Optical coherence tomography
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Optical coherence tomography (OCT) is an interferometric noninvasive imaging technique offering up to multiple millimeter penetration with multiple to sub micrometer axial and lateral resolution. The technique was first demonstrated in 1991 with ~30µm axial resolution, and since then has rapidly developed. Ultra high resolution OCT was established in 2001 and tremendously improved axial resolution to less then a micrometer due to introduction of wide bandwidth light sources. By now OCT has found its place as a widely accepted imaging modality, specially in ophthalmology and other biomedical applications.
Contents 
Introduction
With micrometer resolution and crosssectional imaging capabilities, optical coherence tomography (OCT)^{1} has become a prominent biomedical imaging technique, particularly suited to ophthalmic applications. In tissue imaging, requiring micrometer resolution and millimetre penetration depth, optical coherence tomography (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 former two having poor resolution; the latter lacking millimetre penetration depth^{2,3}.
The fundamentals behind OCT lie in lowcoherence interferometry^{4}. The recombination of backscattered and reference light from a sample and mirror, respectively, gives rise to an interference pattern from which pointspatial dimension and location microstructures can be determined. A crosssectional tomograph (Bscan) may be achieved by laterally combining a series of these axial depth scans (Ascan). En face imaging (Cscan) at an acquired depth is possible depending on the imaging engine used.
Theory
Simple_Interferometer.GIF
OCT_BScan_Setup.GIF
Fullfield_OCT_setup.GIF
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 lenght of the light source. This interference is called auto correlation in a symmetric interferometer (both arms have the same reflectivity), or crosscorrelation 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, <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 \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 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^{5}
 <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 \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 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 Dopplershifted optical carrier are accomplished by pathlength variation. In OCT, the Dopplershifted 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 \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 a 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
<math> \, {l_c} <math> <math>=\frac {2 \ln 2} {\pi} \cdot \frac {\lambda_0^2} {\Delta\lambda}<math> <math>\approx 0.44 \cdot \frac {\lambda_0^2} {\Delta\lambda} \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad (4) <math>
Frequency Domain OCT
In frequency domain OCT the broadband intereference 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 between the auto correlation and the spectrum, the depth scan can be immediatly calculated by a Fouriertransform 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.
Imaging 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 a interferogram with sample information corresponding to a single Ascan (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 twodimensional data set corresponding to a crosssectional image (XZ axes scan), whereas an area scan achieves a threedimensional data set corresponding to a volumetric image (XYZ axes scan), also called fullfield OCT.
Single point OCT
Systems based on single point, or flyingspot time domain OCT, must scan the sample in two lateral dimensions and reconstruct a threedimensional image using depth information obtained by coherencegating through an axially scanning reference arm (Fig. 2). Twodimensional lateral scanning has been electromechanically implemented by moving the sample^{6} using a translation stage, and using a novel microelectromechanical system scanner^{7}.
Parallel OCT
Parallel OCT using a chargecoupled device (CCD) camera has been used in which the sample is fullfield 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 threedimensional representation can be reconstructed. Threedimensional OCT using a CCD camera was demonstrated in a phasestepped technique^{8}, using geometric phaseshifting with a Linnik interferometer^{9}, utilising a pair of CCDs and heterodyne detection^{10}, and in a Linnik interferometer with an oscillating reference mirror and axial translation stage^{11}. 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.
Fullfield OCT
A twodimensional smart detector array, fabricated using a 2µm complementary metaloxidesemiconductor (CMOS) process, was used to demonstrate fullfield OCT^{12}. Featuring an uncomplicated optical setup, each pixel of the 58x58 pixel smart detector array acted as an individual photodiode and included its own hardware demodulation circuitry. In recent developments OCT was demonstrated using a commercial programmable direct readout CMOS camera (Fig. 3). Using the random access capability of the camera a small region of interest (ROI) was sampled very fast and using carrierbased detection a threedimensional surface visualisation of an industrial sample was achieved.
References
1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito and J. G. Fujimoto, "Optical Coherence Tomography", Science, 254: 11781181, 1991.
W. Drexler, U. Morgner, R.K. Ghanta, J.S Schuman, F. X Kärtner, J.G. Fujimoto, Nature Medicine, (2001)
2. S. C. Kaufman, D. C. Musch, M. W. Belin, E. J. Cohen, D. M. Meisler, W. J. Reinhart, I. J. Udell and W. S. V. Meter, "Confocal Microscopy: A Report by the American Academy of Ophthalmology", Ophthalmology, 111(2): 396496, 2004.
3. S. J. Riederer, Current technical development of magnetic resonance imaging, Engineering in Medicine and Biology Magazine. 19: 3441, 2000.
4. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Cambridge, Cambridge University Press, 1999.
5. J. M. Schmitt, "Optical Coherence Tomography (OCT): A Review", Selected Topics in Quantum Electronics, 5(4): 12051215, 1999.
6. J. M. Herrmann, M. E. Brezinski, B. E. Bouma, S. A. Boppart, C. Pitris, J. F. Southern and J. G. Fujimoto, "Two and threedimensional highresolution imaging of the human oviduct with optical coherence tomography," Fertility and Sterility, 70(1), 155158, (1998).
7. J. T. W. Yeow, V. X. D. Yang, A. Chahwan, M. L. Gordon, B. Qi, I. A. Vitkin, B. C. Wilson and A. A. Goldenberg, "Micromachined 2D scanner for 3D optical coherence tomography," Sensors and Actuators A, 117, 331340, (2004).
8. C. Dunsby, Y. Gu and P. M. W. French, "Singleshot phasestepped widefield coherence gated imaging," Optics Express, 11(2), 105115, (2003).
9. M. Roy, P. Svahn, L. Cherel and C. J. R. Sheppard, "Geometric phaseshifting for lowcoherence interference microscopy," Optics and Lasers in Engineering, 37, 631641, (2002).
10. M. Akiba, K. P. Chan and N. Tanno, "Fullfield optical coherence tomography by twodimensional heterodyne detection with a pair of CCD cameras," Optics Letters, 28(10), 816818, (2003).
11. A. Dubois, G. Moneron, K. Grieve and A. C. Boccara, "Threedimensional cellularlevel imaging using fullfield optical coherence tomography," Physics in Medicine and Biology, 49, 12271234, (2004).
12. S. Bourquin, P. Seitz and R. P. Salathé, "Optical coherence tomography based on a twodimensional smart detector array," Optics Letters, 26(8), 512514, (2001).
See Also
External Links
 Carl Zeiss commercial OCT instrument (http://www.meditec.zeiss.com/C125679E0051C774/allBySubject/E3C22400E54CEF94C1256BE6004AE0F4)
 Handbook of Optical Coherence Tomography at Amazon (http://www.amazon.com/exec/obidos/tg/detail//0824705580/qid=1111765621/sr=82/ref=sr_8_xs_ap_i2_xgl14/10395521260510254?v=glance&s=books&n=507846)