 9 is predominantly cylindrical in shape,generated using an optician’s trial lens. Cylindrical aberrations consist mainly offocus and astigmatism modes. The initial conditions correspond to the column

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denoted as Step 0. Note that the DM is flat (meaning that modal coefficients are allzero), the PSF is smeared out to a faint diagonal cloud, and the bar representing theimage metric is relatively small. After proceeding through a set of trial shapes, thebest guess shown in the column denoted as Step 1 is generated. Notice that the DM

Figure 8. Indirect algorithm flow for mode-by-mode amplitude iterations and updates at full steps. Thealgorithm uses a basis function (modal) representation of the wave-front and iteratively determines weightingcoefficients. The metric uses a feature (or combination of features) in the scientific image.

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is taking on a cylindrical shape and the PSF has tightened into a fuzzy spot. Theimage metric has increased sharply. On the successive three steps the DM undergoessubtle adjustments that further tighten the spot and drive the image metric higher.The improvement in the image metric between Step 3 and Step 4 is relatively small,showing that the algorithm is converging.

Example application: retinal imaging

One extremely active area for adaptive optics has been to image the retina of bothhuman and animal subjects. The most common instruments are confocal scanningsystems, OCT systems, as well as traditional flood-illumination. Regardless of the

Figure 9. Example sensorless adaptive-optics algorithm progression for low-order correction. The imagemetric is the integrated intensity squared of a PSF. The PSF image is shown in the top row and the successiveincreases in the image metric value are shown in the second row. The third row shows the evolution of modalcoefficient weightings and the bottom row shows the corresponding DM shape. Note that the majority of theadaptation occurs within the first two full steps.

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modality, however, what happens is that light enters the eye through the pupil in theordinary fashion, a tiny fraction reflects off the retina and travels back out of the eyeand into the instrument. Aberrations are common in the eye, as demonstrated by thenumber of people who need their eyesight corrected by wearing spectacles.

Imaging of animal subjects is common, and often has special challenges due tovariations in the size and shape of their eyes. As mentioned at the outset, mice areparticularly interesting because of their use as model organisms when it comes todeveloping drugs. Figure 10 shows images taken of a mouse retina using an OCTsystem equipped with adaptive optics, which in this case used an iterative indirectcontroller. The top row shows a layer of nerve fibers. The lower two rows showcapillary layers. These layers occur at different axial depths within the sample. Theimprovement between the case when the adaptive optics is off (left column) andwhen it is on (right column) is dramatic. Notice that the total amount of light isenhanced and the image sharpness is increased. Structures that were otherwise onlyfaintly visible are clear through the use of adaptive optics.

4 OutlookLooking ahead, I foresee a continuing demand for high-resolution in vivo imagingdeep into tissue, which will place several demands on companies and individualswho manufacture adaptive-optical systems. The growing popularity of iterativealgorithms places speed demands on DMs and SLMs, while the update rates need tobe as fast as possible to reduce light exposure. Furthermore, tight hardwareintegration into the system is needed. This means that triggering and synchroniza-tion signals must be provided that can coordinate the DM or SLM updates withcamera image acquisition or other events within the system.

Next, the overall ease of use of adaptive-optics systems must continue to improve.Factory calibrated DMs that have predicable open-loop operation and hold theiraccuracy for years are needed. For research-grade systems, these qualities areconveniences. But for commercial systems, these are fundamental requirements.What’s more, flexible, extensible software interfaces for controlling the DMs orSLMs are essential. Given these features, instrument designers can build imagingsystems that are efficient at getting the high quality images in a minimum amount oftime.

Beyond the basics of speed and ease of use, further advances will be required tosupport emerging applications such as laser surgery. These frequently use lasers withmoderate to high power (>0.5 W) so the ability of the DM or SLM to handle this ispivotal. Those devices that support high reflectance dielectric coatings, and comewith features for thermal management such as heat sinking and active cooling will befavored.

Finally, costs must come down. The steady progress in research applications ishelping refine the technology and lower the price. Similarly, growing applications inindustrial systems will increase the production volumes and help lower unit costs.Adaptive optics is currently too expensive for most low-end clinical applications.The good news is not only that the price trend for adaptive-optics technology is

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downward but also that there is growing acceptance of this fascinating technique asa fundamental tool in the research market too.

Additional resourcesBooth M J, DeBarre D and Jesacher A 2012 Adaptive optics for biomedical microscopy Opt.

Photon. News 23 22This is a highly readable paper that reviews accomplishments and challenges in microscopy.

Figure 10. Images of a mouse retina taken with an optical coherence tomography system equipped withadaptive optics. The left column shows the images with the adaptive optics off and the right column shows itwith it on. The top images are of the retinal nerve fiber layer, middle is the inner blood capillary layer, andlower is the outer blood capillary layer. Note that turning the adaptive-optics system on raises the overallsignal return level, increases image sharpness, and reveals details that are otherwise not visible. (Imagescourtesy of M Sarunic and Y Jian, Simon Fraser University.)

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Booth M J 2014 Adaptive optical microscopy: the ongoing quest for a perfect image Light: Sci.Appl 3 e165

Another good, readable review paper by Booth that covers material similar to the OSA paperabove. This one has an extensive reference list for those seeking to dig more deeply.

Born M and Wolf E 1999 Principles of Optics 7th edn (Cambridge: Cambridge University Press)This is a definitive work on optics and related topics. It is a rigorous mathematical treatment.

Where you feel the book by Hecht may not give enough supporting theory, refer to this book.

Hardy J W 1998 Adaptive Optics for Astronomical Telescopes (New York: Oxford UniversityPress)

This book covers adaptive optics at a level depth that most other books don’t. Unfortunately forthe biological imaging researcher, much of the material is aimed at astronomers. In spite ofthis, it can be a useful reference.

Hecht E 2002 Optics 4th edn (San Francisco, CA (Addison-Wesley)This highly readable text sets the standard for covering essentials of optics. Where you feel the

book by Born and Wolf strays too far from the basic conceptual understanding, refer to thisbook.

Jian Y et al 2014 Wavefront sensorless adaptive optics optical coherence tomography for in vivoretinal imaging in mice Biomed. Opt. Exp 5 547

One of the first demonstrations of indirect (sensorless) adaptive optics working at speeds thatmake it an attractive alternative to sensor-based approaches.

Kubby J (ed) 2013 Adaptive Optics for Biological Imaging (Boca Raton, FL: CRC Press)This collection of works includes application examples covering both indirect (sensorless) and

direct (sensor-based) techniques.

Porter J et al 2006 Adaptive Optics for Vision Science (Hoboken, NJ: John Wiley & Sons)This is a very extensive collection of works that cover theory and practice in vision science. Several

example designs are described.

Roorda A et al 2002 Adaptive optics scanning laser ophthalmoscopy Opt. Exp 10 405This details one of the first systems to add adaptive optics to a scanning laser ophthalmoscope for

retinal imaging and demonstrates the benefits in terms of imaging resolution.

Wallace W, Schaefer L H and Swedlow J R 2001 A workingperson’s guide to deconvolution inlight Microscopy Biotechniques 31 1076

This paper, despite being somewhat dated, still holds up well due to the readability and practicalcoverage of the basics of deconvolution.

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