Editing Optical coherence tomography (section)

==Theory==
The principle of OCT is white light, or low coherence, interferometry. The optical setup typically consists of an interferometer (Fig. 1, typically [[Michelson interferometer|Michelson]] type) with a low coherence, broad bandwidth light source. Light is split into and recombined from reference and sample arms, respectively.

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[[File:Full-field OCT setup.png|thumb|375px|Fig. 1 Full-field OCT optical setup. Components include: super-luminescent diode (SLD), convex lens (L1), 50/50 beamsplitter (BS), camera objective (CO), CMOS-DSP camera (CAM), reference (REF), and sample (SMP). The camera functions as a two-dimensional detector array, and with the OCT technique facilitating scanning in depth, a non-invasive three-dimensional imaging device is achieved.]]
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[[File:OCT B-Scan Setup-en.svg|thumb|375px|Fig. 2 Typical optical setup of single point OCT. Scanning the light beam on the sample enables non-invasive cross-sectional imaging up to 3 mm in depth with micrometer resolution.]]
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[[File:Ss-oct.PNG|thumb|375px|Fig. 3 Spectral discrimination by swept-source OCT. Components include: swept source or tunable laser (SS), beamsplitter (BS), reference mirror (REF), sample (SMP), photodetector (PD), and digital signal processing (DSP)]]
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[[File:Fd-oct.PNG|thumb|375px|Fig. 4 Spectral discrimination by Fourier-domain OCT. Components include: low coherence source (LCS), beamsplitter (BS), reference mirror (REF), sample (SMP), diffraction grating (DG) and full-field detector (CAM) acting as a spectrometer, and digital signal processing (DSP)]]
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===Time domain===

:<math> F _ODT \left ( \nu \right ) =  2S_0 \left ( \nu \right ) K_r \left ( \nu \right ) K_s \left ( \nu \right )  \qquad \quad (3) </math>
In time domain OCT the path length of the reference arm is varied in time (the reference mirror is translated longitudinally). A property of low coherence interferometry is that interference, i.e. the series of dark and bright fringes, is only achieved when the path difference lies within the coherence length of the light source. This interference is called autocorrelation in a symmetric interferometer (both arms have the same reflectivity), or cross-correlation in the common case. The envelope of this modulation changes as path length difference is varied, where the peak of the envelope corresponds to path length matching.

The interference of two partially coherent light beams can be expressed in terms of the source intensity, <math>I_S</math>, as

:<math> I = k_1 I_S + k_2 I_S + 2 \sqrt { \left ( k_1 I_S \right ) \cdot \left ( k_2 I_S \right )} \cdot Re \left [\gamma \left ( \tau \right ) \right] \qquad (1) </math>

where <math>k_1 + k_2 < 1</math> represents the interferometer beam splitting ratio, and <math> \gamma ( \tau ) </math> is called the complex degree of coherence, i.e. the interference envelope and carrier dependent on reference arm scan or time delay <math> \tau </math>, and whose recovery is of interest in OCT. Due to the coherence gating effect of OCT the complex degree of coherence is represented as a Gaussian function expressed as<ref name="Fercher"/>

:<math> \gamma \left ( \tau \right ) = \exp \left [- \left ( \frac{\pi\Delta\nu\tau}{2 \sqrt{\ln 2} } \right )^2 \right] \cdot \exp \left ( -j2\pi\nu_0\tau \right ) \qquad \quad (2) </math>

where <math> \Delta\nu </math> represents the spectral width of the source in the optical frequency domain, and <math> \nu_0 </math> is the centre optical frequency of the source. In equation (2), the Gaussian envelope is amplitude modulated by an optical carrier. The peak of this envelope represents the location of the microstructure of the sample under test, with an amplitude dependent on the reflectivity of the surface. The optical carrier is due to the [[Doppler effect]] resulting from scanning one arm of the interferometer, and the frequency of this modulation is controlled by the speed of scanning. Therefore, translating one arm of the interferometer has two functions; depth scanning and a Doppler-shifted optical carrier are accomplished by pathlength variation. In OCT, the Doppler-shifted optical carrier has a frequency expressed as

:<math> f_{Dopp} = \frac { 2 \cdot \nu_0 \cdot v_s } { c } \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad (3) </math>

where <math> \nu_0 </math> is the central optical frequency of the source, <math> v_s </math> is the scanning velocity of the pathlength variation, and <math> c </math> is the speed of light.

The axial and lateral resolutions of OCT are decoupled from one another; the former being an equivalent to the coherence length of the light source and the latter being a function of the optics. The axial resolution of OCT is defined as
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|<math> \, {l_c} </math>
|<math>=\frac {2 \ln 2} {\pi} \cdot \frac {\lambda_0^2} {\Delta\lambda}</math>
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|<math>\approx 0.44 \cdot \frac {\lambda_0^2} {\Delta\lambda} \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad (4) </math>
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where <math> \lambda_0 </math> and <math> \Delta\lambda</math> are respectively the central wavelength and the spectral width of the light source.<ref name="ReferenceA">{{cite book| title= Anterior & Posterior Segment OCT: Current Technology & Future Applications, 1st edition |year=2014| vauthors = Garg A }}</ref>

===Fourier domain===
[[File:Principle-TD-FD OCT.svg|thumb|450px|interference signals in TD vs. FD-OCT]]
Fourier-domain (or Frequency-domain) OCT (FD-OCT) has speed and signal-to-noise ratio (SNR) advantages over time-domain OCT (TD-OCT) and has become the standard in the industry since 2006. The idea of using frequency modulation and coherent detection to obtain ranging information was already demonstrated in optical frequency domain reflectometry<ref name="Eickhoff_1981" /> and laser radar<ref name="Kachelmyer_1989" /> in the 1980s, though the distance resolution and range were much longer than OCT. There are two types of FD-OCT – swept-source OCT (SS-OCT) and spectral-domain OCT (SD-OCT) – both of which acquire spectral interferograms which are then [[Fourier transform]]ed to obtain an axial scan of reflectance amplitude versus depth. In SS-OCT, the spectral interferogram is acquired sequentially by tuning the wavelength of a laser light source. SD-OCT acquires spectral interferogram simultaneously in a spectrometer. An implementation of SS-OCT was described by the MIT group as early as 1994.<ref name="mw_1994" /><ref>{{cite journal | vauthors = Chinn SR, Swanson EA, Fujimoto JG | title = Optical coherence tomography using a frequency-tunable optical source | language = EN | journal = Optics Letters | volume = 22 | issue = 5 | pages = 340–342 | date = March 1997 | pmid = 18183195 | doi = 10.1364/OL.22.000340 | bibcode = 1997OptL...22..340C }}</ref>   A group based in the University of Vienna described measurement of intraocular distance using both tunable laser and spectrometer-based interferometry as early as 1995.<ref>{{Cite journal | vauthors = Fercher AF, Hitzenberger CK, Kamp G, El-Zaiat SY |date=1995-05-15 |title=Measurement of intraocular distances by backscattering spectral interferometry |url=https://dx.doi.org/10.1016/0030-4018%2895%2900119-S |journal=Optics Communications |volume=117 |issue=1 |pages=43–48 |doi=10.1016/0030-4018(95)00119-S |bibcode=1995OptCo.117...43F |issn=0030-4018|url-access=subscription }}</ref><ref>{{cite journal | vauthors = Lexer F, Hitzenberger CK, Fercher AF, Kulhavy M | title = Wavelength-tuning interferometry of intraocular distances | language = EN | journal = Applied Optics | volume = 36 | issue = 25 | pages = 6548–6553 | date = September 1997 | pmid = 18259516 | doi = 10.1364/AO.36.006548 | bibcode = 1997ApOpt..36.6548L }}</ref> SD-OCT imaging was first demonstrated both in vitro and in vivo by a collaboration between the Vienna group and a group based in the Nicholas Copernicus University in a series of articles between 2000 and 2002.<ref>{{cite journal | vauthors = Leitgeb R, Wojtkowski M, Kowalczyk A, Hitzenberger CK, Sticker M, Fercher AF | title = Spectral measurement of absorption by spectroscopic frequency-domain optical coherence tomography | language = EN | journal = Optics Letters | volume = 25 | issue = 11 | pages = 820–822 | date = June 2000 | pmid = 18064195 | doi = 10.1364/OL.25.000820 | bibcode = 2000OptL...25..820L }}</ref><ref>{{cite journal | vauthors = Wojtkowski M, Leitgeb R, Kowalczyk A, Bajraszewski T, Fercher AF | title = In vivo human retinal imaging by Fourier domain optical coherence tomography | journal = Journal of Biomedical Optics | volume = 7 | issue = 3 | pages = 457–463 | date = July 2002 | pmid = 12175297 | doi = 10.1117/1.1482379 | bibcode = 2002JBO.....7..457W | s2cid = 40844236 | doi-access = free }}</ref><ref>{{cite journal | vauthors = Wojtkowski M, Kowalczyk A, Leitgeb R, Fercher AF | title = Full range complex spectral optical coherence tomography technique in eye imaging | language = EN | journal = Optics Letters | volume = 27 | issue = 16 | pages = 1415–1417 | date = August 2002 | pmid = 18026464 | doi = 10.1364/OL.27.001415 | bibcode = 2002OptL...27.1415W }}</ref> The SNR advantage of FD-OCT over TD-OCT was first demonstrated in eye imaging <ref>{{cite journal | vauthors = Wojtkowski M, Bajraszewski T, Targowski P, Kowalczyk A | title = Real-time in vivo imaging by high-speed spectral optical coherence tomography | journal = Optics Letters | volume = 28 | issue = 19 | pages = 1745–1747 | date = April 2003 | pmid = 14514087 | doi = 10.1364/OL.28.001745| bibcode = 2003OptL...28.1745W| url =https://opg.optica.org/ol/abstract.cfm?URI=ol-28-19-1745| url-access = subscription }}</ref> and further analyzed by multiple groups of researchers in 2003.<ref>{{cite journal | vauthors = Leitgeb R, Hitzenberger C, Fercher A | title = Performance of fourier domain vs. time domain optical coherence tomography | journal = Optics Express | volume = 11 | issue = 8 | pages = 889–894 | date = April 2003 | pmid = 19461802 | doi = 10.1364/oe.11.000889 | bibcode = 2003OExpr..11..889L | doi-access = free }}</ref><ref>{{cite journal | vauthors = Choma M, Sarunic M, Yang C, Izatt J | title = Sensitivity advantage of swept source and Fourier domain optical coherence tomography | journal = Optics Express | volume = 11 | issue = 18 | pages = 2183–2189 | date = September 2003 | pmid = 19466106 | doi = 10.1364/oe.11.002183 | bibcode = 2003OExpr..11.2183C | doi-access = free }}</ref><ref>{{cite journal | vauthors = de Boer JF, Cense B, Park BH, Pierce MC, Tearney GJ, Bouma BE | title = Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography | journal = Optics Letters | volume = 28 | issue = 21 | pages = 2067–2069 | date = November 2003 | pmid = 14587817 | doi = 10.1364/ol.28.002067 | bibcode = 2003OptL...28.2067D | url = https://research.vu.nl/en/publications/8596084e-22c8-40a3-801f-9719955645b0 }}</ref>

====Spectral-domain OCT====
Spectral-domain OCT (spatially encoded frequency domain OCT) extracts spectral information by distributing different optical frequencies onto a detector stripe (line-array CCD or CMOS) via a dispersive element (see Fig. 4). Thereby the information of the full depth scan can be acquired within a single exposure. However, the large signal-to-noise advantage of FD-OCT is reduced due to the lower dynamic range of stripe detectors with respect to single photosensitive diodes, resulting in an SNR advantage of ~10 [[decibel|dB]] at much higher speeds. This is not much of a problem when working at 1300&nbsp;nm, however, since dynamic range is not a serious problem at this wavelength range.<ref name="ReferenceA"/>

The drawbacks of this technology are found in a strong fall-off of the SNR, which is proportional to the distance from the zero delay and a [[Sinc function|sinc]]-type reduction of the depth-dependent sensitivity because of limited detection linewidth. (One pixel detects a quasi-rectangular portion of an optical frequency range instead of a single frequency, the Fourier transform leads to the sinc(z) behavior). Additionally, the dispersive elements in the spectroscopic detector usually do not distribute the light equally spaced in frequency on the detector, but mostly have an inverse dependence. Therefore, the signal has to be resampled before processing, which cannot take care of the difference in local (pixelwise) bandwidth, which results in further reduction of the signal quality. However, the fall-off is not a serious problem with the development of new generation CCD or [[photodiode]] array with a larger number of pixels.

[[Optical heterodyne detection|Synthetic array heterodyne detection]] offers another approach to this problem without the need for high dispersion.

====Swept-source OCT====
Swept-source OCT (Time-encoded frequency domain OCT) tries to combine some of the advantages of standard TD and spectral domain OCT. Here the spectral components are not encoded by spatial separation, but they are encoded in time. The spectrum is either filtered or generated in single successive frequency steps and reconstructed before Fourier transformation. By accommodation of a frequency scanning light source (i.e. frequency scanning laser) the optical setup (see Fig. 3) becomes simpler than spectral domain OCT, but the problem of scanning is essentially translated from the TD-OCT reference arm into the swept source OCT light source. Here the advantage lies in the proven high SNR detection technology, while swept laser sources achieve very small instantaneous bandwidths (linewidths) at very high frequencies (20–200&nbsp;kHz). Drawbacks are the nonlinearities in the wavelength (especially at high scanning frequencies), the broadening of the linewidth at high frequencies and a high sensitivity to movements of the scanning geometry or the sample (below the range of nanometers within successive frequency steps).