Quantitative photoacoustic integrating sphere (QPAIS) platform: for Grüneisen parameter, optical absorption & fluorescence quantum yield measurements of biomedical fluids

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(1)QUANTITATIVE PHOTOACOUSTIC INTEGRATING SPHERE (QPAIS) PLATFORM. Quantitative PhotoAcoustic Integrating Sphere (QPAIS) Platform FOR GRÜNEISEN PARAMETER, OPTICAL ABSORPTION & FLUORESCENCE QUANTUM YIELD MEASUREMENTS OF BIOMEDICAL FLUIDS. Yolanda Yecla Villanueva. Yolanda Yecla Villanueva.

(2) QUANTITATIVE PHOTOACOUSTIC INTEGRATING SPHERE (QPAIS) PLATFORM FOR GRÜNEISEN PARAMETER, OPTICAL ABSORPTION AND FLUORESCENCE QUANTUM YIELD MEASUREMENTS OF BIOMEDICAL FLUIDS. Yolanda Yecla Villanueva.

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(4) QUANTITATIVE PHOTOACOUSTIC INTEGRATING SPHERE (QPAIS) PLATFORM FOR GRÜNEISEN PARAMETER, OPTICAL ABSORPTION AND FLUORESCENCE QUANTUM YIELD MEASUREMENTS OF BIOMEDICAL FLUIDS. DISSERTATION. to obtain the degree of doctor at the University of Twente, on the authority of the rector magnificus, Prof.dr. H. Brinksma, on account of the decision of the graduation committee, to be publicly defended on Thursday, the 28th of January 2016 at 16:45h. by. Yolanda Yecla Villanueva born on the 9th of October 1978 in Quezon City, Philippines.

(5) This dissertation has been approved by: Promotor: prof. dr. ir. W. Steenbergen.

(6) Contents Chapter 1. General Introduction ................................................................ 1–1. 1.1. Brief historical background of photoacoustics ................................. 1–2. 1.2. Photoacoustic imaging ..................................................................... 1–2. 1.3. Initial photoacoustic pressure and the Grüneisen parameter ......... 1–4. 1.4. The integrating sphere for optical measurements ........................... 1–6. 1.5. Quantitative photoacoustics using an integrating sphere ............... 1–7. 1.6. Scope and main contributions of this thesis .................................... 1–8. Chapter 2 Photoacoustic measurement of the Grüneisen parameter using an integrating sphere* .................................................................................. 2–15 2.1. Introduction ................................................................................... 2–16. 2.2. Methodology ................................................................................... 2–17. 2.3. Results and Discussion .................................................................. 2–23. 2.4. Conclusion ...................................................................................... 2–27. Chapter 3 Absorption coefficient measurement of scattering liquids using a tube inside an integrating sphere*................................................................ 3–31 3.1. Introduction ................................................................................... 3–32. 3.2. Methodology ................................................................................... 3–33. 3.3. Results and Discussion .................................................................. 3–41. 3.4. Conclusion ...................................................................................... 3–49. Chapter 4 Quantitative Photoacoustic Integrating Sphere (QPAIS) Platform for absorption coefficient and Grüneisen parameter measurements: demonstration with human blood*................................................................ 4–53 4.1. Introduction ................................................................................... 4–55. 4.2. Methodology ................................................................................... 4–56. 4.3. Results............................................................................................ 4–63. 4.4. Discussion ...................................................................................... 4–69. 4.5. Conclusion ...................................................................................... 4–71. Chapter 5 Grüneisen parameter measurement of human knee joint and breast cyst fluids using the Quantitative Photoacoustic Integrating Sphere (QPAIS) ................................................................................................ 5–75 5.1. Introduction ................................................................................... 5–76.

(7) 5.2. Methodology ................................................................................... 5–77. 5.3. Results............................................................................................ 5–79. 5.4. Discussion ...................................................................................... 5–83. 5.5. Conclusion ...................................................................................... 5–84. Chapter 6 Fluorescence quantum yield measurements using an integrating sphere: Initial measurements with Rhodamine 6G*..................................... 6–87 6.1. Introduction ................................................................................... 6–88. 6.2. Methodology ................................................................................... 6–88. 6.3. Results and discussion ................................................................... 6–92. 6.4. Conclusion ...................................................................................... 6–96. Chapter 7. Recommendations .................................................................. 7–99. Summary. .................................................................................................. 109. Samenvatting .................................................................................................. 113 Acknowledgements .......................................................................................... 119 About the author ............................................................................................. 123 List of publications .......................................................................................... 125.

(8) Chapter 1 General Introduction. 1–1.

(9) 1.1. Brief historical background of photoacoustics. Nature has its way for us to observe the physical properties and chemical makeup of things using our own senses. We can feel solid materials, smell gases and taste liquids. We can see light and can hear sound. And it is but natural for us to associate the means to observe a specific material property to a specific sensory faculty. Thus it came to be a remarkable event in history of mankind when in 1880 Alexander Graham Bell first heard the sound of light. In his account given to the American Association for the Advancement of Science, he described how modulated sunlight, when absorbed by a selenium cell produced sound [1, 2]. Bell’s observation has led to his invention of what is known as the photophone [3]. In his book, Bell described how a clear, musical tone was heard when a beam of sunlight focused into one end of an open tube was interrupted, the pitch of which depended upon the frequency of the interruption of the light and the loudness upon the material composing the tube. After observing such emission of sounds by various substances, including fluids, exposed to modulated sunlight, he concluded that “sonorousness” under such circumstances would be found to be a general property of all matter [1]. 1–2. The instrument [photophone] is simplicity itself, but the results are of the highest popular and scientific interest. –John Michels, Editor, Science [4]. 1.2. Photoacoustic imaging. The remarkable discovery of Alexander Graham Bell of the creation of audible sound by modulated sunlight was way ahead of its time and his photophone did not find practical applications until almost a century later. Bell described (1881) in considerable detail the photophone and he demonstrated that the photoacoustic effect in solids was dependent on the absorption of light, and that the strength of the acoustic signal was in turn dependent on how strongly the incident light was absorbed by the material in the cell. However, the experiments were difficult to perform and quantitate since the detector was the investigator's ear. This fact hindered the further development and application of what is now known as the photoacoustic (PA) effect. After this great discovery of the photoacoustic effect in the late 19th century, not much attention was actively given to related scientific research or.

(10) technological advancement. It was only until the invention of lasers in the 1960s that profound interest was given to exploit the applications of this PA phenomenon [5]. Laser sources provided the required high peak power, spectral purity and directionality of various PA measurements that emerged in the decades that followed. The immediate applications were more focused on exploring the gas-phase cell type PA detection in which the laser-induced surface heating generated acoustic waves which propagated in gas [6], in contrast to the nowadays biomedical PA techniques. It was in the 1970s and early 1980s that early research on the potential clinical applications of photoacoustic spectroscopy of the human tissue was reported [7, 8]. Thereafter, first photoacoustic images that stimulated biomedical photoacoustic imaging were obtained by various researchers in the 1990s [911]. The decades that followed witnessed breakthroughs in the development of instrumentation, image reconstruction algorithms, functional and molecular imaging capabilities, both in basic biological research and in vivo clinical applications [12-18]. In PA imaging, modulated electromagnetic radiation usually pulsed with nanosecond timescale is made incident on the target tissue which subsequently generates ultrasound waves that are detected on the surface. Optical wavelengths in the visible and near-infrared (550 nm to 900 nm) which offers greatest optical penetration depth are used in biomedical PA imaging. Optical excitation due to absorption by specific tissue chromophores, for example blood hemoglobin, melanin, water or lipids is followed by very fast conversion to heat accompanied by very small temperature rise that is below the threshold to cause damage to the tissue. If the laser pulse width is much shorter than both the thermal relaxation time that characterizes thermal diffusion and the stress relaxation time that characterizes pressure propagation, the excitation satisfies both thermal and stress confinement conditions. In this case, both heat conduction and pressure propagation are negligible during the laser pulse which consequently leads to the local pressure rise that propagates as PA waves to the surface and gets detected by mechanically scanned ultrasound receiver or array of receivers. Based on the time of arrival of the generated PA waves and at the known speed of sound in the tissue, an image of the absorbing chromophores can be reconstructed similar to the conventional ultrasound pulse echo image reconstruction. In contrast to the mechanical and elastic properties that an ultrasound image represents, PA image gives an impression of the initial pressure distribution generated by the local optical absorption. With some assumptions on the inherent thermal properties of the target, the PA image can be interpreted as proportional to the absorbed optical energy. 1–3.

(11) distribution that depends on the optical properties of the tissue. Consequently, because contrasts in optical absorption between different types of tissue can be much larger than those in acoustic impedance, PA imaging can provide better tissue differentiation and specificity than ultrasound imaging. For example, PA imaging technique is better at visualizing microvasculature. Moreover, the spectroscopic nature of PA effect is used to quantify specific chromophore concentrations that can provide relevant physiological parameters, for example spectroscopic measurement of blood oxygenation.. 1.3. Initial photoacoustic pressure and the Grüneisen parameter. As described above, a photoacoustic image is formed from a set of PA signals and is a representation of the initial pressure V0 which is related to the absorbed optical energy density Ae(r) deposited at the source location r and can be expressed as (1.1). ɐ଴ ሺሻ ൌ Ȟୣ ሺሻ 1–4. where Γ is known as the macroscopic Grüneisen parameter that indicates the conversion of heat energy to pressure. As described in [19], the thermodynamic nature of Γ can be understood by considering the fractional volume expansion upon laser excitation written as (1.2). ሺሻ ൌ െNɐሺሻ ൅ Eሺሻ ሺሻ. where N is the isothermal compressibility (Pa-1), E is the thermal coefficient of volume expansion, V and T are the changes in pressure and temperature, respectively. If the laser pulse width is much shorter than both the thermal relaxation time that characterizes thermal diffusion and the stress relaxation time that characterizes pressure propagation, the excitation satisfies both thermal and stress confinement conditions. In this case, both heat conduction and pressure propagation are negligible during the laser pulse which ୢ୚. consequently leads to negligible volume expansion ( ୚ ൎ Ͳ) and the local pressure rise V0 can be expressed as.

(12) ɐ଴ ሺሻ ൌ. Eሺሻ N. The temperature increase is related to Aeሺሻ as: ሺሻ ൌ. (1.3) K୅౛ ሺ୰ሻ Uେ౒. , K is the. percentage of the absorbed optical energy density that is converted to heat, whereas N is related to the specific heat capacities at constant volume and େ. pressure (CV and CP), mass density U and speed of sound vs as: N ൌ U௩ మು஼. ೞ ೇ. ɐ଴ ሺሻ ൌ. E E‫ݒ‬௦ଶ K௘ ሺሻ ൌ K௘ ሺሻ NU‫ܥ‬௏ ‫ܥ‬௉. (1.4). Equation (1.4) is the photoacoustic signal that is generated at the location of an absorber with the above-mentioned thermal properties E, N, C and vs. In general, if the energy conversion is non-radiative, K is approximately one. If a radiative wave is also produced upon optical absorption, the fluorescence quantum yield )f must also be taken into account for a more accurate measurement of the amplitude of the initial pressure. If the thermal properties of a target absorber are known, an estimation of V0 can easily be determined for a given absorbed energy density Ae = Pa)ሺሻ, where Pa is the absorption coefficient and ) is the incident fluence. Consequently, if ) is also known, Pa is directly determined which is linearly related to the concentration of target chromophores. The material properties in the prefactor in Equation (1.4) above are usually not readily known, particularly for biological fluids which are of interest in biomedical imaging. For the purpose of determining chromophore concentrations, each of these thermal properties does not need to be known a priori. Instead, they are considered collectively as the macroscopic representation of the Grüneisen parameter Γ [19, 20]. From Equation (1.4) Ȟൌ. E Eୱଶ ൌ NU୚ ୔. (1.5). The name comes from the German Physicist Eduard Grüneisen who in 1926 originally proposed an equation of state for solid matter on his lattice vibration theory: ൅ ሺሻ ൌ Ȟሺሻ where e is the specific internal energy, V is the specific volume, G(V) is a function related to the lattice potential and Γ(V) is the microscopic Grüneisen parameter [21]. From Equation (1.1) and (1.5), V0 depends not only on optical parameters but also on various thermodynamic. 1–5.

(13) properties as given by the Grüneisen parameter which may also provide contrast in PA images [22]. Several publications have reported different techniques to measure * of biological chromophores [23-25]. Recently, photoacoustic spectroscopy has been used to measure * of porcine subcutaneous fat tissue and bovine red blood cells [26]. The * value was determined by linearly fitting the photoacoustic spectrum with the absorption spectrum, using a calibrated system with detectors of known sensitivity such that incident fluence is also measured. In another research, the relative change in * with concentrations of inorganic chromophores such as copper and nickel chloride in aqueous dilutions is also measured using photoacoustic spectroscopy [27]. For small concentrations of organic chromophores, for example cyanine-based dyes, dissolved in water, the change in * with dye concentration is negligible [27]. Furthermore, an interferometric technique has also been implemented to measure * of bovine liver tissues. In this technique, * is measured from the plot of the sample surface displacement against incident pulse laser energy [28].. 1–6. The experimental setups in the above-mentioned research require absolute sensitivity measurements of the optical and acoustic signals and involve stringent alignment between the incident light and target absorber and acoustic detector which may not be very convenient for measuring with liquid samples. To address these difficulties and to provide a simple experimental setup, this thesis presents the development of a method and setup for directly measuring the Grüneisen parameter Γ of biomedical fluids using an integrating sphere as a platform for photoacoustic measurements.. 1.4. The integrating sphere for optical measurements. An integrating sphere is an optical instrument commonly used for measuring optical radiation [29]. With its highly reflecting inner wall and spherical geometry, the integrating sphere spatially integrates radiant flux providing homogeneous and uniform illumination within its cavity. Theoretical analysis on this unique property of constant illumination and the multiple reflection of light within the sphere has been studied and reported as early as 1940 [30]. Subsequently, the theory for determining spectral reflectance for non-uniform spherical wall has also been widely investigated [31-33]..

(14) The advantage of measuring the absolute absorbance even when light scattering is present makes integrating spheres very attractive and useful for determining optical properties of various materials, including biological samples. Extensive theoretical descriptions have long been reported [34-42]. Different configurations for mounting the target sample in the integrating sphere system have been described. The sample either filled the entire sphere cavity or was simply placed on a holder at the center [34-38]. Measurement with a falling stream of water through the sphere is also reported [39, 40]. Moreover, with the scattering sample sandwiched between two integrating spheres, simultaneous reflectance and transmittance measurements are also demonstrated [41, 42]. Using the optical output signal collected at a small hole on the sphere wall, the absorption coefficient μa of the scattering sample can be measured. For fluorescent samples, integrating spheres have also been used for measuring fluorescence quantum yield )f [43-45].. 1.5. Quantitative photoacoustics using an integrating sphere. Aside from optical measurements, an integrating sphere can also be used as a platform for measuring photoacoustic signal generated by a target absorber mounted inside the sphere cavity. A simple illustration is shown in Figure 1.1 below. A small transparent tube can be inserted horizontally (on xy-plane) through small holes on opposite ports of an integrating sphere. The absorbing target (for example, a scattering biomedical fluid sample) can be injected into the tube. Pulsed light source can be connected to an input port of the sphere so that light pulses can be made incident onto the sample mounted inside the sphere. Due to photoacoustic effect, pressure waves can be generated which can travel towards the ultrasound detector connected on another port on the sphere wall as shown in Figure 1.1. Using the amplitude of the detected PA signal and a properly calibrated system, an equation for measuring the Grüneisen parameter Γ of the target sample can be derived based on simple energy balance within the sphere. The optical output signals of this sphere can be used to simultaneously determine the absorption coefficient Pa and fluorescence quantum yield )f (for a fluorophore sample) based on the same energy balance within the system. Alternatively, another integrating sphere (air-filled, instead of water filled) can be simultaneously used for optical measurements of Pa and )f of the same target sample in the photoacoustic measurements of Γ. Accurate measurement of these material properties for. 1–7.

(15) various biomedical fluids (such as blood, joint and cyst fluids) is very useful in the growing field of quantitative photoacoustic measurements in biomedicine.. transducer. detected PA signal (Vpp). absorber. initial PA wave. incident pulsed light. z. integrating sphere (water inside). 1–8. Figure 1.1 Illustration of measurements.. 1.6. x. an integrating sphere platform. for. photoacoustic. Scope and main contributions of this thesis. A system and method for measuring material properties relevant to quantitative photoacoustics are presented in this thesis. In Chapter 2, a technique for measuring the Grüneisen parameter * using an integrating sphere as a platform for photoacoustic measurements with absorbing liquids is developed. A small transparent tube mounted through the sphere cavity serves as the holder for the target sample. Calibration of the system is performed using aqueous ink dilutions. Validation of the technique is done by measuring the Grüneisen parameter of ethanol and comparing with calculated values from known thermal properties in literature. In 0, a similar integrating sphere setup is used for measuring the absorption coefficient Pa of absorbing and scattering samples inside the tube. Two models for calculating Pa are proposed. The influence of scattering on the measurable values of Pa is investigated. In 0, as a demonstration on the application of the developed integrating sphere method, * and Pa measurements of human blood are demonstrated. In Chapter 5, the capability of the system to measure * of.

(16) biomedical fluids with weak absorption at near infrared is illustrated using indocyanine green dye. In Chapter 6 the feasibility of measuring fluorescence quantum yield )f using the same integrating sphere-spectrophotometer setup is explored. Chapter 7 enumerates some recommendations for future related research. Finally, a summary of the important contributions and key results in the thesis is given. Quantitative measurements of the Grüneisen parameter *, optical absorption coefficient Pa and fluorescence quantum yield )f of the obtained and prepared absorbing samples are determined in the system that we developed and called Quantitative Photoacoustic Integrating Sphere (QPAIS). Our fruitful collaboration with the Experimental Center for Technical Medicine of the University of Twente and medical doctors from two different hospitals allowed us to demonstrate the capability of our QPAIS method to measure the Grüneisen parameter of biomedical fluids. However, there is no substantial analysis on the physiological state of the obtained human blood, knee joint and breast cyst fluid samples. Consequently, a concrete explanation on the observations and obtained values cannot be given in this book. Further investigations and more measurements using the developed QPAIS platform should be done in order to understand the underlying sources and causes of the measured values. The QPAIS platform that we developed is based on homogenously distributing the incident light onto a scattering sample using an integrating sphere, and subsequently measuring the generated photoacoustic signal. Simultaneously, we measure the absorption spectrum of the same sample using another integrating sphere, even in the presence of scattering. With this double integrating sphere setup, we essentially obtain the Grüneisen parameter in a “single shot”. This simplicity and robustness of our measurement system is in stark contrast to the complexity of other systems reported in literature. The potential contributions and advantages of the QPAIS platform are as follows: (1) it allows uniform illumination on a small volume of the target sample, using an easy fiber coupling with the light source, (2) the method is insensitive to the details of optical coupling which consequently makes it work well with fluids, (3) it enables measurement of the Grüneisen parameter and the absorption coefficient of a scattering sample without the need to measure the local fluence nor the calibration of the sensitivity of detectors, (4) the Grüneisen parameter of biomedical fluids of interest can be determined using a single wavelength which is not necessarily at the absorption region of the. 1–9.

(17) target, for example using contrast agents, (5) scanning multiple wavelengths of incident light is not necessary in determining the sample Grüneisen parameter, (6) the required incident energy per pulse is low such that the laser source can be changed to a compact laser diode provided that the pulse duration is reasonably short, (7) the material properties important to quantitative photoacoustics can be measured simultaneously in a single setup, at varying temperatures, and (8) the QPAIS platform can be used for quantitative characterization of scattering samples (phantoms) to be imaged in a photoacoustic imaging system for calibration and quantitation measurements.. 1–10.

(18) References 1. Bell, A.G., Upon the production of sound by radiant energy. 1881, Washington,: Gibson brothers, printers. 45 p. incl. plates. 2. Bell, A.G., The Production of Sound by Radiant Energy. Science, 1881. 2(49): p. 242-53. 3. Bell, A.G., The Photophone. Science, 1880. 1(11): p. 130-4. 4. The Photophone. Science, 1880. 1(11): p. 121-2. 5. Beard, P., Biomedical photoacoustic imaging. Interface Focus, 2011. 1(4): p. 602-31. 6. Rosencwaig, A. and A. Gersho, Photoacoustic Effect with Solids: A Theoretical Treatment. Science, 1975. 190(4214): p. 556-557. 7. Campbell, S.D., S.S. Yee, and M.A. Afromowitz, Two applications of photoacoustic spectroscopy to measurements in dermatology. J Bioeng, 1977. 1(3): p. 185-8. 8. Rosencwaig, A., Potential Clinical-Applications of Photoacoustics. Clinical Chemistry, 1982. 28(9): p. 1878-1881. 9. Hoelen, C.G.A., et al., Three-dimensional photoacoustic imaging of blood vessels in tissue. Optics Letters, 1998. 23(8): p. 648-650. 10. Kruger, R.A., et al., Photoacoustic ultrasound (PAUS)--reconstruction tomography. Med Phys, 1995. 22(10): p. 1605-9. 11. Ermilov, S.A., et al., Laser optoacoustic imaging system for detection of breast cancer. J Biomed Opt, 2009. 14(2): p. 024007. 12. Maslov, K. and L.V. Wang, Photoacoustic imaging of biological tissue with intensity-modulated continuous-wave laser. J Biomed Opt, 2008. 13(2): p. 024006. 13. Song, K.H. and L.V. Wang, Deep reflection-mode photoacoustic imaging of biological tissue. J Biomed Opt, 2007. 12(6): p. 060503. 14. Kim, C., C. Favazza, and L.V. Wang, In vivo photoacoustic tomography of. chemicals: high-resolution functional and molecular optical imaging at new depths. Chem Rev, 2010. 110(5): p. 2756-82. 15. Mallidi, S., G.P. Luke, and S. Emelianov, Photoacoustic imaging in cancer detection, diagnosis, and treatment guidance. Trends Biotechnol, 2011.. 29(5): p. 213-21. 16. Aguirre, A., et al., Potential role of coregistered photoacoustic and. ultrasound imaging in ovarian cancer detection and characterization.. Transl Oncol, 2011. 4(1): p. 29-37. 17. Xua, M. and L.V. Wang, Photoacoustic imaging in biomedicine. Review of Scientific Instruments, 2006. 77(041101): p. 041101-1 to 041101-22. 18. Heijblom, M., W. Steenbergen, and S. Manohar, Clinical photoacoustic breast imaging: the Twente experience. IEEE Pulse, 2015. 6(3): p. 42-6. 19. Wang, L.V. and H.A. Wu, Biomedical Optics: Principles and Imaging. 2007, New Jersey: John Wiley & Sons, Inc.. 1–11.

(19) 20. Vočadlo, N. and G.D. Price, The Grüneisen parameter — computer calculations via lattice dynamics. Physics of the Earth and Planetaiy Interiors, 1994. 82: p. 261-270. 21. Krehl, P.O.K., History of shock waves, explosions and impact : a chronological and biographical reference. 2009, Berlin: Springer. xxii, 1288 p. 22. Cox, B., et al., Quantitative spectroscopic photoacoustic imaging: a review. Journal of Biomedical Optics, 2012. 17(6). 23. Savateeva, E.V., et al., Optical properties of blood at various levels of. oxygenation studied by time resolved detection of laser-induced pressure profiles. Biomedical Optoacoustics Iii, 2002. 4618: p. 63-75. 24. Yao, D.K., et al., Photoacoustic measurement of the Gruneisen parameter of tissue. Journal of Biomedical Optics, 2014. 19(1). 25. Soroushian, B., W.M. Whelan, and M.C. Kolios, Study of laser-induced thermoelastic deformation of native and coagulated ex-vivo bovine liver tissues for estimating their optical and thermomechanical properties.. Journal of Biomedical Optics, 2010. 15(6). 26. Yao, D.K., et al., Photoacoustic measurement of the Gruneisen parameter of tissue. J Biomed Opt, 2014. 19(1): p. 17007. 27. Laufer, J., E. Zhang, and P. Beard, Evaluation of Absorbing Chromophores. Used in Tissue Phantoms for Quantitative Photoacoustic Spectroscopy and Imaging. IEEE Journal of Selected Topics in Quantum Electronics, 2010.. 1–12. 16(3): p. 600-607. 28. Soroushian, B., W.M. Whelan, and M.C. Kolios, Study of laser-induced. thermoelastic deformation of native and coagulated ex-vivo bovine liver tissues for estimating their optical and thermomechanical properties. J. Biomed Opt, 2010. 15(6): p. 065002. 29. Labsphere. Technical Guide: Integrating Sphere Theory and Applications. 30. Moon, P., On Interreflections. JOSA, 1940. 30: p. 196-205. 31. Jacquez, J.A. and H.F. Kuppenheim, Theory of the Integrating Sphere. Journal of the Optical Society of America, 1955. 45(6): p. 460-470. 32. Jacquez, J.A., et al., An Integrating Sphere for Measuring Diffuse Reflectance in the near Infrared. Journal of the Optical Society of America, 1955. 45(10): p. 781-785. 33. Goebel, D.G., Generalized Integrating-Sphere Theory. Applied Optics, 1967. 6(1): p. 125-&. 34. Elterman, P., Integrating cavity spectroscopy. Appl Opt, 1970. 9(9): p. 2140-2. 35. Edwards, D.K., et al., Integrating Sphere for Imperfectly Diffuse Samples. Journal of the Optical Society of America, 1961. 51(11): p. 1279-&. 36. Fry, E.S., G.W. Kattawar, and R.M. Pope, Integrating cavity absorption meter. Appl Opt, 1992. 31(12): p. 2055-65. 37. Nelson, N.B. and B.B. Prezelin, Calibration of an integrating sphere for determining the absorption coefficient of scattering suspensions. Appl Opt, 1993. 32(33): p. 6710-7..

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(22) Chapter 2 Photoacoustic measurement of the Grüneisen parameter using an integrating sphere* Abstract A method that uses an integrating sphere as a platform for photoacoustic measurement of the Grüneisen parameter * of absorbing liquids is developed. Derivation of a simple equation for determining * is presented. This equation only requires the voltage peak-to-peak value of the photoacoustic signal detected by a flat transducer and the relative energy of the incident light measured by a photodetector. Absolute detector sensitivities are not required. However, a calibration procedure is necessary. An experimental setup is constructed in order to implement and verify the method. Aqueous ink solutions are used as absorbing liquids to determine the calibration (instrument) constants. Validation of the equation is done by determining * of ethanol at room temperature. The obtained value of *ethanol = 0.72 ± 0.06 has a 7% relative difference to the calculated value from known thermal properties reported in literature.. * This chapter is published as Yolanda Villanueva, Erwin Hondebrink, Wilma Petersen and Wiendelt Steenbergen, Photoacoustic measurement of the Grüneisen parameter using an integrating sphere, Review of Scientific Instruments 85, 074904 (2014); doi: 10.1063/1.4890666. 2–15.

(23) 2.1. Introduction. Photoacoustic (PA) imaging is a flourishing technique for visualizing chromophores in biological tissues [1]. It utilizes the absorption of incident light pulses by target absorbers and the subsequent generation of pressure waves due to the PA effect. By detecting the propagated acoustic waves around the target absorber, a three-dimensional view of the distribution of the absorbed optical energy density can be reconstructed in photoacoustic tomography (PAT). Although several PA images of biological samples both invivo and ex vivo, have already been obtained, quantifying chromophore concentrations on such images remains a challenge, here denoted as quantitative photoacoustic imaging [2]. An important step towards quantitation is determining the material properties of biological absorbers. One such property is the Grüneisen parameter which indicates the photoacoustic efficiency of the absorber.[3] It is commonly denoted by * and is related to the specific heat capacity cp, thermal expansion coefficient E and speed of sound vs using * ‫ؠ‬ 2–16. ஒ୴మ ౩ େ౦. [4]. For most biological chromophores, * and these thermal. properties are not always known, although in principle they can be measured individually. In photoacoustics, * relates the absorbed optical energy density Pୟ ) to the amplitude ɐ଴ of the locally generated initial stress in this manner: ɐ଴ ൌ *Pୟ ). [5]. This equation is valid only if the stress confinement condition is satisfied. Here, Pa is the local absorption coefficient and ) is the local fluence. With known absolute values of V0, Pa and ), * can be directly determined as reported by Savateeva et al. [6] using time-resolved photoacoustic technique to measure * of whole blood from anesthetized animals. Recently, photoacoustic spectroscopy has been used to measure * of porcine subcutaneous fat tissue and bovine red blood cells [7]. The * value was determined by linearly fitting the photoacoustic spectrum with the absorption spectrum. In another study, the relative change in * with concentrations of inorganic chromophores such as copper and nickel chloride in aqueous dilutions is also measured using photoacoustic spectroscopy [8]. For small concentrations of organic chromophores, for example cyanine-based dyes, dissolved in water, the change in * with dye concentration is negligible [8]. Furthermore, an interferometric technique has also been implemented to.

(24) measure * of bovine liver tissues. In this technique, * is measured from the plot of the sample surface displacement against incident pulse laser energy [9]. In this chapter, a method for photoacoustic measurement of * using an integrating sphere [10] is explored. This technique has the following advantages: (1) it allows uniform illumination on the target sample, using an easy and convenient fiber coupling with light source; (2) it is insensitive to the details of optical coupling which consequently makes it work well with fluids, and; (3) it has the future potential to provide the Grüneisen parameter and the absorption coefficient of the sample without the need to measure the local fluence. The method presented here does not require stringent alignment of the optical and acoustic detectors. Moreover, a numerical model-based fitting of the detected signals is not necessary, in contrast to other methods previously reported [8]. In Section 2.2, theoretical and experimental descriptions of the method are presented and a derivation of the relevant equation is given. Sample preparations and calibration of the experimental setup are also described. In Section 2.3, experimental results including temporal profiles of the detected acoustic signals, calibration data and measured * values are shown. Validation of the method is done by determining the * of ethanol. A conclusion and summary of important results are given in Section 2.4.. 2.2. Methodology. 2.2.1 Theoretical Description A method for determining the Grüneisen parameter * of liquid absorbing samples is developed based on using an integrating sphere as a platform for PA measurements. An integrating sphere is an optical instrument commonly used to achieve homogeneous illumination on a target material [10]. The absorbing sample is mounted using a hollow transparent tube positioned horizontally through the integrating sphere. An illustration of the experimental setup is shown in Figure 2.1. The sample is homogeneously illuminated by light that has undergone multiple reflections on the sphere wall. Incident light on the sample can be absorbed and can result in acoustic wave generation. The subsequently generated acoustic waves are detected at some distance from the absorber, for example at the position of the transducer shown in Figure 2.1. From the geometry and properties of this integrating sphere system, a simple energy balance can be obtained, resulting in. 2–17.

(25) ୧୬ ൌ ୫ୣୢ୧୳୫ ൅ ୱୟ୫୮୪ୣ ൅ ୵ୟ୪୪ ൅ ୭୳୲. (2.1). The optical energy Ein from the input light pulse is distributed towards the various regions inside the integrating sphere. Emedium, Esample, Ewall and Eout are the absorbed energy by the medium filling up the sphere cavity (for example, water), the absorbing sample in the tube, the sphere wall and the energy escaping the system via the optical output port, respectively. The absorbed energy can also be written in terms of the uniform fluence ) inside the sphere ୧୬ ൌ ୫ ) ൅ ୱ ) ൅ ୵ ) ൅ ୭ ). (2.2). where cm, cs, cw and co are constants which depend on the size and absorption property of the medium, absorbing sample, sphere wall and output port, respectively. If it can be assumed that the entire volume V of the absorber inside the tube is absorbing uniformly with absorption coefficient μa such that, cs = Vμa, Equation (2.2) becomes ୧୬ ൌ ୫ ) ൅ Pୟ ) ൅ ୵ ) ൅ ୭ ). 2–18. (2.3). The second term in Equation (2.3) assumes a constant fluence in the entire cross section of the tube such that the physical volume corresponds to the optical volume of the tube. This can be solved for the uniform fluence ) inside the integrating sphere as indicated below, where c = cm + cw + co. )ൌ. ୧୬ ൅ Pୟ. (2.4). Due to the PA effect, acoustic waves are generated by the absorbing sample. Assuming thermal and stress confinements, the amplitude of the local initial stress V0 is linearly related to the absorbed energy, by ɐ଴ ൌ *Pୟ ), with *. referred to as the Grüneisen parameter is a conversion efficiency factor. Inserting Equation (2.4) yields ɐ଴ ൌ. *Pୟ ୧୬ ൅ Pୟ. (2.5). Equation (2.5) indicates the behaviour of the initial stress distribution V0 at the location of the absorbing sample. However, experimentally, PA signals are measured at the position of the detector at some distance from the absorber. The voltage peak-to-peak Vpp of the detected acoustic signal is assumed to be linearly related to V0, by ୮୮ ൌ ή ɐ଴ , with k representing any acoustic.

(26) attenuation and conversion factor between the initially generated stress and the detected pressure transient. Using this in Equation (2.5) we obtain ୮୮ ൌ. *Pୟ ୧୬ ൅ Pୟ. (2.6). Equation (2.6) indicates that the dependence of the generated PA signal amplitude on Pa is nonlinear. This means that, with all other factors constant, Vpp increases with Pa but approaches an asymptotic value for VPa ‫ ب‬. The constants k and c in Equation (2.6) can be determined from a calibration procedure in which a calibration liquid with known * and Pa is used. Using these calibration constants k and c, and the same setup where PA signals and relative incident energy are measured in the same manner as in the calibration process, the Grüneisen parameter * of an absorbing sample injected in the tube can be determined from the following equation *ൌ. ୮୮ ൫ ൅ Pୟ ൯ ୧୬ Pୟ. (2.7). Here, * can be measured if the sample Pa and volume V are known a priori. Vpp and Ein are factors which can be determined from the detected signals with the absorbing sample inside the tube. The experimental setup and procedure used in validating Equation (2.7) are presented in Section 2.2.2 below.. Figure 2.1 Schematic diagram of the experimental setup for measuring the Grüneisen parameter * of absorbing liquid inside a nylon tube mounted through an integrating sphere.. 2–19.

(27) 2.2.2 Experimental description 2.2.2.1 Description of the integrating sphere setup A schematic diagram of the experimental setup constructed in order to verify the validity of Equation (2.7) is shown in Figure 2.1. An integrating sphere (IS200, Thorlabs, NJ, USA) with a diameter of 50.8 mm is used as a platform for doing PA measurements. The sphere has four ports, each with diameter of 12.7 mm and one smaller port with a diameter of 3 mm. A soft transparent nylon tube (2604 Nylon tubing, Rubber BV, Hilversum, NL) with outer diameter of 0.94 mm and inner diameter of 0.75 mm is used to mount the absorbing liquid inside the integrating sphere. Opposite ends of the tube are inserted in each of the small holes on two opposite ports such that the tube lies horizontally through the sphere. The holes are located 4 mm above the vertical center so that the tube is also 4 mm above the center of the sphere. This ensures that incident light does not directly hit the tube, with consideration to the numerical aperture (NA) of the optical fiber used for light delivery. When the nylon tube is horizontally positioned through the sphere, the absorbing sample is injected, by using a syringe, into one end of tube until it flows out of the other end. 2–20. The absorbing sample inside the tube is uniformly illuminated by multiple reflections of light pulses that enter the sphere through another port, as shown in Figure 2.1. These light pulses with wavelength of 750 nm from an Nd:YAGOPO laser source (Opolette TM 532I, OPOTEK, Inc, CA, USA) and an average pulse energy of 1.25 mJ, measured using a thermal power sensor (S370C, Thorlabs, NJ, USA) connected to a power meter (PM100D, Thorlabs, NJ, USA), are delivered via a fiber (0.37NA, core diameter of 1 mm, Newport, CA, USA) that is tightly connected to the center of the port. The laser beam has a pulse length of 7 ns and a pulse repetition frequency of 20 Hz. A photodetector PD1 (DET10A/M - Si Detector, Thorlabs, NJ, USA) is positioned such that it collects a portion of the laser output is used to monitor the relative energy of the laser beam that is incident on the integrating sphere. Another photodetector PD2 detects the optical output from the integrating sphere, which can be used to monitor the changes in the surrounding fluence with varying absorbing sample in the tube. The optical signals obtained using PD1 and PD2 can in principle be used to determine the unknown absorption coefficient of the absorber in situ, with appropriate calibration. However in this stage a separate measurement of the sample absorption coefficient is performed..

(28) The sphere is filled up with demineralized water to facilitate acoustic matching with a flat ultrasound transducer (NDT V303, 12-mm single element, 1 MHz, 6 dB bandwidth 60.58%, Olympus Panametrics, MA, USA) positioned directly above the center of the nylon tube as shown in Figure 2.1. The detected PA signal is amplified by an ultrasound amplifier (Ultrasonic Preamp 5678, Panametrics NDT, MA, USA ). The optical signals from the laser source and from the integrating sphere output port, as well as the PA signals are viewed using an oscilloscope (TDS 2022C/24C ,200 MHz, 2GS/s, Tektronix, OR, USA) which is interfaced with a computer via a Labview program that allows recording of temporal data. Two oscilloscopes are necessary in order to capture the temporal profiles at different sampling rates, for example, 2.5 u 1010 samples/s for the optical signal, and 5.0 u 107 samples/s for the acoustic signal.. 2.2.2.2 Preparation of absorbing samples A range of absorbing samples is prepared prior to PA measurements. Two types of absorbing samples are needed, one as a calibration liquid for determining the instrument calibration constants and another as a validation liquid for verifying the derived Equation (2.7) for *. Water is chosen as a calibration liquid. However, pure water has very low absorbance at 750 nm wavelength. Thus, a small amount of black ink (Ecoline 700 8265, Royal Talens, Apeldoorn, NL ) is dissolved in deionized water in order to obtain absorbing aqueous ink dilutions that ensure the generation of PA signal for the available incident optical energy. At least three sets of aqueous ink dilutions, with concentrations ranging from 0.1 to 10 vol% are made. These ink solutions mostly contain water molecules such that the * can be assumed equal to that of pure water. This assumes that any absorbed energy by the dye molecules is immediately and adiabatically transferred to the surrounding water. The corresponding Pa values of the various ink concentrations are measured using a spectrophotometer (UV-VIS, Shimadzu, Kyoto, Japan). For validation, ethanol (459844 Ethanol ACS reagent, ≥99.5% (200 proof, absolute, Sigma-Aldrich, MO, USA) is used as an absorbing sample. Similar to water, ethanol has very low absorbance at 750 nm wavelength. To increase the Pa of ethanol at this wavelength, a small amount of indocyanine (ICG) dye (02155020 Indocyanine Green Dye Content: ~90%, Green Powder, MP Biomedicals, CA, USA) is dissolved in ethanol. Six different stock solutions of ethanol with ICG are made. The Pa of each solution is measured via spectrophotometry before using it as an absorbing sample in the PA setup.. 2–21.

(29) Table 2.1 shows a summary of the measured Pa of ethanol plus dye samples. Spectrophotometry and photoacoustic measurements are done on various days, with a new calibration each day. The concentrations of ICG dye in ethanol are chosen such that the Pa of the solution is around 1 mm-1. Using Equation (2.7), * of ethanol is measured and compared with the known literature value of *ethanol = 0.775 [11]. 2.2.2.3 Calibration of the integrating sphere setup The derived equation for determining the Grüneisen parameter * of an absorbing sample requires two experimental constants, k and c, which can be obtained from a calibration procedure that involves an absorber of known *. In order to determine these constants, water with * = 0.120 ± 0.006 (calculated from thermal properties reported in literature [11]) is used as a calibration fluid, with added ink for enhanced absorption. Using Equation (2.6), the values of k and c can be obtained from a plot of Vpp versus Pa with known values of the other parameters *, V and Ein. Moreover, in order to account for any fluctuation on the incident light energy, Equation (2.6) can be rewritten as follows 2–22. *Pୟ ୮୮ ൌ ሖన୬ ൅ Pୟ. (2.6a). Here ሖన୬ is the relative energy of the incident light which is linearly related to Ein. Thus, a calibration plot with. ୚౦౦ ሖ ୉ഠ౤. versus Pa can be used to determine the. constants k and c which also include the necessary conversion factors from pressure and energy values to detectable signals expressed in volts (V). Equation (2.6a) also implies that absolute sensitivity measurements of the transducer and photodetector are not necessary to determine the instrument constants. Instead, a plot of measured. ୚౦౦ ሖ ୉ഠ౤. for varying values of Pa of the. calibration liquid (aqueous ink dilutions) with known * and volume V is sufficient to determine k and c using a rational fitting function of the form ୶ ൌ ୟାୠ୶ similarly as in Equation (2.6a). This procedure is repeated for seven aqueous ink dilutions to obtain enough data points on the calibration plot. After each measurement with a particular ink dilution, the tube is cleaned with demineralized water..

(30) 2.2.2.4 Validation measurement with ethanol Immediately after taking calibration measurements and determining the values of k and c, and after washing the tube with water, an absorbing sample with unknown * (in this case ethanol with ICG) is injected into the tube and the corresponding ሖన୬ and Vpp of the optical and photoacoustic signals, respectively, are measured. The detected signals are processed to determine *ethanol using the integrating sphere system.. 2.3. Results and Discussion. Typical photoacoustic signals generated by the calibration liquid inside the tube for various values of μa are shown in Figure 2.2. Each plot is an average of the photoacoustic waves generated with several laser pulses, for example, five times 128 oscilloscope averages. As a reference, the detected signal (black solid line) with pure water inside the tube is also given.. photoacoustic signal (mV). 20 15. 2–23 Pa umm-1 Pa 0.40mm-1. 10. Pa 0.80mm-1. 5. Pa 1.20mm-1. 0 -5 -10 -15. Pa 1.60mm-1 Pa 2.00mm-1 Pa 5.00mm-1 Pa 9.00mm-1. -20 15. 16. 17. 18. 19. time (Ps) Figure 2.2 Typical photoacoustic signals detected by the transducer for various Pa values of the calibration liquid (aqueous ink dilutions) injected into the tube inside the integrating sphere.. No distinguishable peaks can be observed on this signal. For the rest of the detected signals (dashed and dotted gray lines), prominent peaks appear around 17Ps which correspond to the time of flight of the acoustic wave from.

(31) the medium to the transducer surface positioned at 25 mm vertical distance from the tube. The Vpp amplitudes increase with μa. For the method described in Section 2.2, the equation for determining * only requires measurement of the Vpp amplitude of the PA signal and the relative incident energy ሖన୬ . Moreover, the temporal shape of the PA signal is not relevant and only the variation of its amplitude on varying μa is necessary to calculate for *. Shown in Figure 2.3 are plots of the measured. ௏೛೛ ሖ ாഢ೙. values of the PA signal. against Pa for five sets of measurements. As an illustration, a fitting function (in OriginPro 8.6) similar to Equation (2.6a) indicated by blue line on one set of data, gives the values k = 1.37 (smm3) and c = 4.55u10-5 (mm2). These values are used to determine * using Equation (2.7) rewritten as follows: ܸ௣௣ ൫ܿ ൅ P௔ ܸ൯ ݇P௔. (2.7a). *ൌ ሖ ‫ܧ‬ప௡. For the calculations presented here, the volume V of the target absorber is assumed to be equal to the physical volume of the nylon tube which is 22.4 mm3. 2–24 7x106 6x106. Vpp/E'in (au). 5x106 4x106 expt01 expt02 expt03 expt04 expt05 ave. 3x106 2x106 1x106 0 0. 2. 4. 6. 8. 10. absorption coefficient, Pa (mm ) -1. Figure 2.3 Example of calibration plots of. ௏೛೛ ሖ ாഢ೙. versus Pa for five sets of measurements for. determining the instrument constants k and c. The blue line is a fitting function that gives k = 1.37 (smm3) and c = 4.55u10-5 (mm2) for one measurement, R2 = 0.984 which indicates a measure of how the fit and data points are correlated..

(32) 2.3.1 Measurement of * with constant Pa. photoacoustic signal (mV). With known k and c values, and after cleaning the tube with water, an absorbing sample of ethanol is injected into the tube and the corresponding optical and acoustic signals are measured. Figure 2.4 shows an example of the PA signal generated by the ethanol- absorbing samples labeled E1 to E6. The signal detected (black line) with only ethanol (without dissolved ICG) inside the tube is also shown for comparison. Prominent peaks are visible on the detected signal with ethanol and ICG solutions. 50 40 30 20 10 0 -10 -20 -30 -40 -50 15. ethanol E1 E2 E3 E4 E5 E6 16. 2–25 17. 18. 19. time (Ps) Figure 2.4 Typical PA signals detected with ethanol plus ICG (labeled E1 to E6) inside the tube. The black is the signal detected without ICG dissolved in ethanol. The V pp amplitude of each PA signal is used in Equation (2.7a) to determine the * of ethanol.. Table 2.1 shows a summary of the measured experimental parameters and the corresponding calculated * for each of the ethanol samples. The average and propagated error values are given in Table 2.2. For this set of measurements, calculated * = 0.79 ± 0.34. Based on * ‫ؠ‬. ஒ୴మ ౩ େ౦. and. the known thermal properties of ethanol around 20RC temperature, the calculated literature value is *ethanol = 0.775, which is only 3% different from the measured averaged value. Also, the standard deviation of 0.04 from six measured values is only 5% of the average value. However, it should be noted that the propagated error ߪ* = 0.34 is about 40% of the average which indicates.

(33) that the error in measuring experimental parameters such as Vpp , ‫ܧ‬ሖప௡ and ߤ௔ can significantly increase the range of measurable values of *ethanol. Table 2.3 shows an overview of the measurable values of ߤ௔ , ‫ܧ‬ሖప௡ and Vpp. Here, the tabulated data also include those measurements when the nylon tube is not perfectly aligned with the transducer center, such that there is a large variation in the measureable values of Vpp. Thus, improvement on Vpp measurements can give more precise * values. At least three repetitions of PA measurements are done, with each of E1 to E6 solutions used as the absorbing sample. Here, the average *ethanol is 0.66 for all measurements with E1 to E6 with three different calibration measurements. The standard deviation in these measurements equals 0.10, which is 15% the average value.. Table 2.1 Summary of data for calculating *ethanol for one measurement with each of the ethanol absorbing samples labeled E1 to E6. E1. E2. E3. E4. E5. E6. Average ± SD. μa (mm-1). 1.04. 1.04. 1.03. 1.00. 0.99. 0.99. 1.02 ± 0.02. ࡱሖଙ࢔ (u10-9 Vs). 5.09. 5.12. 5.03. 4.94. 4.99. 4.92. 5.01 ± 0.0773. Vpp (u10-2 V). 8.9. 7.9. 7.9. 8.1. 7.6. 8.2. 8.1 ± 0.42. *. 0.85. 0.75. 0.76. 0.81. 0.76. 0.83. 0.79 ± 0.04. Label. 2–26. Table 2.2 Summary of average and error values (standard deviations and propagated error) in calculating V* for the data given in Table 2.1. ࣆࢇ (mm-1) ࢇ࢜ࢋ࢘ࢇࢍࢋ േ ࡿࡰ. ࡱሖଙ࢔ (u10-9 Vs) ࢇ࢜ࢋ࢘ࢇࢍࢋ േ ࡿࡰ. ࢂ࢖࢖ (u10-2 V) ࢇ࢜ࢋ࢘ࢇࢍࢋ േ ࡿࡰ. * േ ࣌*. 1.02 ± 0.02. 5.01 ± 0.0773. 8.1 ± 0.42. 0.79 ± 0.34. 2.3.2 Measurement of * with varying Pa Measurements are also taken for varying values of Pa of ethanol with ICG solutions labeled E7 to E9 in Table 2.3. Similar profiles of the PA signals, but with varying Vpp amplitudes, are observed. At least three repetitions are.

(34) performed to acquire statistics on measurable * values of ethanol for three different values of Pa. From the collected data, the calculated * does not vary significantly with varying Pa. The average * is 0.72 with a standard deviation of only 8% relative to this average. On the other hand, the propagated error value for each sample is also approximately 0.30, similar to that in the observation above. Moreover, for sample labeled E8 with the same Pa value as in samples E1 to E6, the measured * is also 0.66, but with a higher standard deviation of 0.284. It should be noted that the measurements here are made independently of the ones described above, such that the calibration data, photoacoustic and optical signals are measured with a different batch of ethanol solutions and on a different day. Table 2.3 Summary of data for calculating *ethanol with each of the ethanol absorbing samples of varying μa. V* is the propagated error. Label. E7. E8. E9. ࣆࢇ (mm-1). 0.510 ± 0.004. 1.000 ± 0.002. 1.450 ± 0.023. ࡱሖଙ࢔ (u10-9 Vs). 5.44 ± 0.0364. 5.37 ± 0.123. 5.30 ± 0.131. 6.2 ± 1.1. 8.5 ± 0.7. 13 ± 1.0. 0.78 ± 0.38. 0.66 ± 0.28. 0.72 ± 0.30. ࢂ࢖࢖ (u10-2 V). * ± V*. 2.4. Conclusion. A method for determining * of absorbing liquids using PA measurements in an integrating sphere is designed and implemented. Using an integrating sphere ensures homogenous illumination of the target sample in a small nylon tube mounted within the sphere cavity. It also has the advantage of eliminating tedious alignment between the absorbing medium and the ultrasound detector, as in a free space setup. Inserting a nylon tube makes it possible to do photoacoustic measurements with liquid absorbing media. However, the size of the tube dictates a limitation on the Pa values of the absorbing sample such that incident light could penetrate completely. A simple formula (Equation 2.7a) for calculating * is derived by considering energy balance within the integrating sphere system. The method described in this paper does not require absolute sensitivity measurements of the detectors.. 2–27.

(35) 2–28. However, it is necessary to perform calibration measurements using absorbing liquid with known * in order to determine certain instrument constants. The calibration liquids used are aqueous ink dilutions with Pa values from 0.2 to 10mm-1 and assumed * of water 0.120 ± 0.006 around 22RC. Calibration plots showing the ratio of relative PA amplitudes and incident energy versus Pa give values of instrument constants k = 1.12 ± 0.372 (smm3) and c = 3.06 ± 0.881 (u10-5 mm2) for all the collected data included in this paper. With known instrument constants, validation of the method is done by measuring the * of ethanol. Because ethanol has a very low absorbance at the wavelength available (750 nm), absorbing samples of ethanol are made with dissolved ICG which give Pa values from approximately 1 to 1.5 mm-1. Measurements using nine different ethanol absorbing samples (labeled E1 to E9 above) give * values which are in close agreement with each other. The average and standard deviation among all measurements is * = 0.72 ± 0.06, with a propagated error of 0.30. Comparing those with that expected from literature ( * = 0.775) , the relative difference is only 7% which gives an indication that the method described here is an accurate way of measuring * of absorbing liquids in general. The difference in * values can be attributed to the slight variation in sample temperature which is assumed to be constant and equal to the ambient room temperature. Moreover, it should be noted that a priori knowledge of the absorber Pa is necessary to measure *, and that the method described here is validated only for Pa up to 1.5 mm-1. Measurements with samples of higher Pa values may not be reliable due to the inaccuracy in detecting PA amplitudes. For highly absorbing samples, the incident light does not penetrate the tube completely, such that the assumed constant volume may no longer be valid. However, an improvement on the system can be achieved by using a smaller tube diameter which would allow homogeneous light penetration within highly absorbing samples. Also, with suitable calibration, the absorber Pa can be directly measured using the optical signals on PD1 and PD2. Furthermore, a more consistent way of measuring acoustic and optical signals which does not involve realignment of components can give more precise values of measurable *. Finally, the consequence of the addition of scattering to the sample must be considered in future research. The method described in this paper is a valid and direct way of measuring the * of any absorbing liquid of known Pa, including biological chromophores and nanoparticle suspensions. Knowledge of * values can aid in discriminating the different components in a photoacoustic image..

(36) References 1. Wang, L.V., ed. Photoacoustic imaging and spectroscopy. Optical science and engineering. 2009, CRC Press: Boca Raton. xx, 499 p. 2. Cox, B.T., J.G. Laufer, and P.C. Beard. The challenges for quantitative photoacoustic imaging. in Photons Plus Ultrasound: Imaging and Sensing. 2009. 3. Cox, B., et al., Quantitative spectroscopic photoacoustic imaging: a review. J Biomed Opt, 2012. 17(6): p. 061202. 4. Xu, Z., C. Li, and L.V. Wang, Photoacoustic tomography of water in phantoms and tissue. J Biomed Opt, 2010. 15(3): p. 036019. 5. Wang, L.V., Tutorial on photoacoustic microscopy and computed tomography. IEEE Journal of Selected Topics in Quantum Electronics, 2008. 14(1): p. 171-179. 6. Savateeva, E.V., et al. Optical properties of blood at various levels of. oxygenation studied by time resolved detection of laser-induced pressure profiles. in Biomedical Optoacoustics III. 2002. 7. Yao, D.K., et al., Photoacoustic measurement of the Gruneisen parameter of tissue. J Biomed Opt, 2014. 19(1): p. 17007. 8. Laufer, J., E. Zhang, and P. Beard, Evaluation of Absorbing Chromophores Used in Tissue Phantoms for Quantitative Photoacoustic Spectroscopy and Imaging. IEEE Journal of Selected Topics in Quantum Electronics, 2010.. 16(3): p. 600-607. 9. Soroushian, B., W.M. Whelan, and M.C. Kolios, Study of laser-induced. thermoelastic deformation of native and coagulated ex-vivo bovine liver tissues for estimating their optical and thermomechanical properties. J. Biomed Opt, 2010. 15(6): p. 065002. 10. Elterman, P., Integrating Cavity Spectroscopy. Applied Optics, 1970. 9(9): p. 2140. 11. Haynes, W.M., ed. CRC Handbook of Chemistry and Physics, 94th ed., 2013-2014. 94th ed. 2013-2014, CRC Press.. 2–29.

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(38) Chapter 3 Absorption coefficient measurement of scattering liquids using a tube inside an integrating sphere* Abstract A method for measuring the absorption coefficient μa of absorbing and scattering liquid samples is presented. The sample is injected into a small transparent tube mounted through an integrating sphere. Two models for determining the absorption coefficient using the relative optical output signal are described and validated using aqueous ink absorbers of 0.5 vol% (0.3 mm-1 < μa < 1.55 mm-1) and 1.0 vol% (1.0 mm-1 < μa < 4.0 mm-1) concentrations with 1 vol% (μs ‘ ≈ 1.4 mm-1) and 10 vol% (μs ‘ ≈ 14 mm-1) Intralipid dilutions. The low concentrations give μa and μs values which are comparable to those of biological tissues. One model assumes a uniform light distribution within the sample which is valid for low absorption. Another model considers light attenuation that obeys Lambert-Beer’s law which may be used for relatively high absorption. Measurements with low and high scattering samples are done for the wavelength range 400-900 nm. Measured spectra of purely absorbing samples are within 15% agreement with measurements using standard transmission spectrophotometry. For 0.5 vol% ink absorbers and at wavelengths below 700 nm, measured μa values are higher for samples with low scattering and lower for those with high scattering. At wavelengths above 700 nm, measured μa values do not vary significantly with amount of scattering. For 1.0 vol% ink absorbers, measured spectra do not change with low scattering. These results indicate that the method can be used for measuring absorption spectra of scattering liquid samples with optical properties similar to biological absorbers, particularly at wavelengths above 700 nm, which is difficult to accomplish with standard transmission spectrophotometry. *This chapter is submitted as Yolanda Villanueva, Colin Veenstra, Wiendelt Steenbergen, Measuring absorption coefficient of scattering liquids using a tube inside an integrating sphere for publication.. 3–31.

(39) 3.1 Introduction. 3–32. The technique of using an integrating sphere to determine optical properties of materials has the advantage of measuring the absolute absorbance even when light scattering is present. Extensive theoretical descriptions have long been reported [1-9]. Different configurations for mounting the target sample in the integrating sphere system have been described. The sample either filled the entire sphere cavity or was simply placed on a holder at the center [1-5]. Measurement with a falling stream of water through the sphere is also reported [6-7]. The absorption coefficient μa of the sample is measured using the optical output signal collected at a small hole on the sphere wall. Moreover, with the scattering sample sandwiched between two integrating spheres, simultaneous reflectance and transmittance measurements are also demonstrated [8-9]. In this report, another way of using an integrating sphere as a platform for μa measurements is proposed. A small transparent tube inserted through the sphere is used for introducing a liquid absorbing and scattering sample. This allows measurements that require less sample fluid volume compared to other systems presented in literature. In addition to measuring absorption in scattering liquids, the main motivation for the system presented is the in situ μa measurement with the sample inside a similar integrating sphere setup used for photoacoustic measurement of the Grüneisen parameter recently developed and published [10]. This can replace μ a measurement using a separate spectrophotometer setup, hence further simplifying the Grüneisen parameter measurement. Two models for determining the sample’s μa using the relative optical output signal are presented, so that μa can be determined by using analytical formula [11]. One model assumes a homogenous light distribution within the sample inside the tube whereas the other model considers the light attenuation using Lambert-Beer’s law [12]. A detailed derivation of the necessary equations is presented. Calibration and validation of each model are demonstrated using aqueous absorbing ink samples. Scattering samples are prepared with addition of Intralipid dilutions..

(40) 3.2. Methodology. 3.2.1 Theoretical Description An illustration of an integrating sphere-based setup adapted for absorption coefficient μa measurement is shown in Figure 3.1. An equation for determining μa of absorbing sample mounted inside a transparent tube inserted through the sphere cavity can be derived using the measurable optical output signal Eout on the sphere wall. Two models are proposed here. Model 1 considers a uniform light distribution within the tube which is valid for very low absorption. Model 2 considers a non-uniform distribution of light within the tube such that absorption obeys the Lambert-Beer’s law [12]. Details of the derivation using each model are discussed below.. 3–33. Figure 3.1 Schematic diagram of the experimental setup (top-view) for measuring the absorption coefficient μa of an absorbing liquid sample inside a tube (inner diameter = 0.58 mm) mounted through an integrating sphere (diameter = 50.8 mm). The axis of the tube is positioned approximately 5 mm above the center plane which contains the optical ports.. 3.2.1.1 Model 1: uniform light distribution With uniform light distribution within the absorber inside the tube, the total incident optical energy Ein equals the sum of the magnitudes of the absorbed or otherwise escaping energy by the different parts with the integrating sphere cavity as follows.

(41) ୧୬ ൌ ୟ ൅ ୵ ൅ ୭୳୲. (3.1). Ea is the magnitude of the energy absorbed by the absorber inside the tube and Eout is the optical energy that leaves the system through the output port. Ew represents all the other energy losses within the integrating sphere system, for example, energy absorbed by the medium filling up the entire sphere cavity and wall of the tube. These energy magnitudes can be written in terms of the constant fluence ) within the sphere, for example, ୟ ൌ ୟ ), ୵ ൌ ୵ ) and ୭୳୲ ൌ ୭ ) , where ca, cw and co are constants that depend on geometry and the optical property of the absorber, sphere wall and output port, respectively. For the absorber with absorption coefficient μa inside the transparent tube with volume V, ୟ ൌ Pୟ . Using ୭୳୲ ൌ ୭ ), Equation (3.1) can be written ୧୬ ൌ ൅ Pୟ ୭୳୲ ୚. ୡ౭ ାୡ౥. ౥. ୡ౥. Here, ൌ ୡ and ൌ. (3.2). .. Rearranging Equation (3.2) gives 3–34. ୧୬ (3.3) െ ୭୳୲ Pୟ ൌ Equation (3.3) can be used to determine the μa of an absorber inside the tube if the light is uniformly distributed within the entire tube volume V. ୰ୟ୲୧୭ ൌ. ୉౟౤ ୉౥౫౪. is the ratio between the input and output light energy, a and b are constants which can be determined from a calibration procedure with absorbers of known μa. 3.2.1.2 Model 2: non-uniform light distribution With non-uniform light distribution within the tube, which happens with highly absorbing samples, an equation for determining the absorber’s μa can be derived by considering the total incident light on the sphere surface in terms of the sphere wall reflectance U and absorption by the different parts within the sphere cavity after infinite number of reflections. For a given incident flux Mi, defined as the optical power over an area, the total incident flux Ms on the sphere surface after an infinite number of reflections can be written [11] ɔୱ ൌ. ɔ୧ Uሺͳ െ ሻ ͳ െ Uሺͳ െ ሻ. (3.4).

(42) where U is the known reflectance of the sphere wall and f is the fractional area of the ports and the tube located within the sphere, for example the total area of the ports and tube relative to sphere surface area. Because of a uniform Ms within the sphere, the ratio of the output Mo to input flux Mi is given by Uሺͳ െ ሻ ɔ୭ ൌ ɔ୧ ͳ െ Uሺͳ െ ሻ. (3.5). With known geometry, f is simply ൌ ୮ ൅ ୲ where fp and ft are the fractional area of the ports and tube, respectively, relative to total sphere surface area. However, if the absorber inside the tube does not completely absorb the incident light but instead partially transmits (in a diffuse manner), f t can be written as a product of p1 (the probability that light hits the tube) and p2 (the fraction of light that is absorbed) according to Lambert-Beer’s law as follows ஶ. ଶ ൌ ͳ െ න ሺሻିஜ౗୪ . (3.6). ଴. The second term in Equation (3.6) represents the fraction of light that is partially absorbed and attenuated after passing the absorber in the tube. P(l) indicates the probability that light travels a distance l through the tube and the integral takes all the possible paths dl that light follows within the tube. Equation (3.5) becomes Uሺͳ െ ୮ െ ଵ ଶ ሻ ɔ୭ ൌ ɔ୧ ͳ െ Uሺͳ െ ୮ െ ଵ ଶ ሻ. (3.7). We introduce ൌ Uሺͳ െ ୮ ሻ which can be defined as the fraction of light absorption other than that due to the absorber inside the tube. Equation (3.7) can be written in terms of C instead of the sphere wall reflectance U ͳ െ ୮ ሺͳ െ ୮ െ ଵ ଶ ሻ ɔ୭ ൌ ɔ୧ ͳ െ ሺͳ െ െ ሻ ୮ ଵ ଶ ͳെ. (3.8). ୮. Similar to the derivation in Model 1, Equation (3.8) can be written in terms of Ein and Eout with the assumption that the light flux is linearly related to optical energy within a fixed integration time, so that ɔ୧ ൌ ୧୬ ୧୬ and ɔ୭ ൌ ୭୳୲ ୭୳୲ . Using Eout,0 as the experimentally measurable optical output signal from the integrating sphere when there is no absorbing liquid inside the tube, such that p2=0, Equation (3.8) becomes. 3–35.

(43) (3.9). ͳ െ ୮ ሺͳ െ ୮ ሻ ɔ୭ǡ଴ ୭୳୲ ୭୳୲ǡ଴ ൌ ൌ ɔ୧ ୧୬ ୧୬ ͳ െ ͳ െ ୮ ሺͳ െ ୮ ሻ. Eout,0 includes the conversion factors between input energy Ein and other losses within the sphere. On the other hand, with an absorbing liquid inside the tube, Using. ಞ౥ǡబ ಞ౟ ಞ౥ǡಔ౗ ಞ౟. ஦. ୡ. ୉. ஦౥ǡಔ౗ ஦౟. ൌ. ୡ౥౫౪ ୉౥౫౪ǡಔ౗ ୡ౟౤ ୉౟౤. .. ୉. ൌ ஦ ౥ǡబ ൌ ୡ ౥౫౪୉ ౥౫౪ǡబ ൌ ୉ ౥౫౪ǡబ and substituting equations (8) and (9) ౥ǡಔ౗. ౥౫౪ ౥౫౪ǡಔ౗. ౥౫౪ǡಔ౗. into this relation and rearranging terms lead to ൫ͳ െ ୮ ൯ሺͳ െ ሻ ൅ ଵ ଶ ୭୳୲ǡ଴ ൌ ୭୳୲ǡஜ౗ ሺͳ െ ሻ൫ͳ െ ୮ ଵ ଶ ൯. (3.10). Since p2 is a function of μa, Equation (3.10) can be solved to determine μa for a given p1, C, fp and optical output ratio. 3–36. ୉౥౫౪ǡబ ୉౥౫౪ǡಔ౗. . fp can be determined from the. geometry of the integrating sphere and each of its ports. On the other hand, values of p1 and p2 can be estimated using numerical simulations. If p1, p2 and fp are known, C can be determined from experimental measurements of the relative optical output when an absorbing sample with very high absorbance is inside the tube. Details of the simulations are given below. 3.2.1.3 Description of the numerical simulations The Monte Carlo (MC) simulation method is implemented for modeling photon propagation within the integrating sphere setup. By running the simulation several times, the number of photons Nphotons that can reach a certain region inside the sphere, for example the locations of the tube and the detector, is monitored and counted. The results of the simulation runs, such as ratio of Nphotons reaching the detector without absorber to the Nphotons with absorber inside the tube are compared to the experimental values. A flowchart of the algorithm is shown in Figure 3.2. Initialization sets the necessary input parameters which are comparable to the values in the experimental setup as given in Table 3.1. A photon is launched from the location of the input port with initial weight W = 1. After each reflection from a randomly generated location on the sphere wall, the photon weight is reduced to Ԣ ൌ ɏ, then it continues to propagate within the sphere cavity with further weight reduction depending on the imposed conditions, for example, partial absorption via Lambert-Beer’s and change in trajectory via Fresnel and Snell’s law when it.

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