Lecture 25 Optical Coherence Tomography

Transcription

1 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/ Echo Time Delay of Sound and Light 67ns Electronics: OK 100µm 33fs Too fast to electronics 10µm EEL6935 Advanced MEMS 2005 H. Xie 2

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

3 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

4 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

5 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

6 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 * 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

7 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 ln2 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

8 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

9 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

10 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 ω n R1RCC Q RR 1 2 C R + R C ( ) H s s ω 2 n ( ωn / Q) s+ ωn EEL6935 Advanced MEMS 2005 H. Xie 19 OCT: Detection Electronics Sallen and Key High-pass Filter ( ) H s s ω s 2 2 n ( ωn / Q) s+ ωn 1 CC ω n 1 2 R1 R RCC Q C + C R EEL6935 Advanced MEMS 2005 H. Xie 20

11 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

12 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