Acoustic-feedback wavefront-adapted photoacoustic microscopy

Optical microscopy is indispensable to biomedical research and clinical investigations. As all molecules absorb light, optical-resolution photoacoustic microscopy (PAM) is an important tool to image molecules at high resolution without labeling. However, due to tissue-induced optical aberration


INTRODUCTION
Optical microscopy is crucial to many science and engineering fields.As all molecules absorb light, photoacoustic (PA) microscopy (PAM) is an important technique that employs non-ionizing photons and low-scattering ultrasound to image molecules.By offering universal optical absorption contrast, deep penetration, and label-free capability, PAM is suitable for a wide range of biomedical applications, such as functional imaging of blood oxygenation, tracking of circuiting tumor cells, lipid imaging, and label-free histology [1][2][3][4][5][6].PAM involves both optical excitation and acoustic detection, thereby providing a great diversity of embodiments.When biological tissue is probed with a pulsed and focused light beam, acoustic waves are generated due to absorption-induced heat generation, thus revealing cellular or even sub-cellular structures with high spatial resolution determined by the optical diffraction limit.This modality, termed optical-resolution photoacoustic microscopy (OR-PAM), was first developed in 2008 to image microvasculatures in mice in vivo [7].However, biological tissue is inherently heterogeneous, which distorts the optical wavefront and causes optical aberration as light propagates through.Since the performance of OR-PAM strongly relies on the quality of the excitation focus, it inevitably suffers from degradations in both PA amplitude and spatial resolution while imaging at depths.
OR-PAM relies on optical focusing to achieve high lateral resolution and acoustic time-of-arrival to achieve high axial resolution; it produces a one-dimensional (1D) depth-resolved image (an Aline) per laser pulse.Therefore, the quality of the excitation optical focus is crucially important to the performance of OR-PAM.The first attempt to introduce AO into OR-PAM was in 2010, which aims to correct system-generated aberration [43].By employing an SH sensor to directly measure the backscattered light from a white paper and a deformable mirror (DM) to compensate for the system-generated aberration, significant improvements in both signal strength and lateral resolution were demonstrated [43].In 2022, AO was employed to compensate for the spherical aberration caused by the mismatch of refractive indices between water and a target sample, by using a three-layer liquid crystal device optimized for correcting this specific aberration mode [44].Despite these efforts, however, using AO to correct tissue-induced aberration in OR-PAM has not been demonstrated.This situation may be due to the lack of appropriate guide stars in PAM.On one hand, back-scattered excitation light does not function well, as the back-reflected light may come from different regions from the focal volume.On the other hand, the widely used fluorescent signals do not naturally exist in PAM.To fill this void, we develop acousticfeedback wavefront-adapted PAM (AWA-PAM), which employs acoustic feedback to correct for tissue-induced optical aberration in OR-PAM.In contrast to other AO assisted three-dimensional (3D) optical microscopy techniques that generally abandon the correction for defocus to avoid axial shifting [45], AWA-PAM delightfully takes the correction of defocus into consideration.This choice is because the depth information of PAM is uniquely determined by the time of arrival of the acoustic waves.In this condition, optimizing the depth of the focal plane for each A-line can considerably benefit the imaging of small features at different depths across the field of view.To demonstrate the feasibility of AWA-PAM, we built a microscope system by integrating a liquid crystal based spatial light modulator and an OR-PAM system.The tissue-induced aberration was dynamically compensated point-bypoint by optimizing the phase map displayed on the SLM with a greedy algorithm.We will show in the next section that AWA-PAM effectively corrects for tissue-induced aberration when imaging in vivo zebrafish embryos and mouse ears and significantly improves the image quality, revealing microstructures that are indiscernible with conventional PAM.

A. Principle of AWA-PAM
We start by describing the operational principle of AWA-APM, which is schematically shown in Fig. 1.In conventional PAM, as shown in Fig. 1(a), pulsed light is focused into the biological tissue to locally induce ultrasonic waves, which are subsequently detected by a focused ultrasonic transducer through confocal geometry.The peak-to-valley value of the measured ultrasonic wave, defined as the PA amplitude, is generally used to reflect the local absorption of the tissue within the optical focus.In this condition, the full width at half maximum (FWHM) size of the optical focus determines the lateral resolution.In practice, however, optical aberration aggregates as the excitation light propagates due to the heterogeneity of biological tissue, which broadens the focus and deteriorates the resolution.Moreover, as light is not tightly focused and energy is not highly concentrated, the measured PA amplitude also decreases for small features.As a result, tissue-induced aberration deteriorates both lateral resolution and signal strength.
Inspired by the effectiveness of adaptive optics in fighting against tissue-induced optical aberration in optical microscopy, we developed AWA-PAM to effectively mitigate this issue, as shown in Fig. 1(b).The key enabling point is to modulate the excitation light by using an SLM before it enters the tissue.One would expect that tissue-induced aberration can be compensated by modulating the incident wavefront, resulting in a sharp focus at depths.Due to the special detecting scheme with ultrasound, AWA-PAM adopts an indirect wavefront sensing approach by employing acoustic feedback to estimate the desired phase map through a greedy optimization algorithm.To begin with, the SLM displays a planar phase map such that AWA-PAM effectively functions as conventional PAM.Then, a series of ordered Zernike polynomials are loaded to the SLM in order.These Zernike polynomials are orthogonal to each other over circular pupils [46], and each one effectively represents one type of optical aberration.A feedback loop is established among the SLM, the ultrasonic transducer, and the computer.The corresponding coefficients for each order of the Zernike polynomials are traversed and determined in an ergodic manner [47,48].This feedback loop guarantees continuous enhancement in PA amplitudes after correcting aberrations for each order, leading to the formation of a high-quality focus eventually.The AWA-PAM is relatively simple and does not require direct optical wavefront sensing to determine tissue-induced aberration, which is particularly suitable for PAM with ultrasonic detection.This process is essentially similar to that of feedback-based wavefront shaping with acoustic feedback [49][50][51][52].However, the scattering process inside biological tissue is almost random, which requires a large number of modes to be tested to generate a focus with acceptable quality.Thus, this inefficient method makes it almost impossible to implement for in vivo studies.In comparison, optical aberrations are known to be well-represented by the Zernike polynomials.In this condition, the feedback process is quite efficient, as one needs to consider only a few low-order Zernike polynomials to account for optical aberration.Therefore, point-by-point compensation for spatially inhomogeneous optical aberration can be realized even for live tissue.Furthermore, some of the previous works allow only focusing light to indefinite locations and are not suitable for 3D imaging, unlike AWA-PAM.

B. Compensating for System Aberration
We first compensate for the system aberration by imaging a carbon fiber.The experimental setup of AWA-PAM is schematically shown in Fig. 2(a) with a detailed description in Appendix A. To guarantee sufficient accuracy under static conditions, the step size for traversing the coefficients for a given Zernike mode was set to 0.2 π rads, and the range was from −10 π to +10 π rads.Phase wrapping was performed.Using PA amplitudes as feedback, Fig. 2(b) shows the signal enhancement contributed from each order.Among them, the 1st order (i.e., piston) has no effect, while the 2nd and 3rd orders that correspond to tip and tilt are the two largest contributors.These two corrections mainly account for the misalignment of the SLM.Besides, the correction for the 4th order that corresponds to defocus helps, possibly due to correction for the curvature of the SLM, the use of a lens pair and depth-induced aberration.Corrections for the Zernike polynomials from the 5th order to the 8th order also provide certain contributions.In contrast, the Zernike polynomials after the 10th order have negligible effects, indicating that high-order aberration does not exist in the current system.Overall, compensating for system aberration effectively enhances PA amplitudes by about three times.The image of the focus shown in Fig. 2(c) confirms that, in free space, the lateral resolution can be brought back to the theoretically predicted ∼3 µm after correcting for the system aberration.Since systemgenerated aberration is static, a fixed phase map corresponding to correcting the system aberration is always used as the initial phase map before subsequent wavefront optimization to correct for sample-induced aberration.

C. Imaging Spinal Cords of Zebrafish Embryos In Vivo
The feasibility of AWA-PAM to compensate for tissue-induced aberration was demonstrated through imaging spinal cords of zebrafish embryos in vivo.The zebrafish used for imaging is two days after fertilization.After anesthetizing the zebrafish, we first performed whole-body imaging through conventional PAM, which is shown in Fig. 3(a).Then, we proceeded to execute AWA-PAM to demonstrate its superiority in revealing structures that were hindered by optical aberrations.Given that imaging the whole fish is time-consuming, wavefront correction was performed on a smaller region that mainly contains the spinal cord, which is denoted by the white dashed square in Fig. 3(a).To avoid causing artifacts due to beam drifting, we restrict the orders of the Zernike polynomials from 4 to 10 (i.e., excluding tip, tilt, and piston) during in vivo experiments.The step size of the coefficient for traversing each Zernike order was set to π rads, and the optimization range was from −4π to +4π rads.The isoplanatic patch size was measured to be 15 × 15 µm 2 (with the quantification procedures described in Supplement 1, Note 1) and we used the same corrective wavefront for the measurements taken within the isoplanatic patch.Higher Zernike orders, smaller step sizes, finer isoplanatic patches, and larger optimization ranges can be targeted, which is at the cost of increased imaging time and will be discussed later.Figures 3(b) and 3(c) show the obtained 3D image and its corresponding 2D maximum amplitude projection (MAP) image of the spinal cords of the zebrafish embryo by employing AWA, respectively.As a comparison, the obtained 3D image and 2D MAP image for the same region without using AWA correction are shown in Figs.3(d) and 3(e), respectively.It is clear that AWA-PAM provides richer structural information than that obtained without AWA correction.Notably, AWA correction includes the adjustment of the 4th order of the Zernike polynomials that represents defocusing, allowing spinal cords at different depths to be identified.Such an implementation presents a key difference between AWA-PAM and other AO-assisted 3D optical microscopy.For example, the spinal cord enclosed within the white dashed box in Fig. 3(c) could hardly be seen without AWA correction [Fig.3(e)] but becomes visible with the assistance of AWA correction.The depth information for the 2D MAP image acquired with AWA correction [Fig.3(c)] was extracted based on the time-of-flight information of the ultrasonic wave and provided in Fig. 3(f ).This image shows that different spinal cords are indeed located at different depths.Detailed information on the optimization performance and phase maps at different locations can be found in Supplement 1, Note 2.

D. Imaging Microvascular Structures of Mouse Ear In Vivo
The effectiveness of AWA-PAM was also demonstrated by imaging microvascular structures of mouse ears in vivo.The mouse was anesthetized by isoflurane during the entire experiment, and the ear to be imaged was in a natural state, i.e., without being pressed or flattened, which can otherwise restrain blood flow.The same setting used for imaging zebrafish embryos was used here.Figures 4(a These observations demonstrate the superior performance of AWA-PAM over conventional PAM in revealing microstructures that are wiped out by optical aberrations.Detailed information on the optimization performance and phase maps at different locations can be found in Supplement 1, Note 3.

DISCUSSION
In principle, AWA-PAM relies on the assumption that the tightest focus produces the strongest PA amplitude.Unlike two-photon fluorescent microscopy, which employs nonlinearity, PA is generally considered a linear process.Nonetheless, when imaging capillaries in practice, Supplement 1, Note 4 suggests that the lateral resolution degrades to tens of microns at the depths of a few hundred microns.Since the lateral resolution without AWA correction is larger than the diameters of many capillaries, AWA-PAM can increase the PA amplitude and achieve a tighter focus, thus revealing more microscopic features.Moreover, even for very big vessels shown in Fig. 4, we found a roughly 20%-30% signal enhancement by using AWA correction (detailed in Supplement 1, Note 5).This observation is likely because a tighter focus produces more high-frequency components, which leads to larger signal strengths in OR-PAM where high-frequency ultrasonic transducers are generally employed [53][54][55].It is also worth mentioning that the optical focusing depth was adjusted in AWA-PAM, which is very different from the procedures in conventional AO-assisted 3D microscopy.Such an operation takes advantage of the acoustic detection in PAM and the sparsity of the sample along the depth direction, which is generally true for many biological tissues including vasculatures in mouse ears.In this context, the imaging depth range of AWA-PAM can reach acoustic depth of focus, which is much larger than the optical depth of focus.In short, since PAM detects ultrasound instead of light, using acoustic signals rather than optical signals as a feedback metric is a natural choice.Moreover, the generation of acoustic signals is a rather complicated process that involves light, heat, and sound; the validity of AWA-PAM also relies on the fact that the distribution of the acoustic property of the sample is much more uniform than that of the optical property.
The imaging speed of AWA-PAM can be further improved in future studies.In the current practice, seven measurements were made to determine the optimum coefficients for each Zernike order.With certain prior knowledge of the extent of aberration and a sufficiently high signal-to-noise ratio, 3N or even 2N + 1 measurement could be enough to determine the coefficients of N orders [41,45].Such a decrease in the number of measurements, albeit at the cost of determination accuracy, can effectively improve the imaging speed.Second, for the current imaging system, the bottleneck of the system speed is the low refreshing rate of the SLM (60 Hz).Consequently, optimizing the coefficients of the Zernike polynomials (locating the inflection point) leads to an averaged A-line scanning rate of 1 Hz.Thus, taking the imaging process of mouse ears as an example, acquiring a two-dimensional image of 1 mm 2 takes about 37 min.Although this duration is much longer than that consumed by conventional PAM, AWA-PAM can be further sped up by using micro-electro-mechanical-system-based SLMs that operate up to hundreds of kHz [56][57][58][59], allowing twodimensional images of 1 mm 2 to be formed within ten seconds.Imaging speed can be further improved by choosing an adaptive scanning strategy.For example, by tracking the vessels' profile [60], one can perform fine compensations for optical aberration only in those regions that are of particular interest.Given that more than 60% of the area is informationless, the imaging time could be further reduced with this strategy.To demonstrate the principle, the current system was built in transmission mode.A reflection-mode system will be built in the future to adapt AWA-PAM for various applications [61][62][63].
In this study, AWA-PAM was demonstrated using an imaging system with a numerical aperture (NA) of 0.1 (which is the most widely used value), leading to a 3 µm resolution under the aberration-free condition.The principle of AWA-PAM works for different NAs, and the adaptive correction should be more critical for larger NAs.While it is difficult to characterize resolution enhancement for in vivo studies, this enhancement may be quantified through the employment of tissue-mimicking phantoms with controlled thickness.As detailed in Supplement 1, Note 4, experimental results show that AWA-PAM effectively improves the lateral resolution at all depths tested.In particular, it achieves nearly two-fold improvement in lateral resolution in comparison to conventional PAM at a depth range of 150-200 µm.Nonetheless, since scattering phantoms are mesoscopic homogeneous and do not induce strong optical aberration, we consider the obtained values may be conservative compared to the ones achieved during in vivo experiments.Moreover, as illustrated in Supplement 1, Note 4, AWA-PAM exclusively operates within the quasi-ballistic regime, unable to address optical scattering.Beyond imaging depths of 1 mm in soft tissue, AWA-PAM diminishes its efficacy, and the resolution eventually becomes acoustically determined.
In conclusion, we have developed AWA-PAM to compensate for tissue-induced aberration dynamically.Endogenous optical absorptive objects are employed as internal guide stars to provide acoustic feedback in order to characterize spatially inhomogeneous optical aberration.The feasibility of AWA-PAM was experimentally demonstrated on both zebrafish embryos and mouse ears in vivo.Considerable improvements in both lateral resolution and signal strength were observed, showing that AO effectively helps PAM to generate a more intensified and localized focus at depths.We envision that the demonstrated approach will serve as a useful tool for label-free optical imaging in the quasi-ballistic regime.

Experimental Setup
A pulsed laser (Changchun New Industries, MPL-H-532-30 µJ) operating at 532 nm was used as a light source.A halfwave plate (Thorlabs, WPH05ME-532) and a polarizing beam splitter (Thorlabs, PBS532) controlled the power being dumped into the system and set the output light to be horizontally polarized.The laser has pulse-to-pulse intensity fluctuations up to 10%, which can potentially contaminate the feedback signal.To address this issue, a photodiode (Thorlabs, SM1PA1A) was employed to monitor the intensity of the reflected light from the polarizing beam splitter, and the measured value was used for normalization.Then, the laser beam was expanded through a pair of lenses

Fig. 1 .
Fig. 1.Schematics of the operational principle of AWA-PAM.(a) In conventional PAM, pulsed light is focused into the biological tissue to locally induce ultrasonic waves, which are measured by a focused ultrasonic transducer.The heterogeneity of the biological tissue distorts the wavefront of the focused light, decreasing the signal strength and resolution.(b) In AWA-PAM, a spatial light modulator modulates the wavefront of the pulsed excitation light to compensate for tissue-induced aberration.The phase map displayed by the SLM is the inverse phase of the distorted wavefront, thereby nullifying the distortion and creating a sharp focus at depths.To obtain the desired phase map, a feedback loop between the SLM, the computer, and the ultrasonic transducer is established to optimize the PA amplitude.

) and 4
(b)  show the 3D microvascular images of the mouse ear from two different views obtained with AWA correction, and its corresponding 2D MAP image is also shown in Fig.4(c).In comparison, 3D images and corresponding 2D MAP image obtained without AWA correction are illustrated in Figs.4(d)-4(f ).Although big vessels can be identified in both images, the AWA correction effectively helps to identify microvascular structures at depths.For example, by scrutinizing the regions highlighted by the white dashed boxes in Fig.4(c), one could hardly see similar features in the same regions in the image obtained without AWA correction [Fig.4(f)].Moreover, by comparing the MAP images belonging to different categories, we note that signal strengths obtained with AWA correction are generally stronger than those obtained without AWA correction.Furthermore, Figs.4(g) and 4(h) plot the profiles along the two white dashed lines labeled in Figs.4(c) and 4(f ).A direct comparison shows that richer structural information can be observed with AWA correction (the red solid curve).In contrast, the 1D profiles obtained without AWA correction, denoted by the dashed blue curves, are almost informationless.As before, for the 2D MAP image with AWA correction activated, the depth information based on the time-of-flight information of the ultrasonic wave is provided in Fig.4(i).As we can see from the figure, microvascular structures that are hardly seen in Fig.4(f ) are at a depth that is distinctively different from the focal plane (13.1 mm).

Fig. 3 .
Fig. 3.In vivo imaging of zebrafish embryos.(a) Whole-body image of the zebrafish embryo, captured through conventional PAM.The white dashed square denotes the area of interest with spinal cords.Scale bar: 500 µm.(b) 3D image and (c) its 2D MAP image of the area highlighted in (a) obtained with AWA correction.Image sizes: 0.60 × 0.50 × 0.45 mm 3 (x , y , z).Scale bar, 100 µm.(d) 3D image and (e) its 2D MAP image of the area highlighted in (a) obtained without AWA correction.Image sizes: 0.60 × 0.50 × 0.45 mm 3 (x , y , z).Scale bar, 100 µm.(f ) Depth information of the microstructures in the 2D MAP image in (c).Scale bar, 100 µm.

Fig. 4 .
Fig. 4. In vivo imaging of mouse ears in the natural state.(a), (b) Two different views of the 3D microvascular images obtained with AWA correction.Image sizes: 1.00 × 1.00 × 0.40 mm 3 (x , y , z).(c) Corresponding 2D MAP image obtained with AWA correction.Scale bar, 200 µm.(d), (e) Two different views of the 3D microvascular images obtained without AWA correction.Image sizes: 1.00 × 1.00 × 0.40 mm 3 (x , y , z). (f ) Corresponding 2D MAP image obtained without AWA correction.Scale bar, 200 µm.(g), (h) Line profiles of the dashed lines in (c) and (f ) for the microvascular structures obtained with (red) and without (blue) AWA correction.Scale bars, 200 µm.(i) Depth information of the microvascular structures in the 2D MAP image in (c).Scale bar, 200 µm.