EEL6935 Advanced MEMS (Spring 2005) Instructor: Dr. Huikai Xie Lecture 25 Optical Coherence Tomography Agenda: 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 67ns Electronics: OK 100µm 33fs Too fast to electronics 10µm 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 Lack of in vivo intravascular imaging modalities 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 ( λ 2 / 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., Eye diseases (e.g. glaucoma) Lightlab Imaging Cardiovascular imaging Cancer detection Dentistry Pentax/Lightlab Olympus Many universities Zeiss Stratus OCT 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 Fiber 1 Reference mirror Photo detector 50:50 Beam splitter Fiber 2 y Transverse scanning: 1D or 2D x Electronics Computer z Sample EEL6935 Advanced MEMS 2005 H. Xie 8
OCT Imaging Catheter EEL6935 Advanced MEMS 2005 H. Xie 9 Low Coherence Interferometry Michelson Interferometer Reference mirror E R l R Light source Beam splitter l D E S l S Sample Photo detector E S + E R EEL6935 Advanced MEMS 2005 H. Xie 10
R () E t E t e S ( ) Michelson Interferometer Rm E t E t e Sm [ 2β ω ] j l t () RR [ 2β ω ] j l t () S S Photocurrent of the detector: ηe I ER + E 2 ωz 0 S 2 For monochromatic light source, ηe 1 1 I E + E +R E E ωz 2 2 0 { } 2 2 * Rm RS R S * l R { EE R S} ERmESm cos 2 β( lr ls ) ERmESm 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, Non-dispersive Media 2 τ 2 2σ l τ I e cos 2π λ /2 τ: time delay; σ τ : 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 2ln2 where l FWHM and λ are the full-width at half-maximum axial resolution and spectral bandwidth, respectively. 2 2 2ln2 λ0 λ0 l FWHM 0.44 π λ λ EEL6935 Advanced MEMS 2005 H. Xie 13 OCT: Detection Electronics The photocurrent is a sinusoidal signal, 2 l I cos( ωτ 0 ) cos ω 0 v p Assume the reference mirror moves at a constant speed, i.e., Then l v t 2v r I cos ω0 t v p So, the electrical signal of the detector has a frequency of f ω ω 2vr 2v π π λ D 0 D r 2 2 vp r 0 For example, v r 1m/s, λ 0 1.3µm Then f D 1.5MHz f D 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 2v r λ 2v r 2 λ0 λ f f D λ 1 λ Q 0 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 ( s) 1 ( ) 2 ( ) Vo V s s RR CC + s R + R C + 1 i 1 2 1 2 1 2 1 1 ω n R1RCC Q RR 1 2 C2 2 1 2 R + R C ( ) H s s ω 2 n 2 2 + ( ωn / Q) s+ ωn 1 2 1 EEL6935 Advanced MEMS 2005 H. Xie 19 OCT: Detection Electronics Sallen and Key High-pass Filter ( ) H s s ω s 2 2 n 2 2 + ( ωn / Q) s+ ωn 1 CC ω n 1 2 R1 R RCC Q C + C R 1 2 1 2 1 2 2 EEL6935 Advanced MEMS 2005 H. Xie 20
OCT: Detection Electronics Passive Network Butterworth Filter N th -order low-pass LC ladder network N th -order high-pass LC ladder network Assume equal source and load resistances (R s R L ), cutoff frequency ω c and unity DC gain. The ith L and C. ( 2i 1) π 2R s Li sin ωc 2N ( 2i 1) 2 π Ci sin Rsωc 2N EEL6935 Advanced MEMS 2005 H. Xie 21 OCT: Detection Electronics N th -order Butterworth Bandpass Filter Low-pass to bandpass frequency warping Set ω c 1 rad/s Calculate L i and C i Transform L to L+C Transform C to L//C Bandwidth B ω2 ω1 Midband frequency ωm ωω 2 1 EEL6935 Advanced MEMS 2005 H. Xie 22
OCT: Detection Electronics Demodulation Mixing (multiplier) (( ωc ωs) t φs) icos( ωct φd) cos ± + + 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