Probe beam deflection technique as acoustic emission directionality sensor with photoacoustic emission source

Ronald A. Barnes; Saher Maswadi; Randolph Glickman; Mehdi Shadaram

doi:10.1364/AO.53.000511

1. Introduction

Conventional acoustic detection techniques involve piezoelectric transducers or optical techniques such as interferometry. Optical techniques for measuring acoustic waves provide various desirable features such as passive sensing, lack of ringing effect, and low implementation cost. The ability to measure the direction of a propagating acoustic wave with piezoelectric transducers is accomplished using a piezoelectric array; however, with the proposed probe beam deflection technique (PBDT), the direction of a propagating acoustic wave can be measured with two probe beams from a laser diode. In this work, a photoacoustic source is used to produce an acoustic emission, and this emission is measured through implementation of the PBDT. Though a photoacoustic source is utilized for acoustic emission generation, the focus of this paper is on the capability of the PBDT to measure the propagation direction or angular information of a propagating acoustic emission and not necessarily its capability as a photoacoustic tomography (PAT) sensor modality; however, characteristics of the PBDT do have potential as an acoustic sensor for PAT.

The acoustic-generation mechanism for the demonstration of the directionality capability of the PBDT was chosen to be photoacoustic emission as in PAT. PAT is accomplished by measuring the propagating acoustic energy radiated from a sample of tissue whose thermal expansion is induced by a pulsed laser [1,2]. Light enters a scattering medium where a portion of the energy is absorbed by the tissue in the form of heat, and from this heat a thermal expansion of the tissue occurs. If this temperature increase occurs at a faster rate than the thermal relaxation time and, more importantly, the stress relaxation time of the tissue, an acoustic wave will propagate as a result of the photoacoustic effect. These acoustic waves are currently being measured using piezoelectric transducer arrays placed within a propagation medium at various locations relative to the tissue [1–3] as well as optical techniques such as interferometry using fiber-based detectors and micro-ring resonators for high-frequency ultrasound detection [1,3]. The goal of this paper is to model and evaluate the ability of the PBDT to measure the directionality of acoustic waves emitted in PAT.

The PBDT measures the deflection of laser beams focused through a propagation medium: in the present case, distilled water [4]. An acoustic wave, propagating through the medium, results in a refractive index gradient proportional to the pressure gradient produced by the acoustic wave. Probe beams are focused through the medium, and deflections occur at the intersection between probe beam and wavefronts. In a practical detector, the deflection angle is measured using a quadrant photodiode (QPD). Here, a computer simulation model is developed to predict the deflection of the probe beam and predict the points at which the probe beam will intersect the face of the QPD. A ray-tracing algorithm, for refractive index gradients, is developed in MATLAB to build upon $k$ -Wave simulations for acoustic wave propagation developed in [5–10]. The goal of the computer simulation model is to verify the directionality capability of the PBDT and compare to the results obtained in experiments.

In the past, PAT studies have been performed using tissue phantoms and in vivo measurements and have shown that PAT has the capability of imaging heterogeneous tissue samples with a resolution in the sub-millimeter range and a penetration depth of a few centimeters [1]. PAT has provided much promise in medical applications such as breast cancer imaging and foreign body detection, due to the limited penetration depth required in these applications. Applications such as breast cancer imaging can be achieved by illuminating the breast tissue inducing restricted expansion, such as in blood vessels, causing a pressure wave to propagate to the surface through a nondispersive pathway [1,2]. This pressure wave is a wideband ultrasonic transmission and to date is most commonly measured with piezoelectric transducers. The image can be reconstructed using time reversal or FFT-based methods applied to the piezoelectric transducer signal where the transducer can be variously shaped arrays depending on the application [1,2]. It is well known that optical absorption is closely related to physiological properties, such as oxygen saturation and hemoglobin concentration; thereby the magnitude of the acoustic wave propagating from the tissue source is directly related to the physiological properties of the tissue [1,2]. Improvements in acoustic wave sensors, specifically PBDT, could increase accuracy and speed of tissue image reconstruction through wave directionality measurement, passive measurement, and increased spatial resolution from the absence of the ringing effect. The ringing effect is the continued vibration of a piezoelectric transducer beyond the time course of the excitation pulse, i.e., the acoustic wave [11]. The duration of the ringing is determined by the time necessary to dissipate the mechanical and electrical energy after excitation ceases [11]. PBDT is immune to the ringing effect because the measurement of acoustic waves occurs from the deflection of a laser beam in accordance with Snell’s law; therefore the beam settles without the excess ringing seen with the mechanical transducer.

PBDT, however, cannot be reconstructed with point sensor algorithms; it must instead be treated as a line sensor [12–18]. Much work has been done in PAT concerning reconstruction algorithms based on line sensor topologies; specifically in [12–14] algorithms are presented for thermo-acoustic tomography and PAT with integrating line detectors. Future development of image-reconstruction techniques will be based on algorithms developed in these previous works; however, we hope to improve on the image-reconstruction quality and speed by adding the directionality information acquired through the PBDT technique and implementing multiple beams in hash geometry [19–22].

2. Theory

PAT is defined by the generation of acoustic waves from illuminated tissue, suspended in a nondissipative medium, and is described by Eq. (1) [1]:

(Δ - \frac{1}{ν_{s}^{2}} \frac{\partial^{2}}{\partial t^{2}}) p (r, t) = \frac{β}{c_{p}} \frac{\partial H (r, t)}{\partial t},

where

p

is the acoustic pressure,

β

is the isobaric thermal expansion coefficient,

Δ

is the Laplacian,

ν_{s}

is the speed of sound in the medium,

c_{p}

is the specific heat,

t

is time, and

H

is the density of the absorbed optical energy per unit time.

H

can be expanded by Eq. (2):

H (r, t) = A (r) I (t),

where

A (r)

is the absorbed energy density, and

I (t)

is the temporal function of illumination. Thereby the goal of PAT is to derive

A (r)

from the measurements of

p (r, t)

, the acoustic pressure at a point within the propagation medium. Measurements of

p (r, t)

are the focus of this paper and more specifically the ability to determine the directionality of

p (r, t)

from the deflection angle of the probe beam measured by the QPD.

3. Methods

A. Simulation Setup

The $k$ -Wave computer simulation developed in [4–10] calculates the propagation of linear compression waves in 3D homogeneous and heterogeneous media through implementation of $k$ -space techniques. This simulation has been expanded in this work to include the conversion of pressure to refractive index for ray-tracing purposes. The relationship between pressure and refractive index in a liquid is described by the Lorentz–Lorenz relation shown in Eq. (3):

\frac{n^{2} - 1}{n^{2} + 1} = \frac{4 π}{3} N α,

where

n

is the refractive index,

N

is the number of molecules per unit volume, and

α

is the mean polarizability. From past work [23], experimental results fit the Lorentz–Lorenz relation with slight deviation and the relationship between pressure (Pa) and refractive index (

n

) is shown to be linear for a fixed wavelength and temperature. Consequently, a linear relationship between pressure and refractive index was implemented for conversion in

k

-Wave simulation allowing for the prediction of the refractive index gradients within the medium over a time series. The linear relationship derived from [23] is seen in Eq. (5):

\frac{\partial n}{\partial p} = 1.39 \times 10^{- 5} k {Pa}^{- 1} .

The acoustic wave in PAT is produced by the illumination of soft tissue, and it has been shown that a temperature rise of 1 mK produces a pressure distribution of approximately 0.008 kPa [1]; however, in this paper we are concerned with relative signal amplitude and not absolute measurement. The

k

-Wave simulation will calculate the refractive index gradient of the 3D dataset for every time step of the simulation. The refractive index is stored in the dataset, and each refractive index value is mapped to a voxel at a certain point in time.

k

-Wave also allows for the analysis of phantoms with various shapes and composition, whose thermal expansion and acoustic emission can be described by Eq. (1).

A ray-tracing simulation is implemented to trace the ray path of the probe beam through the enclosure dataset, where the ray encounters a refractive index gradient as it intersects voxels along its trajectory. Voxel traversal is implemented to determine which voxels the ray intersects as it travels throughout the enclosure [24]. An enclosure with dimensions equal to the $k$ -Wave enclosure is mapped to the refractive index data from the $k$ -Wave simulation. A beam origin is defined as a position $μ_{0} = [x, y, z]$ outside the enclosure and an initial beam direction vector $v_{0} = [\partial x, \partial y, \partial z]$ is also defined. Each beam is made up of a user-desired number of rays with fully adjustable initial ray direction and position allowing for accurate representation of any probe beam laser source spot size and shape. In this simulation, we simulate only one ray, as the goal is to determine the ray trajectory, and we are not concerned with the effects of beam waist and spot size on the QPD surface. The voxel traversal is initiated at the origin, and the point at which the ray enters the enclosure is determined by Eq. (5). The intersection point on the enclosure boundary can be found by solving for step size $k$ while setting one of the coordinates of $d$ to the boundary of the enclosure plane first encountered by the beam:

d = u_{0} + k v_{0} .

Once the enclosure boundary intersection point

d

has been determined,

v_{k}

and

u_{k}

can be updated by implementation of Eq. (6). The refractive index values of the intersected voxels are contained in the

k

-Wave dataset. The ray direction will therefore be updated through Snell’s law for each spatial step

k

through the refractive index data set. The number of voxels per enclosure size can be adjusted to increase the trace accuracy. At the enclosure boundary,

n_{k}

is defined as the refractive index of air, and the first voxel intersected is defined as

n_{k + 1}

which is defined by the outer enclosure material; in this case, glass. Every spatial step the ray travels through the enclosure, the position vector

u_{k}

and the direction vector

v_{k}

are recalculated using Eq. (6). The full traversal from enclosure entrance point to enclosure exit point is done for each temporal step for which the

k

-Wave simulation was executed. For each temporal step,

k

-Wave provides a 3D dataset with refractive index values for that given temporal step number. To achieve increased time resolution, the

k

-Wave can be executed with smaller time step sizes at the cost of computation time. To determine the new direction of the ray at each spatial step,

k

through the data set, the vector form of Snell’s law is applied. At the boundary between two voxels, the incident ray refracts as defined by Eqs. (6a) and (6b):

V_{k - 1} = \frac{n_{k}}{n_{k + 1}} V_{k} + ((\frac{n_{k}}{n_{k + 1}}) \cos θ_{k} + \cos θ_{k + 1}) n_{k} n_{k} \cdot - V_{k} \geq 0,

where

V_{k + 1}

is the normalized vector of the resulting refraction,

V_{k}

is the normalized vector describing the direction of the incident ray,

n

is the normalized plane vector,

n_{k}

and

n_{k + 1}

are the refractive indices at both sides of the boundary, respectively, and

θ_{k}

and

θ_{k + 1}

are the incident and refraction angles at each side of the boundary, respectively. The parameter

n

, in the case of the spherical phantom explored in this paper, is defined as the line that intersects both the phantom origin and the point of intersection between incident ray

V_{k}

and the wavefront. This interaction between wavefront and incident beam is illustrated in Fig. 1. For the case of voxel datasets, the normalized plane vector

n_{k}

could be orthogonal to the intersected voxel boundary plane; however, because a spherical phantom has been chosen to illustrate the directional capability of PBDT,

n_{k}

can be calculated by using the technique illustrated in Fig. 1, which also leads to greater accuracy than would be possible if the voxel boundary was considered.

Fig. 1. Diagram of probe beam and acoustic wavefront interaction. The red arrows represent the probe beam at both sides of the wavefront tangent plane. $P$ is the acoustic source, $V_{k + 1}$ is the beam after the intersection boundary, and $V_{k}$ is before the intersection boundary.

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A visual diagram of the simulation model and all of the components is shown in Fig. 2. An initial pressure $P_{0}$ is defined as a photoacoustic waveform, which propagates through the simulated enclosure, based on wave propagation calculated with $k$ -space techniques. The probe beam can be defined as a bundle of rays with any given initial beam propagation, and optical elements such as lenses can also be implemented into the model. In this case, however, we only simulate one ray, as we are more concerned with simulation of the beam movement across the QPD face, then the effects of the probe beam waist on the time resolution.

Fig. 2. Diagram of the PBDT implementation.

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$P_{0}$ is the simulated photoacoustic pressure source, IP designates the point at which the ray is incident on the QPD. The ray travels through the enclosure, traversing Voxel 1 (V1) through Voxel 5 (V5) in increasing order; the ray encounters refractive index (n1) through refractive index (n5). The deflection angle is measured by the simulated QPD, and the $X$ and $Y$ signals are the output.

In simulation, a spherical phantom with a radius of 4 mm was placed inside an enclosure with a volume of $25 {cm}^{3}$ . The voxel volume is $25 {μm}^{3}$ , and the simulation contains 10,000 voxels. The phantom produces a photoacoustic emission from its shell, which has a 0.45 nm thickness; this has been configured in this way to simulate the experiment in which a copper-coated sphere is used. The optical absorption of copper at 535 nm is approximately 70% [25]. A ray was passed in three different locations, and the intersection point between ray and photodiode surface was recorded over time. A simulated QPD is implemented, with differential amplifiers resulting in two signals, $X$ and $Y$ , which were used to determine the location of the probe beam focal spot on the photodiode surface [19–22]. The horizontal and vertical signals ( $X$ , $Y$ ) are derived from the relative incident light intensity in quadrants $A$ , $B$ , $C$ , and $D$ as seen in Eqs. (7a) and (7b). Observing the phase and magnitude of the $X$ and $Y$ signal allowed for the reconstruction of the measured acoustic wave magnitude and propagation direction or trajectory as shown in Fig. 3.

Equations (7a) and (7b) illustrate how the signals $X$ and $Y$ are derived from the relative light intensity incident on the four quadrants $A$ , $B$ , $C$ , and $D$ .

X = \frac{(A + C) - (B + D)}{A + B + C + D},

The differential signal from the horizontal segments is the

x

axis output, and the differential segment from the vertical segments is the

y

axis output. By measuring the peak-to-peak amplitude of

X

and

Y

signals, the propagation vector angle

θ

of the pressure wave can be measured as

\tan θ = \frac{y}{x} .

The measured angle

θ

can be implemented into a reconstruction algorithm such as the 2D Radon transform [13–17]. The ray phantom orientations used for this simulation can be seen in Fig. 4.

Fig. 3. Schematic illustration example of the ability of the PBDT to measure pressure wave direction using a quadrant position detector.

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Fig. 4. Ray orientation looking down the $y$ axis; three different orientations were used in the simulations. Orientation #1 is 135° from the positive $x$ axis, orientation #2 is 90° from the positive $x$ axis, and orientation #3 is 45° from the positive $x$ axis.

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Three probe beam phantom orientations have been chosen for simulation. In the first orientation, the probe beam is oriented 135° from the positive $x$ axis, the second at 90° from the positive $x$ axis, and the third at 45° from the positive $x$ axis.

B. Experimental Setup

The experiment was designed to demonstrate the capability of the PBDT to serve as an acoustic vector sensor and determine the vector direction of photoacoustic waves. Detection was carried out by monitoring the deflection of an optical probe beam as shown in Fig. 5.

Fig. 5. Experimental configuration of PBDT with photoacoustic emission from a copper-coated sphere excited with OPO laser pulses at 335 nm wavelength, 10 ns pulse duration, 10 Hz pulse repetition rate, and 1 mJ output energy. The distance from probe beam source to QPD surface was approximately 50 cm.

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A sphere coated with copper with a 4 mm diameter was used as a sample. Most of the energy is absorbed in the copper coating of the sphere. The sample was immersed in a glass container with transparent windows to allow for optical access of the probe beam. Optoacoustic signals were elicited from the sample, using an optical parametric oscillator (OPO) Opolette HR 355 laser system as the pump and using 535 nm wavelength at 1 mJ energy. The pulse duration of the OPO was 10 ns, and the pulse repetition rate was 10 Hz. The unfocused beam from the pump laser was delivered through optics to illuminate the sample from above with a beam diameter of 6 mm, which covered the entire topside of the sample. A compact diode laser emitting at 670 nm, with 3 mW output power, and focused with a single convex lens, was employed as the probe beam. The probe beam of the diode laser was focused to a beam waist of approximately 75 μm above the sample, but translated at different locations as shown in Fig. 6. The 75 μm beam waist would correspond to a time resolution of 50 ns for the PBDT sensor or frequency response of 20 MHz. Position (1) was above the sample with location up and left from the center (approximately 142° from the positive $x$ axis), position (2) directly above the sample with (about 90° from the positive $x$ axis), and position (3) with location up and right from the center (about 48° from the positive $x$ axis). These angle orientations were measured manually and confirmed using the PBDT.

Fig. 6. Experimental setup diagram. Object was irradiated by an OPO pulsed laser and, through the photoacoustic effect, produced acoustic waves inside the water container. The red points labeled 1, 2, and 3 represent the probe beam orientations looking down the $z$ axis, i.e., directly along the direction of travel of the probe beam.

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A quadrant silicon photodiode (OSI Optoelectonics, model SPOT-9DMI) was chosen for its large active area (about 10 mm diameter) and fast response time as a position sensor. The signals from the four segments of the QPD were individually pre-amplified and then processed through differential amplifiers [19–22]. The $X$ and $Y$ signals obtained were derived using Eqs. (7a) and (7b).

4. Results

A. Simulation

The simulation calculates the trajectory of the beam through the enclosure as well as tracks the beam spot movement across the simulated QPD face and was used to simulate the $X$ and $Y$ signal obtained from the QPD. The signal width is related to the frequency-dependent attenuation of the acoustic emission acting as a low-pass filter, i.e., as the acoustic wave propagates, the high frequencies are attenuated; therefore the measured signal contains the low frequencies of the acoustic emission [26]. In the simulation, the predicted signal width was approximately 300 ns because only one ray was used, and changes in laser beam waist over the propagation distance were ignored. The probe beam photodiode intersection points are illustrated in Figs. 7–9. The $A$ , $B$ , $C$ , and $D$ quadrants are denoted such that they can be related to Eqs. (7a) and Eq. (7b).

Fig. 7. Probe beam orientation #1; 135° from the positive $x$ axis. (a) Simulated QPD and ray intersection points for the simulation duration from time 0 to 360 ns (ray spot location on QPD Face). (b) Simulated QPD $X$ signal. (c) Simulated QPD $Y$ signal.

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Fig. 8. Probe beam orientation #2; 90° from the positive $x$ axis. (a) Simulated QPD and ray intersection points for the simulation duration from time 0 to 360 ns (ray spot location on QPD face). (b) Simulated QPD $X$ signal. (c) Simulated QPD $Y$ signal.

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Fig. 9. Probe beam orientation #3; 45° from the positive $x$ axis. (a) Simulated QPD and ray intersection points for the simulation duration from time 0 to 360 ns (ray spot location on QPD Face). (b) Simulated QPD $X$ signal. (c) Simulated QPD $Y$ signal.

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The time series, of the simulated ray and QPD intersection points, shown in Figs. 7–9, associate unique ray diffractions with unique wavefront propagation directions. As can be seen from these figures, the probe beam movement across the photodiode surface is directly related to the orientation between the probe beam and the phantom in the enclosure. At 90° no $X$ signal is expected; however, the $Y$ signal will have its maximum amplitude. As the orientation approaches 45°, the difference in magnitude in the $X$ and $Y$ signal, approaches zero. Figures 7–9 illustrate this relationship for the three simulated orientations.

The distance from ray to phantom in simulation was set very small such that the simulation time could be limited. We are interested in the trajectory of a single ray; therefore simulating beam waist changes along the ray path is not necessary and has not been done. In this case, orientation #1 and orientation #2 have a ray to phantom distance of 35 μm; orientation #2 has a ray to phantom distance of 25 μm.

B. Experiment

The experimental results were obtained from exposures of a copper-coated sphere to the output of the OPO laser and consist of the actual $X$ and $Y$ signals from the QPD. The same three probe beam orientations were evaluated as those in simulation. Due to the copper coating of the BB used as the excitation object, which absorbed most of the optical energy, the QPD signal width is directly proportional to the coating thickness of the copper BB. The variance in the distances between probe beam and sphere is due to the physical constraints of the experimental apparatus. The signal width for orientations 1–3 is approximately 300 ns, the beam waist after focusing was approximately 75 μm, which gives a time resolution of approximately 50 ns or optical beam time frequency response of 20 MHz.

The distances between the copper sphere and the beam were estimated from the QPD signals as follows: orientation #1 had a distance of 1.2 mm, orientation #2 was 0.5 mm, and orientation #3 was 2 mm.

As can be seen from Fig. 10, the experimental $X$ and $Y$ differential signals match the predicted $X$ and $Y$ differential signals from the simulation results. These experimental results verify that the simulation accurately predicts the interaction between ray and acoustic wavefront and that further simulations can be utilized to optimize probe beam topology, i.e., determine the optimal number of probe beams that should be implemented, the optimal beam origins and the optimal beam shape. This simulation will allow for the optimization of future experiments as well as provide valuable insights into the physics of wavefront beam interaction for PAT, ultrasound, and other acoustic applications. The signal-to-noise ratio (SNR) for the QPD signals obtained in the experiment was not calculated directly; however, from observation, the signal power is much larger than the noise power, and therefore the SNR is sufficient to detect the acoustic wave direction without significant error.

Fig. 10. (Experimental) QPD voltage signal for the three probe beam orientations. (a) Probe beam located to left of tissue source at 142°. (b) Probe beam oriented at 90° relative to tissue source. (c) Probe beam to right of tissue source at 48°.

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5. Discussion and Conclusion

The PBDT is not only limited to PAT but can be applied to a wide variety of applications requiring acoustic wave vector detection, including ballistics, ultrasound, microscopy, etc. [27,28]. PBDT is an alternative to piezoelectric transducers because of the lack of the ringing effect [11] and the ability to measure wavefront directionality. PBDT only changes the method of acoustic wave measurement in PAT and does not change other aspects of classical PAT such as the effects of the coupling medium, tissue excitation, and the acoustic emission. For example, PAT with PBDT can be implemented for small animal imaging by submerging the animal in distilled water and exposing the animal to a pulse laser. The generated acoustic wave will propagate from the tissue into the distilled water coupling medium where it interacts with an array of probe beams. The probe beam array can be implemented to surround the target, such as a small animal, such that the array of probe beams sources and detectors is situated externally, i.e., outside of the water tank. Hash grid geometries can be implemented to simplify the PAT inverse problem for integrating line detectors. This imaging system can be implemented as a handheld device, where the entire acoustic wave sensing system, including probe beam and detector array as well as illuminating source, are contained within the handheld device. It should be noted that the output of the illuminating source will be governed by laser exposure safety limits [29]. The ability to limit probe beam and detector array size is predicted to decrease the size and cost of handheld PAT devices. PBDT is also expected to be a viable alternative to interferometry due to its simple setup and lack of calibration sensitivity; however, this needs to be explored further in future work. PAT based on PBDT will find a variety of biomedical applications such as breast cancer imaging, small animal imaging, foreign body detection, and photoacoustic microscopy.

The simulation, developed in the present work, provides the ability to track the probe beam focal spot on the photodiode surface and predict the $X$ and $Y$ differential signal for any simulated phantom. One of the intended uses of the simulation is to explore the effects of various probe beam phantom orientations, probe beam photodiode orientations, and the number of probe beams implemented in a given detector. With simulation, numerous topologies can be evaluated, and the most effective can be chosen.

The advantage of the wavefront directionality measurement, inherent to the PBDT, has been demonstrated in this paper. Measurement of wavefront directionality shows promise to improve image reconstruction speed and accuracy by providing extra information that can be used in the reconstruction algorithm. As mentioned in the paper, much work has been done in the reconstruction algorithms for PAT based on line detectors; however, none of this past work has implemented wavefront directionality into the reconstruction algorithm, and most work has been focused on interferometry. In conclusion, it has been shown that the direction of a wavefront intersecting a probe beam trajectory can be measured by observing the phase of the QPD $X$ and $Y$ signal.

This work was partly supported by a NSF grant (HRD-0932339), Drs. Demetris Kazakos and Richard Smith, project managers, and by the National Science Foundation Partnerships for Research and Education in Materials (PREM) grant no. DMR-0934218 in collaboration with Northwestern University MRSEC (RDG, SM).

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Probe beam deflection technique as acoustic emission directionality sensor with photoacoustic emission source

Abstract

1. Introduction

2. Theory

3. Methods

A. Simulation Setup

B. Experimental Setup

4. Results

A. Simulation

B. Experiment

5. Discussion and Conclusion

References

Cited By

Figures (10)

Equations (10)

Applied Optics