2.1.

Theoretical Background

The relevant theory governing LUS signal generation in fluids is reviewed in the literature.^{11,12,36–40,42} For a thorough theoretical explanation of LUS see Refs. 11 and 12. The physical mechanism for generating an LUS signal is summarized as follows: (1) a short duration laser pulse impinges on an optically absorptive surface of a material, such as water or biological tissue, (2) the optical energy rapidly and locally converts into localized heat at the laser spot location,⁴⁴ (3) nearly instantaneous expansion of the material due to the localized heating creates a concentration of mechanical stress within the irradiated material, and (4) this stress imbalance dissipates via the propagation of an acoustic pulse from the irradiated region into the material volume. The propagating acoustic pulse is the laser-induced ultrasound wave, the LUS source, which can be utilized for imaging. For this process to occur as described, optical, thermal, and acoustic conditions need to be met by the material and laser pulse. The most critical condition is being the significant absorption of optical energy at the sample surface, relative to optical transmission into the tissue.

This optical condition is described by the characteristic optical penetration depth of light into the material, defined by $l$, with units of (m), as shown in Fig. 1(a). The optical intensity, with units of ($\mathrm{W}/{\mathrm{m}}^2$), of incident light as a function of depth into an absorptive and scattering medium is described as

Fig. 1

Schematic of the three experimental setups employed. (a) Experimental setup one: the generation laser is used to excite an acoustic wave at the surface of the tissue sample, which is detected by the piezoelectric transducer at the bottom of the sample. (b) Experimental setup two: a piezoelectric transducer is lightly contacted with the top of the tissue sample and emits an acoustic wave, which is detected by the piezoelectric transducer at the bottom of the sample. (c) Experimental setup three (imaging setup): the generation laser excites an acoustic wave at the surface of the tissue sample, which is detected by the piezoelectric transducer at the surface of the sample. The mirror scans the generation laser spot along the surface of the sample and the two steel rods serve as test targets.

The thermal condition is the rate of thermal conduction within the material compared with heating time. By analyzing the diffusive terms in the heat equation,¹² one arrives at the equation

The acoustic source condition requires what is often called “stress confinement” in the literature. Physically, this condition means that the mechanical energy generated by the thermal expansion of the material cannot propagate away quicker than the rate of energy delivery.

This condition requires

When the conditions are met, an LUS acoustic source can be efficiently generated in biological tissue.^21,30,31 For biological tissues, with a sufficiently large laser spot diameter, all three conditions are met for optical wavelengths from 800 to 2000 nm.

Theoretical models for an LUS wave in pure water with a smooth surface show that the frequency-domain expression for the waveform is given by Eq. (5) in Ref. 12 and is presented again here with slightly different nomenclature as:

Acoustic attenuation, $\alpha$, is also important when using LUS to image biological tissue. Acoustic attenuation is due to heating and scattering within the tissue. In human tissue, $\alpha =0.5$ to 2 (dB/cm MHz)and in bovine muscle values of 2 to 3 (dB/cm MHz) have been reported.^47,48 Acoustic absorption impacts the depth- and frequency-dependent amplitude, $A$, of an acoustic wave exponentially, as given as

2.2.

Experimental Setup

Three hardware configurations [Figs. 1(a)–1(c)] are utilized for the experiments. The first configuration [Fig. 1(a)] uses the LUS generation laser for exciting an acoustic wave at the surface of the sample and the second configuration [Fig. 1(b)] uses a piezoelectric transducer to generate an acoustic wave at the surface of the sample. The second configuration is employed to isolate the impact of tissue surface roughness for comparison with data from configuration one. The third setup is a pulse echo imaging setup [Fig. 1(c)] that consists of an LUS generation laser to excite an LUS source at the surface and a contact piezoelectric transducer to receive the reflected and direct arrivals from the LUS source.

The generation laser is a Continuum 9030 Panther ($30\text{pulses}/\mathrm{s}$, 9 ns pulses) tunable optical parametric oscillator laser, operating at discrete optical wavelengths from 800 to 2000 nm stepped in 50-nm increments. About 2000 nm is the maximum wavelength used due to generation of laser hardware constraints and significant reductions in the acoustic source amplitude beyond 2000 nm. More specifically, the optical penetration depth becomes much smaller than the acoustic wavelengths of interest causing significant reductions in LUS source efficiency [see Eq. (5)] at the acoustic frequencies of interest (0.5 to 5.0 MHz). Further, theoretical exposure thresholds for skin are 10 times lower beyond 2600 nm. The beam from the laser passes through an adjustable attenuator to a mirror, which directs the beam through a 3-mm iris and then onto the sample. Beneath the iris is a removable power meter to measure the optical power reaching the sample [Fig. 1(a)]. The tissue sample lays underneath the iris on the transducer mounting-bracket, which is mounted on an $x-y$ stage rigidly secured to the optical table [Fig. 1(a)]. The $x-y$ stage enables centering of the laser spot above the piezoelectric acoustic receiving transducer (Olympus V1091). The transducer mount serves as a rigid mount for the transducer and ${\text{Aquasonic}}^{\mathrm{R}}$ 100 ultrasound transmission gel couples the transducer to the tissue sample. The transducer has a 5-MHz center frequency and a usable bandwidth between 0.5 and 8.0 MHz. The piezoelectric, disk-shaped element in the transducer is 3.0 mm in diameter yielding a far-field distance of $\sim 3\mathrm{cm}$ at 5 MHz. A piezoelectric transducer is selected to measure the waveforms to avoid variability in vibrometer sensitivity and SNR due to variation in tissue optical properties between samples. A piezoelectric transducer guarantees consistent detection behavior across different tissue types and samples. After the waveform passes through an Olympus 5077 PR pulser-receiver with a 50-dB gain and a 10-MHz lowpass filter, a Tektronix TDS 2024B 200 MHz oscilloscope digitizes the waveform for collection.

The second setup uses two of the same piezoelectric transducers previously mentioned. The source–transducer connected to an Olympus 5077 PR pulser-receiver is mounted to an adjustable bracket fixed to the optical table. The pulser-receiver generates a one-and-a-half cycle square wave with $0.7\text{-}\mu \mathrm{s}$ duration peaks. The source transducer is centered above the receiving transducer and lightly contacted with the tissue sample using the adjustable mounting bracket. Ultrasound gel couples the source and receives transducers to the sample. The waveform acquisition setup and receiving transducer configuration are identical to the first setup.

Three sample types are tested, bovine muscle, chicken breast with skin, and a pork hock bought from the butcher and approved for use under Massachusetts Institute of Technology Committee on Animal Care protocol number E17-09-0320 for use of animal tissue. All tissue samples are at least 3.5 cm in height such that all data with frequency content $<5\mathrm{MHz}$ are in the far field of both the transducer and LUS source. The bovine sample contains only muscle and fat, while the chicken and pork samples both have skin at the surface with muscle and fat tissue underneath.

The data collection process using the first setup starts by centering the laser spot above the transducer. Next, the generation laser wavelength is manually swept from 800 to 2000 nm at 50-nm increments. Across the spectrum of wavelengths, the laser power is kept at 7.5 mW with a spot area of $0.071{\mathrm{cm}}^2$ (3-mm diameter) yielding a fluence of $3.54\mathrm{mJ}/{\mathrm{cm}}^2$ per pulse, which is skin safe across the entire evaluated optical spectrum to avoid tissue damage. Consequently, this fluence level is also eye safe for wavelengths between 1500 and 1800 nm⁴⁹ with a safety factor just under 10 (30-Hz pulse frequency). The laser power at the samples remains constant by checking the power meter after changing the laser wavelength and correcting the attenuator as needed to maintain constant power.

At each optical wavelength, the LUS source generated by the laser pulse is saved on the oscilloscope for postprocessing, resulting in 25 waveforms for each tissue sample tested. Signals with insufficient SNR are omitted from the dataset.

The data collection process using the second setup starts by centering the source transducer above the receiving transducer. Next, an acoustic pulse propagates from the source transducer through the tissue to the receiving transducer. An oscilloscope attached to the receiving transducer digitizes the incident acoustic waveform on receiving transducer and the resulting data are saved on the laptop for postprocessing. Only data on the bovine samples are collected using the second setup.

The third setup [Fig. 1(c)], referred to from here on as the imaging setup, uses all the same hardware as setup one except the iris is removed to allow scanning of the generation laser spot. The beam diameter at the surface of the sample is 2 mm and the pulse energy is 0.8 mJ, yielding skin safe optical exposure levels from 810 to 2000 nm. The transducer position is now on the sample’s top surface just like the generation laser spot. The data acquisition setup is identical to setup one. The sample under test is bovine shoulder muscle purchased from the butcher with two small metal wires inserted into it.

The data collection process using the imaging setup consists of scanning the generation laser a distance of 5.4 cm in the $x$-direction in 0.54-mmdiscrete steps along the sample surface starting 0.5 cm from the transducer [Fig. 1(c)]. At each of the 101 scan locations, the generation laser excites an LUS source and the transducer, which remains fixed for the scan, records the direct and reflected wave arrivals. Four scans using generation laser wavelengths of 810, 1064, 1550 and 2000 nm comprise the dataset from the imaging setup. The analog gain on the transducer remains constant across all scans. An SAFT algorithm¹⁰ is used to generate an ultrasound image from each scan yielding four images from four different generation laser wavelengths on the same target.

3.1.

Waveforms and Spectra

The LUS source signals in the bovine sample, measured with experimental setup one, exhibit a similar form to LUS source signals observed in water^11,12 [Fig. 2(a)]. The data in Fig. 2(a) are from the bovine samples, data for the pork and chicken are similar and are shown in Sec. 6 Appendix. The spectra of the signals exhibit a peak near 1 MHz and a steady decay in amplitude until the noise floor of the data is reached, near 3.5 MHz, depending on the optical wavelength used [Fig. 2(b)]. The decay in the spectral amplitude with frequency [Fig. 2(b)] is not due to the transducer response, which is shown by the dashed line in Fig. 2(b). The downward slope of the spectra after the 1-MHz peak is roughly twice the expected value for acoustic power law absorption for bovine muscle of $-2.9\frac{\mathrm{dB}}{\mathrm{cm}\mathrm{MHz}}$.⁴⁷ There is also energy that arrives after the first peak in the time-domain signals [Fig. 2(a)], which suggests multiple scattering along the propagation path. It is also possible that scattering of the rough sample surfaces is accounting for the late arrival of energy.

Fig. 2

LUS source waveforms and spectra representative of the full dataset for the bovine sample. (a) LUS source waveforms collected from the bovine sample. (b) Spectra of the waveforms in (a) calculated with a Hanning window roughly over the $-1$ to $1\mu \mathrm{s}$ interval and the frequency response of the receiving transducer.

The SNR of the waveforms collected from the chicken sample at the optical wavelengths of 800 and 850 nm is sufficiently low that the waveforms are excluded from the results. Waveforms from the pork sample at optical wavelengths of 800, 850, 900 and 950 nm are also excluded for the same reason. None of the waveforms collected on the bovine sample are excluded from the results.

3.2.

Impact of Surface Roughness and Attenuation

The impact of surface roughness can be assessed by comparing waveforms collected using setup one (LUS source) with waveforms from setup two (piezoelectric source). In Fig. 3(a), an LUS source signal generated with a 1550-nm pulse in a bovine sample (gray line) is compared with a signal generated by a piezoelectric transducer from setup two (thick black line). The signals are collected on the same sample along the same acoustic path using the same receiver. The LUS signal is also compared with theoretical predictions (thin black line and dashed line).

Fig. 3

Time-domain waveforms and spectra from the bovine sample acquired using experimental setup one and two plotted with theoretical predictions. (a) Time-domain waveforms. The thick black line is the data from setup two using piezoelectric transducer to send and receive the acoustic signal. The gray line is the LUS source waveform acquired in the bovine sample with a 1550-nm wavelength optical pulse. The thin black line is Eq. (6) corrected for acoustic attenuation in bovine muscle ($-2.9\frac{\mathrm{dB}}{\mathrm{cm}\mathrm{MHz}}$), the transducer response, and a surface roughness factor of $\sigma =3.4\times {10}^{-4}\mathrm{m}$. The dashed line is Eq. (5) corrected for the transducer response. (b) The spectra of the signals in (a) with the same line coding. Note the steeper decrease in signal amplitude with frequency for the data from experimental setup one (gray line) compared with setup two (thick black line).

The theoretical prediction (thin black line) for the LUS source waveform using Eq. (6) is corrected for acoustic attenuation, surface roughness, and the transducer frequency response to best predict the observed data collected from the experimental setup and shows good agreement with the observed LUS source signal (gray line) [Figs. 3(a) and 3(b)]. As the acoustic data are not calibrated, Eq. (6) is arbitrarily shifted vertically to compare with the observed data. The key parameters put into the theoretical prediction are ${\mu }_a=730{\mathrm{m}}^{-1}$, $\sigma =3.4\times {10}^{-4}\mathrm{m}$, and $\alpha =-2.9\mathrm{dB}/\mathrm{cm}\mathrm{MHz}$. The value for $\sigma$ is the value that minimizes the mean square error between the model [Eq. (6)] and the data over the 0.5 to 2 MHz spectral band. The values for ${\mu }_a$ and $\alpha$ are taken from the literature.^45,47 The spectra of the time domain signals from Fig. 3(a) are shown in Fig. 3(b). Both spectra are sloping downward as expected. The negative slope of the spectra from setup one is significantly greater than the downward slope from setup two. As both signals experience the same acoustic attenuation, the results suggest surface roughness impacts the bandwidth of LUS signals. The nulls in the spectra from setup two at 2.75 and 5.75 MHz are intrinsic to a square pulse waveform. This comparison is not shown for other tissues because reliable estimates of $\alpha$ for other tissues are not available in the literature.

The experimental LUS signal from the bovine sample in Figs. 3(a) and 3(b) shows agreement with the “corrected” theoretical curves and thus the hypothesis that acoustic absorption and surface roughness play a significant role determining the LUS source characteristics. The dashed lines in Figs. 3(a) and 3(b) are the theoretical prediction for an LUS source waveform generated on a smooth pure-water surface corrected only for the receiving transducer frequency response.

The experimental results are wider in the time domain [Fig. 3(a)] and narrower in the spectral domain [Fig. 3(b)] (gray line) compared with the theoretical predictions for pure water. This is due to surface roughness and attenuation that affect LUS source waveforms in biological tissues. Data collected on water, not shown, are similar to the theoretical curves with high SNR from 1 MHZ up to 9 MHz as well as a narrow pulse.

3.2.1.

Signal power as function of absorption

As shown in Eq. (5), the energy of the LUS source signal should strongly depend on ${\mu }_a^2$ for the experiments conducted. As shown in Figs. 4(a)–4(c), the energy as a function of optical wavelength for each tissue closely follows the ${\mu }_a^2$ curve for water. The energy of the LUS source signals from bovine, chicken, and pork samples as well as the energy compensated by the efficiency factor from Eq. (5) versus optical wavelength are shown in Figs. 4(a)–4(c) on a logarithmic scale. On the second $y$-axis, ${\mu }_a^2$ for water⁴⁵ is plotted on a logarithmic scale [Figs. 4(a)–4(c)]. The energy of an LUS source signal is calculated by integrating the spectrum of each waveform in the 0.5- to 2.5-MHz band.

Fig. 4

Dependence of signal energy uncorrected for efficiency; see Eq. (5) as a function of optical wavelength as compared with ${\mu }_a$ of water for bovine, chicken, and pork samples. (a) Signal energy vs. optical wavelength for bovine sample. (b) Signal energy versus optical wavelength for chicken sample. (c) Signal energy versus optical wavelength for pork sample.

3.2.2.

Impact of generation laser optical wavelength on image quality

The images formed, using an SAFT technique,¹⁰ from the data collected using the third experimental setup clearly show the two rods imbedded in the bovine sample as well as the sample–table interface [Figs. 5(a)–5(d), Fig. 1(c)]. The brightness of the rod and sample-table interface increases with optical wavelength of the generation laser, illustrating a strong dependence of image SNR on the generation laser wavelength for biological tissues [Figs. 5(a)–5d)]. The wires are the bright spots in the images at $z=2.25\mathrm{cm}$ and $z=1.75\mathrm{cm}$ and are indicated schematically by the green dots in Figs. 5(a)–5(d). The rod at $z=2.25\mathrm{cm}$ is not perfectly perpendicular to the imaging plane and fades in and out of the image from $x=1.5$ to 3.0 cm. The bright return at $z=4.0\mathrm{cm}$ is the sample–table interface. The interface appears brighter than the rods despite being located at larger range, because it is a stronger reflector and scatterer of acoustics waves compared with the rods. The interface appears to lift and disappear for $x>3\mathrm{cm}$, this is likely due to side lobe interference and the specular reflections of the boundary. Specular reflections are not always imaged well using SAFT techniques because SAFT was developed for imaging point scatterers¹⁰ like the rods. The energy in the image between the rods and the table is interference likely due to side lobes from the sample–table interface and internal reflections and mode conversion in the elastic rods. All images are acquired on the identical sample with matching scan patterns and displayed on matching color scales.

Fig. 5

Dependence of image quality on the generation laser wavelength. All images are shown on a 32-dB dynamic range and are acquired on the same sample at the same location using identical fluences. The green dots indicate the approximate locations of the metal wires in the images. (a) Image resulting from the dataset using a 810-nm generation laser wavelength. (b) Image resulting from the data set using a 1064-nm generation laser wavelength (c) Image resulting from the dataset using a 1550-nm generation laser wavelength. (d) Image resulting from the dataset using a 2000-nm generation laser wavelength.