Definitions

# computerized axial tomography

computerized axial tomography: see CAT scan.

Optical coherence tomography (OCT) is an optical signal acquisition and processing method allowing extremely high-quality, micrometre-resolution, three-dimensional images from within optical scattering media (e.g., biological tissue) to be obtained. In distinction with other optical methods, OCT, an interferometric technique, is able to penetrate significantly deeper into the scattering medium, for example ~3× deeper than its nearest competitor, Confocal microscopy. Depending on the use of high-brightness and wide-spectrum light sources such as superluminescent diodes or ultrashort pulse lasers, OCT has achieved sub-micrometre resolution (with very wide-spectrum sources emitting over a ~100 nm wavelength range). It is one of a class of optical tomographic techniques. A relatively recent implementation of OCT, frequency-domain OCT, provides advantages in signal-to-noise ratio and therefore faster signal acquisition. OCT systems, now commercially available following years of testing, are finding diverse application areas such as art conservation and diagnostic medicine (notably in ophthalmology where it permits remarkable noninvasive images to be obtained from within the retina).

## Introduction

Starting from white-light interferometry for in vivo ocular eye measurements imaging of biological tissue, especially of the human eye, was investigated by multiple groups worldwide. First devised in 1990 by Naohiro Tanno , then a professor at Yamagata University, and in 1991 by Huang et al., optical coherence tomography (OCT) with micrometer resolution and cross-sectional imaging capabilities has become a prominent biomedical tissue-imaging technique; it is particularly suited to ophthalmic applications and other tissue imaging requiring micrometer resolution and millimeter penetration depth. OCT has also been used for various art conservation projects, where it is used to analyze different layers in a painting. OCT has critical advantages over other medical imaging systems. Medical ultrasonography, magnetic resonance imaging (MRI) and confocal microscopy are not suited to morphological tissue imaging: the first two have poor resolution; the last lacks millimeter penetration depth.

OCT is based on low-coherence interferometry. In conventional interferometry with long coherence length (laser interferometry), interference of light occurs over a distance of meters. In OCT, this interference is shortened to a distance of micrometres, thanks to the use of broadband light sources (sources that can emit light over a broad range of frequencies). Light with broad bandwidths can be generated by using superluminescent diodes (superbright LEDs) or lasers with extremely short pulses (femtosecond lasers). White light is also a broadband source with lower powers.

Light in an OCT system is broken into two arms -- a sample arm (containing the item of interest) and a reference arm (usually a mirror). The combination of reflected light from the sample arm and reference light from the reference arm gives rise to an interference pattern, but only if light from both arms have travelled the "same" optical distance ("same" meaning a difference of less than a coherence length). By scanning the mirror in the reference arm, a reflectivity profile of the sample can be obtained (this is time domain OCT). Areas of the sample that reflect back a lot of light will create greater interference than areas that don't. Any light that is outside the short coherence length will not interfere. This reflectivity profile, called an A-scan, contains information about the spatial dimensions and location of structures within the item of interest. A cross-sectional tomograph (B-scan) may be achieved by laterally combining a series of these axial depth scans (A-scan). En face imaging (C-scan) at an acquired depth is possible depending on the imaging engine used.

## Laypersons Explanation

Optical Coherence Tomography, or ‘OCT’, is a technique for obtaining sub-surface images of translucent or opaque materials at a resolution equivalent to a low-power microscope. It is effectively ‘optical ultrasound’, imaging reflections from within tissue to provide cross-sectional images.

OCT is attracting interest among the medical community, because it provides tissue morphology imagery at much higher resolution (better than 10 µm) than other imaging modalities such as MRI or ultrasound.

The key benefits of OCT are:

• Live sub-surface images at near-microscopic resolution
• Instant, direct imaging of tissue morphology
• No preparation of the sample or subject

OCT delivers high resolution because it is based on light, rather than sound or radio frequency. An optical beam is directed at the tissue, and a small portion of this light that reflects from sub-surface features is collected. Note that most light is not reflected but, rather, scatters. The scattered light has lost its original direction and does not contribute to forming an image but rather contributes to glare. The glare of scattered light causes optically scattering materials (e.g., biological tissue, candle wax, or certain plastics) to appear opaque or translucent even while they do not strongly absorb light (as can be ascertained through a simple experiment — e.g., shining a red laser pointer through one's finger). Using the OCT technique, scattered light can be filtered out, completely removing the glare. Even the very tiny proportion of reflected light that is not scattered can then be detected and used to form the image in, e.g., a scanning OCT system employing a microscope.

The physics principle allowing the filtering of scattered light is optical coherence. Only the reflected (non-scattered) light is coherent (i.e., retains the optical phase that causes light rays to propagate in one or another direction). In the OCT instrument, an optical interferometer is used in such a manner as to detect only coherent light. Essentially, the interferometer strips off scattered light from the reflected light needed to generate an image. In the process depth and intensity of light reflected from a sub-surface feature is obtained. A three-dimensional image can be built up by scanning, as in a sonar or radar system.

Within the range of noninvasive three-dimensional imaging techniques that have been introduced to the medical research community, OCT as an echo technique is similar to ultrasound imaging. Other medical imaging techniques such as computerized axial tomography, magnetic resonance imaging, or positron emission tomography do not utilize the echo-location principle. The technique is limited to imaging 1 to 2 mm below the surface in biological tissue, because at greater depths the proportion of light that escapes without scattering is too small to be detected. No special preparation of a biological specimen is required, and images can be obtained ‘non-contact’ or through a transparent window or membrane. It is also important to note that the laser output from the instruments is low – eye-safe near-infra-red light is used – and no damage to the sample is therefore likely.

## Theory

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

### Time Domain OCT

In time domain OCT the pathlength of the reference arm is translated longitudinally in time. 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, $I_S$, as

$I = k_1 I_S + k_2 I_S + 2 sqrt \left\{ left \left(k_1 I_S right \right) cdot left \left(k_2 I_S right \right)\right\} cdot Re left \left[gamma left \left(tau right \right) right\right] qquad \left(1\right)$

where $k_1 + k_2 < 1$ represents the interferometer beam splitting ratio, and $gamma \left(tau \right)$ is called the complex degree of coherence, i.e. the interference envelope and carrier dependent on reference arm scan or time delay $tau$, and whose recovery 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

$gamma left \left(tau right \right) = exp left \left[- left \left(frac\left\{piDeltanutau\right\}\left\{2 sqrt\left\{ln 2\right\} \right\} right \right)^2 right\right] cdot exp left \left(-j2pinu_0tau right \right) qquad quad \left(2\right)$

where $Deltanu$ represents the spectral width of the source in the optical frequency domain, and $nu_0$ 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 sample under test microstructure, 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

$f_\left\{Dopp\right\} = frac \left\{ 2 cdot nu_0 cdot v_s \right\} \left\{ c \right\} qquad qquad qquad qquad qquad qquad qquad quad \left(3\right)$

where $nu_0$ is the central optical frequency of the source, $v_s$ is the scanning velocity of the pathlength variation, and $c$ 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 coherence length of a source and hence the axial resolution of OCT is defined as

$, \left\{l_c\right\}$ $=frac \left\{2 ln 2\right\} \left\{pi\right\} cdot frac \left\{lambda_0^2\right\} \left\{Deltalambda\right\}$
$approx 0.44 cdot frac \left\{lambda_0^2\right\} \left\{Deltalambda\right\} qquad qquad qquad qquad qquad qquad qquad qquad \left(4\right)$

### Frequency Domain OCT (FD-OCT)

In frequency domain OCT the broadband interference is acquired with spectrally separated detectors (either by encoding the optical frequency in time with a spectrally scanning source or with a dispersive detector, like a grating and a linear detector array). 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. This feature improves imaging speed dramatically, while the reduced losses during a single scan improve the signal to noise 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.

#### Spatially Encoded Frequency Domain OCT (aka Spectral Domain or Fourier Domain OCT)

SEFD-OCT extracts spectral information by distributing different optical frequencies onto a detector stripe (line-array CCD or CMOS) via a dispersive element (see Fig. 1). 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 the lower dynamic range of stripe detectors in respect to single photosensitive diodes, resulting in an SNR (signal to noise ratio) advantage of ~10 dB at much higher speeds. 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.

#### Time Encoded Frequency Domain OCT (also swept source OCT)

TEFD-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 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. 5) 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 (=linewidth) 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)

## Scanning schemes

Focusing the light beam to a point on the surface of the sample under test, and recombining the reflected light with the reference will yield an interferogram with sample information corresponding to a single A-scan (Z axis only). Scanning of the sample can be accomplished by either scanning the light on the sample, or by moving the sample under test. A linear scan will yield a two-dimensional data set corresponding to a cross-sectional image (X-Z axes scan), whereas an area scan achieves a three-dimensional data set corresponding to a volumetric image (X-Y-Z axes scan), also called full-field OCT.

### Single point (confocal) OCT

Systems based on single point, 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 using a translation stage, and using a novel micro-electro-mechanical system scanner.

### Parallel OCT

Parallel 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, using geometric phase-shifting with a Linnik interferometer , utilising a pair of CCDs and heterodyne detection, and in a Linnik interferometer with an oscillating reference mirror and axial translation stage. 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.

#### Smart detector array for parallel TD-OCT

A two-dimensional smart detector array, fabricated using a 2µm complementary metal-oxide-semiconductor (CMOS) process, was used to demonstrate full-field OCT. 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.

## Selected Applications

Optical coherence tomography is an established medical imaging technique. It is widely used, for example, to obtain high-resolution images of the retina. Researchers are also seeking to develop a method that uses frequency domain OCT to image coronary arteries in order to detect vulnerable lipid-rich plaques