REVIEW OF SCIENTIFIC INSTRUMENTS 85, 074904 (2014)
Photoacoustic measurement of the Grüneisen parameter using an integrating sphere Yolanda Villanueva,a) Erwin Hondebrink, Wilma Petersen, and Wiendelt Steenbergen BioMedical Photonic Imaging Group, MIRA Institute for Biomedical Technology and Technical Medicine, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
(Received 13 March 2014; accepted 8 July 2014; published online 30 July 2014) 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. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4890666] I. 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, in or 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 β, and speed of sound vs us2 s 4 . For most biological chromophores, and these ing ≡ βv C p
thermal properties are not always known, although in principle they can be measured individually. In photoacoustics, relates the absorbed optical energy density μa to the amplitude σ 0 of the locally generated initial stress in this manner: σ 0 = μa .5 This equation is valid only if the stress confinement condition is satisfied. Here, μa is the local absorption coefficient and is the local fluence. With known absolute values of σ 0 , μa , and , can be directly determined as reported by Savateeva et al.6 using time-resolved photoacoustic technique to measure of whole blood from anesthesized animals.
a) Author to whom correspondence should be addressed. Electronic mail:
[email protected].
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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 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.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 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 paper, a method for photoacoustic measurement of using an integrating sphere10 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 model-based fitting to the detected signals is not necessary, in contrast to that done in another method.8 In Sec. II, 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 Sec. III, experimental results such as the temporal profile of the detected 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 Sec. IV.
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FIG. 1. Schematic diagram of the experimental setup for measuring the Grüneisen parameter of absorbing liquid inside a nylon tube mounted through an integrating sphere.
that, cs = Vμa , Eq. (2) becomes
II. METHOD AND MATERIALS
Ein = cm + V μa + cw + co .
A. 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. A simple illustration is shown in Figure 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 1. From the geometry and properties of this integrating sphere system, a simple energy balance can be obtained, resulting in Ein = Emedium + Esample + Ewall + Eout .
(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 energy magnitudes absorbed 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: Ein = cm + cs + cw + co ,
(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
(3)
The second term in Eq. (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 : =
Ein . c + V μa
(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 σ 0 is linearly related to the absorbed energy, by σ 0 = μa , with referred to as the Grüneisen parameter is a conversion efficiency factor. Inserting Eq. (4) gives σ0 =
μa Ein . c + V μa
(5)
Equation (5) indicates the behaviour of the initial stress distribution σ 0 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 signal is assumed here to be linearly related to σ 0 , by Vpp = k · σ0 , with k representing any acoustic attenuation and conversion factor between the initially generated stress and the detected pressure transient. Using this in Eq. (5) we obtain Vpp =
kμa Ein . c + V μa
(6)
Equation (6) indicates that the dependence of the generated PA signal amplitude on μa is nonlinear. This means that, with all other factors constant, Vpp increases with μa but approaches an asymptotic value for V μa c.
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The constants k and c in Eq. (6) can be determined from a calibration procedure in which a calibration liquid with known and μa 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: =
Vpp (c + μa V ) Ein kμa
.
(7)
Here, can be measured if the sample’s μa 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 Eq. (7) are presented in Sec. II B below. B. Experimental description
the unknown absorption coefficient of the absorber in situ, with appropriate calibration. However, in this stage a separate measurement of the sample’s absorption coefficient is performed. The sphere is filled up with demineralized water to facilitate acoustic matching with a flat transducer (12-mm single element, 1 MHz, −6 dB bandwidth 60.58%, Olympus Panametrics NDT V303) positioned directly above the center of the nylon tube as shown in Figure 1. The detected PA signal is amplified by an ultrasound amplifier (Panametrics NDT Ultrasonic Preamp 5678). 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 (200 MHz, 2 GS/s, Tektronix TDS 2022C/24C) 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 × 1010 samples/s for the optical signal, and 5.0 × 107 samples/s for the acoustic signal.
1. Description of the integrating sphere setup
A schematic diagram of the experimental setup constructed in order to verify the validity of Eq. (7) is shown in Figure 1. An integrating sphere (Thorlabs IS200) with a diameter of 50.8 mm is used as a platform for doing PA measurements. The sphere has four big ports, each with diameter of 12.7 mm and one small port with a diameter of 3 mm. A soft transparent nylon tube (2604 Nylon tubing from Rubber bv) 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. 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 1. These light pulses with wavelength of 750 nm from an Nd:YAG-OPO laser source (OpoletteTM 532I) and an average pulse energy of 1.25 mJ (measured using Thorlabs S370C connected to PM100D power meter) are delivered via a fiber (Newport, 0.22 NA, core diameter of 1 mm) 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 (Thorlabs DET10A/M—Si detector) 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
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 calibration (instrument) constants and another as a validation liquid for verifying the derived Eq. (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 Ecoline ink (Royal Talens Ecoline 700 8265) 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 μa values of the various ink concentrations are measured using a spectrophotometer (Shimadzu UV-VIS). For validation, ethanol (459844 Sigma-Aldrich Ethanol ACS reagent, ≥99.5%, 200 proof, absolute) is used as an absorbing sample. Similar to water, ethanol has very low absorbance at 750 nm wavelength. To increase the μa of ethanol at this wavelength, a small amount of indocyanine (ICG) dye (02155020 MP Biomedicals Indocyanine Green Dye Content: ∼90%, Green Powder) is dissolved in ethanol. Six different stock solutions of ethanol with ICG are made. The μa of each solution is measured via spectrophotometry before using it as an absorbing sample in the PA setup. Table I shows a summary of the measured μa 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 μa of the solution is around 1 mm−1 . Using Eq. (7), of ethanol is measured and compared with a known literature value of ethanol = 0.775.11
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TABLE I. Summary of data for calculating ethanol for one measurement with each of the ethanol absorbing samples labeled E1–E6. Label μa (mm−1 ) Vpp (V) Ein (V s)
E1
E2
E3
E4
E5
E6
Average ± stdev
1.04 8.9 × 10−2 5.09 × 10−9 0.85
1.04 7.9 × 10−2 5.12 × 10−9 0.75
1.03 7.9 × 10−2 5.03 × 10−9 0.76
1.00 8.1 × 10−2 4.94 × 10−9 0.81
0.99 7.6 × 10−2 4.99 × 10−9 0.76
0.99 8.2 × 10−2 4.92 × 10−9 0.83
1.02 ± 0.02 8.1 × 10−2 ± 4.2 × 10−3 5.01 × 10−9 ± 7.73 × 10−11 0.79 ± 0.04
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 literature11 ) is used as a calibration fluid, with added ink for enhanced absorption. Using Eq. (6), the values of k and c can be obtained from a plot of Vpp versus μa with known values of the other parameters , V, and Ein . Moreover, in order to account for any fluctuation on the incident light energy, Eq. (6) can be rewritten as follows: Vpp Ein
=
kμa . c + V μa
(6a)
Here Ein is the relative energy of the incident light which is V
linearly related to Ein . Thus, a calibration plot with Epp verin sus μa 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 (6a) also implies that absolute sensitivity measurements of the transducer and photodetector are not necessary to determine the instrument constants. Instead, a plot of meaV sured Epp for varying values of μa of the calibration liquid in (aqueous ink dilutions) with known and volume V is sufficient to determine k and c using a rational fitting function of x the form y = a+bx similarly as in Eq. (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.
in Figure 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. 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 17 μs which correspond to the time of flight of the acoustic wave from 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 Sec. II, the equation for determining only requires measurement of the Vpp amplitude of the PA signal and the relative incident energy Ein . 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 . Vpp values of the PA signal are measured and plotted Ein against μa for five sets of measurements as shown in Figure 3. As an illustration, a fitting function (in OriginPro 8.6) similar to Eq. (6a) indicated by blue line on one set of data, gives the values k = 1.37 (s−1 m3 ) and c = 4.55 × 10−5 (m2 ). These values are used to determine using Eq. (7) rewritten as follows: Vpp (c + μa V ) . (7a) = Ein kμa 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 .
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 Ein and Vpp of the optical and photoacoustic signals, respectively, are measured. The detected signals are processed to determine ethanol using the integrating sphere system. III. RESULTS AND DISCUSSION
Typical photoacoustic signals generated by the calibration liquid inside the tube for various values of μa are shown
FIG. 2. Typical photoacoustic signals detected by the transducer for various μa values of the calibration liquid (aqueous ink dilutions) injected into the tube inside the integrating sphere.
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FIG. 3. Example of calibration plots of
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Vpp Ein
versus μa for five sets of mea-
surements for determining the instrument constants k and c. The blue line is a fitting function that gives k = 1.37 (s−1 m3 ) and c = 4.55 × 10−5 (m2 ) for one measurement, R2 = 0.984 which indicates a measure of how the fit and data points are correlated.
A. Measurement of with constant μa
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 4 shows an example of the PA signal generated by the ethanol—absorbing samples labeled E1–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. Table I 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 II. For this set of measurements, calculated = 0.79 2 s and the known thermal proper± 0.34. Based on ≡ βv C p
ties of ethanol around 20 ◦ C 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 δ = 0.34 is about 40% of the average which indicates that the error in measuring experimental parameters such as Vpp , Ein , and μa can significantly increase the range of measurable values of ethanol . Table II shows an overview of the measurable values of μa , Ein , and Vpp . Here, the tabulated data also include those measurements when the nylon tube is not perfectly aligned with the transducer center, such
FIG. 4. Typical PA signals detected with ethanol plus ICG (labeled E1–E6) inside the tube. The black is the signal detected without ICG dissolved in ethanol. The Vpp amplitude of each PA signal is used in Eq. (7a) to determine the of ethanol.
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–E6 solutions used as the absorbing sample. Here, the average ethanol is 0.66 for all measurements with E1–E6 with three different calibration measurements. The standard deviation in these measurements equals 0.10, which is 15% the average value.
B. Measurement of with varying μa
Measurements are also taken for varying values of μa of ethanol with ICG solutions labeled E7–E9 in Table III. Similar profiles of the PA signals, but with varying Vpp amplitudes, are observed. At least three repetitions are performed to acquire statistics on measurable values of ethanol for three different values of μa . From the collected data, the calculated does not vary significantly with varying μa . 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 μa value as in samples E1–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 II. Summary of average and error values (standard deviations and propagated error) in calculating δ for the data given in Table I. μa ± δμa (mm−1 ) 1.02 ± 0.02
Ein ± δEin (V s) 5.01 × 10−9 ± 7.73 × 10−11
Vpp ± δVpp (V) 8.1 × 10−2 ± 4.2 × 10−3
± δ 0.79 ± 0.34
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TABLE III. Summary of data for calculating ethanol with each of the ethanol absorbing samples of varying μa . δ is the propagated error. Label μa ± δμa (mm−1 ) Ein ± δEin (V s) Vpp ± δVpp (V) ± δ
E7
E8
E9
0.510 ± 0.004 5.44 × 10−9 ± 3.64 × 10−11 6.2 × 10−2 ± 1.1 × 10−2 0.78 ± 0.38
1.000 ± 0.002 5.37 × 10−9 ± 1.23 × 10−10 8.5 × 10−2 ± 0.7 × 10−2 0.66 ± 0.28
1.450 ± 0.023 5.30 × 10−9 ± 1.31 × 10−10 13 × 10−2 ± 1.0 × 10−2 0.72 ± 0.30
IV. 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’s 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 μa values of the absorbing sample such that incident light could penetrate completely. A simple formula (Eq. (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. 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 μa values from 0.2 to 10 mm−1 and assumed of water 0.120 ± 0.006 around 22 ◦ C. Calibration plots showing the ratio of relative PA amplitudes and incident energy versus μa give values of instrument constants k = 1.12 ± 0.372 (s−1 m3 ) and c = 3.06 × 10−5 ± 8.81 × 10−6 (m2 ) 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 μa values from approximately 1 to 1.5 mm−1 . Measurements using nine different ethanol absorbing samples (labeled E1–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’s
μa is necessary to measure , and that the method described here is validated only for μa up to 1.5 mm−1 . Measurements with samples of higher μa 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’s μa 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 μa , including biological chromophores and nanoparticle suspensions. Knowledge of values can aid in discriminating the different components in a photoacoustic image. ACKNOWLEDGMENTS
The authors gratefully acknowledge The Netherlands Technology Foundation STW Project 10831 for the financial support given to this research. 1 L.
V. Wang, Photoacoustic Imaging and Spectroscopy (CRC Press, Boca Raton, 2009). 2 B. T. Cox, J. G. Laufer, and P. C. Beard, Proc. SPIE 7177, 717713 (2009). 3 B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, J. Biomed. Opt. 17(6), 061202 (2012). 4 Z. Xu, C. Li, and L. V. Wang, J. Biomed. Opt. 15(3), 036019 (2010). 5 L. V. Wang, IEEE J. Sel. Top. Quantum Electron. 14(1), 171–179 (2008). 6 E. V. Savateeva, A. A. Karabutov, S. V. Solomatin, and A. A. Oraevsky, Proc. SPIE 4618, 63–75 (2002). 7 D. K. Yao, C. Zhang, K. Maslov, and L. V. Wang, J. Biomed. Opt. 19(1), 017007 (2014). 8 J. Laufer, E. Zhang, and P. Beard, IEEE J. Sel. Top. Quantum Electron. 16(3), 600–607 (2010). 9 B. Soroushian, W. M. Whelan, and M. C. Kolios, J. Biomed. Opt. 15(6), 065002 (2010). 10 P. Elterman, Appl. Opt. 9(9), 2140 (1970). 11 W. M. Haynes, CRC Handbook of Chemistry and Physics, 94th ed. (CRC Press, 2013–2014).
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Photoacoustic measurement of the Grüneisen parameter using an integrating sphere Yolanda Villanueva,a) Erwin Hondebrink, Wilma Petersen, and Wiendelt Steenbergen BioMedical Photonic Imaging Group, MIRA Institute for Biomedical Technology and Technical Medicine, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
(Received 13 March 2014; accepted 8 July 2014; published online 30 July 2014) 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. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4890666] I. 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, in or 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 β, and speed of sound vs us2 s 4 . For most biological chromophores, and these ing ≡ βv C p
thermal properties are not always known, although in principle they can be measured individually. In photoacoustics, relates the absorbed optical energy density μa to the amplitude σ 0 of the locally generated initial stress in this manner: σ 0 = μa .5 This equation is valid only if the stress confinement condition is satisfied. Here, μa is the local absorption coefficient and is the local fluence. With known absolute values of σ 0 , μa , and , can be directly determined as reported by Savateeva et al.6 using time-resolved photoacoustic technique to measure of whole blood from anesthesized animals.
a) Author to whom correspondence should be addressed. Electronic mail:
[email protected].
0034-6748/2014/85(7)/074904/6/$30.00
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 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.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 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 paper, a method for photoacoustic measurement of using an integrating sphere10 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 model-based fitting to the detected signals is not necessary, in contrast to that done in another method.8 In Sec. II, 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 Sec. III, experimental results such as the temporal profile of the detected 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 Sec. IV.
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FIG. 1. Schematic diagram of the experimental setup for measuring the Grüneisen parameter of absorbing liquid inside a nylon tube mounted through an integrating sphere.
that, cs = Vμa , Eq. (2) becomes
II. METHOD AND MATERIALS
Ein = cm + V μa + cw + co .
A. 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. A simple illustration is shown in Figure 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 1. From the geometry and properties of this integrating sphere system, a simple energy balance can be obtained, resulting in Ein = Emedium + Esample + Ewall + Eout .
(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 energy magnitudes absorbed 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: Ein = cm + cs + cw + co ,
(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
(3)
The second term in Eq. (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 : =
Ein . c + V μa
(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 σ 0 is linearly related to the absorbed energy, by σ 0 = μa , with referred to as the Grüneisen parameter is a conversion efficiency factor. Inserting Eq. (4) gives σ0 =
μa Ein . c + V μa
(5)
Equation (5) indicates the behaviour of the initial stress distribution σ 0 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 signal is assumed here to be linearly related to σ 0 , by Vpp = k · σ0 , with k representing any acoustic attenuation and conversion factor between the initially generated stress and the detected pressure transient. Using this in Eq. (5) we obtain Vpp =
kμa Ein . c + V μa
(6)
Equation (6) indicates that the dependence of the generated PA signal amplitude on μa is nonlinear. This means that, with all other factors constant, Vpp increases with μa but approaches an asymptotic value for V μa c.
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The constants k and c in Eq. (6) can be determined from a calibration procedure in which a calibration liquid with known and μa 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: =
Vpp (c + μa V ) Ein kμa
.
(7)
Here, can be measured if the sample’s μa 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 Eq. (7) are presented in Sec. II B below. B. Experimental description
the unknown absorption coefficient of the absorber in situ, with appropriate calibration. However, in this stage a separate measurement of the sample’s absorption coefficient is performed. The sphere is filled up with demineralized water to facilitate acoustic matching with a flat transducer (12-mm single element, 1 MHz, −6 dB bandwidth 60.58%, Olympus Panametrics NDT V303) positioned directly above the center of the nylon tube as shown in Figure 1. The detected PA signal is amplified by an ultrasound amplifier (Panametrics NDT Ultrasonic Preamp 5678). 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 (200 MHz, 2 GS/s, Tektronix TDS 2022C/24C) 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 × 1010 samples/s for the optical signal, and 5.0 × 107 samples/s for the acoustic signal.
1. Description of the integrating sphere setup
A schematic diagram of the experimental setup constructed in order to verify the validity of Eq. (7) is shown in Figure 1. An integrating sphere (Thorlabs IS200) with a diameter of 50.8 mm is used as a platform for doing PA measurements. The sphere has four big ports, each with diameter of 12.7 mm and one small port with a diameter of 3 mm. A soft transparent nylon tube (2604 Nylon tubing from Rubber bv) 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. 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 1. These light pulses with wavelength of 750 nm from an Nd:YAG-OPO laser source (OpoletteTM 532I) and an average pulse energy of 1.25 mJ (measured using Thorlabs S370C connected to PM100D power meter) are delivered via a fiber (Newport, 0.22 NA, core diameter of 1 mm) 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 (Thorlabs DET10A/M—Si detector) 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
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 calibration (instrument) constants and another as a validation liquid for verifying the derived Eq. (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 Ecoline ink (Royal Talens Ecoline 700 8265) 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 μa values of the various ink concentrations are measured using a spectrophotometer (Shimadzu UV-VIS). For validation, ethanol (459844 Sigma-Aldrich Ethanol ACS reagent, ≥99.5%, 200 proof, absolute) is used as an absorbing sample. Similar to water, ethanol has very low absorbance at 750 nm wavelength. To increase the μa of ethanol at this wavelength, a small amount of indocyanine (ICG) dye (02155020 MP Biomedicals Indocyanine Green Dye Content: ∼90%, Green Powder) is dissolved in ethanol. Six different stock solutions of ethanol with ICG are made. The μa of each solution is measured via spectrophotometry before using it as an absorbing sample in the PA setup. Table I shows a summary of the measured μa 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 μa of the solution is around 1 mm−1 . Using Eq. (7), of ethanol is measured and compared with a known literature value of ethanol = 0.775.11
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TABLE I. Summary of data for calculating ethanol for one measurement with each of the ethanol absorbing samples labeled E1–E6. Label μa (mm−1 ) Vpp (V) Ein (V s)
E1
E2
E3
E4
E5
E6
Average ± stdev
1.04 8.9 × 10−2 5.09 × 10−9 0.85
1.04 7.9 × 10−2 5.12 × 10−9 0.75
1.03 7.9 × 10−2 5.03 × 10−9 0.76
1.00 8.1 × 10−2 4.94 × 10−9 0.81
0.99 7.6 × 10−2 4.99 × 10−9 0.76
0.99 8.2 × 10−2 4.92 × 10−9 0.83
1.02 ± 0.02 8.1 × 10−2 ± 4.2 × 10−3 5.01 × 10−9 ± 7.73 × 10−11 0.79 ± 0.04
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 literature11 ) is used as a calibration fluid, with added ink for enhanced absorption. Using Eq. (6), the values of k and c can be obtained from a plot of Vpp versus μa with known values of the other parameters , V, and Ein . Moreover, in order to account for any fluctuation on the incident light energy, Eq. (6) can be rewritten as follows: Vpp Ein
=
kμa . c + V μa
(6a)
Here Ein is the relative energy of the incident light which is V
linearly related to Ein . Thus, a calibration plot with Epp verin sus μa 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 (6a) also implies that absolute sensitivity measurements of the transducer and photodetector are not necessary to determine the instrument constants. Instead, a plot of meaV sured Epp for varying values of μa of the calibration liquid in (aqueous ink dilutions) with known and volume V is sufficient to determine k and c using a rational fitting function of x the form y = a+bx similarly as in Eq. (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.
in Figure 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. 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 17 μs which correspond to the time of flight of the acoustic wave from 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 Sec. II, the equation for determining only requires measurement of the Vpp amplitude of the PA signal and the relative incident energy Ein . 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 . Vpp values of the PA signal are measured and plotted Ein against μa for five sets of measurements as shown in Figure 3. As an illustration, a fitting function (in OriginPro 8.6) similar to Eq. (6a) indicated by blue line on one set of data, gives the values k = 1.37 (s−1 m3 ) and c = 4.55 × 10−5 (m2 ). These values are used to determine using Eq. (7) rewritten as follows: Vpp (c + μa V ) . (7a) = Ein kμa 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 .
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 Ein and Vpp of the optical and photoacoustic signals, respectively, are measured. The detected signals are processed to determine ethanol using the integrating sphere system. III. RESULTS AND DISCUSSION
Typical photoacoustic signals generated by the calibration liquid inside the tube for various values of μa are shown
FIG. 2. Typical photoacoustic signals detected by the transducer for various μa values of the calibration liquid (aqueous ink dilutions) injected into the tube inside the integrating sphere.
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FIG. 3. Example of calibration plots of
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Vpp Ein
versus μa for five sets of mea-
surements for determining the instrument constants k and c. The blue line is a fitting function that gives k = 1.37 (s−1 m3 ) and c = 4.55 × 10−5 (m2 ) for one measurement, R2 = 0.984 which indicates a measure of how the fit and data points are correlated.
A. Measurement of with constant μa
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 4 shows an example of the PA signal generated by the ethanol—absorbing samples labeled E1–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. Table I 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 II. For this set of measurements, calculated = 0.79 2 s and the known thermal proper± 0.34. Based on ≡ βv C p
ties of ethanol around 20 ◦ C 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 δ = 0.34 is about 40% of the average which indicates that the error in measuring experimental parameters such as Vpp , Ein , and μa can significantly increase the range of measurable values of ethanol . Table II shows an overview of the measurable values of μa , Ein , and Vpp . Here, the tabulated data also include those measurements when the nylon tube is not perfectly aligned with the transducer center, such
FIG. 4. Typical PA signals detected with ethanol plus ICG (labeled E1–E6) inside the tube. The black is the signal detected without ICG dissolved in ethanol. The Vpp amplitude of each PA signal is used in Eq. (7a) to determine the of ethanol.
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–E6 solutions used as the absorbing sample. Here, the average ethanol is 0.66 for all measurements with E1–E6 with three different calibration measurements. The standard deviation in these measurements equals 0.10, which is 15% the average value.
B. Measurement of with varying μa
Measurements are also taken for varying values of μa of ethanol with ICG solutions labeled E7–E9 in Table III. Similar profiles of the PA signals, but with varying Vpp amplitudes, are observed. At least three repetitions are performed to acquire statistics on measurable values of ethanol for three different values of μa . From the collected data, the calculated does not vary significantly with varying μa . 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 μa value as in samples E1–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 II. Summary of average and error values (standard deviations and propagated error) in calculating δ for the data given in Table I. μa ± δμa (mm−1 ) 1.02 ± 0.02
Ein ± δEin (V s) 5.01 × 10−9 ± 7.73 × 10−11
Vpp ± δVpp (V) 8.1 × 10−2 ± 4.2 × 10−3
± δ 0.79 ± 0.34
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TABLE III. Summary of data for calculating ethanol with each of the ethanol absorbing samples of varying μa . δ is the propagated error. Label μa ± δμa (mm−1 ) Ein ± δEin (V s) Vpp ± δVpp (V) ± δ
E7
E8
E9
0.510 ± 0.004 5.44 × 10−9 ± 3.64 × 10−11 6.2 × 10−2 ± 1.1 × 10−2 0.78 ± 0.38
1.000 ± 0.002 5.37 × 10−9 ± 1.23 × 10−10 8.5 × 10−2 ± 0.7 × 10−2 0.66 ± 0.28
1.450 ± 0.023 5.30 × 10−9 ± 1.31 × 10−10 13 × 10−2 ± 1.0 × 10−2 0.72 ± 0.30
IV. 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’s 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 μa values of the absorbing sample such that incident light could penetrate completely. A simple formula (Eq. (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. 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 μa values from 0.2 to 10 mm−1 and assumed of water 0.120 ± 0.006 around 22 ◦ C. Calibration plots showing the ratio of relative PA amplitudes and incident energy versus μa give values of instrument constants k = 1.12 ± 0.372 (s−1 m3 ) and c = 3.06 × 10−5 ± 8.81 × 10−6 (m2 ) 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 μa values from approximately 1 to 1.5 mm−1 . Measurements using nine different ethanol absorbing samples (labeled E1–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’s
μa is necessary to measure , and that the method described here is validated only for μa up to 1.5 mm−1 . Measurements with samples of higher μa 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’s μa 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 μa , including biological chromophores and nanoparticle suspensions. Knowledge of values can aid in discriminating the different components in a photoacoustic image. ACKNOWLEDGMENTS
The authors gratefully acknowledge The Netherlands Technology Foundation STW Project 10831 for the financial support given to this research. 1 L.
V. Wang, Photoacoustic Imaging and Spectroscopy (CRC Press, Boca Raton, 2009). 2 B. T. Cox, J. G. Laufer, and P. C. Beard, Proc. SPIE 7177, 717713 (2009). 3 B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, J. Biomed. Opt. 17(6), 061202 (2012). 4 Z. Xu, C. Li, and L. V. Wang, J. Biomed. Opt. 15(3), 036019 (2010). 5 L. V. Wang, IEEE J. Sel. Top. Quantum Electron. 14(1), 171–179 (2008). 6 E. V. Savateeva, A. A. Karabutov, S. V. Solomatin, and A. A. Oraevsky, Proc. SPIE 4618, 63–75 (2002). 7 D. K. Yao, C. Zhang, K. Maslov, and L. V. Wang, J. Biomed. Opt. 19(1), 017007 (2014). 8 J. Laufer, E. Zhang, and P. Beard, IEEE J. Sel. Top. Quantum Electron. 16(3), 600–607 (2010). 9 B. Soroushian, W. M. Whelan, and M. C. Kolios, J. Biomed. Opt. 15(6), 065002 (2010). 10 P. Elterman, Appl. Opt. 9(9), 2140 (1970). 11 W. M. Haynes, CRC Handbook of Chemistry and Physics, 94th ed. (CRC Press, 2013–2014).
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