Acousto-optic systems for advanced microscopy

Acoustic waves in an optical medium cause rapid periodic changes in the refraction index, leading to diffraction effects. Such acoustically controlled diffraction can be used to modulate, deflect, and focus light at microsecond timescales, paving the way for advanced optical microscopy designs that feature unprecedented spatiotemporal resolution. In this article, we review the operational principles, optical properties, and recent applications of acousto-optic (AO) systems for advanced microscopy, including random-access scanning, ultrafast confocal and multiphoton imaging, and fast inertia-free light-sheet microscopy. As AO technology is reaching maturity, designing new microscope architectures that utilize AO elements is more attractive than ever, providing new exciting opportunities in fields as impactful as optical metrology, neuroscience, embryogenesis, and high-content screening.


Introduction
Cornerstones in developing new optical technologies are systems capable of directly controlling light. Efforts in this direction have led to transformative advances in both research and industry, ranging from optical fibers for communication [1] to complex optical traps for laser cooling [2]. Among these technologies, advanced optical microscopy showcases the success of developing innovative strategies for guiding, focusing, splitting, and modulating light. Here, the optimal control of light directly determines the amount of information that can be retrieved from a sample. As such, modern microscopy architectures have come hand in hand with novel methods to increase speed, precision, and resolution at which light can be focused onto and collected from a sample. For instance, laser-scanning microscopes such as confocal [3] or multiphoton [4] systems-presently the tool-of-choice for cellular and functional tissue imaging-have flourished thanks to methods for precisely and swiftly scanning a focused laser beam across a sample. Similarly, the growing interest of light-sheet and structured-illumination microscopes (SIMs) [5] in the life sciences is mostly due to new approaches for shaping light beams [6,7]. All in all, improvements in light control have radically changed optical microscopes, rendering them quantitative tools for characterizing living specimen with unprecedented spatial and temporal detail.
Several approaches exist to control illumination and detection of light in optical microscopes. They can be broadly divided into two groups: passive and active systems. The first group includes lenses, beam splitters, and diffractive optical elements, producing a static output for a given light input. While quality and customization has improved thanks to modern fabrication technologies such as three-dimensional (3D) printing of optical components [8,9], their operational principle and implementation have remained largely unchanged. The second group, active systems, is capable of dynamically shaping light, and has seen a tremendous progress over the last decades. Examples include, spatial light modulators for multi-point illumination [10] and adaptive optics for reduction of aberrations [11], resonant scanning mirrors for reduced photobleaching [12], varifocal systems for fast axial focusing [13], and electro-optical scanners for fast imaging [14] and 3D particle tracking [15]. Among active systems, the family of acousto-optic (AO) devices stands out because of its versatility. AO devices enable high-speed modulation, deflection, splitting, filtering, and focusing of light. These features, combined with their ease of implementation, have rendered them essential components of advanced optical microscopes.
In this review, we provide a comprehensive introduction to AO systems and their applications to optical microscopy. First, we describe the operation principles and properties of various AO devices, emphasizing the differences between members of the AO family and their early use in optical microscopes. Next, we survey recent developments in advanced microscopy that feature AO devices as enabling elements, including random-access scanning microscopes and fast volumetric imaging systems. They provide clear examples of the numerous possibilities that AO systems offer in imaging applications. Finally, we discuss how AO devices can help to continue shaping the present and future of optical microscopy.

How acousto-optic systems work
The large family of AO devices provides a complete toolkit for controlling light in microscopy applications, ranging from splitting to focusing beams as well as amplitude and frequency modulation. Despite the significant differences between AO devices, they all operate under the same physical principle, the so-called AO effect. This phenomenon consists of the diffraction of light by ultrasound waves [16]. Briefly, ultrasound is used to create regions of compression and rarefaction in an optical medium, which in turn, produce local changes in the refractive index ( figure 1(a)). For typical AO materials (crystals and liquids) and ultrasound intensities, the maximum change in refractive index (∆n) ranges from 10 −4 to 10 −5 . When a beam of light propagates through such an acoustically perturbed medium, it undergoes a phase transformation, resulting in singular diffraction effects.
Depending on the properties of the vibrating medium (static refractive index n 0 , thickness L, speed of sound c s ), the wavelength of light (λ), and the frequency of ultrasound (f), two different regimes can be identified leading to distinct diffraction patterns. While no sharp transition exists between them, it has proved useful to identify the two regimes by the parameter Q [17], defined as: The parameter Q quantifies the effective thickness of the vibrating medium. Depending on the magnitude of Q, two distinct diffraction phenomena are possible. When Q ≪ 1, known as the Raman-Nath regime, the diffraction pattern consists of a fan of beamlets symmetrically spread with respect to the undiffracted beam (zero order). As shown in figure 1(b), each beamlet is diffracted at a fixed angle θ m = mλf/n 0 c s , and experiences a frequency shift mf, where m is an integer denoting the diffraction order. Thus, an AO device operated in this regime acts as a moving thin phase grating [18]. Although the splitting of light into multiple beams forming an optical frequency comb is of great interest in microscopy, it comes with a caveat. The intensity of each beamlet is different, rapidly decaying for higher orders, and never reaching more than the 34% of the incident intensity. However, as detailed in the next sections, new AO devices used in microscopy for fast axial focus control or generating interference patterns do operate in this regime.
When Q ≫ 1, known as the Bragg regime, the diffraction pattern typically contains a single diffraction order. For this to occur, the incident beam needs to enter the AO device at a particular angle, called the Bragg angle θ B , given by the expression: As shown in figure 1(c), such a condition, known as phase-or momentum-matching, leads to the deflection of the diffracted beam by an angle equal to θ B , with a frequency shift of the light wave of ±f depending on the sign of the incident angle. Hence, the Bragg regime is optically equivalent to a moving thick phase grating. Notably, the beam diffracted after the AO device maintains most of the incident intensity, with typical maximum values in the range of 60%-100%. Such a high diffraction efficiency facilitates the integration of AO devices in optical microscopes as add-on modules (no need to increase the illumination power). It also helps to design systems for controlling light in different directions by cascading multiple AO devices.
The previous description, although general, does not provide a complete picture of the AO effect. Additional aspects need to be considered when selecting or designing an AO device for microscopy. Among them, the type of ultrasound waves-longitudinal or transverse and traveling or standing-is essential. In general, AO devices make use of longitudinal waves. However, transverse waves are preferred in specific applications such as beam deflection at high spatial resolution. Traveling waves are prevailing in most AO devices, particularly in those operating at the Bragg regime. In this case, besides the ultrasound generator, the AO device needs to incorporate an acoustic absorber at the opposite side to prevent unwanted sound reflections that may reduce the intensity of the diffracted beam. The main advantage of traveling waves is a continuous operating frequency band. Alternatively, standing waves are generally used with Raman-Nath diffraction. Because a resonant cavity is needed here that may be susceptible to temperature fluctuations, feedback systems are required to maintain the diffraction pattern at the discrete resonant conditions. Note, though, that diffraction generated by standing waves depends on time. Therefore, once steady-state is reached, it is possible to select different light patterns at high speed-only limited by the driving frequency [19]. Resonance also allows for minimal driving power of the ultrasound actuators.
The optical anisotropy of the medium also plays a pivotal role in AO devices, with direct consequences for microscopy applications. By using birefringent materials, the incident and diffracted angles are no longer the same. Thus, the range of incident beam angles, or the operative frequency bandwidth of AO devices can be significantly increased [20]. As detailed in the following section, most AO deflectors and all AO tunable filters use birefringent materials. Particularly, uniaxial crystals, exhibiting a crystal axis with a refractive index different from the other two. As a result of the anisotropy of these materials, careful attention must be paid to the polarization direction of both incident and diffracted beams relative to the orientation of the AO device. Thus, additional optical elements, such as adjustable waveplates, are normally required to successfully integrate AO devices into microscopes.

Types of acousto-optic devices
The need for optimizing the many facets of light control has spurred the development of an entire family of AO devices. They all operate under the same principle and also feature the same key elements, including an AO medium transparent to light, an ultrasound source (normally a piezoelectric transducer), and the control electronics. The latter enables adjusting frequency and amplitude of the driving signal, and consequently, the ultrasound waves and the diffraction regime. Because all AO devices achieve light control without the inertia of moving mechanical components, they have typical response times well below milliseconds. Despite these similarities, each AO device has distinct characteristics suitable for performing a specific task, as briefly summarized in table 1. Understanding these characteristics is vital for microscopy applications, where strict requirements exist regarding focusing precision and photon collection efficiency [21]. Next, we detail the main features of a selected number of AO devices that are relevant for advanced microscopy.

AO modulators
One of the most widely used AO devices in microscopy is the acousto-optic modulator (AOM). It is a common component in laser-scanning microscopes, including confocal or two-photon systems, for elegant electronic control of the illumination intensity. It is also used for generating a synchronization signal and for laser pulse picking. In all these applications, the AOM acts as a high-speed light attenuator. AOMs consist of a piezoelectric actuator bonded to a facet of a rectangular solid medium-typically a birefringent crystal or fused silica. As shown in table 1, AOMs are operated in the Bragg regime at a fixed driving frequency  MHz range), producing the splitting of an incident beam into two beamlets at a fixed angle. By tuning the sound amplitude, the relative intensity between the two beamlets can be modulated. Although both beamlets can be used for light modulation, the diffracted beam is usually preferred in microscopy. The latter grants high contrast between the minimum and maximum light intensity-from no light to about 70% of the incident light, given by the typical diffraction efficiency of AOMs. A central aspect of AOMs is their high-modulation speed, determined by the time to reach the maximum or minimum values of the diffracted light (rise and fall time). For a Gaussian beam of size w, the rise time is related to the acoustic access time τ, namely the time the ultrasound wave needs to traverse the light beam: Thus, an AOM typically features a small aperture, which requires it to be placed between two lenses, one for focusing and one for re-collimation of the beam. Using this strategy, the diffraction efficiency is reduced, but the benefit is a decrease in modulation time, down to tens of nanoseconds.

AO deflectors
Acousto-optic deflectors (AODs) are AO devices optimized to function as fast electronic beam scanners (see table 1). They are implemented in advanced laser-scanning systems to maximize the laser deflection speed, and consequently, the spatiotemporal resolution retrieved from dynamic samples [22]. They are also used to shift the frequency of the incident beam by a controlled amount. In this case, they are also known as acousto-optic frequency shifters (AOFS).
AODs share many resemblances with AOMs regarding design, geometry, and operational mode (Bragg regime). However, some singular and important differences exist. In AODs, beam scanning is obtained by tuning the driving frequency-the angle of the diffracted beam (Bragg angle) depends on this parameter (see equation (2)). Thus, an electronic driver capable of operation over a wide frequency range is needed. Blocking of the undiffracted beam is also required. Importantly, to maintain a high diffraction efficiency over a broad angular range ∆θ d , AODs normally make use of birefringent materials. As previously described, for a fixed angle of incidence, the phase-matching condition only occurs at a given acoustic frequency. Birefringent materials, operated around the so-called tangential phase-matching, allow overcoming this issue and achieve an extended frequency band ∆f, typically of 50 MHz or above.
In microscopy, maximizing ∆f is not only crucial to achieve a high ∆θ d , but also to increase the number of resolvable focal spots N, defined as: where τ is the acoustic access time (see equation (3)). Notably, due to unavoidable beam divergence, resolution increases with beam diameter. Consequently, AODs commonly have an aperture much larger than AOMs. An aspect to consider is that both N and ∆θ d are larger for materials featuring a low speed of sound. Therefore, resolution and scanning range come at the cost of sacrificing speed: the response time of AODs is up to 4 orders of magnitude slower than AOMs, and within hundreds of microseconds. Still, AODs are amongst the fastest beam steering devices. It is also worth noting that the large acoustic bandwidth of AODs allows driving them with a multifrequency signal. In this case, each harmonic component diffracts the incident beam at its corresponding Bragg angle, resulting in an array of independently controlled beamlets.

AO tunable filters
Acousto-optic tunable filters (AOTFs) are AO devices that operate as electronically adjustable narrow-band-pass filters [23]. They are typically implemented in the beam-combining unit of laser-scanning systems to control intensity and wavelength of multiple laser lines. They can also be used as fast tunable beam splitters for multi-color imaging [24,25]. AOTFs, similarly to AODS, also operate in the Bragg regime, exhibit a rectangular geometry, use birefringent crystals, and require electronic drivers with a wide frequency range. Indeed, by changing the driving frequency, the central wavelength λ c of the passband that fulfills the phase-matching condition varies as: where ∆n is the birefringence of the crystal. Critical parameters for selecting an AOTF in microscopy are the spectral resolution ∆λ and wavelength scan rate. Commercial AOTF can have a ∆λ as narrow as one nanometer or below. The scan rate, defined as the time needed to switch between beam wavelengths, depends on the acoustic access time, with typical values of a few microseconds. A particular feature of AOTFs is the possibility to be implemented in the detection arm of a microscope for precise spectral imaging. Note, though, that the loss of light passing through the device, even if only 10%, is not ideal for fluorescence systems, in general having a low photon budget.

AOF device
Acousto-optofluidic devices (AOFs) function as electronic beam shapers to generate tunable optical patterns. They can be used for increasing imaging speed in laser-scanning systems or for producing light patterns in super-resolution techniques such as SIM.
In contrast to the AO devices previously described, AOFs consist of a liquid-filled chamber containing two pairs of orthogonally oriented piezoelectric actuators. Each actuator pair forms an acoustic resonant cavity. When driven on resonance, they produce ultrasound standing waves that diffract an incoming beam into an array of beamlets. Thus, the direct construction of 2D beam arrays is possible when both cavities are operative [26]. Interestingly, by adding a focusing lens between the device and the objective lens, the beamlets interfere, generating 3D patterns in the focal plane of the objective [19]. Note, although the latter is also possible with AODs, unavoidable crystal defects can deteriorate the pattern quality [27]. AOFs are operated at the Raman-Nath regime-as the significant acoustic attenuation of liquids at high frequencies makes it challenging to reach the Bragg regime. As such, AOFs offer a wide acceptance angle for the incident light, which eases alignment procedures and facilitates integration in microscopy systems.
The main features of AOFs are their high tunability and speed. By controlling the frequency and amplitude of the driving signal, the properties of the diffraction pattern, such as the number, spacing, and intensity of the diffraction orders, can be selected with the only constraint that the diffracted beams are not independent from each other. Also, the use of standing waves offers an extra control parameter. Employing synchronized pulsed illumination, the temporal phase difference between light pulses and the ultrasound wave enables to select a diffraction pattern faster than the acoustic access time. Given typical operation frequencies in the 0.5 − 5 MHz range, AOFs can operate at a timescale below 1 µs.

TAG lens
Tunable acoustic gradient (TAG) lenses are AO devices operating as fast varifocal lenses. They are typically used in microscopy to extend the depth-of-field of high numerical aperture (NA) objective lenses, and as fast axial scanners for high-speed volumetric imaging. Under certain conditions, they can also be used to generate Bessel beams [28][29][30][31].
TAG lenses have a cylindrical geometry, unique within the family of AO devices. They consist of a piezoelectric tube filled with a liquid. When driven on resonance, an ultrasound standing wave is formed, which can be described with a Bessel function [32]. Typically, a TAG lens requires the illumination beam clearly underfilling its aperture, in order to remain smaller than the central lobe of the Bessel function. In this mode, a TAG lens acts as a parabolic gradient-index lens, with the optical power δ (t) that periodically varies over time [29]: where F lens is the focal length of the lens, L is the length of the tube, ω the angular driving frequency, and n a is a constant that depends on ω and the liquid properties. The normal frequency range of a TAG lens is between 50 kHz and 1 MHz, and thus falls in the Raman-Nath regime. The effective NA of a TAG lens is low-as the aperture is limited by the central lobe of the Bessel function. Thus, for microscopy applications, TAG lenses are always used in combination with high NA objectives. By placing the TAG lens in a conjugate plane of the back focal plane of a microscope objective, magnification effects can be avoided, and the lens enables fast z-focus scanning. Such continuous z-focusing at microsecond time scales is faster than the integration time of many optical detectors. In this case, the simultaneous collection of multiple focal planes leads to an image with virtual extended depth-of-field. Notably, if synchronized stroboscopic illumination or fast detectors with appropriate electronics are used, information from multiple axial positions can be acquired. When illuminated with a beam larger than the central lobe of the Bessel function, the TAG lens acts as an axicon with a user-selectable cone angle [32]. In this case, a Bessel-like beam is formed. Such a beam is of interest in microscopy, particularly in applications where fast interrogation of a volume without the need for axial resolution is required, as in some aspects of neuroimaging.

Recent applications of acousto-optic systems for advanced microscopy
The enormous advantages that AO devices offer regarding fast control of light have previously been utilized in microscopy. However, their use was limited to a small number of niche applications, such as laser power control (AOMs) and fast filters (AOTFs). With the advent of new technologies, including fast optical detectors, electronics, and digital acquisition cards, new opportunities for the use of AO devices in microscopy have emerged. Here we provide examples of how novel schemes, designed around AO devices, can help to enhance the performance of optical microscopes, allowing us to characterize relevant dynamic events at unprecedented spatiotemporal resolution.

Fast z-scanning volumetric microscopy
Maximizing the amount of spatial and temporal 3D-information retrieved from a sample is crucial in scientific and industrial applications ranging from cell imaging to optical inspection. Typically, 3D microscopes operate by acquiring a z-stack, namely a sequence of optical sections at different focal planes. Such a strategy requires techniques capable of optical sectioning, that is the virtual slicing of a sample into 2D sections [5]. In addition, the focus position must be axially translated. Unfortunately, fast z-focus scanning, a key factor in determining the overall volumetric imaging speed, has been technically challenging. Even today, most state-of-the-art 3D microscopes feature piezoelectric actuators for z-focusing via sample or objective lens translation. Due to inertia, the z-scanning rate is limited to a maximum of about 100 Hz. Thus, the z-axis has traditionally been the slowest scanning axis in a microscope system, imposing a burden when imaging fast dynamic processes. The implementation of AO systems, in particular the TAG lens, into 3D microscopes has helped to change this paradigm, effectively overcoming the restrictions in z-scanning speed.

Non-synchronized z-scanning
By conjugating the TAG lens to the back-aperture of a microscope objective lens, continuous z-focus scanning is attained at microsecond timescales. Such speed is faster than the exposure time or pixel dwell time of conventional microscope cameras. When using continuous illumination and/or non-synchronized detection, information from multiple focal planes is collected in a single-camera frame, obtaining an image with a dynamic extended depth-of-field [28]. The extent of the depth-of-field depends on the z-scanning range, which in turn is given by the driving voltage amplitude at the TAG lens and the NA and focal length of the objective lens. Typically, the depth-of-field can reach an extension of up to one order of magnitude relative to the native value of the focusing lens. Note, though, that the sinusoidal z-scanning produced by the TAG lens results in a non-uniform extended depth-of-field, with the scanned edges more intense than the central part [33][34][35]. This effect is more pronounced as the scanned range increases, but it can be partially compensated by using synchronized illumination [36,37] (see section 3.1.2). Also, the increase in spherical aberration as one moves away from the native focal plane of the objective lens, a usually detrimental effect when trying to maximize the extended depth-of-field, can help here to render the scanned volume uniform [13]. TAG lens-enabled bright-field microscopes, combined with edge detection methods or other image processing algorithms, have become valuable tools for 'extended depth-of-field' imaging in fast industrial metrology applications and quality-control tasks [38]. Additionally, the tunable depth-of-field of the TAG lens has been used in two-photon microscopy [28], optical coherence tomography [39] and photoacoustic microscopy [40] for rapid interrogation of volumes and enhanced image quality.
Interestingly, full 3D information from a sample can be retrieved in a light-sheet microscope featuring extended depth-of-field detection. In such microscopes, the sample is selectively illuminated with a thin sheet of light placed at the focal plane of an orthogonally oriented detection objective. Volumetric imaging is then performed by acquiring a z-stack where both illumination and detection objectives need to move synchronously. Given the slow speed of z-focus translation, such an operation can be time-consuming. Variable focal elements that provide remote z-focus control can relax these speed constraints [13,41]. An even faster approach is to use an objective with an extended depth-of-field in the detection arm [42,43]. Because an in-focus image is obtained for any plane at any position, the sole translation of the light-sheet suffices to collect the z-stack. In addition, volumetric imaging speed only depends on camera frame rate, light-sheet translation speed, and signal-to-noise ratio (SNR). As shown in figure 2(a), by using AOD scanning for translating the light sheet, a TAG lens for dynamic extended depth-of-field and a high-speed camera (10 000 frames s −1 ), dark-field 3D images at sub-cellular resolution and rates as high as 200 volumes per second have been obtained. The same microscope has proven effective for fast in vivo imaging of biological systems ( figure 2(b),c).
The acquisition rate can potentially be doubled by using two Gaussian beams and sweeping them across the field of view synchronously, using a CMOS camera with a double rolling shutter [46]. Despite the high-speed capabilities of light-sheet microscopes with extended depth-of-field detection, extending the depth-of-field normally comes at the cost of losing signal. Parallelized illumination with multiple light sheets can significantly mitigate this effect [47].

Synchronized z-scanning
An alternative method for obtaining fast 3D images is to synchronize the TAG lens z-scanning with pulsed illumination [29,30,[48][49][50]. Provided the pulse duration is shorter than the time it takes to hop from one plane to another (sub-microseconds), a particular z-position can be selected. The resulting imaging speed is no longer limited by z-focusing, but rather by the camera frame rate or, ultimately, the SNR. Note that such a strategy results in a significant reduction of SNR. Indeed, collecting light is limited to a fraction of the entire camera exposure or pixel dwell time. Still, current light sources, such as light-emitting diodes or certain lasers, are capable of pulsed operation, which makes synchronized strobing illumination easy to implement. This approach has been successfully used for fast micro-particle velocimetry inside microchannels [48] or optical inspection of consumer goods [38]. Importantly, the use of strobing light with an inter-pulse separation longer than the triplet state relaxation time of the fluorescent dyes, can have the added benefit of reducing photobleaching or phototoxicity [13,51].
A fast 3D stack can also be collected by synchronizing the TAG lens with fast optical detection [45,52]. By tagging the photons with their arrival time relative to the TAG lens position, a z-stack can be reconstructed in a post-processing step. Note that such operation requires detectors and data acquisition hardware with sub-microsecond response time. Thus, this strategy is more suitable for laser-scanning microscopes such as confocal or two-photon systems that feature point detectors. Similarly, fast electronics cards based on field programmable gate arrays are preferred for data acquisition [53]. Despite the added complexity regarding electronics, this approach offers two important advantages compared to synchronized illumination. First, valuable information can be collected during the entire pixel dwell time, resulting in improved SNR. Secondly, the number of sections of the z-stack can be arbitrarily selected during a post-processing step. As shown in figures 2(d)-(f), TAG lens-enabled microscopes with synchronized detection have been successfully implemented in several applications. They include fast fluorescence correlation spectroscopy [54], confocal microscopy [52], flow cytometry [55], or two-photon in vitro [31] and in vivo imaging [45,53]. It is worth to note that the high-speed 3D light control offered by a laser-scanning microscope featuring a TAG lens can be used for operations beyond imaging, such as single-particle tracking [15], sample movements tracking [56,57], or combined laser photo-stimulation with functional imaging [58].

Random-access scanning microscopy
Random-access microscopy or RAM is an imaging method implemented in laser-scanning microscopes and characterized by focusing a laser beam at a discrete number of individual and user-selectable sites of a specimen. The rationale of this approach is to drastically reduce acquisition time by interrogating a limited number of pre-selected points or regions of interest within the sample. As described in section 3.1, confocal or two-photon microscopes retrieve information from a volume by sequentially scanning an extensive collection of pixels, each requiring a particular illumination time (pixel dwell time). In sparse samples or when only specific parts of the sample are of interest, interrogating the entire volume is inefficient. RAM addresses this issue by restricting the collection of information to only selected regions of interest by using a two-step process. First, the regions of interest are selected. This task is performed by acquiring a conventional confocal or two-photon 3D image. Second, the laser focus is programmed to hop from one position to another. To minimize waiting time, light hopping should occur as fast as possible. High speed and accuracy of beam positioning have rendered AODs the tool-of-choice for implementing RAM.

2D-RAM
As described in section 2.1, varying the driving frequency of AODs allows for scanning a laser beam along one direction (1D scan). Such scanning can be performed either continuously [59,60], or at discrete positions [61,62]. Since AODs do not use movable mechanical parts and are not limited by inertia, changing the deflection angle can be extremely fast, down to microsecond timescales [63]. Importantly, 1D scans can be extended to 2D scans by properly arranging two orthogonal AODs in series [61,62]. In this scheme, each AOD controls the x-and y-axis deflections independently, enabling illumination of an arbitrary number of spots within a plane. The high versatility of 2D-AOD scanning has been exploited in optogenetics, where selective illumination of a sample is key. Examples include mapping the functional synaptic connections between neurons in vitro [64] and in vivo [65] as well as studying the role of GABA receptors in orthodromic propagation of axonal action potentials [66]. However, the central application of AODs has arguably been RAM.
The first RAM systems were implemented using 2D-AOD scanners and single-point detectors in a non-descanned configuration. While not capable of optical sectioning and featuring a relatively low spatial resolution, they enabled beam re-positioning in only 3-5 µs and acquisition rates as high as 200 ksamples s −1 [61]. Integration of 2D-AODs into confocal microscopes enabled a five-fold enhancement in the axial resolution while maintaining impressive frame rates, as high as 25 kHz [67]. Such a system, though, comes at the cost of increased complexity. Specifically, an array of pinholes is required in the detection arm. To this end, a digital micromirror device (DMD) can be used. Unfortunately, the effective pinhole size using a DMD is typically two-fold larger than in conventional confocal systems, resulting in reduced rejection of out-of-focus light .
Today, RAM is almost exclusively used with two-photon microscopes. In this case, tightly focused femtosecond laser pulses confine light emission to the focal volume [68], obviating the need for detection pinholes. Thus, the integration of 2D-AOD systems into two-photon microscopes comes at relative ease. Additionally, the core advantages of AO systems (speed, versatility) and two-photon microscopes (3D sub-cellular imaging at depth) are preserved. All these properties have rendered RAM particularly suitable for in vivo monitoring of dynamic events that are sparsely located. Given that such settings are typically found in neuroscience applications, particularly in functional brain imaging, it comes as no surprise that RAM has found its niche application in this field.
Even if two-photon systems are the prevailing RAM technology, they can face issues regarding the spatiotemporal dispersion of short laser pulses induced by the diffractive nature of AODs. Temporal dispersion broadens the pulse width, lowering the laser peak-power and, hence, the two-photon excitation efficiency. Spatial dispersion results in the spectral decomposition of the laser pulse, significantly reducing the number of resolvable spots of the AOD scanner. Both effects can be compensated, but careful attention is needed. In the case of temporal dispersion, pre-chirping of the laser pulse is the most common strategy. It is generally implemented with a pair of two identical prisms that introduce a negative dispersion depending on their separation. While an inter-prism separation of 65 cm has proven sufficient for compensating ∼90% of the dispersion introduced by the AODs [22], in some instances it may take distances as long as 4 metersimpracticable in many laboratories or commercial systems. Fortunately, more compact approaches such as stacked-prisms [69] or placing a tilted prism before the AODs offer viable alternatives [70][71][72]. Regarding spatial dispersion, the straightforward solution would be to use longer laser pulses (300-700 fs) which feature a narrower spectral bandwidth [73,74]. Unfortunately, such pulse durations also results in lower two-photon signal, which can be detrimental in applications where excitation efficiency is low. In these cases, compression of the laser pulse by a diffraction grating [69,75], an AOM [76], or a single prism [22] is possible. Interestingly, the latter two can be used to compensate for both spatial and temporal distortions.
RAM systems featuring 2D-AODs with well-compensated spatiotemporal distortions have been successfully used to characterize several key processes in the field of neurosciences. Examples include multisite uncaging of neurotransmitters at high spatial resolution (∼0.75 µm) [75], monitoring fast neural events such as synaptic or action potentials, rapid (frame rates 0.5-1.5 kHz) recording of calcium transients from several (up to 80) spines of the dendritic tree [73], identifying the direction of neural network activation with single-cell resolution in brain slices to study epilepsy [77], or obtaining fluorescence measurements from various neurons (up to 91) at a sampling rate of 180-490 Hz from layer L2/3 of mouse cortices in vivo. 11

3D-RAM
The RAM systems presented so far restricted fast scanning to a single 2D plane. Given the complex 3D organization of cellular structures such as the brain, extending fast scanning to a whole volume is a central aspect in RAM. While several variable optical elements exist for fast z-scanning [13], two pairs of 2D-AOD scanners operating in series can also be used for this purpose. As shown in figure 3(a), each pair of scanners must be driven by chirped and counter-propagating acoustic waves [62,78,79]. Such a combination results into two independent effects: (1) the beam is deflected in one direction with an angle proportional to the difference between the central frequencies of the AODs; (2) beam convergence or divergence is introduced because the AODs act as a cylindrical lens with a focal length inversely proportional the to the rate of change in frequency (chirp) [80]. Therefore, orthogonally cascading two scanners results in beam deflection in x and y, together with a 3D spherical change of the beam collimation. Optically conjugating the pair of 2D-AODs with a focusing lens enables fast x, y, z focus control ( figure 3(b)). Note that, because four AODs are used in such a 3D-scanning system, only the effects of temporal dispersion must be taken into consideration. However, changing the collimation of the incident beam for z-scanning can result in spherical aberration [13]. This issue can be addressed by using synchronized illumination, in which case the AODs can act as beam shapers [81,82].
Over the last decade, RAM utilizing 3D-AOD scanners has become an increasingly popular technique in neuroscience. As shown in figure 3(c), such systems have been used for monitoring 3D localized calcium transients at rates as high as 10 kHz in vitro [78], as well as in vivo with synthetic [85] and long-wavelength genetically encoded indicators [86]. Note that, to maximize the scanned volume, wide-band AODs capable of wider deflections are required [87]. With such AODs, volumes as large as 700 × 700 × 1400 µm 3 were scanned at sub-millisecond speed and sub-cellular spatial resolution, enabling recording the calcium activity of more than 500 neurons [83].
An important aspect when applying 3D-RAM in awake behaving animals are motion artifacts, induced by heartbeat, respiration, as well as any muscle contraction [84,88]. As this can change the location of tissue details relative to the pre-selected scanning sites, dynamic correction is necessary for long-term experiments. Such an effect can be corrected by a nonlinear (parabolic) chirp of the acoustic waves. Thus, pre-selected scanning points can be converted into small 3D lines, surfaces, and volumes (ribbons) that can used to compensate for possible focal shifts. As shown in figure 3(e), this strategy enabled measurements of neuronal activity on behaving animals, down to the spiny dendritic segments, over an axial range of 650 µm.

Frequency-division multiplexing microscopy
Besides fast z-scanning and hopping from one region to another within a sample, AO devices can be used to boost the 2D imaging speed. The straightforward application is to use AODs for rapid scanning in confocal or two-photon microscopes [89]. In these cases, though, even faster approaches exist such as the widely commercialized resonant galvo-scanners [90]. More recent applications have combined parallelization methods with AO devices. Examples include the use of beam-splitting gratings [91] and multiple illumination paths, each resulting in a different z-focus position [92]. Among them, frequency-division multiplexing (FDM) microscopy offers arguably the fastest 2D imaging speed.
The essence of FDM is to simultaneously illuminate multiple points of a sample, each at a specific temporal frequency. Thus, there is a univocal relationship between modulated frequency and position. In other words, the position is encoded in the frequency. The overall signal from the sample is recorded with a single photodetector. By decoding the signal in the frequency domain, e.g. using a Fourier transform, the intensity of each frequency component can be retrieved, and consequently, an image can be reconstructed.  [93] 2013. (c) Left: scheme of an FDM system with wide-field detection used for super-resolution imaging. Each laser is sinewave-modulated at F/2, F/3, and F/4, with F being the camera frame rate. Center: 2D images of mitochondria (magenta) and microtubules (green). Right: 3D image of microtubules color-coded for Z-position (from 300 nm, blue, to 500 nm, yellow). Reproduced from [100]. CC BY 4.0.
As in FDM used in telecommunications, this strategy increases the rate of data recording by dividing the available detection band into multiple non-overlapping frequency channels, each carrying a separate signal. Compared to sequential scanning methods, and provided a frequency bandwidth large enough, FDM can increase the imaging speed by a factor equal to the number of illuminating points. Note, though, that this imaging modality typically needs relative long acquisition times to resolve the individual frequency components, depending on their period duration. Therefore, it is essential to modulate the excitation light at high frequencies. The ability of AO devices to frequency-shift the diffracted light renders them optimal tools for modulating light in the MHz-range. At such high-modulation frequencies, FDM enables imaging at rates at thousands of frames per second.
Given the intrinsic high speed of single-point photodetectors, FDM is most commonly implemented in laser-scanning systems [93][94][95][96]. As shown in figure 4(a), the typical elements consist of a single AOD and an AOFS. By driving the AOD with different radiofrequencies, a 1D comb of beamlets is obtained, each with a given deflection angle and frequency shift (tone). By interfering such multi-tone comb with the beam providing from the output of the AOFS (reference beam), the intensity of each beamlet can be modulated at MHz-range. Indeed, the interfering process results in frequency beats, whose frequency is the difference between the tone of each beamlet and that of the reference beam. When illuminating a fluorescent or scattering sample [97,98] with such a comb of modulated beamlets, the univocal relationship between position and modulation frequency is established. Combining two AODs can result in 2D-combs of beamlets, enabling direct reconstruction of 2D images [99]. In most common implementations, though, the sample is illuminated with only 1D-line, thus requiring additional scanning for 2D or 3D images. While traditional galvo-scanners can be used [95], this extra degree of freedom is intrinsic to imaging flow cytometry systems. In this case, the temporal displacement of objects flowing in microfluidic channels acts as an additional scanned axis (see figure 4(b)). By using the 1D-comb of modulating beamlets to illuminate the direction perpendicular to the flow, 2D fluorescence confocal images have been acquired at kHz rates [93], with the main speed limited being imposed by the fluorescence lifetime of the fluorophore [94]. By combining flow imaging with z-focusing methods, z-stacks can be acquired. Using this strategy, 3D images of microalgal cells have been acquired at 100 volumes per second without motion blurring [94].
FDM can also be implemented in wide-field imaging systems, such as light-sheet [101] and super-resolution microscopes based on single molecule localization approaches [100]. These systems cannot perform as fast as the previously described ones due to the limited frame rate of cameras. Still, they can outperform traditional implementations. For instance, by modulating different colors, each with a particular frequency, simultaneous super-resolution multi-color imaging using a monochromatic camera becomes possible (figures 4(c)-(e)). The gain in speed is proportional of the number of colors detected, while the localization precision of the native microscope is maintained.
Advantages of FDM, besides speed, are the possibility to improve the SNR of the reconstructed image. By applying lock-in detection algorithms, each unique beat frequency can be retrieved while filtering out any external source of noise. However, the shot-noise of each point (plane) is shared by all the multiplexed points (planes). This can be specially detrimental when imaging bright objects close to dim ones, however synthetically extending the acquisition time by phase-matching techniques can mitigate this effect [95]. Another advantage of the technique is the compatibility with highly scattering samples. Specifically, FDM combined with wavefront shaping has been successfully used to enhanced the laser focused intensity by a factor of 125 inside a 3 mm-thick chicken breast [99]. Special consideration must be given to the modulation bandwidth of AO devices and crosstalk between frequency beats. Typically, a large tone spacing is desirable to facilitate image reconstruction and avoid crosstalk. Unfortunately, the limited modulation bandwidth of AO devices determines the number of points that can be simultaneously illuminated. Strategies to increase such bandwidth include quadrature amplitude modulation [94]. Also, by properly selecting the phase of each tone or using machine-learning algorithms [102], crosstalk effects can be reduced. Today, state-of-the-art FDM systems feature about 100 comb lines with tone spacing of 1 MHz and a bandwidth of 200 MHz.

Summary and future outlook
The inertia-free nature and tunability of AO devices enables unprecedented light control in optical microscopy, opening the door to advancing research in important areas such as optical inspection, metrology or biology. Here we provided some key examples to illustrate how the unique properties of AO devices enable novel microscope designs capable of volumetric imaging at high spatiotemporal resolution. Thus, the fast z-scanning of a TAG lens allows rapid collection of a z-stack or dynamic extension of the depth-of-field of a microscope, significantly reducing 3D acquisition time. Similarly, selection and superimposition of the acoustic frequencies applied to an AOD has been recognized as the primary enabler of advanced scanning strategies in confocal and two-photon microscopes that further boost imaging rates by scanning pre-selected points of a volume or encoding spatial information in the frequency domain. As a result of these new developments, it is possible today to study fast dynamic processes such as neuronal communication at the cellular level and sub-millisecond resolution. The future of AO for optical microscopy looks even brighter. As progress will be made in the speed and sensitivity of light detectors [103,104], volumetric imaging will be performed at even higher spatial resolution and speed. Combined with the help of artificial intelligence [105] or fast algorithms [106,107], AO devices will increasingly become a fundamental tool of advanced imaging systems.
In order to keep this review compact, certain topics were not addressed here, including the use of AO devices for improving the spatial resolution of microscopes beyond the diffraction limit. In this regard, AOD systems have already been used in super-resolution systems based on single molecule localization [100], stimulated emission depletion microscopy [108], or SIM [27]. As new AO devices are being developed for dynamic light pattern generation, such as the recently implemented AOF [19], faster super-resolution methods with minimal photobleaching will become possible. Based on these results, we envision future AO systems that will continue to push the limits of optical microscopy, offering new opportunities to study biological processes at high spatiotemporal resolution and over a large volume, thus providing a clearer picture of living organisms and their functions from the molecular to the macroscopic scale.