Cellular-resolution in vivo tomography in turbid tissue through digital aberration correction

Noninvasive tomographic imaging of cellular processes in vivo may provide valuable cytological and histological information for disease diagnosis. However, such strategies are usually hampered by optical aberrations caused by the imaging system and tissue turbidity. State-of-the-art aberration correction methods require that the light signal be phase stable over the full-field data acquisition period, which is difficult to maintain during dynamic cellular processes in vivo. Here we show that any optical aberrations in the path length difference (OPD) domain can be corrected without the phase stability requirement based on maximum intensity assumption. Specifically, we demonstrate a novel optical tomographic technique, termed amplitude division aperture synthesis optical coherence tomography (ADAS-OCT), which corrects aberrations induced by turbid tissues by physical aperture synthesis and simultaneously data acquisition from sub-apertures. Even with just two sub-apertures, ADAS-OCT enabled in vivo visualization of red blood cells in human labial mucosa. We further demonstrated that adding sub-apertures could significantly scale up the aberration correction capability. This technology has the potential to impact a number of clinical areas where noninvasive examinations are preferred, such as blood count and cancers detection.


Introduction
Imaging pathophysiological processes at the cellular level is critical for understanding and diagnosis of human diseases, which is routinely realized through cytological or histological examinations following biopsies in clinical settings. Because biopsy is associated with sampling errors and complications due to its invasive and destructive nature, it is not suitable for screening a large population or imaging over a large tissue area. Moreover, cytology and histology procedures are time-consuming which may result in delayed diagnosis. Tomographic imaging modalities are the mainstay of noninvasive diagnostic tools, including ultrasound imaging [1], computed tomography [2], magnetic resonance imaging [3] and positron emission tomography [4]. Although these existing tools have fundamentally changed clinical practice and basic research, cellularlevel cytological and histological information is still not available in tomograms in vivo due to the limited spatial resolution.
Optical tomography techniques are capable of achieving cellular-level spatial resolution in thin tissue sections or semi-transparent tissues [5][6][7]. However, imaging through thicker (> 300 μm) tissues in vivo is still highly challenging because the spatial resolution is degraded by optical aberrations, which can be roughly classified into system aberrations and sample-induced aberrations. System aberrations are generally inherent effects arising due to the focusing optics, such as defocus and inevitable imperfections in the optics used in endoscopic applications [8,9]. Sample-induced aberrations in turbid tissues generally vary spatially and temporally. They must be corrected before clear images of cells can be obtained in vivo.
The straightforward way to correct these aberrations is using hardware-based adaptive optics (HAO), which measures the wavefront distortion and cancels it by modulating the incident light wavefront. With an HAO correction, a set of correction parameters is valid only over a sufficiently small volume and over a sufficiently short period of time during which the sample-induced aberrations are constant. Consequently, it is time consuming to screen a large tissue volume [10,11]. From a practical point of view, the system complexity and cost also impede its applications.
In OCT, optical aberrations result in not only the suboptimal coupling of signals at the detection pinhole but also interferometric wavefront distortions, which compromise both the coherence gating and the transverse focusing. Fortunately, the optical aberrations are recorded as the interferometric wavefront distortions that are detected optoelectronically, which opens up the possibility of correcting the aberrations digitally. Wide-field computational techniques, such as sub-aperture correlation [12,13], computational adaptive optics [14][15][16], and model-based methods [17][18][19] have been developed to overcome the above-mentioned system complexity and speed issue with HAO. However, these techniques usually require high phase stability over the full-field acquisitions, which is challenging for imaging dynamic cellular processes in vivo, especially in endoscopic scenarios.
To overcome the limitation in phase stability, synthetic aperture OCT has been developed and demonstrated to be effective in digitally correcting the spherical aberration of the focusing optics [20]. However, it divides the aperture central-symmetrically by wavefront [20] or sequentially by time [21,22] so that it is not possible to correct the sample-induced aberrations. In this study, we report a novel technique, termed amplitude division aperture synthesis optical coherence tomography (ADAS-OCT), which corrects both the sample-induced aberrations and spherical aberrations without any phase stability requirement. We show that ADAS-OCT can deliver clear images of rapidly moving blood cells by restoring the spatial resolution degraded by the aberrations caused by the human mucosa in vivo.

Working principle of aberration correction in ADAS-OCT
In typical point-scanning confocal optics, when the wavefront of the optical beam is distorted by aberrations, destructive interference may occur at the detection pinhole, resulting in a broadened three-dimensional (3D) point-spread function (PSF) with a lower peak intensity compared with the diffraction-limited PSF (Fig. 1). Assuming the full aperture can be segmented into a number of sub-apertures, the aberrations in the optical path difference (OPD) domain can be digitally corrected if the OPD of light rays encircled in each sub-aperture can be recorded separately in the electrical signals. In spectral-domain OCT (SD-OCT), recording of the OPD is achieved by interference between the sample light with the reference light, governed by the following simplified formulation: where I(k) is the spectral interference signal detected by the spectrometer, S(k) is the spectral distribution of the light source and will be omitted in the following derivations, I r (k) and I s (k) are the electric field reflectivity from the reference arm and the sample arm at the depth of z, respectively. In the sample arm, one can synthesize the aperture of the objective lens by dividing the illumination beam by its amplitude and displace them evenly along the radial direction ( Fig. 1). In the pupil plane, each beamlet creates a sub-aperture with distinct center spatial frequency, which defines both an illumination light path and a detection light path. The OPD of each distinct round-trip path can be shifted by a fixed length using an optical path encoder ( Fig. 1) so that the corresponding interferometric signals do not overlap with each other in the OPD domain. In such an ADAS-OCT system, the m-th (m = 1, 2, …, 2n-1, represents the round-trip path number) depth-encoded cross-correlation term is given by the expression where C. C. stands for complex conjugate. Fourier transform (ℑ) of these crosscorrelation terms give the standard SD-OCT images obtained through individual paths Correction of aberrations in the OPD domain can be simply achieved by eliminating the phase delay α m of m-th cross-correlation term I m with regard to I 1 . Assuming that the aberration-free condition is met when the local intensity of coherently summed image reaches its maximum, the problem is equal to finding α coh m which is the best estimate of α m so that the local intensity maxfiðzÞj z∈½z 0 ;z 00 g reaches its maximum, where ið zÞ ¼ P 2n−1 m¼1 ℑ ½I m ðkÞ Á expðiα m Þ is the coherent summation of the Fourier transform of the cross-correlation terms denoted by Eq. (2), [z ' , z '' ] is the local depth range with 1 ≤ z ' ≤ z '' ≤ N, and N is the length of Fourier transformation. Then the resultant aberration corrected A-line is given by While the interferometric signals from the local scatterer (z '' − z ' = 10 coherence length) are coherently summed, those from the out-of-focus scatterers are suppressed due to OPD mismatches between light paths through different sub-apertures. Thus, this digital aberration correction mechanism can restore both the spatial resolution and the peak signal intensity degraded by aberrations. To produce the aberrationuncorrected control A-line, we incoherently summed the Fourier transform of the cross-correlation terms denoted in Eq. (2) so that iðzÞ ¼ P 2n−1 m¼1 j ℑ ½I m ðkÞ Á expðiα m Þ j, and then found the optimal phase value for α m so that global intensity max{| i(z)‖ z ∈ [1, N] } reaches its maximum. Therefore, the aberration-uncorrected control A-line is given by,

ADAS-OCT imaging system
We developed an ADAS-OCT system on an SD-OCT platform ( Supplementary Fig. 1). Specifically, we created two sub-apertures using a birefringent beam displacer (Fig. 2a, Supplementary Fig. 2(a)-(c) and Supplementary Table 1), with which we obtained three cross-correlation terms with the aid of a quarter-wave plate: I 1 (k), I 2 (k), and I 3 (k) are from the oo-path, the oe/eo-path, and the ee-path, respectively (Supplementary Fig.  2(d)). By adding a second birefringent beam displacer (Fig. 2b, Supplementary Fig. 2(e)-(f) and Supplementary Table 2), we were able to create three sub-apertures and adjust the displacement between them, with which we could tailor the aberration correction performance.
A light source with a spectral bandwidth of 180 nm centered at 800 nm was used to achieve an axial resolution of 1.50 μm in water (refractive index = 1.33). Meanwhile, the effective numerical aperture of the focusing optics of the SD-OCT platform was set to 0.13 (1% power level) to achieve a transverse resolution of 2.75 μm (full width at half maximum, FWHM) and a depth of focus of 30 μm (confocal parameter). This spatial resolution allowed us to clearly visualize cellular structures under the aberration-free condition. Details of the system construction and signal transduction are provided in the Supplementary Notes 1 and 2.

Correction of sample-induced aberrations ex vivo
To demonstrate the ability to correct sample-induced aberrations, we first imaged a simplified tissue phantom that consisted of a collection of polystyrene microparticles with a mean diameter of 6 μm and that was uniformly suspended in agarose gel (See Fig. 2 Schematics of sample arms in ADAS-OCT with one (a) and two (b) calcite beam displacers demonstrating two and multiple distinctive apertures, respectively. SMF1-2, single mode fiber; L1-4, lens; CBD1-3, calcite beam displacer; QWP1-2, quarter wavelength plate Supplementary Note 3 for details of phantom preparation). We focused the sample light to the upper half of the phantom through a chicken breast tissue with thickness of 289 μm in air (Fig. 3a), resulting in broadened transverse and axial profiles of the particles in the control image (Fig. 3c, e, g) compared with an representative image obtained without the tissue on the phantom (Fig. 3b). In the aberration corrected image, both the transverse and axial profiles of the microparticles were significantly restored (Fig.  3d, f, h). For quantitative comparison, the FHWM values showed a mean improvement of 24.1% and 16.0% in the transverse and axial directions, respectively ( Fig. 3i and j). In addition, a mean improvement in the peak intensity of 53.7% was obtained in favor of the signal-to-noise ratio (Fig. 3k). The image contrast and clarity of the chicken breast tissue were also significantly improved (boxes in Fig. 3c, d). k Signal intensity is also restored in the ADAS-OCT image (green rectangle) with respect to the control image (red triangle). Here, "Control" and "ADAS" represent the aberration-uncorrected and aberration-corrected images with chicken breast given by Eqs. (4) and (5) respectively, while "SD-OCT" is the conventional OCT image of the particle phantom only without aperturedivision. Transverse and vertical scale bars: 100 μm

Correction of sample-induced aberration in vivo
RBCs are ideal image phantoms due to their characteristic axial scattering profiles and spatial sparsity in blood vessels. According to our previous observations in zebra fish larvae, a typical OCT image of an RBC consists of two coherence-length limited reflection signals from the upper and lower boundaries of the cell's biconcave disk [23]. Under the aberration-free condition, RBCs should be easily identified in OCT images since the platelets and white blood cells are much fewer and present very different scattering characteristics [24,25]. We imaged the labial mucosa of human volunteers with the focal region aligned to the lamina propria (See Supplementary Note 3 for details of sample preparation). The optical thickness (refractive index =1.33) was approximately 300 μm from the surface of the stratified squamous epithelium to the RBCs in focus. In a representative aberration-corrected ADAS-OCT image (Fig. 4b, d), we could clearly identify six pairs of reflectance signals, presumably six RBCs (Fig. 4e). In contrast, in the corresponding control image (Fig. 4a, c), two reflective surfaces of RBCs numbered 4-6 are difficult to discern due to aberrations. It is obvious that aberration correction significantly enhanced the peak signal intensity of RBCs as compared with the control image (Fig. 4f), which contributed to the visibility of RBCs. In one of the other images, we could recover signals of RBCs even when one or both reflection signals were lost due to aberrations ( Supplementary Figs. S3 and S4).

Scalable imaging performance
The performance of the ADAS-OCT technique can be enhanced by scaling up the number of sub-apertures and increasing the displacement between them. Using the dual beam displacer setup ( Fig. 2b and Supplementary Fig. 2(e)-(f)), we obtained three equally displaced sub-apertures: oo, ee, and oe/eo. The displacement between the centers of the sub-apertures Δx was adjusted in terms of R by rotating the second displacer (R = 1.3 mm is the radius of the illumination beam measured at the 1% power level).  scalability was demonstrated by correcting defocus, which is the simplest aberration but represents a general problem in microscopy and endoscopy. As before, we used the tissue phantom consisting of 6-μm-diameter microparticles suspended in agarose gel. At a sample location 250 μm above the focal plane, the mean transverse FWHM of the particles was degraded to 24.1 μm, 25.6 μm, and 27.1 μm in the control images (Fig. 5a-c and red line in j-l).
For the group of two sub-apertures (oo and ee), the transverse FWHM was found to improve by 9.1% (for displacement between sub-apertures, Δx = 0.2R), 25.8% (for Δx = 1R) and 57.2% (for Δx = 1.8R) (Fig. 5d-f and green line in j-l). Larger displacement results in better correction also held true in the group of three sub-apertures (oo, ee, and oe/eo) (Fig.  5g-i and blue line in j-l). In the largest displacement of 1.8R between the oo sub-aperture and the ee sub-aperture, the mean transverse FWHM was 9.2 μm with three subapertures, which was 69.4% better than that of the control image data (Fig. 5l), while the mean transverse FWHM was 11.6 μm with two sub-apertures. It is suggested that the number of sub-apertures is related to the improvement of the transverse FWHM.
Wavefront distortions between sub-apertures in the path delay domain are digitally corrected by matching the optical path delay of light rays encircled in sub-apertures. By scaling up the sub-apertures number, wavefront distortions (such as IW in Fig. 1) in the aperture plane could be sampled finer to achieve a more accurate approximation. If we could have an infinitely large number of sub-apertures, we will be able to compensate for higher-order Corresponding aberration-corrected images using two sub-apertures: oo and ee. g-i Corresponding aberration-corrected images using three sub-apertures: oo, ee, and oe/eo. Insets: illustrations of subapertures. j Comparison of the transverse FWHM of the microparticles ongoing from the control image (a) to the corrected image with two sub-apertures (d) to the corrected image with three sub-apertures (g). k Comparison of the transverse FWHM of the microparticles ongoing from the control image (b) to the corrected image with two sub-apertures (e) to the corrected image with three sub-apertures (h). l Comparison of the transverse FWHM of the microparticles ongoing from the control image (c) to the corrected image with two sub-apertures (f) to the corrected image with three sub-apertures (i). Mean transverse FWHMs of each plot is indicated in (j-l). SA, sub-apertures; R, radius of the illumination beam. Transverse and vertical scale bars: 100 μm wavefront distortions, but it will never achieve the same diffraction limited transverse resolution as a standard focusing system with an aperture being all the sub-apertures combined since ADAS refocusing is one dimensional (depth) instead of three dimensional.

Discussion
ADAS-OCT is based on the same depth-priority point-scanning mechanism as the most of current endoscopic and intracoronary OCT systems, so that it can be potentially developed into an endoscopic technology that performs high-speed circumferential and helical scanning. In contrast, to maintain phase stability high enough to guarantee coherent aperture synthesis, existing computational-based aberration-correction methods have to rely on special scanning mechanisms such as line-field scanning or time-domain lateral priority scanning [14][15][16], which are not suitable for endoscopic applications in tubular organs. An ADAS-OCT endoscopic probe could be realized in practice by incorporating a beam displacer and a polarizer into a classical fiber-optic design [26]. Beam splitter (BS) is an alternative beam displacer ( Supplementary Fig. 5, see Supplementary Note 4 for details of beam division). However, it is not easy to fabricate this two-surface coating BS with a diameter of 1-2 mm in an ADAS-OCT endoscopic probe. Considering the design, the manufacture, and the test of beam displacer, birefringent crystal should be a better choice. Using a calcite beam displacer, the two-beam separation angle could be 2.2°with a probe diameter of 2 mm and a rigid length of 21.2 mm, based on optical simulation results using Zemax software (Zemax, LLC, Kirkland, Washington, USA) ( Supplementary Fig. 6). This probe diameter should be compatible with the instrument channel of a standard video endoscope [27] or in a tethered capsule endomicroscope [26,28].
Once developed, such an ADAS-OCT endoscope may enable tomographic diagnosis of mucosal abnormalities at the cellular basis in internal organs. Potential clinical benefits may include the early detection of intraepithelial neoplasia and metaplasia in the gastrointestinal tract. Such early detection can be missed by standard video endoscopy and random biopsy procedures if the lesions are focally and heterogeneously distributed over a large mucosal area, leading to a lack of morphological features at the mucosal surface. ADAS-OCT could potentially improve screening and diagnostic outcomes by capturing the cellular hallmarks of the precancerous lesions invisible to standard-ofcare tools, such as goblet cells in Barratt's esophagus and specialized intestinal metaplasia in the stomach.
Looking towards the goal of tomographic diagnosis at the cellular level, future efforts will focus on the development of a clinically viable endomicroscopic ADAS-OCT system. The diameter and rigid length of the probe may be further reduced by using materials with larger birefringence, such as yttrium orthovanadate (YVO4). Space constraints could be further mitigated by employing a tethered capsule that can accommodate largerdiameter optics. The ranging depth of the spectrometer (Supplementary Fig. 7) could be extended through the use of spectral combination [23], linearization [29], and circular interferometric ranging [30].

Conclusion
ADAS-OCT offers a relatively simple route to cellular-level resolution tomography through turbid tissues in vivo. Our approach avoids the phase stability issue encountered by existing computational-based aberration-correction methods. Current computational formulations require full-field data acquisition, during which motion-induced phase instability is inevitable. ADAS-OCT is inherently insensitive to motion-induced phase variations or spatially variant wavefront distortions because it collects scattered signals from all sub-apertures simultaneously. Therefore, to the best of our knowledge ADAS-OCT is the first method that can correct tissue induced aberrations during a rapid cellular process, such as blood flow.
This technical advance may enable noninvasive blood count, which will potentially address many challenges in diagnosis, management, and treatment of diseases. Neonatal blood sampling represents one type of clinical challenges where blood volume and accessible veins are limited for needle puncture, and capillary skin puncture may be associated with increased risk of infection, injury, pain, and maternal anxiety [31,32]. While, blood count monitoring during chemotherapy represents another type of challenges where the venipuncture-based blood test may lead to complications, and delays and/or dose reductions of subsequent courses of chemotherapy [33,34]. A non-invasive blood count device enabled by ADAS-OCT could potentially reduce the number of blood samples from newborns and allow rapid tailoring the dosage and improve the life quality of patients undergoing chemotherapy.