1. 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

2. 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.

3. 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)

4. 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.

5. 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.

6. 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 )

7. 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

8. 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

9. Goal How can this artifact be removed?

10. Solution

11. The Complex FD-OCT Schematic 1 2

12. 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

13. Results The removal of the complex conjugate artifact

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

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

16. 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)