1.5 Outline
2.1.1 Optical Coherence Tomography
Fundamentals. Optical coherence tomography is an imaging modality that makes use of low coherent near-infrared light to acquire depth information in a region of interest (ROI). It is based on the principle of interferometry and functions similar to a Michelson interferometer. A low-coherence light source emits a beam that is split up in two, such that a part of the beam hits a reference mirror, and the other part hits the ROI. Light is reflected back from the reference mirror and the ROI, interferes, and finally hits a detector. Inside the ROI, light is usually partially reflected at multiple surfaces along the beam’s direction. When the reference arm’s light and the reflected light from the ROI travel the same distance, positive interference occurs, which is characterized by a high intensity at the detector [136]. In order to acquire a full 1D depth image (A-Scan), the
Reference Mirror
Spectrometer
Region Interest Light
Source
SplitterBeam
of
I(n)
I
n
|F(I)|
d d
Broadband
Fig. 2.1: Simplified depiction of the SD-OCT principle. Arrows represent light beams.
Own elaboration based on [207]. The spectral imagefS(n)(n)can be trans-formed to an intensity imagefI(d).
reference arm length needs to be changed continuously in standard time-domain OCT (TD-OCT). A 2D scan can be acquired by repeatedly acquiring A-Scans at different lateral locations, resulting in a 2D image (B-Scan). Adding another lateral scanning direction leads to 3D volumes (C-Scans) [207]. Typically, lateral scanning is performed by using mirrors, redirecting the light beam. Finally, 4D image sequences can be acquired by repeatedly acquiring 3D volumes over time.
Besides TD-OCT, Fourier domain OCT (FD-OCT) has been proposed. One of its vari-ants is spectral-domain OCT (SD-OCT) which recently gained popularity. This method does not require a moving reference arm, as a broadband light source is used to capture information at different depths. The recombined signal is captured by a spectrometer and a line scan camera. A Fourier transform directly results in a depth profile. This leads to much higher A-scan rates and an improved signal to noise ratio [285]. SD-OCT systems typically use a wavelength of800 nmto900 nm, which allows for an imaging depth of a few millimeters [61]. A simplified setup for SD-OCT acquisition is shown in Figure 2.1.
Swept-Source OCT (SS-OCT) represents another FD-OCT method for OCT image acquisition. Here, the light source is a tunable swept laser that emits light at a single wavelength at each point in time. The laser sweeps across a large range of wavelengths over time, which are captured by a single photodetector. SS-OCT uses longer wave-lengths above 1000 nm, which is higher than SD-OCT and allows for deeper tissue imaging. Also, higher acquisition speed can be achieved easier with SS-OCT [76]. On the other hand, SS-OCT’s spatial resolution is limited due to the limited amount of wavelengths that can be scanned [12].
Axial and Lateral Resolution. An important property of OCT is the independence of axial and lateral resolution. For FD-OCT, the axial resolution is, in principle, determined by the bandwidth and central wavelength of the light source. Assuming a Gaussian
2.1 Image Data Representations
W0
2W0
2z0
z
Fig. 2.2: Profile of the Gaussian beam, following [61]. The depth of focus is defined by 2z0 and the waist sizeW0determines the lateral resolution.
spectrum, the axial resolution is given by
∆la = 2 log(2)λ2b
π∆λb (2.1)
whereλb is the central wavelength and∆λb is the bandwidth [61]. In practice, OCT systems offer an axial resolution of up to2µm[12].
The imaging depth along the axial direction is limited by the light’s penetration depth and the physical limitations of the detector. For example, for SD-OCT, the imaging depth is determined by the spectral range that can be captured by the spectrometer with a finite number of pixels. Following the Nyquist-Shannon theorem, the spectrometer’s spatial grid should be spaced by half the axial resolution in order to avoid aliasing effects [61].
Assuming that the bandwidth∆λbis sampled byNλpixels, the maximum imaging depth is given by
zmax = λ2b 2∆λNb
λ
. (2.2)
The lateral resolution, on the other hand, depends on the light beam characteristics and the focused spot size. Typically, a light beam is modeled by a Gaussian beam model, which is defined by its waist sizeW0, the Rayleigh rangezo, and radius of curvature [61].
A model of the beam’s intensity profile is shown in Figure 2.2. The depth of focus is defined by2z0, which resembles the axial depth with sufficient beam collimation. The beam’s profile with respect to the axial direction has its minimum radius atW0, which is also referred to as the spot size and determines the lateral resolution for this model.
Temporal Resolution.OCT system’s temporal resolution is often measured by their A-Scan rate. Typical SD-OCT systems offer an A-Scan rate of 40 kHz to 100 kHz [12]. While these frequencies allow for fast A-Scan and B-Scan acquisition, real-time volumetric imaging is still difficult, especially if techniques like A-Scan averaging are applied to improve image quality. Thus, newer systems also offer A-Scan rates in the MHzrange [252], which allow for fast volumetric imaging [449].
Speckle Noise. An important property of OCT systems is the phenomenon of speckle.
Speckle results from random interferences of waves that are mutually coherent, which were reflected on or inside the ROI [433]. In OCT images, it appears as a granular
Fig. 2.3: B-Scan of the human eye [134] with granular speckle noise.
structure with no relation to the actual texture of the structure it was reflected from. An example is shown in Figure 2.3.
Speckle constitutes an issue to be considered as it reduces image quality. It is difficult to filter out, but some techniques such as averaging help reducing its negative influence [478]. For some applications, speckle can be useful as it remains almost constant for small movement in the OCT volume. It can be used for tracking tasks where frame to frame comparisons are made [167].
Multi-Dimensional Data Representations. Overall, OCT systems naturally provide 1D A-Scan data. For scanning at a target location, optical fibers can be used. Due to the fiber’s small size, they can be integrated into small instruments such as needles to provide image guidance and information during an intervention [294]. Acquiring several 1D scans over time results in 2D spatio-temporal data, often also referred to as an M-Scan. Examples for A-Scan and B-Scan data are shown in Figure 2.4.
Alternatively, scan heads containing adjustable mirrors enable lateral scanning and thus spatial 2D and 3D image data acquisition. Example images for this type of data acquisition are shown in Figure 2.5. This type of data is typically used for imaging of the eye, for example, to detect and track disease progression of age-related macular degeneration, diabetic retinopathy, or retinal dystrophies [7]. By repeating the scan head’s scan pattern over time, 3D spatio-temporal data (a sequence of B-Scans) or 4D spatio-temporal data (a sequence of C-Scans) can be acquired. Spatio-temporal OCT data is often used for angiography, which allows imaging of the retina’s microvasculature [479].
Another method of data acquisition is employed for intravascular OCT (IVOCT), which is used to scan coronary arteries from the inside of a catheter [58]. Here, an OCT catheter is inserted into a target artery using a guiding catheter and a guidewire. A
2.1 Image Data Representations
Noise Metal Surface
Scattering Epoxy Layer
OCT Fiber
Time
Intensity
Depth Depth
1D A-Scan 2D M-Scan
Fig. 2.4: Example for a 1D A-Scan (left) and a 2D M-Scan (right) consisting of multiple A-Scans. An OCT fiber images an epoxy layer which is capped by a metal layer. The epoxy layer is deformed over time. See Gessert et al. [162] for details.
Fig. 2.5: Examples for a 2D B-Scan (top) and 3D C-Scan (bottom). In the B-Scan, the A-Scan direction is indicated. In the C-Scan, the B-Scan direction is indicated.
The images show a pig’s ex-vivo heart valve.
Tissue
Infrared Light Catheter OCT Probe
with Prism
Catheter Tissue
(a) Scanning Device (b) Scanning Pattern
Fig. 2.6: The scanning setup for IVOCT data acquisition. A schematic drawing of a scanning device (a) and a cross section of the acquisition pattern (b) is shown.
Due to simultaneous rotation and pullback the pattern in (b) results in a helix.
rotating probe with a prism close to the catheter’s tip emits the infrared light and captures the back-scattered light. During acquisition, the probe rotates and is pulled back while continuously acquiring A-Scans. The acquisition process is depicted in Figure 2.6.
This scanning strategy results in a long M-Scan, however, the spatial locations of the A-Scan’s point of acquisition form a helix pattern. Thus, image reconstruction is required for assigning A-Scans to their respective spatial locations. A simplified method of reconstruction is to cut the M-Scan into consecutive B-Scans. The cutting points can be determined based on rotation frequency and A-Scan acquisition frequency. The resulting B-scans are usually referred to as the polar representation, as the 2D image’s coordinates are the imaging depthdand angle θ. Using a coordinate transform with x=dcos(θ)andy=dsin(θ), the polar images can be transformed into Cartesian space.
This results in 2D cross-sectional image slices of the artery that are easier to interpret for a clinical practitioner. An entire 3D volume can be reconstructed by stacking the Cartesian 2D slices. All three data representations are shown in Figure 2.7.
Note that this type of image reconstruction is a simplified approximation. When cutting the M-Scan into B-Scans, we assume that the rotation frequency is significantly faster than the pullback speed. In this way, we can disregard the helix pattern and assume that the starting point of a single rotation approximately coincides with the ending point.
Also, when reconstructing the 3D volume, we assume that all scans are acquired along some center line. In reality, the catheter is subject to bending and movement, which is not reflected in this type of reconstruction. An additional external catheter tracking technique such as digital subtraction angiography (DSA) [99] or magnetic particle imaging (MPI) [272] can be used to obtain more accurate 3D volume reconstructions.
Summary. OCT allows for diverse applications with subsurface imaging on a mi-crometer scale with a centimeter-level FOV. Different scanning techniques and high acquisition frequencies lead to a variety of data representations ranging from 1D to 4D image data. There are different 2D data representations, including spatio-temporal data, cross-sectional B-Scans, and polar and Cartesian representations. While sharing the same underlying imaging principle, these data representations come with different properties and potentially different requirements for deep learning-based processing. A summary of all data representations is given in Table 2.1.
2.1 Image Data Representations
(a) Polar image representation. (b) Cartesian image representation.
(c) Volume rendering.
Fig. 2.7: The different data representations of IVOCT images.
Tab. 2.1: Overview of the different OCT data representations.
Acquisition Type Dimensionality Typical Application Single Fiber 1D Spatial
Surgical Guidance 2D Spatio-Temporal
Scan Head
2D Spatial
Tissue Imaging 3D Spatial
3D Spatio-Temporal
Angiography 4D Spatio-Temporal
Catheter
2D Spatial (Polar)
Intravascular Imaging 2D Spatial (Cartesian)
3D Spatial