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EEL6935 Advanced MEMS (Spring 2005) Instructor: Dr. Huikai Xie Lecture 25 Optical Coherence Tomography Agenda: Ê Ê Ê OCT: Introduction Low-Coherence Interferometry OCT Detection Electronics References: Bouma and Tearney, Handbook of Optical Coherence Tomography, Marcel Dekker, Inc, 2002 EEL6935 Advanced MEMS 2005 H. Xie 4/11/2005 1 Echo Time Delay of Sound and Light 100µm 67ns Electronics: OK 10µm 33fs Too fast to electronics EEL6935 Advanced MEMS 2005 H. Xie 2 Measuring Ultrafast Optical Echoes Nonlinear optical gating Kerr shutter Second harmonic generation o High intensity o Short pulses Interferometric detection Low coherence interferometry White light interferometry EEL6935 Advanced MEMS 2005 H. Xie 3 Michelson Interferometer EEL6935 Advanced MEMS 2005 H. Xie 4 Optical Coherence Tomography Heart disease and cancer are the top two killers in US ¾ Lack of in vivo intravascular imaging modalities ¾ Lack of high-resolution imaging for early cancer diagnostics X-ray (safety, dye, resolution, …) Ultrasound (~100µm) Optical Coherence Tomography first demonstrated by Prof. Fujimoto et al. in 1991 Non-invasive or minimal invasive Based on low coherence interferometry High Resolution (∝ λ2/∆λ, ~10µm) cross-sectional images EEL6935 Advanced MEMS 2005 H. Xie 5 Optical Coherence Tomography EEL6935 Advanced MEMS 2005 H. Xie 6 Optical Coherence Tomography Carl Zeiss Meditec Inc., ¾ Eye diseases (e.g. glaucoma) Lightlab Imaging ¾ Cardiovascular imaging ¾ Cancer detection ¾ Dentistry Zeiss Stratus OCT Pentax/Lightlab Olympus Many universities Lightlab Imaging OCT System EEL6935 Advanced MEMS 2005 H. Xie 7 Optical Coherence Tomography Schematic of a simplified OCT setup Axial scanning, z Broadband source Reference mirror Fiber 1 Transverse scanning: 1D or 2D 50:50 Photo detector Fiber 2 Beam splitter y x Electronics EEL6935 Advanced MEMS 2005 H. Xie Computer z Sample 8 OCT Imaging Catheter EEL6935 Advanced MEMS 2005 H. Xie 9 Low Coherence Interferometry Michelson Interferometer Reference mirror ER lR ES Light source lS Beam splitter lD Photo detector EEL6935 Advanced MEMS 2005 H. Xie Sample ES+ ER 10 Michelson Interferometer ER ( t ) = ERm (t )e ES ( t ) = ESm (t )e − j [ 2 β R lR −ωt ] − j [ 2 β S lS −ωt ] Photocurrent of the detector: I= ηe E R + ES 2 ω Z0 For monochromatic light source, I= ηe ω Z0 2 1 2 2 1 * 2 ERm + 2 ERS + ℜ ER ES { } ∆l ℜ ER ES* = ERm ESm cos 2β ( lR − lS ) = ERm ESm cos 2π λ/2 { } The interference has a period of λ/2 relative to the length mismatch ∆l. EEL6935 Advanced MEMS 2005 H. Xie 11 Low Coherence Interferometry For partially coherent light source, I ∝e ∆τ 2 − 2 2στ Non-dispersive Media ∆l cos 2π λ/2 ∆τ: time delay; στ: standard deviation of the temporal width which is inversely proportional to the spectral bandwidth The interference changes periodically but the intensity decays exponentially. EEL6935 Advanced MEMS 2005 H. Xie 12 Low Coherence Interferometry Full-width at half-maximum (FWHM): FWHM = 2σ 2 ln 2 where ∆lFWHM and ∆λ are the full-width at half-maximum axial resolution and spectral bandwidth, respectively. ∆lFWHM = EEL6935 Advanced MEMS λ2 2 ln 2 λ02 ≈ 0.44 0 π ∆λ ∆λ 2005 H. Xie 13 OCT: Detection Electronics The photocurrent is a sinusoidal signal, 2∆l I ∝ cos (ω0τ ) = cos ω0 v p Assume the reference mirror moves at a constant speed, i.e., ∆l = vr t Then 2v I ∝ cos ω0 r t v p So, the electrical signal of the detector has a frequency of fD = fD ω ωD 2v = 0 2vr = r λ0 2π 2π v p For example, vr = 1m/s, λ0 = 1.3µm Then fD = 1.5MHz is the Doppler shift due to the moving reference mirror. EEL6935 Advanced MEMS 2005 H. Xie 14 OCT: Detection Electronics Relations Between Electrical and Optical Frequencies The electrical signal of the detector has a frequency of f = ∆f ≈ 2vr λ 2vr λ02 ∆λ ∆f ∆λ 1 ≈ → Q f D λ0 The equivalent quality factors of both electrical and optical signals are equal. EEL6935 Advanced MEMS 2005 H. Xie 15 OCT: Detection Electronics Block Diagram of OCT Electronics EEL6935 Advanced MEMS 2005 H. Xie 16 OCT: Detection Electronics Transimpedance Amplifier v = iR C for stability and high-frequency suppression EEL6935 Advanced MEMS 2005 H. Xie 17 OCT: Detection Electronics Bandpass Filters 1. Active Sallen and Key Cascade Filter • Cascading a low-pass S/K filter and a high-pass S/K filter 2. Passive Network Butterworth Filter EEL6935 Advanced MEMS 2005 H. Xie 18 OCT: Detection Electronics Sallen and Key Low-pass Filter H (s) = ωn = H (s) = EEL6935 Advanced MEMS Vo ( s ) Vi ( s ) 1 s 2 R1 R2C1C2 + s ( R1 + R2 ) C1 + 1 = 1 R1 R2C1C2 Q= R1 R2 R1 + R2 C2 C1 ωn2 s 2 + (ωn / Q ) s + ωn2 2005 H. Xie 19 OCT: Detection Electronics Sallen and Key High-pass Filter H (s) = ωn = EEL6935 Advanced MEMS ωn2 s 2 s + (ωn / Q ) s + ωn2 2 1 R1 R2C1C2 2005 H. Xie Q= C1C2 C1 + C2 R1 R2 20 OCT: Detection Electronics Passive Network Butterworth Filter Nth-order low-pass LC ladder network Nth-order high-pass LC ladder network Assume equal source and load resistances (Rs = RL), cutoff frequency ωc and unity DC gain. The ith L and C . Li = 2 Rs ωc EEL6935 Advanced MEMS ( 2i − 1) π sin 2N Ci = ( 2i − 1) π sin Rsωc 2N 2 2005 H. Xie 21 OCT: Detection Electronics Nth-order Butterworth Bandpass Filter Low-pass to bandpass frequency warping • • • • Set ωc = 1 rad/s Calculate Li and Ci Transform L to L+C Transform C to L//C Bandwidth B = ω2 − ω1 Midband frequency ωm = ω2ω1 EEL6935 Advanced MEMS 2005 H. Xie 22 OCT: Detection Electronics Demodulation • Mixing (multiplier) ∝ cos ( (ωc ± ωs ) t + φs )icos (ωc t + φd ) Phase control • Envelope detection ~ EEL6935 Advanced MEMS ~ 2005 H. Xie 23 OCT: Detection Electronics Noise • Thermal noise • Shot noise • Relative intensity noise • Amplified spontaneous emission (ASE) Design Issues • Design for shot-noise limited sensitivity • Trade-offs between resolution, power, speed and sensitivity EEL6935 Advanced MEMS 2005 H. Xie 24