CHAPTER 3: GAS-COUPLED LASER ACOUSTIC DETECTION
Conventional contacting piezoelectric transducers for ultrasonic wave detection are highly sensitive and tuned for real-time imaging with €xed array geometries. However, optical detection provides an alterna-tive to contacting piezoelectric transducers when a small sensor footprint, a large frequency bandwidth, or non-contacting detection is required. Typical optical detection relies on a Doppler-shi‰ed reƒection of light from the target, but Gas Coupled-Laser Acoustic Detection (GCLAD) provides an alternative optical detection method for photoacoustic and ultrasound imaging that does not involve surface reƒectivity. In-stead, GCLAD is a line-detector that measures the deƒection of an optical beam propagating parallel to the sample, as the refractive index of the air near the sample is a‚ected by particle displacement on the sample surface.
We describe the underlying principles of GCLAD and derive a formula for quantifying the surface dis-placement from a remote GCLAD measurement. We discuss a design for removing the location-dependent displacement bias along the probe beam and a method for measuring the aŠenuation coe•cient of the surrounding air. GCLAD results are used to quantify the surface displacement in a laser-ultrasound ex-periment, which shows 94% agreement to line-integrated data from a commercial laser vibrometer point detector. Finally, we demonstrate the feasibility of photoacoustic imaging of an artery-sized absorber using a detector 5:8 cm from a phantom surface.
Photoacoustic and laser-ultrasound modalities utilizing optical detection have the potential to substantially improve non-invasive medical imaging capabilities. However, hardware design toward a clinically feasible modality is not without challenges. Important considerations for detection of laser-induced acoustic waves include frequency bandwidth, detection aperture, and element size [Beard, 2011]. When a PA or LUS wave travels through a sample, its surface is displaced. Traditional ultrasound piezoelectric transducers detect this movement using piezoelectric crystals, while optical “point” methods measure the change in optical path length with a probe beam perpendicular to the surface motion. Here, we present Gas-Coupled Laser Acoustic Detection (GCLAD) [Caron et al., 1998] for detecting PA and LUS waves through air. GCLAD was developed for materials evaluation, and images of composite materials using a C-scan geometry have been shown [Caron et al., 2000]. Here, we explore the possibility of GCLAD as an integrating line detector for PA and LUS imaging.
Employing traditional ultrasound piezoelectric transducers for photoacoustic imaging is aŠractive, as it allows photoacoustic capabilities to be incorporated with commercially available ultrasound modalities. However, several characteristics of piezoelectric transducers are undesirable for photoacoustic imaging. Delivery of the source light in reƒection mode is complicated with piezoelectric transducers, as most are contacting, relatively large and opaque devices that require an acoustic coupling medium. Photoacoustic waves are inherently broadband, thus the narrow frequency bandwidth of piezoelectric elements limits the size and depth of structures that can be imaged with a given piezoelectric transducer. Furthermore, the sensitivity of piezoelectric transducers decreases with element size. Œe assumption of a point detector required by most reconstruction algorithms is thus poorly satis€ed, resulting in degraded images [Paltauf et al., 2007].
Optical detection of ultrasound addresses many of the challenges associated with piezoelectric transducers. Examples include optical interferometers [Speirs and Bishop, 2013], Fiber Bragg detectors [Rosen-thal et al., 2011], micro-ring resonators [Ling et al., 2011], and Fabry-Perot´ sensors [Zhang et al., 2008]. Œese detectors have the bene€t of broadband sensitivity and a point-like detection spot, therefore, spatial resolution is higher compared to piezoelectric transducers. However, interferometric detection on scaŠer-ing or absorbing surfaces, such as skin, o‰en requires a reƒective medium to be incorporated [Johnson et al., 2014]. Rousseau et al. [2012b] and Rousseau et al. [2012a] have shown adequate sensitivity with a fully non-contacting confocal Fabry-Perot´ interferometer by employing a high-energy, pulsed probe beam. Likewise, Hochreiner et al.  used a two-wave mixing interferometer without the need for a coupling medium. However, interferometric detectors are di•cult to parallelize, thus a single point is scanned across the sample surface for two- and three-dimensional imaging.
Integrating line detectors are a promising alternative to point detectors for photoacoustic imaging. While 2D imaging with point detectors of €nite size is degraded by out-of-plane e‚ects, waveforms ac-quired by line detectors strictly obey the two-dimensional wave equation when the line is much larger than the target [Paltauf et al., 2007]. Additionally, line detectors suppress signals with a wavelength such that destructive interference takes place along the line. In exploration geophysics, geophone groups are commonly used to suppress surface waves (o‰en termed “ground-roll”) at the bene€t of body-wave reƒec-tions from the targets of interest, by making the group-size equal to the wavelength of the surface-wave energy [Section 4.4.2 of Kearey et al., 2002]. Analogously, line detection can suppress surface waves that interfere with the longitudinal waves of interest in medical laser-ultrasound imaging. Œe feasibility of Mach-Zehnder and Fabry-Perot´ line detection in water has been shown [Grun¨ et al., 2009], and three-dimensional photoacoustic images of phantoms and insects were demonstrated using a Fabry-Perot´ line detector [Grun¨ et al., 2010].
In this chapter, we present GCLAD as a quantitative integrating line detector. GCLAD is based on the deƒection of an optical beam by ultrasound [Born and Wolf, 1999], where the change in refractive index due to a propagating ultrasound wave is probed by a laser. Œis approach uses simple optics relative to interferometric techniques and requires minimal alignment. GCLAD is independent of surface reƒectivity, and is therefore purely non-contacting and does not contribute to energy exposure. Œis is optimum for imaging when access to the target is required, or contact with the sample could cause discomfort or harm. Parallelization is straight-forward, and hardware is inexpensive, hence detector arrays for simultaneous acquisition of full-€eld data is possible.
Recently, the e‚ects of gold nanoparticle concentration on photoacoustic waveforms have been mon-itored using beam deƒection [Khosroshahi and Mandelis, 2015]. Further, photoacoustic waveforms have been detected with beam deƒection in water, where Barnes et al.  demonstrated the ability to obtain directionality information, and Khachatryan et al.  designed a photoacoustic microscopy device us-ing a C-scan approach. However, detection through air requires enhanced sensitivity, and the potential for line detection has not been studied until now.
In Section 3.3, we derive the theory of GCLAD; Section 3.4 presents a series of characterization experi-ments, demonstrating the feasibility of using GCLAD as a quantitative detector for photoacoustic and laser-ultrasound imaging; in Section 3.5, we present a two-dimensional PA imaging experiment with GCLAD; and in Section 5.5, we provide our discussion and conclusions. Œroughout this chapter, all automation and data acquisition is controlled using PLACE, as described in Appendix B.
Gas-Coupled Laser Acoustic Detection
Œe surface displacement resulting from a PA or LUS wave propagating to the surface of a sample causes density variations in the surrounding air as the transmiŠed wave couples to the air. GCLAD detects these pressure variations by measuring the motion of an optical beam perpendicular to the acoustic propagation with a position-sensitive detector (PSD, ‹arktet, Silver Spring, Maryland, USA). Caron  found that the theoretical, frequency-dependent sensitivity of GCLAD is comparable to an ideal confocal Fabry-Perot interferometer [Monchalin and Heon, 1986], as reproduced in Fig. 3.1. However, the bandwidth of GCLAD is also dependent on the probe beam diameter, and more favorably compares with interferometers when a narrow beam width is used.
Relationship between refractive index and pressure in air
Here we derive a relationship between spatial and temporal variations in air pressure (caused by particle displacement in a sample), and the refractive index of air n. Œe Lorentz-Lorenz formula describes the relationship between the refractive index and the molar refractivity A of a substance [Born and Wolf, 1999]:
where is density, and M is molecular mass. Œe refractive index of a gas can be found by taking the €rst-order Taylor expansion of Eq. 3.1 at n=1:
and the ambient constants for refractive index n0 and density 0 can be related Œe density of acoustic waves varies adiabatically with pressure p, thus and we can integrate to solve for the density of air for a given pressure Substituting Eq. 3.5 into Eq. 3.2 and de€ning the pressure of an acoustic wave p(r; t), we have a formula relating refractive index to pressure:
Ray theory of beam deƒection
When an optical beam encounters a medium with a continuously varying refractive index, the beam is refracted according to the ray equation [Kopeika, 1998]:
where n is the refractive index, s is the path length of the light ray, and r is the location of the ray in space (Fig. 3.2). For light propagating along an x-axis, ds ’ dx and Eq. 3.7 becomes the paraxial ray equation Combining Eq. 3.6 and Eq. 3.8 for an acoustic plane wave propagating in the z-direction (Fig. 3.3) gives us.
Dependence on acoustic source position
In a traditional beam deƒection setup (Fig. 3.3), the total position change Z is proportional to the distance from the acoustic wave to the detector (Eq. 3.17). As such, beam deƒection is greater for a unit perturbation farther from the PSD than for one close to the PSD. To rectify this bias, a convex lens is placed in front of the position sensitive detector, as in Fig. 3.4. Caron  showed that incorporating a lens reduces the system size without compromising sensitivity. Here, we look at the e‚ects of the lens on amplitude measurements. Œe position change at the PSD a‰er passing through the lens can be determined from ray transfer (ABCD) matrix analysis. Œe contribution from a deƒected ray is [Caron, 2008]:
and a displaced ray (traveling parallel to the original ray path) is where f is the focal length of the lens. When x0 f, the displacement term is negligible, and the deƒected term is both proportional to and independent of x1 Placing a lens at x0 f is advantageous for line detection, as the amplitude is proportional to the change in pressure, but independent of the location of the acoustic waves along the probe beam. Furthermore, the sensitivity of the system can be tuned by varying the focal length of the lens (and changing x0 accordingly), with the trade-o‚ between sensitivity and compactness. Œe focal length of the lens is also proportional to the focal spot size. Œe spot size increases with f and reduces the amplitude sensitivity on the PSD, further supporting the use of a compact system where f is small. It is noted that spherical abberations should also be considered when the beam diameter becomes large compared to the lens.
†antifying surface displacement from beam deƒection
‹antitative measurements of the displacement at the sample surface are possible given the beam deƒection measured remotely. Upon reaching the surface of a sample, a propagating acoustic wave will displace the surface by a distance . Considering a planar surface, the wave will continue to propagate as a plane wave in the air de€ned [Towne, 1967]:
where is the frequency of the wave, ! = 2 , k is the wavenumber !c , is the aŠenuation coe•cient, and z is the distance from the surface.
Substituting Eq.’s 3.16 and 3.21 into Eq. 3.20, we have an equation relating the total position change at the detector to the surface displacement of the sample:
GCLAD as an unbiased line detector
Next, we compare GCLAD as an integrating line detector between a conventional beam deƒection setup, and the unbiased approach described in Sec. 3.3.3. First, we measure the GCLAD signal for an acoustic source at multiple positions along the probe beam using beam deƒection as in Fig. 3.3. A 500 kHz piezo-electric transducer (V101, Panametrics, Olympus) driven by a 300 V square wave (5077PR, Olympus) with a 100 Hz repetition rate is used to generate acoustic waves. Œe piezoelectric transducer is mounted on a linear stage (M-IMS300LM, Newport, Irvine, CA, USA) 6 cm from the probe beam and scanned at 1 mm increments parallel to the detection line. Œe acoustic wave propagates through air to the probe beam, and the amplitude of the detected wave is recorded at each increment. In this con€guration, the maximum amplitude is proportional to x1 (Fig. 3.5). Second, we place a convex lens with a 60 mm focal length in front of the PSD where x0 f and repeat the scan. As predicted by Eq. 3.20, the amplitude becomes uniform across the length of x1.
Signal strength and laser ƒuence proportionality
For any quantitative acoustic detector, the amplitude of the detected wave must be proportional to the initial pressure distribution. To validate this property for GCLAD, we generate LUS waves using four discrete light ƒuences and detect the elastic waves with GCLAD. A 3:3 cm thick solid phantom is composed of 1% Intralipid (Fresenius-Kabi, Uppsala, Sweden), 1% agar gel (A0930-05, U.S. Biological, SwampscoŠ, MA, USA), and 0.35% India ink, corresponding to an absorption coe•cient of 20 cm 1 [Cubeddu et al., 1997]. Œe phantom is placed 9 mm from a GCLAD beam with a beam waist of 800 µm before the lens. A collimated 1064 nm source laser (‹anta-Ray, Spectra Physics, Newport, Irvine, CA, USA) with an 8 mm diameter is incident on the opposite side of the phantom (Fig. 3.6(a)). Laser-ultrasound waves are generated with laser ƒuences in the range of 70 100 mJ=cm2 in 10 mJ=cm2 increments at 10 Hz, and 64 waveforms were averaged for each ƒuence. As expected, Fig. 3.6(b) demonstrates that the signal amplitude is proportional to the incident laser ƒuence, and therefore the initial pressure of the LUS wave. A constant o‚set is observed due to a non-zero initial position of the probe beam on the PSD, causing a DC o‚set in the recorded signal.
Air gap dependence
A comprehensive understanding of the waveforms acquired by GCLAD a‰er propagation through air is important for accurate analysis and reconstruction. Measuring relevant properties, such as velocity and aŠenuation, allow these parameters to be included in a reconstruction model.
To study the e‚ects of the air gap for laser-generated ultrasound modalities, LUS waves are generated with a 1064 nm Nd:YAG laser on a 1:5 cm thick solid tissue phantom composed of 1% Intralipid and 1% agar (Fig. 3.8a). An opaque tape with an unknown absorption coe•cient is placed on the phantom surface to generate a localized LUS wave at the phantom surface. Œe source laser is collimated with an 8 mm diameter and pulse energy of 150 mJ=cm2. Œis ƒuence is beyond the maximum permissible exposure for biological tissue [ANS, 2007]; however, the energy is absorbed by the tape, rather than the tissue sample in this example. Œe wave€eld propagates through the phantom, and is detected with GCLAD on the opposite side of the sample. An average of 200 waveforms is acquired every 1 mm up to 10 cm away from the phantom (Fig. 3.8b).
A slope correction obtained via linear regression corrects for the additional time travel through air and determines the velocity in air (344:3 m s 1). With only the time-travel correction, the correlation co-e•cient for the direct wave is 0.91. Œe remaining di‚erence is aŠributed to aŠenuation. Œe wave€eld can be approximated by a plane wave when it crosses the phantom surface and geometric spreading is therefore minimal. Œe maximum amplitude decreases exponentially with an aŠenuation coe•cient of 0:6 dB cm 1 (Fig. 3.8c), corresponding to a frequency of 270 kHz in Fig. 3.8(d). Œe aŠenuation coe•cient in air varies dramatically with temperature, pressure, and volume; however, our measurements are consis-tent with published aŠenuation models [Hickling and Marin, 1986, Jakeviciusˇ et al., 2010]. Œe frequency dependence of the aŠenuation coe•cient is found by €rst ploŠing the power spectrum in decibels versus frequency for the signals recorded at each z-position (Fig. 3.7). For each discrete frequency, the relationship between power and z-position is found to be linear. Œe slope of each of these frequency lines is ploŠed versus frequency to obtain Fig. 3.8(d), which shows a frequency-dependent aŠenuation coe•cient (slope) of 2:7 dB cm 1MHz 1.
A‰er the direct LUS arrival, several reƒections within the phantom are detected. Œe amplitude of each subsequent wave is decreased, with the exception of a slight increase in amplitude of the third arrival compared to the second. With each pass through the phantom, the LUS wave becomes more planar. Œe increase in amplitude seen in the third arrival indicates that it is more planar than the waves detected prior, thus the integrated signal along the GCLAD beam is higher. Œis highlights that amplitude quanti€cation is dependent on the assumption of a plane wave, which is most accurate for waves travelling long distances.
Œese results con€rm that higher frequencies are aŠenuated more strongly, therefore imaging small structures with high frequency content requires a small air gap, while larger structures with low dominant frequencies can be imaged farther from the sample. As the acoustic properties of air vary with environmen-tal conditions, a reference air scan can be acquired at the time of data acquisition to calibrate the velocity and aŠenuation model.
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
1.1 All-optical Photoacoustic and Laser-Ultrasonic Imaging
1.2 esis Outline
1.3 Scientic Contributions
2 WAVE-EQUATION BASED IMAGE RECONSTRUCTION
2.3 Generating Solutions to the Acoustic Wave Equation
2.4 Ultrasound Reconstruction and Imaging with Reverse-Time Migration
2.5 Photoacoustic Reconstruction with Time-Reversal
2.6 Velocity Optimization and Sampling
3 GAS-COUPLED LASER ACOUSTIC DETECTION
3.3 Gas-Coupled Laser Acoustic Detection
3.4 Characterization Experiments
3.5 Two-Dimensional Imaging with GCLAD
4 NONCONFOCAL PHOTOACOUSTIC AND LASER-ULTRASONIC ANALYSIS WITH A SINGLE SOURCE
4.3 Materials and Methods
5 NONCONFOCAL LASER-ULTRASOUND AND PHOTOACOUSTIC IMAGING
5.1 Abstract .
6 PHOTOACOUSTIC AND LASER-ULTRASOUND IMAGING OF DISEASED ARTERIAL TISSUE
6.3 Photoacoustic and Laser-Ultrasound Imaging
7 ELIMINATION OF REFLECTION ARTIFACTS IN 2D PHOTOACOUSTIC IMAGING WITHMARCHENKO FOCUSING
7.2 Numerical Model
7.3 eory and Implementation
7.4 Results and Discussion .
8 CONCLUSIONS AND FUTURE WORK
8.2 Future Work
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ALL-OPTICAL PHOTOACOUSTIC AND LASER-ULTRASONIC IMAGING IN HETEROGENEOUS TISSUE