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«POLARIZATION-SENSITIVE OPTICAL COHERENCE TOMOGRAPHY USING POLARIZATION-MAINTAINING FIBERS A dissertation submitted to the Faculty of the Graduate ...»

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POLARIZATION-SENSITIVE OPTICAL COHERENCE TOMOGRAPHY

USING POLARIZATION-MAINTAINING FIBERS

A dissertation submitted to the Faculty of the Graduate School of the

UNIVERSITY OF MINNESOTA

by

MUHAMMAD K. AL-QAISI

in partial fulfillment of the requirements for the degree of

DOCTOR OF PHILOSOPHY

Adviser: Taner Akkin December 2010 © Muhammad K. Al-Qaisi December 2010

ACKNOWLEDGEMENTS

I want to start by thanking my adviser Prof. Taner Akkin for his valuable guidance.

Working in his lab was an insightful experience, from which I learned a lot. I started with Prof.

Akkin in the early stages of the lab, and I am delighted to see the progress that we have collectively accomplished. In every event I choose to thank Prof. James Leger, a distinguished researcher with outstanding teaching skills; thanks Dr. Leger for being always helpful, and for reading my dissertation. I appreciate Prof. Robert Tranquillo’s service on my committee, and his dedication heading the department; I will always remember the department’s summer parties in your backyard! Thanks to Prof. Shai Ashkenazi for the interesting ultrasound class, and for being a reader of my thesis and a committee member on my final defense.

I want to thank my labmates: John Becker, Aarthi Sivaprakasm, Hui Wang and Adam Black; I wish every one of you the best in his/her endeavors. The discussions I had with you have helped me improving the content of this dissertation, and elevating the level of my understanding of the topic. I want to also thank Prof. Victor Barocas and his lab members: Rouzbeh Amini, Julie Whitecomb, and Sara Jouzdani; collaborating with you was fun and indeed productive. Thanks for the good neighbors and the caffeine suppliers, thanks to everyone in Lori’s coffee. I must thank Mahmoud Shahin for the valuable advice he always offered, and my writing comrade, Omar Tesdell, for the good times at Saint Paul library and for reading this manuscript and commenting on it.

i I strongly appreciate the scholarship from the Jordan University of Science and Technology. Without their support, I may not have been able to come to Minnesota. I would also like to acknowledge the National Institute of Health for supporting this research, and the Graduate School at the University of Minnesota for supporting me in the last semester at the university through the Doctoral Dissertation Fellowship.

I must thank my parents and siblings for their constant support and availability to help; the good environment they created is always cherished. Thank you father and mother for, well, everything! I learned from you patience and dedication; and I promise to grasp onto the values you exemplified. I can not express my appreciation to my wife’s support; thanks Mysoon for being always the best despite the long days I have spent away working on this manuscript, and thanks for always understanding and endorsing me. It is now your turn to come back to school, Mysoon! And you, little Khaled, you may not yet understand, but I must thank you for the pleasure your smiles has brought to my heart!

–  –  –

Optical Coherence Tomography (OCT) is a sensitive imaging technique that generates cross-sectional images of turbid tissues with a micrometer-scale resolution. Polarization-Sensitive (PS) OCT adds additional contrast to OCT by detecting polarization alterations within tissues, and provides accurate OCT images in polarization-altering tissues. Common approaches to build PSOCT are either: simple but difficult to incorporate in clinics and laboratories, or fiber-based and flexible but expensive, sophisticated, and computationally demanding.

We have developed a new approach to build PSOCT using Polarization-Maintaining Fibers (PMF). A single depth scan is sufficient to calculate reflectivity, retardance, and axis orientation information using computationally-inexpensive algorithms. We present novel PMFbased PSOCT systems and demonstrate sensitivity figures larger than 100 dB, equivalent to common approaches. The developed PMF-based interferometers are used to measure minute Faraday rotations in tissue-mimicking phantoms, and the polarization properties of unmyelinated nerves. A novel algorithm is also developed to correct for errors calculating the birefringence of samples, and generate interpretable PSOCT images.

–  –  –

Acknowledgements

Dedication

Abstract

Table of Contents

List of Figures

List of Abbreviations

Notations

CHAPTER 1 Introduction

1.1 Motivation

1.2 Organization of the Dissertation

CHAPTER 2 Background

2.1 Light Extinction in Tissues

2.2 Low-Coherence Interferometry

2.3 Optical Coherence Tomography (OCT)

2.3.1. Time-Domain (TD) OCT

2.3.2. Fourier-Domain (FD) OCT

2.3.3. Signal to Noise Ratio

2.3.4. Phase noise

2.4 Polarization of Light

2.5 Birefringence

2.6 Form-Birefringence

2.7 Polarization-Sensitive (PS) OCT

2.7.1. Polarization-Diversity Reflectivity

2.7.2. Imaging Retardance and Optical Axis Orientation





CHAPTER 3 PMF-Based PS-OCT in Time-Domain using Frequency-Multiplexing.... 23 3.1 Introduction

3.2 Common TD PSOCT Implementations

v 3.3 Polarization-Maintaining Fiber (PMF)

3.4 Hardware Setup of the PMF-Based Interferometer

3.4.1. Frequency Multiplexing

3.4.2. Aligning the Coherence Functions

3.4.3. Dispersion Compensation

3.4.4. Axial Scanning

3.4.5. Data Acquisition

3.5 Theory

3.5.1. Jones Calculus

3.5.2. Signal Processing

3.6 System Characterization

3.6.1. Axial Resolution

3.6.2. Birefringence Measurements

3.7 Tissue Imaging

3.8 Discussion

3.8.1. Ghost Images

3.8.2. Accurate Splicing of the PMF

3.8.3. Unequal Losses in the Reference Arm

3.8.4. External Effects

3.9 Conclusion

CHAPTER 4 Sensitive Measurement of Faraday Rotation in Reflection Mode.............. 49 4.1 Introduction

4.2 Concept of the Measurement

4.3 Method

4.3.1. Hardware Setup

4.3.2. Mathematical Formulation

4.3.3. LCI Measurement

4.3.4. Data Acquisition and Signal Processing

4.4 Results

4.4.1. Phase Sensitivity

4.4.2. Faraday Rotation in Clear Liquids

4.4.3. Faraday Rotation in Turbid Phantoms

4.5 Discussion and Future Guidelines

vi 4.6 Conclusion

CHAPTER 5 Birefringence in Unmyelinated Nerves

5.1 Introduction

5.2 Nerve Preparation

5.2.1. Dissection and Ringer Solutions

5.2.2. The Nerve Chamber and Electrical Stimulation

5.3 Evaluating the Nerve Preparation

5.3.1. Crossed-Polarizers Setup

5.3.2. Results

5.4 PMF-based LCI for Measurement of Minute Linear Birefringence

5.4.1. Mathematical Formulation

5.4.2. Data Acquisition and Signal Processing

5.4.3. LCI Measurement

5.4.4. Precise Adjustment of the Modulation

5.4.5. Adaptive Alignment for Improved Long Term Stability

5.5 Results

5.5.1. System Characterization

5.5.2. Retardance Images of the Nerve

5.5.3. Attempts to Measure Retardance Change due to Neural Activity................ 86 5.6 Discussion and Future Directions

5.7 Conclusion

CHAPTER 6 PMF-Based Fourier Domain PSOCT for Imaging

6.1 Introduction

6.2 Hardware Setup

6.2.1. Aligning the Coherence Functions

6.2.2. Balanced-Detection

6.2.3. Signal Amplification and Acquisition

6.3 Signal Processing

6.4 System Characterization

6.4.1. Optical Spectrum

6.4.2. Alignment of the Coherence Functions

6.4.3. Signal to Noise Measures

6.4.4. Sensitivity of PMF- versus SMF-based Interferometers

vii 6.4.5. Imaging Characteristics of PMF- versus SMF-based OCT

6.4.6. Imaging Range

6.4.7. Birefringence Measurements

6.4.8. Temperature Effect

6.5 Tissue Imaging

6.5.1. Area Imaging

6.5.2. Absolute Optical Axis Orientation Image

6.5.3. Volume Imaging

6.6 Discussion

6.6.1. Polarization Leakage

6.6.2. Errors Due to Leaks

6.6.3. Absolute Axis Orientation Images

6.7 Conclusion

CHAPTER 7 Correcting the Birefringence Images

7.1 Introduction

7.2 Analysis

7.2.1. Theory

7.2.2. Example Data

7.3 Method

7.3.1. Correcting Retardance Images

7.3.2. Correcting Optical Axis Orientation Images

7.3.3. Rejecting the High-Noise Regions in Axis Orientation Images................. 129 7.4 Results

7.4.1. Images of Tissues with Low Cumulative Retardance

7.4.2. Retardance Images of High-Birefringence Tissues

7.4.3. Optical Axis Orientation Images of High-Birefringence Tissues............... 136 7.5 Discussion

7.5.1. Automatic Adjustment of the Gaussian Window of Canny Edge Detector 137 7.5.2. Towards a Fully-Automated Algorithm

7.5.3. Phase Reversal Correction in Axis Orientation Images

7.6 Conclusion

CHAPTER 8 Summary

References

viii Appendix A The OCT Equation

Appendix B General OCT Design Considerations

Appendix C Time Domain OCT

Appendix D Fourier Domain OCT

–  –  –

Figure 1.1 PMF-based PSOCT systems retain the flexibility exhibited by conventional fiber systems, and employ the compensation-free algorithms used in bulk optics systems.

2 Figure 2.1 (a) Milk is commonly used to emulate the scattering behavior of tissues. When a cup of milk is illuminated from the bottom, the scattered light can be viewed from any angle. (b) Under Rayleigh scattering regime, the scattering coefficient is inversely proportional to wavelength, and a piece of turbid glass looks blue under white light. Red light, which has a longer wavelength, penetrates deeper in scattering media. 7 Figure 2.2 Extinction of the light wave in tissue occurs due to a number of factors. The scattering coefficient decreases at longer wavelengths, while water absorption dramatically increases. OCT is operated in the range when light extinction in the target tissue is minimal. 8 Figure 2.3 Schematic of Michelson interferometer. The beam splitter splits the light of the source into the sample and reference arms. Light reflected from the known reference and unknown sample interfere at the beam splitter, and the interference pattern is recorded on the photodetector.

–  –  –

Figure 2.5 (a) Illustration of a sample of three reflecting surfaces, where τ = 0 is at the top of the sample.

(b) The A-line of the sample shows a coherence function corresponding to each reflector in the sample. The axial resolution ρa, and the modulation interval 2π/f are indicated. 13

–  –  –

Figure 2.7 (a) Illustration of the reflectivity profiles mapped using OCT of two samples with the same reflectivity, but one of them is birefringent.

The variations in reflectivity due sample birefringent are misleading. (b) When two orthogonal polarization states are recorded, a representative polarization-diversity reflectivity profile of the birefringent sample can be calculated. 20 Figure 2.8 Reflectivity images of the birefringent porcine iris tissue. OCT images are shown in (a) and (b), and PSOCT polarization-diversity reflectivity image shown in (c). When (a) and (b) are compared to (c), regions with lower reflectivities can be observed. OCT reflectivity images are misleadingly altered by the birefringence of the tissue, whereas PSOCT provides more accurate representation of the iris reflectivity. The differences between (a) and (b) are due to different stresses applied to the fiber. 21 Figure 3.1 Cross section of the PMF. The two stress elements create a uniaxial stress on the core and generate constant birefringence in the fiber. Two orthogonal and independent linear polarization states propagate simultaneously in PMF. 26 Figure 3.2 (a) Splicing the PMF at 0° couples the polarization state in the first fiber into the same polarization channel of the second fiber (slow to slow in the figure). (b) A 90° splice couples light from one channel in the first fiber into the other channel of the second fiber (shown slow to fast).

Figure 3.3 Schematic diagram of the PMF-based PSOCT.

SLD – Superluminscent diode, FSI – free-space isolator, C – collimator, EO – Phase Modulator – electro-optic LiNbO3 modulator, L – lens, GM – mirror mounted on a galvanometer, M – mirror, QWP – quarter-wave plate, PD – photodetector, and A2D – analog to digital converter. All fibers are PMF. 28 Figure 3.4 The delay l1 and l2 between the orthogonal channels in the sample and reference beams, respectively, are unequal, resulting in l2 - l1 displacement between the coherence functions. 30

–  –  –

Figure 3.7 (a) Retardance measurement of a voltage-controlled VR using single and dual detector setups.

(b) Retardance after unwrapping plotted against the manufacturer’s test data. 40

–  –  –

Figure 3.9 Images of the same section of a mouse tail acquired using dual-detector (a) and (b), and single-detector (c) and (d) setups.

Polarization-diversity reflectivity images (a) and (c) exhibit the same dynamic range, and retardance images (b) and (d) are comparable. 42 Figure 3.10 Dual-detector images of a mouse foot. (a) Polarization-diversity reflectivity, (b) retardance, and (c) relative axis orientation images. The birefringence images clearly show the extensor tendons that are not easily recognized in the reflectivity image. 44

–  –  –

Figure 4.1 Schematic diagram of the PMF-based PSLCI configured for measuring minute Faraday rotation.



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