Optical coherence tomography

${\displaystyle F_{O}DT\left(\nu \right)=2S_{0}\left(\nu \right)K_{r}\left(\nu \right)K_{s}\left(\nu \right)\qquad \quad (3)}$

In time domain OCT the pathlength 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 auto correlation in a symmetric interferometer (both arms have the same reflectivity), or cross-correlation in the common case. The envelope of this modulation changes as pathlength difference is varied, where the peak of the envelope corresponds to pathlength matching.

The interference of two partially coherent light beams can be expressed in terms of the source intensity, ${\displaystyle I_{S}}$, as

${\displaystyle I=k_{1}I_{S}+k_{2}I_{S}+2{\sqrt {\left(k_{1}I_{S}\right)\cdot \left(k_{2}I_{S}\right)}}\cdot Re\left[\gamma \left(\tau \right)\right]\qquad (1)}$

where ${\displaystyle k_{1}+k_{2}<1}$ represents the interferometer beam splitting ratio, and ${\displaystyle \gamma (\tau )}$ is called the complex degree of coherence, i.e. the interference envelope and carrier dependent on reference arm scan or time delay ${\displaystyle \tau }$, 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[4]

${\displaystyle \gamma \left(\tau \right)=\exp \left[-\left({\frac {\pi \Delta \nu \tau }{2{\sqrt {\ln 2}}}}\right)^{2}\right]\cdot \exp \left(-j2\pi \nu _{0}\tau \right)\qquad \quad (2)}$

where ${\displaystyle \Delta \nu }$ represents the spectral width of the source in the optical frequency domain, and ${\displaystyle \nu _{0}}$ 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

${\displaystyle f_{Dopp}={\frac {2\cdot \nu _{0}\cdot v_{s}}{c}}\qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad (3)}$

where ${\displaystyle \nu _{0}}$ is the central optical frequency of the source, ${\displaystyle v_{s}}$ is the scanning velocity of the pathlength variation, and ${\displaystyle c}$ is the speed of light.

interference signals in TD vs. FD-OCT

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

${\displaystyle \,{l_{c}}}$	${\displaystyle ={\frac {2\ln 2}{\pi }}\cdot {\frac {\lambda _{0}^{2}}{\Delta \lambda }}}$
	${\displaystyle \approx 0.44\cdot {\frac {\lambda _{0}^{2}}{\Delta \lambda }}\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad (4)}$

where ${\displaystyle \lambda _{0}}$ and ${\displaystyle \Delta \lambda }$ are respectively the central wavelength and the spectral width of the light source.[20]

In frequency domain OCT (FD-OCT) the broadband interference is acquired with spectrally separated detectors. Two common approaches are swept-source and spectral-domain OCT. A swept source OCT encodes the optical frequency in time with a spectrally scanning source. A spectral domain OCT uses a dispersive detector, like a grating and a linear detector array, to separate the different wavelengths. Due to the Fourier relation (Wiener-Khintchine theorem between the auto correlation and the spectral power density) the depth scan can be immediately calculated by a Fourier-transform from the acquired spectra, without movement of the reference arm.[21][22] This feature improves imaging speed dramatically, while the reduced losses during a single scan improve the signal to noise ratio proportional to the number of detection elements. The parallel detection at multiple wavelength ranges limits the scanning range, while the full spectral bandwidth sets the axial resolution.[23]

Spatially encoded frequency domain OCT (SEFD-OCT, spectral domain or Fourier 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 (signal to noise ratio) advantage of ~10 dB at much higher speeds. This is not much of a problem when working at 1300 nm, however, since dynamic range is not a serious problem at this wavelength range.[20]

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-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 can not 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.

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

Time encoded frequency domain OCT (TEFD-OCT, or swept source OCT) tries to combine some of the advantages of standard TD and SEFD-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 SEFD, but the problem of scanning is essentially translated from the TD-OCT reference-arm into the TEFD-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 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).

Schematic view of a full-field OCT

An imaging approach to temporal OCT was developed by Claude Boccara's team in 1998,[24] with an acquisition of the images without beam scanning. In this technique called full-field OCT (FF-OCT), unlike other OCT techniques that acquire cross-sections of the sample, the images are here "en-face" i.e. like images of classical microscopy: orthogonal to the light beam of illumination.[25]

More precisely, interferometric images are created by a Michelson interferometer where the path length difference is varied by a fast electric component (usually a piezo mirror in the reference arm). These images acquired by a CCD camera are combined in post-treatment (or on-line) by the phase shift interferometry method, where usually 2 or 4 images per modulation period are acquired, depending on the algorithm used.[26][27] More recently, approaches that allow rapid single-shot imaging were developed to simultaneously capture multiple phase-shifted images required for reconstruction, using single camera.[28] Single-shot time-domain OCM is limited only by the camera frame rate and available illumination.

The "en-face" tomographic images are thus produced by a wide-field illumination, ensured by the Linnik configuration of the Michelson interferometer where a microscope objective is used in both arms. Furthermore, while the temporal coherence of the source must remain low as in classical OCT (i.e. a broad spectrum), the spatial coherence must also be low to avoid parasitical interferences (i.e. a source with a large size).[29]

Line-field confocal optical coherence tomography (LC-OCT) is an imaging technique based on the principle of time-domain OCT with line illumination using a broadband laser and line detection using a line-scan camera.[30] LC-OCT produces B-scans in real-time from multiple A-scans acquired in parallel. En face images can also be obtained by scanning the illumination line laterally.[31] The focus is continuously adjusted during the scan of the sample depth, using a high numerical aperture (NA) microscope objective to image with high lateral resolution. By using a supercontinuum laser as a light source, a quasi-isotropic spatial resolution of ~ 1 µm is achieved at a central wavelength of ~ 800 nm. On the other hand, line illumination and detection, combined with the use of a high NA microscope objective, produce a confocal gate that prevents most scattered light that does not contribute to the signal from being detected by the camera. This confocal gate, which is absent in the full-field OCT technique, gives LC-OCT an advantage in terms of detection sensitivity and penetration in highly scattering media such as skin tissues.[32] So far this technique has been used mainly for skin imaging in the fields of dermatology[33] and cosmetology.[34]

Systems based on single point, confocal, or flying-spot time domain OCT, must scan the sample in two lateral dimensions and reconstruct a three-dimensional image using depth information obtained by coherence-gating through an axially scanning reference arm (Fig. 2). Two-dimensional lateral scanning has been electromechanically implemented by moving the sample[22] using a translation stage, and using a novel micro-electro-mechanical system scanner.[35]

Parallel or full field OCT using a charge-coupled device (CCD) camera has been used in which the sample is full-field illuminated and en face imaged with the CCD, hence eliminating the electromechanical lateral scan. By stepping the reference mirror and recording successive en face images a three-dimensional representation can be reconstructed. Three-dimensional OCT using a CCD camera was demonstrated in a phase-stepped technique,[36] using geometric phase shifting with a Linnik interferometer,[37] utilising a pair of CCDs and heterodyne detection,[38] and in a Linnik interferometer with an oscillating reference mirror and axial translation stage.[39] Central to the CCD approach is the necessity for either very fast CCDs or carrier generation separate to the stepping reference mirror to track the high frequency OCT carrier.

A two-dimensional smart detector array, fabricated using a 2 µm complementary metal-oxide-semiconductor (CMOS) process, was used to demonstrate full-field TD-OCT.[40] Featuring an uncomplicated optical setup (Fig. 3), each pixel of the 58x58 pixel smart detector array acted as an individual photodiode and included its own hardware demodulation circuitry.

Ocular (or ophthalmic) OCT is used heavily by ophthalmologists and optometrists to obtain high-resolution images of the retina and anterior segment. Owing to OCT's capability to show cross-sections of tissue layers with micrometer resolution, OCT provides a straightforward method of assessing cellular organization, photoreceptor integrity,[41][42][43][44] and axonal thickness in glaucoma,[45] macular degeneration,[46] diabetic macular edema,[47] multiple sclerosis[48] and other eye diseases or systemic pathologies which have ocular signs.[49] Additionally, ophthalmologists leverage OCT to assess the vascular health of the retina via a technique called OCT angiography (OCTA).[50] In ophthalmological surgery, especially retinal surgery, an OCT can be mounted on the microscope. Such a system is called an intraoperative OCT (iOCT) and provides support during the surgery with clinical benefits.[51]

In the setting of cardiology, OCT is used to image coronary arteries in order to visualize vessel wall lumen morphology and microstructure at a resolution 10 times higher than other existing modalities such as intravascular ultrasounds and x-ray angiography (intracoronary optical coherence tomography). For this type of application, approximately 1 mm in diameter fiber-optics catheters are used to access artery lumen through semi-invasive interventions such as percutaneous coronary interventions.

The first demonstration of endoscopic OCT was reported in 1997, by researchers in James Fujimoto laboratory at Massachusetts Institute of Technology, including Prof. Guillermo James Tearney and Prof. Brett Bouma.[52] The first TD-OCT imaging catheter and system was commercialized by LightLab Imaging, Inc., a company based in Massachusetts in 2006. The first FD-OCT imaging study was reported by the laboratory of Prof. Guillermo J. Tearney and Prof. Brett Bouma based at Massachusetts General Hospital in 2008.[53] Intravascular FD-OCT was first introduced in the market in 2009 by LightLab Imaging, Inc.[54] and Terumo Corporation launched a second solution for coronary artery imaging in 2012. The higher imaging speed of FD-OCT enabled the widespread adoption of this imaging technology for coronary artery imaging. It is estimated that over 100,000 FD-OCT coronary imaging cases are performed yearly, and that the market is increasing by approximately 20% every year.[55]

Intravascular OCT has been investigated for use in neurovascular applications, too, including imaging for guiding endovascular treatment of ischemic stroke and brain aneurysms.[56] Clinical use has been limited to proximal intracranial anatomy of patient with limited tortuosity, showing the potential of OCT for the imaging of neurovascular disease. [57] An intravascular OCT imaging catheter design tailored for use in tortuous neurovascular anatomy has been proposed in 2020.[58]

Further developments of intravascular OCT included the combination with other optical imaging modalities (multi-modality imaging). OCT has been combined with fluorescence molecular imaging to enhance its capability to detect molecular/functional and tissue morphological information at the same time.[59] In a similar way, combination with near-infrared spectroscopy has been also demonstrated.

Endoscopic OCT has been applied to the detection and diagnosis of cancer and precancerous lesions, such as Barrett's esophagus and esophageal dysplasia.[60]

The first use of OCT in dermatology dates back to 1997.[61] Since then, OCT has been applied to the diagnosis of various skin lesions including carcinomas.[62][63][64] However, the diagnosis of melanoma using conventional OCT is difficult, especially due to insufficient imaging resolution.[65] Emerging high-resolution OCT techniques such as LC-OCT have the potential to improve the clinical diagnostic process, allowing for the early detection of malignant skin tumors – including melanoma – and a reduction in the number of surgical excisions of benign lesions.[66] Other promising areas of application include the imaging of lesions where excisions are hazardous or impossible and the guidance of surgical interventions through identification of tumor margins.

Researchers in Tokyo medical and Dental University were able to detect enamel white spot lesions around and beneath the orthodontic brackets using swept source OCT.[67]

Researchers have used OCT to produce detailed images of mice brains, through a "window" made of zirconia that has been modified to be transparent and implanted in the skull.[68] Optical coherence tomography is also applicable and increasingly used in industrial applications, such as nondestructive testing (NDT), material thickness measurements,[69] and in particular thin silicon wafers[70][71] and compound semiconductor wafers thickness measurements[72][73] surface roughness characterization, surface and cross-section imaging[74][75] and volume loss measurements. OCT systems with feedback can be used to control manufacturing processes. With high speed data acquisition,[76] and sub-micron resolution, OCT is adaptable to perform both inline and off-line.[77] Due to the high volume of produced pills, an interesting field of application is in the pharmaceutical industry to control the coating of tablets.[78] Fiber-based OCT systems are particularly adaptable to industrial environments.[79] These can access and scan interiors of hard-to-reach spaces,[80] and are able to operate in hostile environments—whether radioactive, cryogenic, or very hot.[81] Novel optical biomedical diagnostic and imaging technologies are currently being developed to solve problems in biology and medicine.[82] As of 2014, attempts have been made to use optical coherence tomography to identify root canals in teeth, specifically canal in the maxillary molar, however, there is no difference with the current methods of dental operatory microscope.[83][84] Research conducted in 2015 was successful in utilizing a smartphone as an OCT platform, although much work remains to be done before such a platform would be commercially viable.[85]