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

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.

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)

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.

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.

FD-OCT Signal Processing

Amplitude Vs. pixelsAmplitude Vs. Pixels

•Di[km] .S[ Km].(RR+Rs+2√(RRRs) cos(2∆xkm +I))

Subtract DC

Di[km] .S[ Km] 2√(RRRs) cos(2∆xkm +I)

•Fourier transform: Di[Xn] = Di[km]e-

(j2(kmXn))

Di[xn] S[xn] 2√(RRRS)((xn+∆x)+(xn-∆x))

Amplitude Vs. Pixels

Di[km] .S[ Km] 2√(RRRs) cos(2∆xkm +I)

Fourier Transform

Amplitude Vs.Position

• 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

Goal

How can this artifact be removed?

Setting up andaligning thespectrometer

Simultaneousdetecting from both

cameras

Connecting thefibers and calculatingthe coupler splitting

ratios

Minimizedispersion

Lab viewDrive

the system Process

data

3X3fiber coupler

2spectrometers

Creat a complexinterferometric signal

Solution

The Complex FD-OCT Schematic

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

1

2

3x3 algorithms

•Signal 1 ( I1) -DC: Di[km] .S[ Km] 2√(RRRs) cos(2∆xkm +I)

•Signal 2 (I2) -DC: Di[km] .S[ Km] 2√(RRRs) cos(2∆xkm +I)

•Complex equation: real part + j imaginary part

If we assume that I1= the real part

the imaginary part can be obtained by the following equation:

I1cos(∆) - I2

Iim=

Sin(∆)

Graph of , I2/ I1 Graph of ∆Graph of CCD1Vs. CCD2

Results

• The removal of the complex conjugate artifact

Did it Work?

Single CCD ImageHalf screenSingle CCD Image

Full screen

Single CCD ImageFull screen

Two CCD ImageFull screen

Acknowledgments

•Center for Adaptive Optics, a National

Science Foundation Science and technology

Center(STC), AST-987683.

•UC Davis medical Center.

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)