## Abstract

We proposed a single-shot spatial angular compounded optical coherence tomography angiography (AC-Angio-OCT) for blood flow contrast enhancement. By encoding incident angles in B-scan modulation frequencies and splitting the modulation spectrum in the spatial frequency domain, angle-resolved independent subangiograms were obtained and compounded to improve the flow contrast. A full space of the spatial frequency domain allows a wide modulation spectrum. To get access to the full space of the spatial frequency domain and avoid the complex-conjugate ambiguity of the modulation spectrum, a complex-valued OCT spectral interferogram was retrieved by removing one of the conjugate terms in the depth space. To validate the proposed concept, both flow phantom and live animal experiments were performed. The proposed AC-Angio-OCT offers a $\sim 50\%$ decrease of misclassification errors, and an improved flow contrast and vessel connectivity, which contributes to the interpretation of OCT angiograms.

© 2016 Optical Society of America

Motion-contrast optical coherence tomography angiography (Angio-OCT) provides a label-free, depth-resolved, and high-speed imaging of the microvasculature with high motion sensitivity [1 –4]. It eliminates the requirement of contrast injection, and can be used as frequently as required for clinical and scientific research purposes. Typically, the blood flow contrast is achieved by mathematically analyzing the temporal dynamics of light scattering, and using a threshold to isolate the dynamic blood flow from the static tissue bed. However, in typical Angio-OCT, the dynamic and static signals exhibit a residual overlap, resulting in misclassification errors and a limited flow contrast [5]. To facilitate the interpretation of OCT angiograms, effective methods are in demand for a higher flow contrast Angio-OCT.

According to the statistical analysis in Angio-OCT [5], the motion contrast can be improved by averaging of independent angiograms. Referring to the methods used for speckle reduction, independent angiograms may be achieved by the methods, like wavelength diversity [6], angular diversity [7], and polarization diversity [8]. On the basis of the similar concept of wavelength diversity, Jia *et al.* have proposed a split-spectrum Angio-OCT, in which the full wavelength spectrum is split into several different subbands and each subband generates an independent angiogram [3]. Nevertheless, splitting the full wavelength spectrum results in decreasing axial resolution. As mentioned above, independent angiograms may also be acquired by angular diversity. In this Letter, we present a single-shot angular compounded (AC) Angio-OCT method by splitting the full-space B-scan modulation spectrum for enhancing the flow contrast, and quantitatively demonstrate the superiority of the proposed method.

A typical sample arm in an OCT system is depicted in Fig. 1(a). The collimated probe beam is centered on the pivot of the scanning mirror. Because a large size of the illumination beam before the objective lens is desired for high lateral resolution, the incident light away from the beam center corresponds to an off-pivot offset ($\delta $). As we know, a slight off-pivot offset would induce a continuous B-scan modulation of the sample arm path length and thus the phase as the probe beam is scanned in the lateral direction, and the B-scan modulation frequency (${f}_{m}$) is linearly proportional to the offset ($\delta $) [7,9 –11], as shown in Fig. 1(b). ${f}_{m}$ can be expressed by

where $k$ is the central wavenumber of the light source, and $\omega $ is the angular velocity of the scanning mirror. As a consequence, different incidence angles ($\theta $) are encoded by different modulation frequencies (${f}_{m}$), which has been used for speckle reduction [7]. By splitting the spectrum of B-scan modulation, independent subangiograms are generated from the angle-resolved subbands. However, because the real-valued spectral interferogram is recorded by an OCT spectrometer, its Fourier transform in the lateral direction is Hermitian and one cannot distinguish the negative and positive frequencies of B-scan modulation (i.e., being equivalent to $\pm \delta $ or $\pm \theta $), as shown in Fig. 1(c). Therefore, a complex-valued spectral interferogram is desired.The raw spectral interferogram for a spectral domain OCT (SDOCT) B-frame is a two-dimensional real-valued array $S(k,x)$ with $x$ being the fast-scan direction. Fourier transform of $S(k,x)$ along the wavenumber $k$ direction generates reflectivity profile $A(z,x)$ in the depth space ($z$-space). A half of its Fourier $z$-space in a typical SDOCT configuration corresponds to a $\sim 3\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{mm}$ imaging range, which is able to satisfy most of the applications in high-scattering samples. By situating the sample solely on one side of zero path length, the conjugate images are resolved, and the complex-valued spectral interferogram $\tilde{S}(k,x)$ is reconstructed by removing one of the conjugate parts in the $z$-space using Heaviside function, as depicted in Fig. 2. Then the Fourier transform of $\tilde{S}(k,x)$ along the $x$ direction generates a conjugate-free B-scan modulation spectrum in the spatial frequency ($\nu $) domain. Assuming a Gaussian shape for the modulation spectrum, the bandwidth of the full spectrum is determined, and then a Gaussian filter bank is created to split this full spectrum into several different subbands. In this concept-proof study, the full spectrum is equally divided into two subbands. The bandwidth of each filter is one half of the full spectrum for uncorrelated subbands. The filter spacing is the same as the bandwidth of the filter for a full use of the spectrum. Finally, angle-resolved independent subangiograms are generated from the subbands and compounded for a new angiogram. In this method, the complex-valued spectrum is achieved by sacrificing a half of the depth space (i.e., imaging range), but the full space in the spatial frequency domain is accessible for a wide modulation spectrum.

To validate the proposed concept of AC-Angio-OCT, both flow phantom and live animal experiments were performed. The flow phantom and animal preparations were similar to the description in [5]. The system setup was built based on a typical configuration of SDOCT. MB-mode scanning protocol was used for statistical analysis. Each B-scan was formed by 512 A-lines, determining a rate of 190 frames per second. A total of 1000 repeated B-scans were sequentially acquired in the same cross section within $\sim 5.3\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{s}$, generating a raw data cube $(k,x,n)$, where $n$ is the B-frame index, equivalent to the time dimension. The amplitude differential (AD) Angio-OCT algorithm was applied to extracting the flow signals by subtracting the amplitudes $A(z,x,n)$ between adjacent B-frames:

Totally, 999 cross-sectional angiograms were generated for the statistical analysis of Angio-OCT signals. The dynamic and static regions were identified in the angiograms. From each region, five spatial points were randomly selected to generate a total of $4995(5\times 999)$ elements of amplitudes for statistics. The histograms of the static and dynamic signals were computed separately. According to [5], the probability density function (PDF) of the conventional AD-Angio-OCT ${f}_{\text{AngioOCT}}$ follows a truncated Gaussian distribution. In addition, averaging of two independent angiograms with PDFs ${f}_{\mathrm{AngioOCT}1}$ and ${f}_{\mathrm{AngioOCT}2}$ yields a new distribution ${f}_{\overline{\mathrm{AngioOCT}}}$, given by

where $*$ represents convolution computation. The histograms of the experimental data were further fitted using the theoretical model, and the agreement was evaluated by $R$-squared (${R}^{2}$) statistic. Commonly, distributions of the dynamic and static Angio-OCT signals have a residual overlap, which is defined as the classification error rate (CER). Using the CER criterion, the improved flow contrast of our angular compounded method was quantitatively evaluated. A stepwise raster scanning protocol was used for volumetric imaging. Overall, 200 steps were scanned in the slow-scan ($y$) direction and five repeated B-frames were acquired at each step [12].Representative cross-sectional phantom angiograms of the conventional and AC-Angio-OCT are shown in Figs. 3(a) and 3(b), respectively. The correlation between the phantom subangiograms is less than 0.1, indicating the independence of the subangiograms generated in AC-Angio-OCT. As described in the partial enlarged views, the AC method presents higher flow contrast than the conventional one. The yellow asterisks and pluses, respectively, indicate the selected points from the dynamic fluid and static gel that are used for the following statistical analysis. The histograms and their fitting curves of the selected Angio-OCT signals are shown in Figs. 3(c)–3(f). Here, the curves of AC-Angio-OCT signals [Fig. 3(f)] are achieved from two subangiograms [Figs. 3(c) and 3(d)] using the model of Eq. (3). All the $R$-squared (${R}^{2}$) statistics are higher than 0.95, indicating good agreement between the experimental outcome and the theoretical prediction. The CERs of the conventional and AC-Angio-OCT are 0.24 and 0.11 (a fall of $\sim 50\%$), respectively. Moreover, in mouse cortex *in vivo*, similar distributions of the dynamic and static Angio-OCT signals can also be observed, and the CER of AC-Angio-OCT imaging decreases by $\sim 50\%$ in comparison with that of the conventional method.

Figure 4 shows 3D angiograms of the conventional and AC-Angio-OCT in mouse cortex *in vivo*. Figure 4(a) is a 3D rendering of vasculature. Figures 4(b) and 4(c) are the *en face* slices at a superficial depth of conventional and AC-Angio-OCT, respectively, and Figs. 4(d) and 4(e) are the slices at a deeper position. As indicated by the arrows, the AC method presents an enhanced flow contrast and a better vascular connectivity. The processing time of the conventional Angio-OCT algorithm was $\sim 361\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{s}$, while that of the proposed AC-Angio-OCT algorithm was $\sim 433\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{s}$ mainly due to the additional computation load of generating a full-space modulation spectrum.

In our AC-Angio-OCT, the full space of the spatial frequency domain allows a wide B-scan modulation spectrum and incident angle ($\theta $) range, which is helpful for compensating the degradation of lateral resolution induced by splitting the spectrum in the spatial frequency domain. To get access to the full space of the spatial frequency domain and avoid the complex-conjugate ambiguity of the modulation spectrum, a complex-valued OCT spectral interferogram is retrieved by removing one of the conjugate terms in the depth space, rather than the conventional full-range complex SDOCT using off-pivot illumination of the scanner where half the space of the spatial frequency domain is sacrificed for full-range imaging in the depth space [9 –11].

A similar concept of angular compounding by encoding the B-scan Doppler shift has been previously used for speckle reduction in OCT structural imaging [7], but our method is different from their report. In [7], to distinguish the complex conjugate of the B-scan modulation spectrum, the probe beam is deliberately decentered from the pivot axis of the scanning mirror, so as to shift the whole spectrum of B-scan modulation to one side of dc. However, complete separation of the complex conjugate entails dense A-scans in one B-scan to ensure enough sampling points to acquire the Doppler shifts, which limits the imaging speed. In addition, only half the space of the spatial frequency domain can be used for encoding in their approach [7], which limits the efficiency of angular compounding and the lateral resolution, as discussed above.

In brief, we have proposed a single-shot AC-Angio-OCT for blood flow contrast enhancement. By encoding different incident angles in different B-scan modulation frequencies and splitting the modulation spectrum in the spatial frequency domain, angle-resolved independent subangiograms are obtained and compounded to improve the flow contrast. The proposed concept has been validated through both phantom and live animal experiments, demonstrating a $\sim 50\%$ decrease of misclassification errors, and an improved flow contrast and vessel connectivity. In addition, angle-resolved OCT signals can be used for calculating absolute Doppler velocity, and compounding of multiangular subangiograms may be beneficial to revealing the features shadowed by the upper vessels.

## Funding

National Natural Science Foundation of China (NSFC) (61475143, 11404285, 61335003, 61327007 and 61275196), Zhejiang Provincial Natural Science Foundation of China (LY14F050007), Zhejiang Province Science and Technology Grant (2015C33108), National Hi-Tech Research and Development Program of China (2015AA020515), Fundamental Research Funds for the Central Universities (2014QNA5017), and Scientific Research Foundation for Returned Scholars, Ministry of Education of China.

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