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A Picosecond Optoelectronic Cross Correlator Using a Gain Modulated Avalanche Photodiode for Measuring the Impulse Response of Tissue

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A Picosecond Optoelectronic Cross Correlator Using a Gain Modulated Avalanche Photodiode for Measuring the Impulse Response of Tissue A Picosecond Optoelectronic Cross Correlator using a Gain Modulated Avalanche Photodiode for Measuring the Impulse Response of Tissue. David R. Kirkby B.Sc. M.Sc. Department of Medical Physics and Bioengineering, University College London. Thesis submitted for the degree of Doctor of Philosophy (Ph.D.) at the University of London. Supervisor: Professor David T. Delpy, FRS. Second supervisor: Dr. Mark Cope. April 1999. 2 Abstract Human tissue is relatively transparent to light between 700 and 1000 nm in the near infra- red (NIR). NIR spectroscopy is a technique that can measure non-invasively and safely, the optical properties of tissue. Several different types of spectroscopic instrumentation have currently been developed, ranging from simple continuous intensity systems, through to complex time and frequency resolved techniques. This thesis describes the development of a near infra-red time-resolved system, using an inexpensive avalanche photodiode (APD) detector and a microwave step recovery diode (SRD) in a novel way to implement a totally electronic cross- correlator, with no moving parts. The aim of the work was to develop a simple instrument to monitor scattering changes in tissue during laser induced thermal therapy. The APD was gain-modulated by rapidly varying the bias voltage using electrical pulses generated by the SRD (120 ps full width half maximum (FWHM) and8Vinamplitude). The resulting cross-correlator had a temporal resolution of 275 ps FWHM - significantly faster than the 750 ps FWHM of the APD when operating with a conventional fixed bias voltage. Spurious responses caused by the SRD were observed, which were removed by the addition of Schottky diodes on the SRD’s output, although this slightly degraded the system temporal resolution from 275 to 380 ps FWHM. The ability of the system to monitor scattering changes was tested using an IntralipidTM phantom containing infra-red absorbing dye. An 800 nm fibre coupled mode-locked (2 ps pulse width) laser source was used with the cross-correlator measuring the temporal point spread function (TPSF) at 5 to 30 mm away from the source fibre. Five different numerical algorithms to derive the scattering coefficient from the measured TPSF were compared. The optimum choice of algorithm was found to depend on whether absolute accuracy or minimum computation time is the most important consideration. 3 Acknowledgements I would like to thank the following for their help during this research. Dr. Klaus Berndt, whose research publications first got the idea for the project going and for very helpful discussions at one of the SPIE conferences. My supervisor, Professor David Delpy FRS, for first noting the publications of Dr. Berndt and then helping me write the grant proposal, which finally secured funding. His help at every stage of the research was invaluable. Elizabeth Hillman, for proof reading parts of my thesis and her invaluable help with dispelling doubts I had about the Monte Carlo results. Beth, within a few months of starting her Ph.D., made what was probably the most significant single contribution of anyone else, towards me getting this Ph.D. finished. Thanks Beth. Barry Hall, Joy Hall and Dr. Jeremy Chipchase, all of whom proof read parts of my thesis. They are of course in no way responsible for any remaining mistakes. Dr. Jem Hebden, who had the very useful habit of suggesting computer programmes that were appropriate and for helping me implement some of them. Also for the time he spent in meetings with my supervisor and I discussing aspects of this work. Dr. Mark Cope, for his help on several aspects, especially the phantom construction, noise characteristics of lock-in amplifiers, but also countless other things. Marks superb knowledge base that makes him so popular with his students, was tapped by me on several occasions. Dr. Paul Ripley, for his advice on PDT and LITT. Veronica Hollis for her help in using with the CCD spectrometer, which had been put together and optimised by Dr. Roger Springett. My wife Linda, for her support during the whole of the Ph.D. and who so often met me at Althorne Station for the 2220 or 2301 train, to save me the 1.5 mile walk home - most of which is up hill. Thanks for all your help Lin. 4 My Father, Robert William Kirkby, for his encouragement throughout the whole duration of the work. Denzil Booth, Geoff Brown, Stewart Morrison and Billy Raven from our mechanical workshop, who all helped me make various mechanical pieces. The members and former members, of our research group, but in particular Dr. Simon Arridge, Dr. Matthew Clemence, Dr. Martin Fry, Dr. Michael Firbank, Dr. Mathias Kohl, Dr. Louise Lunt, Dr. Roger Springett, Florian Schmidt and Dr. Martin Schweiger. Lastly, but not least, to the former Science and Engineering Research Council (now EPSRC) who supplied funding for the project. 5 Dedication This thesis is dedicated to the memory of my late Grandmother, Dorothy May Impey, who would have so much enjoyed to see her Grandson get the title "Doctor". 6 List of Tables. .................................................... 12 Abbreviations. .................................................... 22 Symbols. ........................................................ 24 Chapter 1. Introduction. ..................................................... 29 1.1 Purpose. ................................................... 29 1.2 Guide to this thesis. ........................................... 29 1.3 Medical uses of optical radiation. ................................. 31 1.3.1 Photodynamic therapy (PDT). ................................. 31 1.3.2 Laser induced thermal therapy (LITT). ........................... 32 1.3.3 Near infra-red spectroscopy (NIRS). ............................. 33 1.3.4 Laser Doppler blood flow measurements. ......................... 34 1.3.5 Tissue spectrophotometry. .................................... 35 1.4 Terminology in tissue optics. .................................... 36 1.4.1 Absorption. .............................................. 38 1.4.2 Scattering. ............................................... 40 1.4.3 Temporal point spread function (TPSF). .......................... 42 1.4.4 Typical values of the optical properties of tissue. .................... 43 1.5 Modelling light transport in tissue. ................................ 44 µ µ 1.5.1 Why model to obtain a and s. ................................ 44 1.5.2 Kubelka-Munk (KM) model. .................................. 45 1.5.3 The diffusion equation approximation of the radiative transfer equation. .... 47 1.5.3.1 Solution of the diffusion equation by finite-element modelling (FEM). 51 1.5.4 Monte Carlo models of light transport in tissue. ..................... 54 1.5.5 Comparison of modelling methods and why Monte Carlo was selected. .... 56 µ µ 1.6 Hardware for finding a and s without measuring the TPSF. .............. 59 1.6.1 Simple CW hardware. ....................................... 59 1.6.2 Frequency domain phase fluorometer. ............................ 60 1.6.3 Frequency domain phase measurements for tissue optics. .............. 62 1.7 Measurement of the temporal point spread function (TPSF). .............. 66 7 1.7.1 Measurement of the TPSF with a photo-detector and sampling oscilloscope. 66 1.7.2 Measurement of the TPSF with a streak camera. .................... 68 1.7.3 Measurement of the TPSF with a sampling optical oscilloscope. ......... 69 1.7.4 Temporal response of optical pulses by intensity auto-correlation using second harmonic generation. ....................................... 70 1.7.5 Measurement of the TPSF using time-correlated single-photon counting. 71 1.7.6 Temporal response of optical signals using a cross-correlation method. .... 75 1.7.7 Hardware for TPSF measurement using a cross-correlation technique. ..... 76 1.7.8 Other methods of TPSF Measurement. ........................... 79 1.8 Design methodology for the instrument. ............................. 79 1.9 Initial design specifications of the instrument. ........................ 80 Chapter 2. Short Pulsed Laser Sources. .......................................... 82 2.1 Introduction. ................................................ 82 2.2 Q-switched Lasers. ........................................... 83 2.2.1 Q-switching with a rotating mirror. ............................. 84 2.2.2 Active Q-switching using an electro-optic modulator. ................. 84 2.2.3 Passive Q-switching using a saturable absorber. ..................... 84 2.2.4 Q-switching of semiconductor diode lasers. ........................ 85 2.3 Mode-locking. ............................................... 85 2.3.1 Active mode-locking. ....................................... 87 2.3.2 Passive mode-locking. ...................................... 87 2.3.3 Mode-locking of semiconductor diode lasers. ...................... 88 2.4 Gain-switching of semiconductor lasers. ............................ 88 2.5 Laser used for this project. ...................................... 89 Chapter 3. Fast Semiconductor Detectors. ........................................ 90 3.1 PN/PIN photodiode. ........................................... 90 3.1.1 Equivalent circuit. ......................................... 91 3.1.2 Small signal response of a pin photodiode. ........................ 91 3.1.3 Large signal response of a pin photodiode. ........................ 92 3.1.4 Noise of pin photodiode. ..................................... 93 8 3.1.5 Frequency response of the pin photodiode. ........................ 96
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