Three dimensional tracking for volumetric spectral-domain optical coherence tomography

We present a three-dimensional (3D) tracker for a clinical ophthalmic spectral domain optical coherence tomography (SD-OCT) system that combines depth-tracking with lateral tracking, providing a stabilized reference frame for 3D data recording and post acquisition analysis. The depth-tracking system is implemented through a real-time dynamic feedback mechanism to compensate for motion artifact in the axial direction. Active monitoring of the retina and adapting the reference arm of the interferometer allowed the whole thickness of the retina to be stabilized to within ±100 μm. We achieve a relatively constant SNR from image to image by stabilizing the image of the retina with respect to the depth dependent sensitivity of SD-OCT. The depth tracking range of our system is 5.2 mm in air and the depth is adjusted every frame. Enhancement in the stability of the images with the depth-tracking algorithm is demonstrated on a healthy volunteer. © 2007 Optical Society of America OCIS codes: (170.3890) Medical optics instrumentation; (170.4500), Optical coherence tomography; (110.6880) Three-dimensional image acquisition; (170.3880) Medical and biomedical imaging; (170.4470) Ophthalmology; (200.4560) Optical data processing References and Links 1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, "Optical coherence tomography," Science 254, 1178-1181 (1991). 2. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, "Measurements of intraocular distances by backscattering spectral interferometry," Opt. Commun. 117, 43-48 (1995). 3. M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, "In vivo human retinal imaging by Fourier domain optical coherence tomography," J. Biomed. Opt. 7, 457-463 (2002). 4. N. Nassif, B. Cense, B. H. Park, S. H. Yun, T. C. Chen, B. E. Bouma, G. J. Tearney, and J. F. de Boer, "In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography," Opt. Lett. 29, 480-482 (2004). 5. T. C. Chen, B. Cense, M. C. Pierce, N. Nassif, B. H. Park, S. H. Yun, B. R. White, B. E. Bouma, G. J. Tearney, and J. F. de Boer, "Spectral domain optical coherence tomography Ultra-high speed, ultra-high resolution ophthalmic imaging," Arch. Ophthalmol. 123, 1715-1720 (2005). 6. S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, "Motion artifacts in optical coherence tomography with frequency-domain ranging," Opt. Express 12, 2977-2998 (2004). 7. R. D. Ferguson, D. X. Hammer, L. A. Paunescu, S. Beaton, and J. S. Schuman, "Tracking optical coherence tomography," Opt. Lett. 29, 2139-2141 (2004). 8. D. X. Hammer, R. Daniel Ferguson, Nicusor V. Iftimia, Teoman Ustun, G. Wollstein, H. Ishikawa, Michelle L. Gabriele, William D. Dilworth, Larry Kagemann and Jeol S. Schuman, "Advanced scanning methods with tracking optical coherence tomography," Opt. Express 13, 7937-7947 (2005). #86578 $15.00 USD Received 17 Aug 2007; revised 14 Nov 2007; accepted 18 Nov 2007; published 3 Dec 2007 (C) 2007 OSA 10 December 2007 / Vol. 15, No. 25 / OPTICS EXPRESS 16808 9. N. A. Nassif, B. Cense, B. H. Park, M. C. Pierce, S. H. Yun, B. E. Bouma, G. J. Tearney, T. C. Chen, and J. F. de Boer, "In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve," Opt. Express 12, 367-376 (2004). 10. N. V. Iftimia, B. E. Bouma, J. F. de Boer, B. H. Park, B. Cense, and G. J. Tearney, "Adaptive ranging for optical coherence tomography," Opt. Express 12, 4025-4034 (2004). 11. G. J. Tearney, B. E. Bouma, and J. G. Fujimoto, "High-speed phaseand group-delay scanning with a grating-based phase control delay line," Opt. Lett. 22, 1811-1813 (1997). 12. B. H. Park, M. C. Pierce, B. Cense, and J. F. de Boer, "Real-time multi-functional optical coherence tomography," Opt. Express 11, 782-793 (2003). 13. N. V. Iftimia, C. E. Bigelow, T. Ustun, J. F. de Boer, R. D. Ferguson, "Hybrid retinal imager using linescanning laser ophthalmoscopy and spectral domain optical coherence tomography," Opt. Express 14, 12909 12914 (2006). 14. D. X. Hammer, R. Daniel Ferguson, John C. Magill, Lelia A. Paunescu, Siobahn Beaton, Hiroshi Ishikawa, Gadi Wollstein, Joel S. Shuman, "Active retinal tracker for clinical optical coherence tomography," J. Biomed. Opt. 10, Art. No. 024038 (2005). 15. M. Mujat, R. C. Chan, B. Cense, B. H. Park, C. Joo, T. Akkin, T. C. Chen, and J. F. de Boer, "Retinal nerve fiber layer thickness map determined from optical coherence tomography images," Opt. Express 13, 94809491 (2005). 16. S. L. Jiao, R. Knighton, X. R. Huang, G. Gregori, and C. A. Puliafito, "Simultaneous acquisition of sectional and fundus ophthalmic images with spectral-domain optical coherence tomography," Opt. Express 13, 444-452 (2005).


Introduction
Optical coherence tomography (OCT) is a highly sensitive noninvasive imaging modality based on light reflectivity from within the tissue [1]. Recent advances in OCT technology have led to the development of spectral-domain OCT (SD-OCT) with improved sensitivity and speed [2][3][4][5]. In SD-OCT, a depth profile (or optical A scan) is obtained by Fourier transforming the spectral interferogram obtained through a spectrometer in the detection arm of a Michelson interferometer. Motion artifacts during retinal imaging, including lateral and axial motion of the eye, are of major concern [6] due to the discontinuities within and in between OCT frames leading to the loss of image quality and improper registration of 3-D volumetric data. Lateral movement of the retina is inevitable due to the involuntary eye movements, and limits the capability of imaging a targeted region in the retina. Undesirable lateral movement of the retina is corrected for in our system by implementing a lateral-tracking mechanism that was described in detail previously [7,8]. Retinal imaging of patients is performed with our SD-OCT system using a modified slit-lamp designed with head and chin rests as shown in Fig. 1. In spite of the head and chin rests, one of the other motion artifacts during imaging is axial eye motion, caused by back and forth head movement. In an OCT measurement, the ranging depth is quite limited and the axial motion may displace the retinal image to an undesired location in depth. Moreover in an SD-OCT system, the sensitivity degrades with depth due to the limited spectral sampling resolution of the spectrometer [9]. Hence, limiting the image of the retina to within a very short distance in depth provides better sensitivity and relatively constant signalto-noise ratio (SNR) over the entire OCT scan.
An adaptive ranging technique [10] was previously developed to adjust the coherence gate offset within a lateral scan (frame) for a time-domain OCT (TD-OCT) system. As TD-OCT systems are relatively slow compared to SD-OCT systems, it was possible to correct for depth shifts in between A-lines.
In this paper, we present a complete 3D tracking system that, in addition to lateral tracking, enables active monitoring and stabilization of the retina's depth position. For depth tracking, we derive and show experimentally that a relatively constant SNR is maintained from frame to frame by confining the image of the retina to a relatively fixed location. Our system is capable of tracking a distance of 5.2 mm in air.

Materials and methods
The 3D tracking retinal imaging system is based on our clinical SD-OCT system that was previously described by Nassif et al. [9]. The setup, which includes the recent upgrades of simultaneous scanning laser ophthalmoscope (SLO) imaging, lateral tracking and depth tracking, is depicted in Fig. 1. In brief, the SD-OCT system is a fiber-based interferometer that is illuminated by a superluminescent diode (SLD) with a full-width at half maximum (FWHM) bandwidth of 50 nm at a center wavelength of 840 nm. A grating based rapid scanning optical delay (RSOD) line [11] is incorporated in the reference arm, with a reflection grating (300 lines/mm), scan lens (f = 80 mm), and galvanometer scanner 6800 HP with a 3 x 7 mm mirror (Cambridge Technology). The RSOD line utilizes a mirror mounted on a rotational galvanometer to introduce an optical pathlength delay in the reference arm. It is used mainly for adjusting the two arms of the interferometer and for compensating unbalanced dispersion. The dispersion mismatch between the reference and sample arms is minimized by optimizing the location of the diffraction grating [11]. This RSOD line provides a 5.2 mm range of pathlength delay at high speeds and it is used for the depth tracking. Light reflected from the retina is interferometrically combined with the light reflected from the reference arm and the spectral interference is analyzed using a high-speed spectrometer. The measured axial resolution of the SD-OCT system, evaluated at -3 dB (FWHM) of the intensity peak (power) reflected from the sample arm, is approximately 4.7 μm in tissue (assuming a refractive index of 1.38). Individual depth profiles or axial scans (A-lines) are acquired at the rate of 14.5 kHz with each frame or image consisting of 500 consecutive A-lines, allowing 29 frames per second (fps) acquisition. Data acquisition and processing software based on thread architecture similar to the one described in Ref. [12] is used to handle functionalities such as triggering, acquisition, processing, displaying and saving simultaneously. The computer used is a dualcore processor (Intel Pentium IV Xeon) that controls the system through three National An SLO fundus imaging and lateral tracking system (~10μm RMS) developed by Physical Sciences Inc. [7,8,13,14] is integrated into the SD-OCT system and is currently controlled by a separate computer. The SLO system provides real time imaging of retina for proper focusing of the OCT light onto the retina and for precise aiming of the lateral tracking beam before acquisition of the OCT scans. The improvement in OCT imaging due to lateral tracking is demonstrated in Fig. 2 showing examples of the integrated reflectance image [15,16] a) without and (b) with active lateral tracking. Figure 2(a) shows several discontinuities due to lateral eye motion and fixation loss, while Fig. 2(b) contains no visible discontinuities or lateral jumps.
Axial motion of the sample results in pathlength difference between the sample arm and the fixed reference arm that manifests as a vertical motion of the target (retina) within the ranging depth. The depth range of our SD-OCT system is measured to be 2.58 mm in air (1.87 mm in tissue) and the sensitivity of our system decreases by 12 dB over a depth of 2 mm in air with 5 dB reduction over the first 1 mm [9]. Therefore, it is highly desirable to keep the image of the retina within this 1 mm imaging range in order to achieve the best sensitivity possible and also to maintain a relatively constant SNR from frame to frame. With an actual thickness of the retina in air around 500 μm and taking into account an additional 300 μm for the curvature, the whole thickness of the retina needs to be stabilized to within about ±100 μm. A depth-tracking system and algorithm is used to continuously adjust the length of the reference arm. The depth-tracking algorithm measures the change of sample arm pathlength by analyzing the acquired retinal images and adjusts the reference arm pathlength in the RSOD in order to minimize the pathlength difference.
The depth-tracking algorithm is described in Fig. 3 using a block diagram. The voltage signal V sent to the RSOD galvanometer is initially set to zero. First, the depth position of the retina is measured and calculated by processing the acquired SD-OCT images. The 2D cross sectional image (frame) consists of a set of axial scans or depth profiles (D) each of which consists of a number of points or pixels (N). For each processed image, a weighted first (4) For a flat horizontal retina in the image (as in small area scans), σ is relatively small with respect to W, and therefore P and W are almost the same. However, for a curved retina (as in a large area scan), σ becomes significant and reduces the value of P. By stabilizing the depth position P to the reference position P ref , the algorithm pulls the image down preventing any clipping at the top of the image due to the retina curvature. One can use a scaling factor in front of σ in Eq. (4) to account for a large variability in patient measurements and scan protocols; however, here a scaling factor was not included. This procedure allows the algorithm to adjust itself to the changes in curvature. Images of 500 A-lines can be processed at a rate of 20 fps, slower than the actual acquisition rate of 29 fps. To provide rapid feedback in the closed loop, the processing speed is increased by processing only one quarter (every 4 th A-line) of the A-lines for each frame. The algorithm updates the output to the RSOD galvanometer at the start of each frame, synchronized with the frame rate of the SD-OCT imaging. The RSOD galvanometer responds to its input with a settling time of around 1 millisecond. Therefore, the dynamics of the RSOD galvanometer are considered negligible compared to the frame rate.
As a first step in designing the feedback controller, the absolute time delay in system response, i.e. the time delay between the voltage output from the algorithm to the RSOD galvanometer, and its effect in the measured position of the retina was determined to be 2 frames (~0.07sec). The software processes the first frame during the acquisition of the second frame and can update the voltage only at the start of the acquisition of the third frame, accounting for the 2-frame delay. With the known propagation delay of the system, a proportional integral (PI) controller is designed for the depth-tracking algorithm. Alternatively a proportional integral derivate (PID) controller could be used however we found that the derivative term was enhancing the measurement noise. The algorithm calculates the position error between the reference position and the measured position of the retina where γ is a conversion factor for converting the position error in image pixel unit to the voltage for the RSOD galvanometer, p K is a proportional gain that is empirically determined, and 2 − i V is the voltage applied two frames prior to the RSOD galvanometer as determined by the time delay in system's response. In case the frame delivering the correction voltage 2 − i V was not processed, it was assigned a zero value. The conversion factor from RSOD voltage to optical pathlength change was measured to be 1.4 mm/V.
For each subsequent image of the retina, the calculated depth position is constantly compared to the set reference value and the updated voltage is continuously applied to stabilize the image of the retina. The voltages sent to the RSOD are stored to record axial eye motion. A reference position, P ref corresponding to a desired location of the retina in the image is initially set, however the operator is given the freedom to change this desired position during the initial patient alignment, before starting the data acquisition.

Characterization of the depth-tracking algorithm
The closed-loop response of the depth-tracking algorithm was characterized by imaging a stable sample (rough metal surface mounted in a model eye) and introducing an external disturbance into the system. The system response was measured as shown in Fig. 4. The the induced disturbance (P disturbance ) and the results are shown in Fig. 5. Figure 5(a) shows the system response to an external disturbance at 2.42 Hz. The amplitude of the response is almost the same as that of the disturbance, whereas the phase is delayed by 60 0 with respect to the disturbance. The ratio of the peak-to-peak amplitude of the response and the disturbance is taken at each frequency and is shown in Fig. 5(b). At very low frequencies, the disturbance and the response nearly coincide with negligible phase difference. As the frequency is increased, we can observe that the response falls behind in time relative to the disturbance and the resulting phase difference is plotted in Fig. 5(c). At a frequency of 7.25 Hz, the phase delay is 180 degrees. This frequency corresponds to a 2-frame delay in response to a disturbance or error in the real-time measurement. The depth-tracking range is limited by the linear scan range of RSOD galvanometer without reducing the detected spectral bandwidth of the light source and is measured to be 5.2

Results
In order to demonstrate the depth-tracking ability of our system, the retina of a healthy human volunteer was imaged with our SD-OCT system, yielding a movie sequence as shown in Fig.  6. The image size is 6.9 x 1.66 mm 2 with a pixel size of 13.8 x 3.65 μm 2 . The images were cropped in the lateral directions to remove artifacts generated by galvanometer fly-back. The first 40 pixels of each depth profile were cropped to remove artifacts associated with low frequency wavelength dependent spectral modulation. In a span of around 29 seconds, a sequence of 840 images was taken at the same location (Y galvanometer was stationary) with active depth-tracking. Instead of the volunteer moving his head, a controlled movement of the head in axial direction over the depth-tracking range, is simulated by manually changing the length of the reference arm. Figure 6(a) shows the movement of the retina if the depth tracking would have been inactive. It is a depiction of the retinal movement that is hypothetically constructed using the known linear relationship between the offset voltage and movement of the retina (1.4 mm/volt). Figure 6(b) shows the retinal image with active depthtracking demonstrating that the image is kept relatively stable (standard deviation of 60 μm) within the imaging range at the level pre-selected by the user. Once the image of the retina is constrained within the imaging range with a relatively constant SNR using the depth-tracking algorithm, the stability of the retina can be further improved through software as shown in Fig. 6(c). The software stabilization is done by cross-correlating pairs of adjacent images, finding the shift in the cross-correlation, and translating back the second image by this shift [15]. With the standard deviation of 60 μm, the stabilization error for the measurement was determined to be ± 60 μm. The associated reference arm length changes (image displacement) from the RSOD galvanometer are shown in Fig. 6(d) as a function of the frame number. The horizontal axis in Fig. 6(d) can also be converted to time given the video-rate acquisition of 29 fps. Volumetric retinal imaging with active three-dimensional tracking is demonstrated in Fig. 7. Fig. 7(a) shows the enface image of the retinal scan over optical nerve head and Fig   Fig. 7. Movie of the retina illustrating volumetric SD-OCT imaging with three-dimensional tracking. a) Enface image over optical nerve head (6.4 x 6. 7(b) shows the corresponding cross sectional fly through of the retinal scan. It can be observed that the algorithm as described in section 2, stabilizes the image taking the retinal curvature into the account The shadows seen in the image are due to the blood vessels that prevent the light penetrating through them due to blood scattering and absorption and can be observed in the enface image as shown in Fig. 7(a).

Discussion
We can evaluate the velocity at which a patient can move with the current depth-tracking system. As described in section 2, to be able to keep the image of the retina within 1mm range, assuming the retinal thickness around 500 μm in air, and allowing about 300 μm for retina curvature, the maximum allowed axial motion turns out to be ±100 μm. With a 2-frame propagation delay for the error correction, the sample (retina) may be allowed to move by ± 50 μm/frame or close to ±1.45 mm/sec in order to track the retina continuously. In the measurement described above, the maximum velocity was calculated to be around 0.464 mm/sec however it should be noted that the measurement was a simulation of the axial eye motion by manually changing the length of the reference arm. In a clinical setting, the velocities at which the subject could move may vary considerably.

Conclusions
Active 3D eye tracking for removing involuntary eye motions during OCT measurements was demonstrated here by combining lateral tracking with a new depth-tracking system. Depth tracking is achieved through active monitoring of the retina position relative to a fixed set location. A scaled voltage necessary to stabilize the image of the retina is dynamically fed into the RSOD located in the reference arm to offset any pathlength mismatch between the reference arm and the sample arm. Our SD-OCT system can stabilize the image of the retina to within ±100 μm as long as the movement of the head in the axial direction stays within ±2.6 mm. The OCT system combines lateral and axial tracking to provide an absolute 3D stabilization and provides a relatively constant sensitivity by reducing the effect of depth dependent sensitivity decay. Absolute 3D stabilization and constant sensitivity are expected to provide significant improvements for longitudinal studies monitoring progression in ocular diseases such as glaucoma and macular degeneration. Functional retinal testing such as blood flow, spectroscopic OCT, or in combination with adaptive optics for testing photoreceptor responses are other important applications that are expected to significantly benefit from the 3D image stabilization.