Optical Coherence Tomography Zhongping Chen, Ph.D. Optical imaging in turbid media Coherence and interferometry Optical coherence tomography Functional Optical Coherence Tomography Hecht Chapter 7, 9, 12

Absorption spectra and imaging

Fluorescence Spectrum and Imaging Tryptophan

Optical Imaging Microscope Fluorescence Imaging Confocal Microscopy Two/Multi-Photon Fluorescence Microscopy Time Domain Optical Imaging Polarization Imaging Surface Imaging

Cross sectional Imaging and Tomography Biopsy Histology “Optical Biopsy”? Noninvasive cross sectional imaging

Optical Tomographic Imaging of Tissue Structure and Physiology Mean free scattering path: Skin tissue: 1/µ s ~ 50 µm Blood: 1/µ s ~ 8 µm Challenge: Scattering of photon destroy localization scatterer non-scattering media scattering media

Technology: Time of flight (only ballistic photons or minimally scattered photons are selected) Photon migration (amplitude and phase of photon density wave are measured) Optical coherence tomography (coherence gating are used to select minimally scattered photons) Optical Tomographic Imaging of Tissue Structure and Physiology

Optical Coherence Tomography: Coherence Gating Photon path length Back scattered photons Coherence gating scatterer scattering media

Optical Coherence Tomography

Interference of monochromatic light Electromagnetic wave: E=Acos(  t+  ) A: amplitude  : phase Interference: Superposition of waves E = E 1 + E 2 =A 1 cos(  t+  1 ) +A 2 cos(  t+  2 ) Phase difference:  =  2 -  1 Detection of light waves: I  c= 3x10 8 m/s, =5x10 14 Hz, T=2x sec, Detector response time ~10 -9 s,-> =0

I  = If I 1 =I 2 =I 0 Detection of light waves: In phase  =0, 2 , 4 ,..... I = 4I o Out of phase  = , 3 , 5 ..... I = 0  =  2 -  1 Interference of monochromatic light

Coherent Sources Monochromatic Definite and constant phase relation Methods to obtain two coherent sources: I.Wave front splitting II. Amplitude splitting E = E 1 + E 2 =A 1 cos(  t+  1 ) +A 2 cos(  t+  2 )

Young’s Interference Experiment Optical path length difference:  L=dsin  Phase difference:  =2  L/ Constructive interference: 2  dsin  / =2m  -> sin  m =m /d m=0,1,2,..... Destructive interference: 2  dsin  =(2m+1)  -> sin  m =(m+1/2  /d m=0,1,2,.....

Michelson interferometer

Optical path length difference:  L=2(L 2 -L 1 ) Phase difference:  L  Detected Light Intensity: Constructive interference:  L/ =2m   L=m m=0,1,2,..... Destructive interference:  L  =(2m+1)   L=(m+1/2) m=0,1,2,3,.. Michelson interferometer

Photon sources Atoms or molecules radiate wavetrains of finite length More than one wavelength (spectral bandwidth) Fixed phase relation only within individual wavetrain cc I 

Coherence Correlation of light wave at two points in space-time:  r 1,t 1 ;r 2,t 2 ) = Temporal Coherence (longitudinal)  = Spatial Coherence (lateral)  = EcEc EdEd EaEa EbEb k

Coherence time: The time for the elementary wavetrain to pass a single point Temporal Coherence Correlation of light wave along the light propagation direction  = = EaEa EbEb cc LcLc Coherence length: The length of the wavetrain where there is definite phase relation. L c =c  c k

A high (good) temporal coherence gives a narrow spectral bandwidth (“pure” light of single wavelength (color)) t E(t) Temporal Coherence Temporal coherence is a measure of spectral bandwidth cc A( )  Fourier transform pair  c  1/ 

Coherence lengths of light sources

The effect of finite coherence length Path length difference r 2 -r 1 << L c same wavetrain overlap Interference fringe observable Path length difference r 2 -r 1 >> L c Different wavetrain overlap No interference fringe observable

Partially Coherent Sources  Coherent source: Monochromatic: same wavelength Constant phase relation Incoherent source: Broad spectrum band P( ) Random Phase Partially coherent source: Broad spectrum band (  =10~100 nm), P( ) Definite phase relation within coherence length L c (2~15 µm) If  L<L c, Interference observed If  L>>L c, Interference disappeared 

 1  1       2  L  )] Interference with Partial Coherence Light Source Laser 1 Laser 2 Phase change:  L   2  2       2  L  )] Interference terms 

2222 1111 Interference with two light sources of different frequency    1  2  Laser 1 Laser 2

 1  1       2  L  )] Interference with Partial Coherence Light Source Laser 1 Laser 2  2  2       2  L  )]  3  3       2  L  )]   m  2       2  L  )] Laser 3 Laser m   

   1  2     1    3     1    7  Interference with Partial Coherence Light Source

Interference with partial coherence light source Broad band source For light with continue spectra given by the spectral density of S( ) : S( ) I (  ) For light with discrete wavelengths I( i ):

Interference with partial coherence light source Broad band source For continuous spectra with spectral density of S( ): S( ) For discrete light with different wavelength

Interference of partially coherent light Assuming the electrical fields from the partial coherent source light coupled into the interferometer is written as an harmonic superposition Where: E(t) is electrical field amplitude emitted by a low coherent light source; A( ) is the corresponding spectral amplitude at optical frequency. Because phase in each spectral component are random and independent, cross spectral density of A( ) satisfies, Where:S o ( ) is the source power spectral density [W/Hz];  (  ’) is the Dirac delta function satisfying and  (  ’) ’ Source spectrum

Interference of partially coherent light Assume light coupled equally into reference arm and sample arm with spectral amplitude of A o ( ). The light coupled back to the detect from the sample and reference arm is given by: A 0 ( ) A r ( )A s ( ) A 0 ( ) Optical path length difference:  L=2(L 2 -L 1 )

If the time delay (  ) between light in reference and sample paths is changed by translating the reference mirror, total power detected at the interferometer output is given by a time-average of the squared light amplitude Assuming that there is no spectral modulation in the reflectivity of both the sample and reference arms If the source spectral distribution is a Gaussian function Where L c is the coherence length of the partial coherence source given by Interference of partially coherent light

Optical Coherence Tomography S( )  LcLc L c =    Interference fringes observed only when optical path lengths are matched within coherence length of the source

Optical Coherence Tomography ––– Michelson interferometer with a broad band partially coherent source Axial spatial resolution: L c =   

Coherence function LL Narrow Spectrum Broad Spectrum  FWHM ~ 75 nm  FWHM ~ 25 nm L c ~15 µm L c ~5 µm Source spectrum L c =    Fourier Transformation Interference with Partial Coherence Light Source

Optical Coherence Tomography Fringe amplitude proportional to backscattered light Longitudinal (depth) resolution: L c Coherence length: L c =    (2~15 µm) Lateral resolution by focusing optics (1~10 µm) Probing depth: 1/µ’ s ~ 5/µ’ s ––– Michelson interferometer with a broad band partial coherent source

Interference Coherence sources I  Partially coherence sources Source power spectrum L c =    Coherence function LcLc

Optical Coherence Tomography Interference fringes is observed only when optical path lengths are matched within the coherence length of the source Fringe amplitude is proportional to the backscattered light intensity Longitudinal (depth) resolution: coherence length L c given by L c =    (2~15 µm) Lateral resolution: focusing optics (1~10 µm) Probing depth: 1/µ’ s ~ 5/µ’ s ––– Michelson interferometer with a broad band partial coherent source

Sample with Scattering Surfaces (internal and external) Low Coherence “Laser” Light Source Reference mirror Photodetector Beam splitter Operating Principles of OCT { {

Reference Beam Path Length Three scattering surfaces Low Coherence Light Source Reference mirror Photodetector Beam splitter

Fiber Based OCT Setup Michelson Interferometer Source Mirro r Pre amp Band pass Filter Detector Demodulation AD Converter A Scan

Optical Biopsy OCT in vivo image of a human hand 200 µm

Optical biopsy: Speckle averaged OCT image

Visualization of neonatal freeze lesion Investigating epilepsy in animal model 4.7T MRI (1.8 x 1.3 cm)OCT (2 x 1.8mm)Histology Cortex WM R. D. Pearlstein, Z. Chen, et al.

Epithelium Lamina Propria Muscularis Mucosa Circular Muscle Optical biopsy: OCT image of rat esophagus

Optical Doppler Tomography Doppler frequency shift:  s s f0+fDf0+fD f0-fDf0-fD Velocity: V=  f D /(2cos(  ))

Optical Doppler Tomography LcLc Combining Doppler velocimetry with optical sectioning capability of OCT

Optical Doppler Tomography