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An Alternative Method of Extending Imaging Window of Fourier Domain – Optical Coherence Tomography by Using a Complex Conjugate Removal Technique Amine Bouchti University California Davis Research Advisor: John S. Werner Research Supervisor: Robert J Zawadzki

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Optical Coherence Tomography (OCT) –An interferometric technique that offers, in vivo, cross-sectional views of biological microstructure tissue such as the human retina. –The depth structure of the sample is reconstructed from backscattered light by Fourier domain OCT (FD-OCT). –The images are generated by scanning the incident light beam at different axial depths and transverse positions.

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What is Fourier Domain ? Fourier domain is the analysis of functions or signal with respect to frequency. It relates to the Fourier transform by decomposing a function into a finite number of frequencies. Fourier transform functions are complex ( they have Amplitude and phase.) In standard FD-OCT only the magnitude of Fourier transform is displayed. Position(z)

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Main Applications of OCT The axial resolution of OCT in retinal tissue is about 1-15 µm, which is 10 to 100 times better than ultrasound or MRI. It enables visualization of the internal architectural morphology of the retina noninvasively; in real time and provides a 3 dimensional view of the retina. OCT can detect and diagnose early stages of disease before physical symptoms and irreversible vision loss can occur.

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OCT apparatus Schematic of the OCT System SLD: Superluminescent diode source. PC:polarization controllers. NDF: Neural density filter. FI: Faraday isolator. M: Mirror. DG: Diffraction grating. CCD: CCD cameras.

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FD-OCT Signal Processing Amplitude Vs. pixels Amplitude Vs. Pixels D i [k m ].S[ K m ].(R R +R s +2(R R R s ) cos(2xk m + I )) Subtract DC D i [k m ].S[ K m ] 2(R R R s ) cos(2xk m + I )

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Fourier transform: D i [X n ] = D i [k m ]e - (j2 (kmXn)) D i [x n ] S[x n ] 2(R R R S )( (x n +x)+ (x n -x)) Amplitude Vs. Pixels D i [k m ].S[ K m ] 2(R R R s ) cos(2xk m + I ) Fourier Transform Amplitude Vs.Position

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In Standard FD-OCT only half of the imaging window can be used. Due to a reflection at + X that cannot be distinguished from a reflection at -X. This is called Complex Conjugate Artifact. Limitations

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Goal How can this artifact be removed?

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Solution

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The Complex FD-OCT Schematic 1 2

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3x3 algorithms Signal 1 ( I 1 ) -DC: D i [k m ].S[ K m ] 2(R R R s ) cos(2xk m + I ) Signal 2 (I 2 ) -DC: D i [k m ].S[ K m ] 2(R R R s ) cos(2xk m + I ) Complex equation: real part + j imaginary part If we assume that I 1 = the real part the imaginary part can be obtained by the following equation: I 1 cos( ) - I 2 I im = Sin( ) Graph of, I 2 / I 1 Graph of Graph of CCD1 Vs. CCD2

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Results The removal of the complex conjugate artifact

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Did it Work? Single CCD Image Half screen Single CCD Image Full screen Single CCD Image Full screen Two CCD Image Full screen

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Acknowledgments Center for Adaptive Optics, a National Science Foundation Science and technology Center(STC), AST-987683. UC Davis medical Center.

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References University of California Davis Medical center, http://vsri.ucdavis.edu/. Marinko V.Sarunie, Michael A. Choma, Changhuei Yang, Joseph A. Izatt, Instantaneous complex conjugate resolved spectra domain and swept-source OCT using 3x3 fiber coupler,Opt.Express 13,957- 967 (2005) Michael A. Choma, Changhuei Yang, Joseph A. Izatt, Instantaneous quadrature low-coherence interferometry with 3x3 fiber-optic couplers, Opt.Lett.28, 2162-2164 (2003) N.A. Nassif, B. Cense, B.H. Park, M.C. Pierce, S.H. Yun, B.E. Bouma,G.J.Tearney, In vivo high-resolution video-rate spectral-domain optical coherence tomography of the human retina and optic nerve, Opt.Express 12,367- 376 (2004)

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