Aberration-diverse optical coherence tomography for suppression of multiple scattering and speckle.

Multiple scattering is a major barrier that limits the optical imaging depth in scattering media. In order to alleviate this effect, we demonstrate aberration-diverse optical coherence tomography (AD-OCT), which exploits the phase correlation between the deterministic signals from single-scattered photons to suppress the random background caused by multiple scattering and speckle. AD-OCT illuminates the sample volume with diverse aberrated point spread functions, and computationally removes these intentionally applied aberrations. After accumulating 12 astigmatism-diverse OCT volumes, we show a 10 dB enhancement in signal-to-background ratio via a coherent average of reconstructed signals from a USAF target located 7.2 scattering mean free paths below a thick scattering layer, and a 3× speckle contrast reduction from an incoherent average of reconstructed signals inside the scattering layer. This AD-OCT method, when implemented using astigmatic illumination, is a promising approach for ultra-deep volumetric optical coherence microscopy.

This adds complexities in live imaging environments where dynamic sample fluctuations can occur. Another class of techniques for MS suppression exploits different correlation characteristics between SS and MS photons [20][21][22], in which the MS signal becomes decorrelated across multiple acquisitions, while the SS signal maintains its correlation. Other related methods have been demonstrated to produce decorrelated speckle patterns [23,24]. This class of techniques for MS/speckle reduction is usually accompanied by confocal and/or coherence gating for further MS suppression.
Previously, we demonstrated OCT with hybrid adaptive optics (hyAO) [25] to enhance the volumetric imaging throughput of optical coherence microscopy (OCM), by splitting the work of image formation between both hardware and computation. In [25], we utilized an astigmatic illumination beam produced via hardware adaptive optics (HAO) to enhance signal collection compared to a standard Gaussian beam, and the resolution penalty of this intentionally applied aberration was mitigated in post-processing via computational adaptive optics (CAO) [26]. However, hyAO relies on single scattered photons to achieve a good CAO reconstruction, and imaging performance can be degraded in highly scattering samples [25].
In this paper, we use aberration-diverse OCT (AD-OCT) to extend this astigmatic imaging into the MS regime, by exploiting phase correlation behaviors (similar with [20,22]) to distinguish SS from MS photons in volumetric reconstructions. AD-OCT takes advantage of the principle that a diversified illumination point spread function (PSF) passes through different spatial regions of a scattering medium, and therefore generates differing realizations of MS signal. By using various aberrated illumination PSFs (such as a rotating astigmatic PSF in this paper), the patterns formed by multiple realizations of the MS field decorrelate between acquisitions, while the SS field remains deterministically correlated. A coherent accumulation of multiple volumes then extracts the SS signal while suppressing the MS components. Meanwhile, since the aberration diversity also generates multiple decorrelated realizations of speckle, an incoherent accumulation can reduce the speckle contrast. By using AD-OCT, we achieved a 10 dB enhancement in signal-to-background ratio (SBR) when imaging a USAF target hidden beneath a scattering layer consisting of TiO 2 beads with 7.2 scattering mean free paths (MFP), and a 3× reduction in speckle contrast within this layer.

Theory
When imaging inside a scattering medium, the complex signal reconstructed from a spectral domain OCT (SD-OCT) system can be described by the superposition of the following components: In Eq. (1), OCT S  is the detected OCT signal at a particular depth 0 z imaged with certain orientation angle θ , defined as the orientation of the first astigmatic line focus in the transverse (xy-) plane. SS S  is the single-scattered signal from the sample after CAO reconstruction, and in theory it does not depend on astigmatism rotation angleθ after the aberration has been removed. The background BG S  (which is not related to the selfinterference signal from the OCT reference arm) includes the MS contribution MS S  and OCT system noise SYS S  (e.g. optical shot/intensity noise or thermal/electronic noise), that is The OCT system noise SYS S  is assumed to be circularly Gaussian distributed in the shot noise limit and can be reduced by temporal averaging [27][28][29]. However, the MS contribution MS S  is not inherently randomized in time. Suppressing MS S  requires inducing a decorrelation of the MS signal (e.g. by rotating the astigmatic angle θ ) across multiple acquisitions and can be accomplished via imaging with a diverse set of aberrated PSFs in AD-OCT. In this paper, AD-OCT utilizes astigmatism as the aberration and rotates the astigmatic angle across volumetric acquisitions. Since the optical illumination and collection paths in the scattering medium are altered by this rotation, the patterns formed by MS photons at the detector become decorrelated. However, the SS signals, as acquired with different astigmatic PSFs, still converge to the same correlated signal after CAO reconstruction. Therefore, as illustrated in Fig. 1 where SS,i S  and BG,i S  represent the single-scattered and background contributions respectively, from the i th aberration state. Although the coherent average is able to suppress the background, it cannot reduce the speckle contrast (in the context of this paper, speckle refers to the interference pattern formed by both sub-resolution SS scatterers and MS photons), because this coherent process generates a new speckle pattern that has the same statistics as the old one. However, since AD-OCT acquires decorrelated speckle patterns resulting from aberration diversity, an incoherent magnitude-based average can achieve speckle reduction, with the speckle contrast reduced by a factor of N [24,[30][31][32], that is In Eq. (4) having a mean individual sp magnitude S  In summa can suppress using an incoh

Experime
The AD particles inside a silicone medium, which consisted of 1:10:100 w/w/w of RTVb, RTVa (Momentive, RTV615) and silicone oil, respectively. The scattering MFP was measured from the exponential decaying confocal responses fused with multiple focal depths inside the layer, as described in [33], with the sensitivity fall-off removed by simultaneously adjusting the sample and reference arm. The USAF target helped to characterize the improvement of SBR and speckle reduction, and was placed at the second line foci of the astigmatic beam. The DM in the sample arm was used to rotate the astigmatism across acquisition volumes. In the experiment, the astigmatism induced by the deformable mirror resulted in a line foci separation of 100 μm (in air), and a complete rotation (180°) was covered by 100 volumes (corresponding to 100 astigmatic states). As shown and discussed later in the paper, using only 12 states (equally spaced over the 100 astigmatic states; 15° angular separation between volumes) was adequate to observe significant improvements. The purpose of acquiring more states than necessary was to demonstrate a saturation effect when finer angular separation was applied.

Data processing
The workflow in AD-OCT post-processing involves standard OCT reconstruction, phase registration across volumes, and CAO aberration compensation. Standard OCT reconstruction corrects for dispersion mismatch between the sample and reference arms, resamples the wavenumber to a linear spacing, and performs a Fourier transforms along wavenumber to convert the signal into the space domain.
Phase registration corrects phase drifting which takes place across multiple volumes and is essential for a coherent average of sequentially acquired volumes. The first step is to utilize the upper surface of the cover glass as a phase reference, which is then used to conjugate the phase across the entire A-scan. The details of this phase stabilizing approach can be found in [34,35].
The second step is to account for any tilt in the optical system alignment or sample, which produces an offset in the Fourier-domain OCT signal with respect to the center of the computed pupil coordinate system. If the Fourier-domain OCT signal bandwidth is not centered in the computed pupil coordinate system, the application of CAO defocus or astigmatic correction centered about the pupil origin will lead to a residual 2D phase ramp in the CAO-corrected Fourier-domain signal. For a given Fourier-domain signal offset, the magnitude and orientation of the residual 2D phase ramp depends on the magnitude and orientation of the astigmatic correction. Therefore, application of different astigmatic CAO correction kernels, corresponding to the rotating astigmatic line foci, will produce a residual 2D linear phase ramp in the CAO-corrected Fourier domain signal whose orientation rotates with the orientation of the astigmatic line foci. This 2D linear phase ramp with rotating orientation in the CAO-corrected Fourier domain signal leads to an astigmatic-statedependent shift of the spatial-domain image, resulting in a 'wobbling' FOV, as shown in Fig.  3b. Assuming the Fourier domain offset is constant across data sets, one solution to this FOV wobble is to correct the residual astigmatic-state-dependent phase ramp, or alternatively (as we implemented in this paper), to remove the offset of the Fourier-domain OCT signal before applying the CAO correction. The final step is to fix small, bulk space-domain offsets using cross correlation, and adjust the constant phase offsets (i.e. piston aberration), across the acquired volumetric data sets. CAO reco aberration-fre detailed proce for astigmatis (made with th 0.1%) to ma (controlled by CAO is able t the maximum complex OCT

Quantita
In this subsec and single-sta plane, and se domain OCT coherent ADnot show a s single-state c optical shot/i mirror shape. The level order to quan speckle contr (plane  in F focus), the sig target bar is e the red region from the glass depth of the U inside the sca 100 μm above standard devi pattern from scatterers at th tive comparis ction, a more q ate control is s elected intensi T acquisition. F -OCT data. By imilar level of oherent averag ntensity noise 6. Intensity profile rget, extracted fro ce plane, averaged 4. of enhanceme ntify this effec rast. As shown Fig. 4, at a de gnal was taken expected to app n where no SS s surface of the USAF plane). I attering layer e the first astig iation was calc the thick laye hat depth.  Fig. 7(a), epth of 7.2 sca n as the average pear, and the b S event is expe e USAF target In Fig. 7 (Fig. 9(b)) on to the utili reduction to sc for a small val otation states. tigmatic PSFs Section 5.

Combine
We have seen OCT for spec states, can the to achieve sim In Fig. 10, except that th means that M averaged to a (giving an ang states with u incoherent av 5) of the cohe speckle. 9 [9]. ration has thorough ironments ibute this orrelation nitude or t requires l-to-noise ttenuation CAO even with the forward model [37], as attenuated portions of the signal aperture may be fall below the noise floor. For in vivo/vitro live imaging, sample motion may cause phase instabilities that degrade the CAO reconstruction of each volume and the coherent average across multiple volumetric acquisitions. Nevertheless, achieving the necessary phase stability for AD-OCT of live samples may still be feasible through increased acquisition speed and/or the use of additional phase registration algorithms [38]. For example, the use of swept-source FDML lasers can support video-rate volumetric acquisition [39][40][41]. On our current SD-OCT system, AD-OCT may still be feasible for ultra-deep cross-sectional imaging. A potentially feasible acquisition scheme would involve the acquisition of smaller, aberration diverse volumetric data sets, with the length of the slow-axis dimension being just long enough to enclose the full transverse width of the aberrated PSFs (this will typically be much smaller than the length of the fastaxis dimension). The fast refresh rate of the DM (~1 ms in open loop) can be leveraged to rapidly switch aberration states between the acquisition of each small volume, and a crosssectional AD-OCT image can be reconstructed at the central slice position along the slow axis. In our SD-OCT system, assuming the use of a comparable level of astigmatism to that used in this study, we estimate a total acquisition time of less than 25 seconds for a 12 state AD-OCT cross-sectional image with FOV 1 × 1 mm 2 (depth × fast axis, 1024 × 1500 × 100 voxels per aberration state, at 75 kHz line scan rate) at 2 μm isotropic FWHM resolution. For in vivo AD-OCT applications, even though saturation can be a potential concern for absolute performance in MS suppression, sample motion may not allow for the acquisition of a sufficient number of stable volumes to reach the saturation limit. When compared to other methods for ultra-deep or speckle-reduced imaging [20][21][22]24], even though AD-OCT may encounter an earlier saturation at the current level of astigmatism, it offers a larger depth coverage than similar approaches using SD-OCT [22,24] (due to the use of hyAO [25]), and can serve as a cross-sectional complement to the en face techniques [20,21].
In this paper, we placed the USAF target plane at the second line focus of the astigmatic beam, in order to obtain a good illumination intensity. One question that remains open is how sample placement will affect the decorrelation level of MS or speckle provided by the aberration diversity. For example, it is worthwhile to investigate whether there is any difference to place the USAF target at the first line focus, plane of least confusion, or second line focus, given the same scattering layer thickness that the imaging beam passes through. This depth dependency with respect to the astigmatic beam structure needs to be studied in future work, as it may lead to the development of alternative PSF conventions for volumetric AD-OCT.
The functionality of the DM in AD-OCT could in principle be performed with other alternatives, such as a cylindrical lens, a liquid-crystal-on-silicon spatial light modulator (LCoS SLM), or a digital micro-mirror device (DMD). For example, a cylindrical lens in conjunction with a mechanical rotation stage would be able to support a comparable data acquisition scheme. However, the use of wavefront shaping devices may provide more precise wavefront control and better high-speed phase stability due to a lack of bulk moving parts during astigmatism rotation, and offer greater flexibility to enable a wide range of applications in the future, including simultaneous realization of AD-OCT and HAO correction of sample-induced aberrations [42][43][44][45]. An SLM or DMD can also provide realtime wavefront shaping capabilities. However, compared to a DM, an SLM has a slower refresh rate that may impose limitations for high speed imaging and can only impart a group delay to the optical wavefront when the required peak-to-valley correction is less than a wavelength, and a DMD has a poorer diffraction efficiency that degrades the quality of the wavefront [46]. Therefore, a DM with high-speed, precise aberration control is an attractive choice for AD-OCT.

Conclusion
We have presented AD-OCT as a novel approach for MS suppression and speckle reduction. AD-OCT uses aberration diversity to randomize the MS field and obtain decorrelated speckle realizations across CAO-reconstructed volumes. A coherent average of these reconstructed aberration-diverse volumes provides suppression of MS, and an incoherent average leads to speckle reduction. We utilized AD-OCT to demonstrate a 10 dB SBR improvement of a USAF target hidden beneath a scattering layer via coherent accumulation, and a 3× speckle contrast reduction inside the scattering layer via incoherent accumulation. The total level of aberration diversity can also be split between a partial MS suppression and partial speckle reduction. AD-OCT extends astigmatic beam imaging into the MS regime, and thus is potentially beneficial for various biomedical applications that require volumetric imaging inside a scattering medium. Future work will investigate the ultimate imaging depth limits of AD-OCT, compare its performance to Gaussian confocal gating, and explore additional or alternative options for aberration diversity.

Funding
This research was supported in part by a Cornell Discovery and Innovation Research Seed Award; National Institutes of Health (1R21EY028389, NIBIB-R21EB022927); National Science Foundation (CAREER: CBET-1752405).