some aspects of Optical Coherence Tomography

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1 some aspects of Optical Coherence Tomography SSOM Lectures, Engelberg Ch. Meier 1 / 34

2 Contents 1. OCT - basic principles (Time Domain Frequency Domain) 2. Performance and limiting factors 3. Mirror ambiguity in FD-OCT 4. Dispersion in OCT 5. Conclusion 2 / 34

3 Time Domain OCT Michelson Interferometer setup with moving reference mirror Source S(λ) z0 z1 Detector 3 / 34 z

4 Time Domain OCT Broadband source = low coherence Interferences are localized Source S(λ) z0 z1 Detector 4 / 34 z

5 Time Domain OCT Broadband source = low coherence, interferences are localized Source S(λ) z0 z1 Detector Degree of coherence 5 / 34 z

6 Source Spectrum - Degree of Coherence Wiener Khinchin theorem: The correlation function and the spectrum form a Fourier pair The normalized correlation function is the degree of coherence. For a gaussian Spectrum The coherence length (FWHM) Bandwidth 6 / 34 Coherence length 20 nm 14 um 50 nm 5.6um 150 nm 1.9um

7 Time Domain OCT The signal envelope represent the reflectivity depth profile Source S(λ) z0 z1 Detector 7 / 34 z

8 Resolution Lateral resolution = spot diameter Beam diameter and focal length Axial resolution = coherence gate In OCT Systems axial resolution is independent of Numerical Aperture NA! depends on source spectrum 8 / 34

9 Frequency/Fourier Domain OCT Broadband source coupled to SM fiber Source S(λ) z0 Suppose gaussian Spectrum with bandwidth z1 z Spectrometer sample In wavenumber: 9 / 34 Ch. Meier

10 Frequency/Fourier Domain OCT Interferences due to optical path difference Source S(λ) z0 Amplitude reflectivities z1 z Spectrometer sample Frequency in k-space is proportional to OPD 10 / 34 Ch. Meier

11 Frequency/Fourier Domain OCT Interferences due to optical path difference Source S(λ) z0 Amplitude reflectivities z1 z Spectrometer sample Frequency in k-space is proportional to OPD Time domain signal is obtained by a Fourier transformation 11 / 34 Ch. Meier

12 FD OCT, post processing Signal after Fourier Transformation Axial resolution The Fourier transformation of a real signal is symmetric. Only the half measuring range is usable 12 / 34 Ch. Meier

13 FD OCT, post processing Signal power drops for higher OPD due to finite spectrometer resolution. Scanning range or measuring range Spectral resolution Measurement from home build FD System ( ) 13 / 34 Ch. Meier

14 Time Domain vs Frequency Domain Time Domain Frequency Domain Scan rate Slow (< 1kHz) Mechanics Mechanical scanning reference arm Fast ( 50 khz, >100 khz with swept source and CMOS cameras) no mouvable parts SNR Scan range Limited by reference arm Signal power decreases with depth Mirror ambiguity bisect scanning depth 14 / 34

15 FD OCT, post processing The symmetry property of the Fourier Transform can produce image artifacts. How to overcome the mirror ambiguity in FD-OCT? Several systems are proposed to achieve full range FD-OCT Bildquelle: Wojtkowski 15 / 34 Ch. Meier

16 Full Range FD-OCT by Phase shifting Consecutive acquisition of two ore more phase shifted signals Piezo z1 Time consuming Expensive References Wojtkowski,.. Optics Letters, 2002 Leitgeb,.. Optics Letters / 34 Ch. Meier

17 Full Range FD-OCT by 3x3 coupler Parallel acquisition with a 3x3 fiber coupler 120 phase delay between output ports (for even power splitting ration ) Expensive Bildquelle: Sarunic 2005 References Sarunic, Optics Express, / 34 Ch. Meier

18 Full Range FD-OCT by heterodyne techniques Reference Bachmann, Optics Express / 34 Ch. Meier

19 Full Range FD-OCT Phase shift by moving reference mirror over one B-scan Construction of complex signal by Hilbert Transformation in x direction References Wang, Applied Physics Letters, / 34 Ch. Meier

20 Full Range FD-OCT by Dispersion encoding The dispersion mismatch in the interferometer can be used to Improve signal quality perform full range FD-OCT The algorithm was recently published by B. Hofer, group of W. Drexler, Cardiff. Bernd Hofer, Boris Pova\v{z}ay, Boris Hermann, Angelika Unterhuber,Gerald Matz, Wolfgang Drexler Dispersion encoded full range frequency domain optical coherence tomography, Opt. Express, / 34 Ch. Meier

21 Dispersion in OCT The propagation constant depend on frequency In a Taylor series expansion we have: The interpretation of the three terms are: Wave number Group velocity Second Order Dispersion With 21 / 34 vacuum speed of light and the vacuum wavelength Ch. Meier

22 Dispersion in OCT reference The dispersion mismatch is modeled by the element with thickness L, group index ng and second order dispersion D z0 ng, D L 22 / 34 z sample Ch. Meier

23 Dispersion mismatch Signal without DC term one reflecting surface Positive Dispersion Positive OPD Phase is determined by Hilbert transformation 23 / 34 First derivative is prop. to frequency Second derivative is prop. to dispersion mismatch Ch. Meier

24 Dispersion mismatch Signal without DC term one reflecting surface Positive Dispersion Negative OPD The sign of OPD = sign of the measured dispersion 24 / 34 Ch. Meier

25 Dispersion Compensation 1st surface 2nd surface Glass Dispersion in the interferometer degenerate: axial resolution SNR 25 / 34

26 Dispersion Compensation The FD-signal is multiplied by a complex phase factor j k FDc k = e 2 FD k 3 k = a 2 k a 3 k... The factors a2, a3, are determined by the second derivative of the phase function. 26 / 34 c2 L D 2 FD k cos 0 2 z n g L k k... 2 Ch. Meier

27 Dispersion Compensation Signal before and after dispersion compensation Dispersion of 25 mm glass in sample arm SNR improvement 8 db Axial resolution improvement factor 4.6 FWHM = 9 um compensated = 44 um uncompensated 27 / 34

28 Dispersion encoded Full Range The dispersion mismatch is used to identify the sign of OPD x 28 / 34

29 Dispersion encoded Full Range Original ROI Filter 29 / 34

30 FD TD Find Max TD FD FD TD 30 / 34

31 FD TD Find Max Sub. sym. TD FD FD TD FD TD 31 / 34

32 FD TD Find Max Sub. sym. TD FD FD TD FD TD 32 / 34

33 Application of DeFR in actual project High measurement range zrange > 6 mm Resolution dz = 10 um A-scan rate > 100 Hz The challenges are: 33 / 34 Compact module Large measuring range Low manufacturing cost

34 Conclusion Removal of the mirror ambiguity in FD-OCT is a issue Dispersion handling enables signal enhancement and full range FD-OCT Dispersion handling is software based, don't need expensive and time consuming hardware FD-OCT with low-cost elements is feasible Thank you for your attention 34 / 34

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