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We present a dual-beam Doppler optical coherence tomography system for visualizing the microvasculature within the retina. The sample arm beams from two identical spectral domain optical coherence tomography (SD-OCT) systems are combined such that there is a small horizontal offset between them at the retina. Thereby we record two tomograms which are slightly separated in time. Phase-resolved Doppler analysis is performed between these two data sets. This system allows blood capillary imaging with high flow sensitivity and variable velocity range. To demonstrate the performance of our system we present images of the microvascular network around the fovea and around the optic nerve head of the human eye.
After its first introduction in the 1990s , optical coherence tomography (OCT) has found a variety of applications, especially in medical research and ophthalmology . Since 1995 OCT was further developed into Doppler OCT (DOCT) [3-5], a technique that is not only capable of providing 2D and 3D micro structural images of the sample but also recognizes moving particles within the object. Various different Doppler OCT systems can be found in literature as for example: phase-resolved Doppler OCT (PR-DOCT) [6-8], resonant Doppler flow imaging , joint spectral and time domain imaging , optical micro-angiography (OMAG)  or single-pass volumetric bidirectional blood flow imaging (SPFI) . Despite the huge variety of DOCT systems, PR-DOCT is still the most widely used technique. PR-DOCT measures the phase difference between adjacent A-scans, which have to be recorded at overlapping positions within the sample. This phase difference Δ is directly proportional to the velocity of the moving particle:
In this equation vaxial denotes the speed of the particle in measurement direction, λ is the central wavelength of the measurement beam, τ is the timing interval between two consecutive A-scans and n denotes the refractive index of the medium. Furthermore, the measured velocity depends on the angle α between the incident light and the flow direction of the particle, which is known as the Doppler angle:
From both equations one can see that the maximum detectable flow speed depends on the 2π ambiguity of the phase shifts whereas the minimum measureable velocity depends on the phase noise of the system. The range from the minimum to the maximum detectable velocity can in principle be arbitrarily shifted by changing the time difference τ between both phase measurements. But for in vivo measurements the minimum detectable flow speed is further limited by the measurement time. If one wants to measure the microvasculature within the human retina, where the flow speed is approximately in the range of a few 100 μm/s, the timing between two adjacent A-scans has to be larger than ~1ms. This measurement speed would, on the one hand make the time which is necessary to acquire a 3D capillary flow image in vivo prohibitively long, on the other hand, the phase washout due to bulk sample motions occurring at these long integration times would severely degrade the signal quality. Additionally, when imaging the human retina, the measurement beam is almost perpendicular to the blood vessel and hence the Doppler angle approaches 90° which further degrades the minimum detectable velocity.
Recently important steps towards the visualization of small blood vessels in tissue were introduced. The systems described in [13,14] use ultra fast SD-OCT setups to reduce motion artifacts and hence allow contrasting of very small details such as cone photoreceptors or capillary vessels. Other systems are based on Doppler OCT and use different scanning protocols to change the dynamic range of the flow measurement [15-17]. Rather than performing the Doppler measurements between adjacent A-scans (fast scanning direction), these systems apply their Doppler analysis between consecutive B-scans (slow scanning direction). Because a single B-scan usually consists of several hundreds of A-scans, the timing between the two required measurements is large enough to contrast the slow flow within a microvasculary network. But nevertheless these methods require strong oversampling between sequential B-scans and hence the measurement time needed for a full 3D scan limits in vivo imaging at human subjects.
Based on this measurement approach and the OMAG technology  Wang et al.  presented a system which is capable of visualizing the microvascular network around the fovea region in vivo. OMAG is based on full range complex OCT [19-22] and introduces a constant modulation frequency along the fast scanning direction (x-scan direction) which after applying the algorithm, separates the backscattering signal of a moving object from the surrounding static tissue. In their recent work  they applied this algorithm along the slow scanning axis (y-scan direction) and hence increased the timing between two adjacent measurements. Their system provides good images of the capillary network around the fovea, but it also puts some additional requirements on the measurement apparatus. In order to apply the OMAG algorithm along the slow scanning direction the fast scanning axis time has to be chosen adequately. They used a spectral domain OCT (SD-OCT) system with a CMOS line scan camera and set the integration time to be 7.4 μs. With 256 A-scans per B-scan and a duty cycle of 75% this resulted in a B-scan time of 2.5 ms. This rapid measurement period, which is needed for the OMAG algorithm, places not only high demands on the line scan camera speed but also reduces the system sensitivity (~90 dB in their case). In order to regain sensitivity and hence increase the image quality they had to acquire eight B-scans at the same lateral position .
In this paper we present a different approach for visualizing the capillary structure within the human retina in vivo. The idea behind our system is related to the work by Makita et al.  and on our dual beam full range complex OCT setup . The sample beams of two identical SD-OCT setups are scanned over the object at different lateral positions. Therefore two tomograms which are slightly separated in time are recorded. During the post processing we overlay both data sets again and apply an extended PR-DOCT algorithm to extract a 3D capillary network tomogram of the retina. The separation between both sample beams can be adjusted arbitrarily and hence the velocity measurement range can be freely chosen.
A schematic diagram of our dual beam PR-DOCT system is shown in Fig. 1. It consists of two identical SD-OCT setups. As light sources we use two super luminescent diodes (SLD) with a center wavelength of 840 nm and a full width at half maximum of 50 nm. The SLDs are coupled into single mode fibers and split into reference and sample arm by two 50:50 fiber beam splitters. Both sample beams are combined by a bulk optic 50:50 beam splitter such that they form a small angle and displacement with each other. This angle and the offset between them at the beam splitter is optimized such that they hit the pivot point of the fast axis scanning mirror of the galvanometer scanner and that they illuminate the retina with a desired horizontal offset (see Fig. 1). Note that it is important for both beams to be centered at the pivot point of the scanner. Otherwise they would undergo an additional phase shift which would disturb the phase resolved measurement of the object. The inherently present small phase shift arising from the slow axis scanner does not influence the performance of the system. Two 50 mm lenses are used to guide the sample beams (1.6 mm in diameter) to the object.
In the reference arm both beams are combined with another bulk optic 50:50 beam splitter such that there is a small vertical displacement between them. Afterwards both beams pass a variable neutral density filter which is used to adjust the light power at the detection unit and a prism pair which compensates the dispersion in the sample arm. This reference arm arrangement is used to reduce phase noise and drifts between the two SD-OCT systems.
Two identical detection units consist of diffraction gratings with 1200 lines/mm, 200 mm focal lenses and line scan cameras with 2048 pixels. The cameras were operated at 20 kHz and with a sample beam intensity of 2 × 0.35 mW we measured a sensitivity of 95 dB for each SD-OCT system. This lower sensitivity as compared to other spectral domain setups, can be explained by the fact that we lose 3 dB with the additional 50:50 beam splitter in the sample arm and another 3 dB due to the limited total probing power on the eye.
For alignment purposes we retrieved the light which is otherwise lost due to the 50:50 beam splitter in the sample arm (see Fig. 1) by the combination of a lens and a mirror. A small portion of this light is back reflected into the fiber and the signal which arises by this mirror is monitored before the start of a measurement to check if both SD-OCT systems are well aligned with respect to each other and to set the phase difference between them approximately zero. This can be done by adjusting the reference arm lengths accordingly.
Due to the horizontal displacement between both sample beams at the retina we record two tomograms which are slightly separated in the fast scanning direction but not in the slow scanning direction. During post processing we overlay both complex data sets again by removing a certain amount of A-scans from each B-scan. By doing this we, first of all, regain 3 dB sensitivity for the intensity images and secondly, it allows us to perform a phase-resolved Doppler analysis along the fast scanning direction on our data. By looking at Fig. 1 it is obvious that sample beam 1 will measure the same lateral position as sample beam 2 but with a temporal displacement. The lateral separation Δx between both beams can be set arbitrarily. Because of this we can define the delay between the two phase measurements which are required for PR-DOCT analysis. Therefore we can overcome the problem that a conventional phase resolved Doppler technique along the fast scanning direction is too fast to resolve the slow motion in the microvasculary structure within the human retina (see Introduction). Additionally we do not have to lower the integration time of our line scan camera, hence reducing the sensitivity, in order to perform a Doppler measurement along the slow scanning direction.
The post processing algorithm which reveals the capillary network within the retina works as follows. After overlaying both recorded tomograms as mentioned above, we first calculate the phase difference between both data sets. In these images moving particles will be displayed as localized regions where there is a phase difference between both measurements, whereas static tissue will introduce no phase shift. This ideal case holds true as long as there is no bulk sample movement during the measurement and in case there is no additional phase shift coming from the measurement apparatus, e.g. off pivot point illumination of the galvoscanner. But due to the fact that we use two individual SD-OCT setups which are based on Michelson interferometers, we will always suffer from slow but random phase drifts. Figure 2a shows a typical phase difference measurement result of our dual beam PR-DOCT system. Displayed is a single B-scan around the fovea region. The phase difference is calculated for pixels whose intensity is above a certain threshold to exclude the background noise. One can see that due to the unavoidable phase drifts between the two interferometers, the phase difference along a B-scan varies slowly. But still the phase shifts which are additionally introduced due to moving particles are visible within this picture (see zoom in of Fig. 2a). The vessels are now extracted by a histogram based normalization method. Assuming that there are no phase drifts along a single A-scan, except by moving blood cells and that we observe more static tissue than vessels, we calculate a histogram plot of the phase difference for each A-scan. This histogram should reveal the global phase difference between both interferometers at the current A-scan position. The maximum value of the histogram is then subtracted from each pixel along the corresponding A-scan. The result of this calculation is shown in Fig. 2b. The phase difference of this B-scan is now normalized such that static tissue exhibits no phase difference and blood vessels are now clearly visible. Note that due to this normalization method phase wrapping might occur on some vessels. This method is therefore not suitable for distinguishing artery from veins.
As a next post processing step we combine the phase difference images with the corresponding intensity scans. This is schematically shown in Fig. 3. First we exclude all the data points from the Doppler maps which exhibit no phase difference. For this purpose we define a symmetric range around zero phase difference, usually in the range of ± 20° (the exact value is manually adjusted for maximum image quality). Every data point of the phase difference image that lies within this range is set to zero. The remaining pixels which correspond to moving particles are set to the value 1. In this way we generate a binary image in which 0 corresponds to static tissue and 1 to moving blood cells. This image is then multiplied with the corresponding intensity image (see Fig. 3b). Buy doing this we extract only those pixels out of the intensity scan which have a counterpart in the reduced phase difference image (see Fig. 3c). In this way we generate a three dimensional map of the capillary network within the retina which is based on a phase-resolved Doppler analysis combined with the inherently present intensity images.
To present the performance of our dual beam PR-DOCT system we show images of the human nerve head and the fovea in vivo. All images shown beneath are recorded with a scanning angle of 6.5° and with a scanning pattern of 512 A-scans times 256 B-scans. The distance between sample beam 1 and 2 was adjusted to be 50 A-scans. With an A-scan speed of 20 kHz this separation corresponds to 2.5 ms or approximately 190 μm at the retina.
Figure 4 shows a typical measurement result of our dual beam PR-DOCT system around the fovea region. Displayed are three en face images which are summed over different depth regions (these regions are labeled as 4a-4c in Fig. 3a). Figure 4a shows an en face projection over the inner limiting membrane until the outer limiting membrane (the nomenclature of these layers was taken from ). Additional to the larger blood vessels which are radial arranged around the fovea, the microvascular network and the avascular zone in the middle of the fovea are clearly visible. By comparing Fig. 4b with Fig. 4c one can see that these micro capillaries are mainly located below the larger blood vessels. The images shown in Fig. 4 are generated by the algorithm described above. Afterwards we apply a 2D median filter and optimize brightness and contrast.
The timing separation of 2.5 ms or 50 A-scans was chosen, because this configuration showed the best results. Figure 5 shows measurement results around the fovea region for different separations of the two probing beams. The depth integration region is the same as in Fig. 4a. In Fig. 5a the distance between sample beam 1 and 2 was adjusted to be 30 A-scans which corresponds to 1.5 ms time delay between both measurements. Larger vessels and part of the microvasculature can be visualized but due to the short timing separation, most of the micro vessels cannot be resolved. Figure 5b shows the same image as Fig. 4a which was recorded with 50 A-scans separation. In Fig. 5c the displacement of the measurement beams was 80 A-scans or 4 ms. Larger vessels and the microvasculature can be resolved but stronger phase noise and microsaccades limit the image quality.
In order to compare our results with a classical PR-DOCT analysis, we also present an image where the phase difference was calculated from adjacent A-scans. For this purpose a classical phase resolved Doppler analysis on both data sets was calculated and the same post processing algorithm was applied (note that phase shifts due to bulk sample motion are compensated by our histogram based phase normalization algorithm described in section 2.2). The resulting images for both data sets were overlaid and averaged. The result is shown in Fig. 6a. One can see that this method is hardly capable of extracting even the larger vessels around the fovea. This en face image was summed over the same depth region as in Fig. 4b.
Figure 6b shows an intensity image en face projection over the same depth length as Fig. 4a. In this image the larger vessels and part of the microvasculature are visible but are hard to distinguish from the surrounding tissue.
Figure 7a shows a capillary network map around the optic nerve head which was recorded with the same measurement settings and stitched together from two measurements. Additional to the main vessels, smaller vasculature which also originate from the optic disk and the microvasculature which is located below them can be seen. Figure 7b shows the classical PR-DOCT analysis which shows only the main vessels. By comparing both images it is obvious to see that our new dual-beam PR-DOCT method has a huge advantage as compared to the classical one. Note that due to the fast blood velocity in the major vessels and large time separation between the two phase measurements, phase wrapping occurs and therefore not every point of the vessel will be recorded by our algorithm since some pixels might exhibit a phase difference of zero. Anyhow these leaking points are filled up again by others in the enface projection (see Fig. 7).
Figure 8 shows an image which is stitched together from several measurements ranging from the optic disk towards the fovea. Note again that all of these images were recorded with the same system settings and especially the separation between both measurement beams was kept constant at 50 A-scans.
The presented data above shows the good performance and the large dynamic range of our dual beam PR-DOCT system for visualizing the capillary network. It is not only capable of contrasting the major vessels in the human retina in vivo but also manages to display the microvasculature. Due to our dual beam scanning approach we do not have to adjust acquisition speed hence either sacrificing measurement speed or system sensitivity. The fact that the lateral displacement between the two sample beams and therefore the delay between both phase measurements can be set arbitrarily makes this device also suitable for other applications such as vasculature examination of other biological samples. Throughout this work the displacement between the two beams was kept constant at 50 A-scans corresponding to 2.5 ms time delay between the phase measurements. A further separation showed no increase in terms of flow sensitivity, whereas a reduction reduced the visibility of the microvasculature.
The main advantage of our system is that the velocity range can be arbitrarily adjusted by tuning the separation between both measurements beams. With a time delay of τ = 2.5 ms between the phase measurements we calculated the minimum resolvable flow speed vaxial,min to be approximately 10.3 μm/s. This value was calculated by using formula (1) and replacing Δ by Δerror which corresponds to the phase noise. The phase noise was calculated by Δerror = 1/SNR1/2 . The signal to noise ratio (SNR) was calculated by taking the mean intensity of all vessels within a 3D data set divided by the standard deviation of the noise in the measurement range. Additionally we calculated the minimum detectable flow speed for a classical Doppler analysis between adjacent A-scans. With an A-scan rate of 20 kHz the timing between two phase measurements is 50 μs and vaxial,min was calculated to be approximately 517 μm/s. This shows that our system is able to decrease the minimum detectable flow speed by more than an order of magnitude compared to a classical PR-DOCT system. The maximum resolvable flow speed is usually limited by the 2π ambiguity of the phase shift, but since we are only interested in visualizing the vessels rather than measuring the absolute flow speed we are not restricted to this limit.
The main disadvantage of our setup is the same as for every Doppler OCT system, namely its sensitivity to involuntary sample motion. If the object moves during the measurement, the two phase measurements will be recorded at different lateral positions resulting in a totally random phase difference. For our extraction algorithm this means that if there is involuntary sample movement during a B-scan, almost every pixel of the intensity image will be extracted into the final vessel image due to the random phase relation. This causes those B-scans to appear as white lines within the extracted vessel maps (see images above). Figure 9 shows two measurement results from another healthy subject including several microsaccades. The capillary network is still nicely extracted but due to the involuntary sample movement the image quality is severely reduced. The lateral displacement of the vessels could in principle be compensated by applying a motion artifact correction algorithm based on B-scan cross correlation, but the elimination of the white stripes would require a refinement of our extraction algorithm.
One limitation of our current setup is that we are not able to resolve the capillary network in the choroid region. Images in this region show no meaningful results because the penetration depth and therefore the sensitivity is too low. This problem could be overcome by changing the central wavelength of our SLDs from 840 nm to 1050 nm, because this wavelength region enhances the visualization of choroidal structures [27,28].
A way to further improve our system would be to calculate the absolute flow velocity within the micro vessels. But since the Doppler angle is not easily accessible, one would need to increase the system complexity either during post processing [29,30] or during the measurement by implementing another sample beam [31,32].
At the end we want to compare our work with another dual-beam Doppler OCT system especially with the one by Makita et al. . Both systems use a dual-beam scanning approach to delay the timing between two consecutive phase measurements in order to increase the sensitivity to slow flowing particles. The main difference between both setups is the way how these measurement beams are provided. Makita et al.  use only one interferometer and separate the two scanning beams via a Wollaston prism which splits the incoming light into two polarization components. Both polarized beams are recombined in the interferometer and split up again by a polarizing beam splitter in the detection unit (a similar approach has previously been reported for measuring phase differences in differential phase contrast OCT [33,34]). This approach has no need for using a second interferometer and hence overcomes the problems of phase instabilities. Difficulties of this approach might be that different layers within the human eye (e.g. cornea or retinal nerve fiber layer) alter the polarization state of the incoming beam. This might cause a crosstalk between both scanning beams at the detection unit. The system presented in this work uses two individual SD-OCT systems to provide the two scanning beams. This approach has no need for any polarizing elements and cannot experience any crosstalk in the detection unit. On the other hand it suffers from the phase drifts between the two interferometers. But this problem can be overcome either by implementing an active phase stabilization system into the setup or, as we have shown, during the post processing.
In conclusion we experimentally realized a dual beam PR-DOCT system which is capable of visualizing not only the major vessels but also the microvasculature within the human retina in vivo. The two laterally displaced sample beams make it possible to apply a phase-resolved Doppler analysis along the fast scanning direction. This approach allows us to delay the time between the two necessary phase measurements arbitrarily without the need to adjust the acquisition time. By combining the phase difference information with the recorded intensity images we are able to generate 3D maps of the capillary network of the human retina with a high dynamic range.
The authors would like to thank H. Sattmann and C. Wölfl for technical assistance, the Austrian Science Fund (Grant Number P19624-B02) and the European Union (project FUNOCT, FP7 HEALTH, contract no. 201880) for financial support.
OCIS codes: (170.3880) Medical and biological imaging; (170.4500) Optical coherence tomography; (170.3340) Laser Doppler velocimetry.