1. Introduction

Advances in optical imaging techniques have revolutionized biomedical research and clinical applications [1, 2]. In the field of deep tissue imaging, two photon microscopy [3, 4] and optical coherence tomography (OCT) [5–7] have enabled dramatic improvements in imaging depth and contrast. Yet optical techniques suffer from random scattering and the resulting exponential decay of the ballistic component of the wavefront. Therefore optical imaging in tissue is currently limited to a depth of ~1mm [8]. Besides the attenuation of the signal, tissue scattering also severely degrades the quality of an optical focus, which in turn lowers the spatial resolution and contrast of the imaging system. Adaptive optics has the potential to drastically improve the signal strength and image quality in deep tissue imaging and might enable even deeper imaging depth than the current state of the art in two photon microscopy and OCT.

Recently, many techniques for adaptive optics for two photon imaging have been presented [9–13]. Most of them have in common that the two photon fluorescence signal or an image metric is iteratively optimized by manipulating the excitation wavefront. While more recently it has been shown that such an approach is suitable for deep tissue imaging by estimating complex wavefronts of up to 1000 spatial modes [13], a feedback based on fluorescence has some inherent limitations. Firstly, the number of fluorescence photons is limited by photobleaching. This limited “photon budget” needs to be distributed between wavefront optimization and the actual imaging for the (biological) experiment.

Secondly, the fluorescence emission rate is limited by fluorophore saturation, i.e. at a certain threshold, more excitation light will not linearly yield more fluorescence photons. This fundamentally limits the speed of the wavefront optimization.

Using backscattered light instead of fluorescence removes these shortcomings, however poses new challenges. The nonlinearity of the two photon process enables a feedback signal that is confined in 3D space and allows localized wavefront estimations. In stark contrast, backscattering of photons can happen anywhere in the sample and is therefore completely un-localized. However, coherence gating of broadband light sources, the working principle of OCT, allows for the discrimination of scattering events in the axial direction. Using light sources with spectral bandwidths above 100nm, the axial resolution can reach similar values than the point spread function (PSF) in two photon microscopy [14].

In ophthalmology many systems and successful applications of OCT combined with adaptive optics have been reported [15]. However, these systems have been optimized for the fast correction of spatially slowly varying aberrations introduced by the human eye and not for random scattering in tissue.

Coherence gating has been applied to adaptive optics in a two photon microscope using a widefield OCT geometry [16]. However, only correction of low order spatial modes has been demonstrated. The presented system is not ideally suited for deep tissue imaging, as CCD array detectors have a limited dynamic range. Furthermore, high spatial frequency wavefront information may have been lost by averaging over multiple locations to suppress speckles in the interferograms that have been used to measure the wavefront [16].

Here we present a novel approach for deep tissue adaptive optics based on coherence gated backscattered light. In our scheme, the feedback signal is collected in a configuration similar to optical coherence microscopy (OCM) [17, 18]. OCM synergistically combines confocal detection using a pinhole and coherence gating to achieve high spatial confinement in the measurement of the backscattered light. A deterministic and parallel optimization method is used to find a suitable wavefront correction for the illumination and detection path for OCM.

We simulated the performance of our approach for random scattering media and we experimentally demonstrated successful focusing through tissue phantoms and fixed brain slices. To our knowledge these are the first demonstrations of deep tissue adaptive optics based on backscattered light.

2. Adaptive optics OCM

In principle our system is an OCM microscope that is equipped with a wavefront correcting element. Ideally, this element corrects the illumination wavefront to form a proper focus in the sample plane and corrects the backscattered wavefront to form an ideal image on the detector at the same time. The crucial part is to find the appropriate wavefront correction to do so.

Here, we use a technique that was originally introduced for focusing light through atmospheric turbulence [19] and more recently has been modified for optical microscopy [20]. The basic idea is to bring a beam that is phase modulated at a certain frequency and a reference beam to interference in the sample. The signal detected from a small target within the sample (e.g. a strong scatterer) will also be modulated at the same frequency, but will lag in phase. This phase difference is the desired correction needed to maximize the interference between the two beams at the target. Lock-in detection of the interference signal at a specific frequency allows for straightforward parallelization of multiple beams that are phase-modulated at different frequencies.

So far this technique has only been applied for single pass corrections, i.e. transmission experiments or two photon imaging where only the excitation wavefront needs to be corrected.

Here, we demonstrate a dual pass approach where the in- and outgoing wavefront is optimized at the same time. A spatial light modulator is placed near the pupil plane of the objective and a fraction (50% or less) of its pixels are modulated, each at a unique frequency. The illumination light passes over the SLM and is focused onto the sample. The backscattered light is collected by the same objective, passes again over the SLM and is brought to interference with a reference beam (that serves as the coherence gate) at a point detector.

Besides a DC component, the measured signal will be modulated at different frequencies. For the wavefront correction, the following components are of interest:

Components 1 and 2 are modulated at the original drive frequencies of the pixels and contain the desired phase information.

In addition, sum frequencies will occur when light is modulated on both paths (ingoing and outgoing), but assuming a large number of pixels, each sum frequency will be of small magnitude and will be neglected here. Thus the dominant contribution at the detector is the interference of component 1 and 2 with the external reference beam.

The phase information can be determined by performing a temporal Fourier transform of the data acquired by the point detector and analyzing the phase at each pixel drive frequency. The recovered phase values are then displayed stationary on the SLM on the corresponding pixels and another fraction of the SLM is modulated. This procedure is repeated until the phase values for all pixels have been determined [20].

Experimentally, our system operates in the following way: a sequence of phase patterns is displayed on the SLM one after the other. For each individual pixel pattern that is displayed, a complete oscillation of the interference signal between the sample beam and the reference beam is measured. To this end, the piezo mirror in the reference path is oscillated continuously and one period of the oscillation signal is sampled and digitized. From this data the amplitude is computed and is used as the feedback signal for the optimization algorithm. It is important to note that in our implementation, the amplitude measurement is performed once all SLM pixels have reached a stationary phase value, i.e. the SLM pixels are not continuously oscillating.

Ideally, only scatterers within the OCM detection volume, determined by the coherence gate and the confocal pinhole, can contribute to the detected signal. Within this volume, the outlined procedure will lock on a dominant scatterer, i.e. optimize focusing light onto and detecting light from this location. If there are multiple strong scatters within a diffraction limited volume, the wavefront correction scheme will not be able discriminate them, because the ideally corrected focus will be diffraction limited as well (or only slightly exceeding this limit [21, 22]).

However, random scattering and severe aberrations in deep tissues will widen the OCM detection volume drastically, allowing more scatterers to contribute to the detected signal and making the wavefront correction less localized. Multiple iterations of the outlined phase optimization procedure are expected to help the convergence towards a single scatterer and to form a high quality focus [13, 20].

In our implementation, the wavefront is optimized to essentially focus light into the pinhole, whereas earlier implementations of this wavefront correction technique optimize directly the focus in the sample plane [13, 19, 20]. It is conceivable to design an OCM microscope that optimizes the wavefront of the input path alone, representing a similar approach as presented in the previous studies. Besides the increased complexity of the setup (separate illumination and detection paths) we found via simulations that such a scheme performs worse than the dual pass approach. We assume that in the dual pass approach, the signal improvement upon successful wavefront optimization is twofold, as more light reaches the scatterer and more light is reaching the detector. This results in higher gains and presumably better convergence compared to the single pass approach applied to OCM.

3. Simulation

In order to validate our concept and to find its limits, we simulated light scattering in a random scattering sample and the wavefront optimization process. The scattering medium was simulated by randomly placing blobs of two micron diameter in a 30x30x30 micron Volume with a volumetric density of 30%. The real part of the refractive index of these blobs followed a linear distribution from 1 to 1 + n_max. The imaginary part of the refractive index was set to zero, therefore the blobs only affect the phase of the e-field. The upper value n_max was chosen such that the desired mean scattering path length resulted, defined by the exponential decay constant of the ballistic component of the wavefront.

In the focal plane, a random distribution of beads with one micron diameter was simulated at a density of 40%. The imaginary part of the beads’ refractive index was uniformly distributed from 0 to 1 while the real part was set to 0. Having the beads and thus the amplitude modulation confined to one plane was chosen to simulate an ideal coherence gate.

The image formation in OCM was simulated the following way: an e-field first propagates through an objective lens with NA 0.4 and is then incident on the sample. Plane by plane the e-field is forward propagated until it reaches the focal plane. There the amplitude of the e-field is multiplied by the beads’ scattering potential. From the beads plane, the resulting e-field is back-propagated through all the layers of the sample and is propagated through the objective lens and a tube lens to form an image. In the image plane, a point detector (diameter of one wavelength) measures the intensity.

The wavefront optimization procedure was simulated by adding a spatial phase modulation in the pupil plane of the objective. The phase modulation was divided into 24x24 pixels and each pixel modulated the phase at a distinct frequency. For one optimization run, first one half (or a different fraction) of the pixels were kept at a constant phase while the other half modulated the incoming and also outgoing e-field. Then the phase for each modulated pixel was determined with a temporal Fourier transform of the detector signal. The determined phase was then applied to the corresponding pixels and held constant while the other remaining pixels where modulated. The subsequent determination of the phase value for those pixels concluded one optimization round. For better convergence, the procedure was iterated several times (using the previously determined wavefront as a starting point).

The simulation results (and then later verified by experiments) suggested that it is advantageous to split the SLM into six pixel groups (in contrast to a 50% split reported in a transmission only configuration).

As a first simulation, a scattering medium with a mean scattering path length of 4.5 was simulated. In Fig. 1(a) the initial light intensity in the focal plane is shown. Figures 1(b)–1(d) show the evolution of the light intensity in the focal plane from one to three wavefront optimization iterations. A single focus emerges already after one iteration, but the peak intensity increases once more after finishing the third iteration.

 

Fig. 1 Simulation of the wavefront optimization. (a)-(d) Light intensity distribution at the focal plane in a tissue phantom with a mean scattering path length of 4.5 after 0, 1, 2 and 3 wavefront optimization iterations. (e)-(h) Light intensity distribution at the focal plane in a tissue phantom with a mean scattering path length of 6 after 0, 1, 2 and 3 wavefront optimization iterations

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Next we simulated a scattering medium with a mean scattering path length of 6. Figure 1(e) shows the initial light intensity distribution in the focal plane. The corresponding results after one, two and three wavefront optimization iterations are shown in Figs. 1(f)–1(h). In the first two iterations the algorithm has difficulties to select a single focus. After iteration three a single focus with higher peak intensity emerges, but still some speckles in the background remain. Thus the simulation results suggest that around a mean scattering path length of six the limits of our technique are reached.

4. Experiments

4.1 Setup

Our experimental setup is shown in Fig. 2 . A mode locked Ti:Sapph laser (Synergy M1, Femtolaser Produktions Gmbh, Vienna, Austria), delivers laser pulses with around 110nmspectral bandwidth, centered at 790nm. After passing through an optical isolator and a beam expander, the light is split by a beamsplitter into a reference and a sample arm. In the sample arm, the light passes through a polarizing beamsplitter and a quarter waveplate (QWP) and is then reflected by a SLM with 492 pixels (MulitDM, Boston micromachines corporation, Cambridge, MA).

 

Fig. 2 Experimental setup: BS, beamsplitter, PBS, polarizing beamsplitter, QWP, quarter waveplate.

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After passing the QWP again, the polarization is rotated by 90 degrees and subsequently the light is reflected by the polarizing beamsplitter and focused into the sample by a Nikon NA 0.5 20X objective. The backscattered light is collected by the same objective and passes again over the SLM via the polarizing beamsplitter and the QWP. The reference beam is focused with another Nikon NA 0.5 20X objective onto a small mirror that can be rapidly moved with a Piezo actuator. A double pass through a QWP turns the polarization of the returning light by 90 degrees.

The dispersion in the reference arm was closely matched to the one in the sample arm. Both beams are recombined by the beam splitter and have normal polarization to each other. A tube lens focuses the beams through a confocal pinhole. After the pinhole a Wollaston Prism (oriented 45 degrees relative to the polarization state of the two beams) is used to interfere the reference and sample beam on a pair of balanced photodiodes (Newport, Irvine, CA) and the difference between the two signals is digitized by a NI PCI 6115 acquisition card. This arrangement suppresses the detection of power fluctuations and DC signals and is more sensitive to the coherent interference signal in comparison to a measurement with a single photodiode.

For each iteration 1986 phase patterns were needed to determine the phase of all SLM pixels. The update rate of the SLM was 2.5 kHz and the piezo mirror in the reference path was oscillated at 400Hz. One iteration, including processing of the data, took about 7s to complete. The update rate of the SLM and the acquisition rate of the data was limited by our control software. Potentially the operation speed could be improved by more than an order of magnitude. Especially the measurement of the oscillation signal could be done much faster using higher drive frequencies for the piezo mirror and lock-in detection. Thereby the update rate of the SLM would become the rate limiting step.

In order to evaluate the quality of the focus in the object plane, we used a second objective (Nikon NA 0.75 40X) to image the transmitted light onto a CCD camera (DMK21BU04, The Imaging Source, Charlotte, NC). An additional, same camera was used to form a widefield image of the backscattered light. For that purpose, a small portion of the reference and sample beam was picked up in front of the pinhole.

4.2 Tissue phantom

To test the proper working of our system, we fabricated a composite tissue phantom. We mixed 6 micron dia. polystyrene microspheres with Agar and produced a layer of 500 micron thickness (anisotropy factor: 0.89, scattering coefficient: −2.99 /mm, 95% confidence bounds: −3.1/-2.9 /mm) An additional thin (>100 micron thickness) layer of a mixture of Agar and 1.5 micron polystyrene microspheres was added behind the first layer. The tissue phantom was sandwiched between two coverslips and sealed with nail polish. The purpose of the thick layer with the large spheres was to distort the focus. The thin layer with the small beads provided the targets for the focus optimization.

The imaging sequence was as follows: first the sample was focused such that the blurred, yet strong reflection of the coverslip at the backside of the sample could be imaged on the widefield camera that records the backscattered light (reference arm blocked for this step). The piezo actuated mirror was driven by a sinusoidal signal and the coherence gate was adjusted to the coverslip position, producing a strong oscillatory signal on the balanced photodiode detector.

The transmission objective was then also focused on the coverslip at the backside of the sample. The sample was subsequently translated until the first small targets beads came into focus on the transmission camera. Displaying rapidly changing random phase patterns on the SLM combined with the strong scattering generated a pseudo-incoherent widefield illumination that allowed us to find and focus the beads. Such an image is shown in Fig. 3(c) , illustrating the density of the target beads. In order to make the test more challenging, the illumination objective was defocused such that a larger area of the target bead layer was illuminated. Therefore multiple beads in the target layer were illuminated and felt, albeit weakly, into the OCM detection volume.

 

Fig. 3 (a) Distorted focus after propagation through a tissue phantom, as imaged in transmission. A uniform phase profile was displayed on the SLM. A gamma correction with a factor of 0.5 was applied to better highlight the weak features of the distorted focus. (b) Corrected focus after three wavefront optimization iterations. A magnified view of the focus is shown in the inset. (c) Pseudo incoherent widefield image of the target bead layer as imaged in transmission. (d) Wavefront correction corresponding to image (b).

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After the coherence gate was adjusted to the bead target layer, the wavefront optimization procedure was initiated. In Fig. 3(a) a transmission image of the distorted focus before the wavefront correction is shown.

Figure 3(b) shows a transmission image of the corrected focus after three wavefront optimization iterations. The peak to background ratio (defined as the peak intensity divided by the average intensity around the peak) corresponds to 69. The corresponding wavefront correction is shown in Fig. 3(d).

Occasionally the algorithm focused light on more than one bead, forming two or multiple foci. Changing the initial conditions slightly (i.e. shifting the sample by a few microns) before the start of a new optimization could help to find a single focus in those cases. In our experience, the problem of multiple foci is much less pronounced if there is initially a small ballistic focus left that can be moved on a scatterer.

This initial experiment demonstrates that the z position of the focus can be defined by the coherence gate alone, but we found that it is advantageous to overlap the focus and the coherence gate. This ensures higher detected signal (more light reaching the scatterer and the detector), reduces the risk of double foci and lateral focus shift.

4.3 Fixed brain tissue

To demonstrate focusing through biological tissues, we prepared fixed rat brain sections of 300 and 500 micron thickness. The rat (long Evans), was perfused with 4% formaldehyde in 0.1M phosphate buffer at pH7.4 and subsequently postfixed in the same solution for 12h at 4 degrees C. The sections were cut on a vibratome (Leica Model VT 1200 S) at approximately + 2.6 to −6.4 Bregma. All work involving vertebrate animals was approved by Janelia Farm’s Institutional Animal Care and Use Committee and was conducted at an AAALAC accredited facility.

We subsequently embedded the brain sections in Agar. Since it turned out that the matching of the coherence gate to the focal plane was crucial, we added 10 micron silica microspheres in sparse concentration into the Agar. The beads helped to find a coarse setting of the coherence gate to the backside of the brain tissue. The sample was sandwiched between two coverslips and was sealed with nail polish.

The sample was first observed in transmission and a bead close to the brain tissue was brought into focus and the coherence gate was adjusted onto it. Then the sample was translated such that the focal plane lied within the brain tissue and the coherence gate was moved accordingly. After a strong enough backscattering signal (by observing the OCM oscillatory signal) was found by moving the sample laterally and iteratively adjusting the coherence gate, the wavefront optimization algorithm was started with three iterations.

Figure 4(a) shows a transmission image of the distorted focus after propagating through a 300 micron thick brain section without any wavefront correction. The beam is largely distorted but still shows a small ballistic component. In Fig. 4(b) the corrected focus after three wavefront optimization iterations is displayed. Figure 4(d) shows a cross section through the corrected focus in Fig. 4(b) (solid line) and the uncorrected focus in Fig. 4(a) (dashed line). The ratio between the ballistic component in the uncorrected focus and the peak of the corrected focus equals to ~5 and the peak to back ground ratio is 51. In Fig. 4(c) the wavefront correction that was applied for the corrected focus in Fig. 4(b) is shown.

 

Fig. 4 Focusing onto scattering sources inside the brain: (a) Distorted focus after propagation through a 300 micron thick fixed brain section, as imaged in transmission. A uniform phase profile was displayed on the SLM. (b) Corrected focus after three wavefront optimization iterations. (c) Wavefront correction corresponding to image (b). (d) Cross section through the corrected (solid line) and uncorrected focus (dashed line) corresponding to the images shown in (b) and (a), respectively. (e) Distorted focus after propagation through a 500 micron thick fixed brain section. A uniform phase profile was displayed on the SLM. (f) Corrected focus after three wavefront optimization iterations. (g) Wavefront correction corresponding to image (f). (h) Cross section through the corrected (solid line) and uncorrected focus (dashed line) corresponding to the images shown in (e) and (f), respectively.

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Figure 4(e) shows a transmission image of the distorted focus after propagating through a 500 micron thick brain section. The focus has become a random speckle field. In Fig. 4(f) the corrected focus is shown. Figure 4(h) shows a cross section through the corrected focus in Fig. 4(f) (solid line) and the uncorrected focus in Fig. 4(e) (dashed line). The peak to background ratio for the corrected focus amounts to 19. In Fig. 4(g) the wavefront correction that was applied for the corrected focus in Fig. 4(f) is shown.

By comparing the intensity of the ballistic focus (without correction) formed after the 500 micron thick brain section and the peak intensity obtained by focusing through an area void of brain tissue, we estimated the mean scattering path length to ~3.5.

For comparison, we also focused on a bead that was located below a 500 micron thick fixed brain tissue. In Fig. 5(a) , the distorted focus after propagation through the brain tissue is shown. A gamma correction of 0.5 was applied to better highlight the weak features of the distorted focus. In Fig. 5(b) the corrected focus after three wavefront iterations is shown. The corresponding wavefront correction is shown in Fig. 5(c). The peak to background ratio for the corrected focus amounts to 51.

 

Fig. 5 Focusing through brain tissue on a polystyrene bead: (a) Distorted focus after propagation through a 500 micron thick fixed brain section, as imaged in transmission. A uniform phase profile was displayed on the SLM. A gamma correction with factor 0.5 was applied to the image. (b) Corrected focus after three wavefront optimization iterations. (c) Wavefront correction corresponding to image (b).

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In order to investigate over what area the wavefront correction remains valid, we established a focus through a 300 micron thick fixed brain slice and then translated the sample with a differential micrometer in one dimension. Every two microns we acquired a transmission image of the focus and computed the peak intensity. The focus at nine different sample positions is shown in Fig. 6(a) and the applied wavefront correction is shown in Fig. 6(b). The corresponding peak intensities of the foci are displayed in Fig. 7 . About 6 microns away from the center, the peak intensity decays to half of the maximum value.

 

Fig. 6 Lateral shift dependence of the corrected focus through a 300 micron thick fixed brain slice: (a) Corrected focus as observed in transmission for different lateral shifts. Scale bar: 5 microns. (b) Applied wavefront correction. The phase is indicated in radians.

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Fig. 7 Peak intensity of the corrected focus versus lateral displacement measured on a 300 micron thick brain slice.

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5. Conclusions

We have demonstrated focusing of light through random scattering media using only backscattered light as a feedback. The combination of a confocal pinhole and a coherence gate using laser pulses of ~10fs duration enabled localized, complex wavefront corrections.

Using backscattered light, our technique has no fundamental speed limit, in contrast to fluorescence based techniques. Furthermore, our method could be ideally combined with two photon microscopy since it will not induce significant sample bleaching. For that purpose, the input beam (sample and reference arm) would be highly chirped during the wavefront measurement, avoiding fluorescence excitation. The chirp does not change the resolution in OCM, as long as the same dispersion is added to both arms. Once the wavefront is determined, the dispersive optical element is removed from the beam and the two photon imaging can be performed.

A drawback compared to two photon based wavefront optimization techniques is that there is no nonlinearity involved in the scattering process. The square dependance of the two photon signal on the excitation intensity favors a single focus solution, since it yields a higher signal than distributing the excitation light on multiple foci. Further it is expected that a nonlinear feedback signal leads to a faster convergence of the optimization process (simulation data not shown).

However, we have shown numerically that with the OCM detection, our method can handle up to six mean scattering path lengths. Our experiments with the tissue phantom also illustrate the notable fact that the algorithm can still select a single scatterer even when the incident beam is totally unfocused. If a double foci was formed, it could be rectified by restarting the optimization with new initial settings.

Without a transmission image, a double (or higher) foci can’t be detected right away. By scanning an image, however, it is expected that suitable image metrics (e.g. sharpness or contrast) can distinct between multiple foci and a single focus.

Our experimental setup is similar to time domain OCT and the coherence gate has to be carefully adjusted to the selected scatterer. Using a spectrometer for detection as it is done in Fourier domain OCT [23, 24] and OCM [25] would dispense with the moving mirror. Thereby information for different coherence gate settings would be acquired instantaneously and the strongest interference signal could be selected by software.

For our proof of principle experiments we omitted a scanning mechanism that would enable the acquisition of lateral, en-face images. With the possibility to acquire en-face OCM images of the sample, the slightly cumbersome procedure to focus on the sample as outlined in chapter 4.2 could be avoided. In a recent publication impressive brain tissue imaging via OCM was presented [25], indicating that OCM has sufficient sensitivity to map suitable scattering sources for wavefront correction in biological tissue.

A complex wavefront correction remains only effective over a small field of view for deep tissue imaging. To image larger field of views, subimages with local wavefront corrections can be stitched together as demonstrated by Tang et al [13]. This limitation is mainly caused by the placement of the SLM in the pupil plane, which might be the worst place if shift-variant aberrations are present. We are currently investigating other arrangements that enable direct imaging of large field of views in highly scattering media.

It is important to note that despite the small FWHM of the peak intensity vs displacement curve (which can be as small as 7 microns for 400 micron thick fixed tissue [13]) one can still image areas larger than this value. The reason is that the degraded focus remains compact and can have still more intensity than an uncorrected focus [13].

In summary we have shown adaptive optics with complex wavefront corrections using only backscattered light, which is an intrinsic contrast mechanism. Therefore no artificial guide star or fluorescence labeling is needed. The determined wavefront could be used for two photon imaging, where only the input wavefront needs to be corrected, but also for OCM imaging itself, where both paths need correction to form a sharp image.

We envision that our technique will find applications in adaptive optics for two photon microscopy where the fluorescence budget is limited or high speed corrections are mandatory. Applied to OCM, it might allow even deeper imaging with higher clarity. Further applications may include photo-activation or stimulation, where light has to be focused on a target.