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= Spectral Domain Optical Coherence Tomography for Tissue Diagnostics =

Short Summary
Spectral-Domain Optical Coherence Tomography (SD-OCT) is a biomedical imaging method that stems from a foundation of the decades old imaging modality termed Optical Coherence Tomography (OCT). It combines principles from Optical Coherence Tomography and Low-Coherence Interferometry to produce cross sectional tomographic and spectroscopic imaging by measuring the spectrum of the backscattered light from a sample. This method produces high resolution images where spectral information of the sample is extracted and further analyzed. Spectral Domain OCT is slowly becoming accepted as a means for tissue diagnostics in current research studies.

Optical Coherence Tomography
OCT is a widely used imaging technique that uses low-coherence light to capture micrometer resolution, 2D and 3D images from within a sample that contains optical scattering media. This configuration typically consists of an infrared light source, which is a relatively long wavelength in order to allow penetration into scattering media. This technique produces cross sectional images, where layers of the sample can be viewed and further analyzed. Due to its principles being based on a detection of time-delay in light waves, it is often described as the optical analog to ultrasound, the main difference being OCT uses a light source while ultrasound utilizes sound waves. However, both are considered a method for depth-range imaging.

OCT has become a standard of care in ophthalmology, and has opened the doors to many applications in clinical specialties, fundamental research, and manufacturing.

Low-Coherence Interferometry
By taking a look into an OCT system, one would find optical components set up in a way that is representative of an interferometer. Because light is a wave, we can use interference to measure the effect of very small changes in spacing.

In a low-coherence interferometer, the main light source used for illumination of the sample is one that consists of a broad optical bandwidth. The light coming out of the source is split by a beam splitter into two paths called the reference and sample arms of the interferometer. The light from each arm hits two different mirrors and is reflected back to the beam splitter. The beam splitter recombines the paths and the recombined signal becomes incident at the detector. An interference effect is seen at the detector only if the time travelled by light in the reference and sample arms is nearly equal. This occurs when the mirrors are placed at equal distances, so the signals would overlap and you would get a positive constructive interference. So the plot at the right represents the combined signal incident on the detector. And at the highest peak of the recombined signal, the mirrors were placed at equal distances since purely constructive interference will occur in that path. Thus, this presence of interference serves as a relative measure of the distance travelled by light.

By removing the sample mirror and replacing it with a biological sample, one can think of the biological tissue as a sample of many small mirrors. Thus, different layers and parts of the tissue will reflect differently which will then affect the overall signal that is reflected back to the beam splitter and then recombined with the reference arm. In this case, the reference arm is scanned in a controlled manner and the resulting light intensity is recorded on the detector. The modulation interference pattern occurs when the mirror is the same distance from the beam splitter as one of the reflecting structures in the sample. This interference pattern can be processed to register the presence of that structure. Even though the light beam passes through different structures in the sample, low-coherence interferometry helps to distinguish the amount of reflection from each unique structure in the path of the beam. In doing so, the material scattering, and structure, can be measured as a function of depth [1].

Using a low-coherent signal, the source will output a bunch of random peaks and valleys almost similar to white noise where there is no particular pattern. When the recombined signal overlaps, a peak forms meaning the path length matched in that moment. Any light that is not within a coherence length will not interfere. This low-coherent signal is useful in that it allows the peaks from the recombined signal to be resolvable, thus improving axial resolution of the system.

Image Specifications
OCT will be able to create an image based on the differences collected between the reference and sample arm. One can collect 1D images called A scans and then add up the columns of A scans to create a 2D image called B scans. After processing these scans, one can see a cross sectional image of a tissue sample, where different levels of reflectivity represent different layers of tissue.

Lateral resolution is limited by the size of the spot. The size of the spot is equal to central wavelength divided by 2*NA. NA is numerical aperture, which is how wide of an angle the objective is able to make as a converging beam onto the sample. Axial resolution is limited by the coherence length which is inversely related to bandwidth source. The shorter the coherence length, the more resolvable the peaks are meaning the better resolution.

Fourier-Domain OCT
Fourier Domain OCT includes a low-interferometer configuration, but includes a spectrometer as the main form of detection. This configuration provides an even more efficient way to implement the low-coherence interferometry described earlier. Instead of recording intensity at different locations of the reference mirror, the intensity is recorded as a function of the wavelengths or frequencies of the light. The intensity modulations when measured as a function of frequency are called spectral interference.

When imaging a biological sample, the rate of variation of intensity over different frequencies is indicative of the location of the different reflecting layers in the sample. It can be shown that a Fourier transform of spectral interference data provides information equivalent to that which would be obtained by moving the reference mirror.

Fourier-Domain OCT encompasses two different imaging methods: SD-OCT and Swept-Source OCT.

Spectral-Domain OCT
In spectral-domain OCT (SD-OCT), a broadband light source delivers many wavelengths to the sample, and all are measured simultaneously using a spectrometer as the detector. Using this set up, SOCT is able to perform cross sectional tomographic and spectroscopic imaging by measuring the spectrum of the backscattered light. Thus, specific spectral features can be extracted through signal processing.

Spectral information
Once the data is processed, one can perform further analysis to extract specific spectral features. For example, if you take the short-time Fourier transform, one may obtain the power spectrum of the sample. Since tissue scattering follows a power law dependence with wavelength, this could be a good way to characterize specific tissues.

$$\text{STFT}(k,d;w)=\int_{-\infty}^{\infty}i_d(d')w(d-d';\Delta d)e^{-ikd'}d(d') $$

where w is a spatially confined windowing function that extracts spatially-localized frequency information by suppressing information from outside of the window, commonly a Gaussian distribution, centered around d with width delta d.

Furthermore, one can describe this power spectrum using Beer’s law. If one is familiar with Beer’s law, one will know that the scattering coefficient and absorption coefficient can then be extracted. These values can also provide a lot of information to users about the biological sample being studied.

$$S(d)=\xi \cdot \mu_{b,NA}e^{-2\mu_{OCT}d} $$

$$\mu_{OCT}=\mu_{t}=\mu_{s}+\mu_{a} $$

S(d) is the power spectrum as a function of depth, while mu_OCT is the signal attenuation coefficient. In order to fully extract scattering and absorption coefficients from the attenuation coefficient, one will need to perform least squares fitting [2].

$$\mu_{OCT}=a \cdot \lambda^{-b}\textstyle \sum_{i} \displaystyle (c_i \mu_{a,i}) $$

Application
By extracting spectral information such as the power law coefficients, absorption coefficients, and scattering coefficients from a biological sample, one may diagnose healthy v. unhealthy tissues using these parameters. Current research applications are utilizing SD OCT to provide further spectral information on biological samples induced with certain diseases. One may also use this information to assist in determining the stages of disease that the biological sample is exemplifying [2].