Localized measurement of ultrasonic waves using a Fabry–Perot sensor illuminated by a Bessel beam

A. Interrogation System

To test the concept of interrogating an FP ultrasound sensor using a Bessel beam, a beam design was chosen that would provide a core diameter of 29 µm, with a depth of focus of 54 mm [24]. To visualize the beam’s characteristics, its 2D cross-sectional spatial intensity profile and angular spectrum [20] were calculated [25] and are plotted in Figs. 1(a) and 1(b). As expected, the profile shows the focused core surrounded by several concentric rings of decreasing intensity. Meanwhile, the angular spectrum comprises a single ring centered on 2.29° with a full-width half-maximum (FWHM) of approximately 0.05°.

To enable interrogating an FP sensor with this beam, an experimental system was constructed. The system is shown in Fig. 1(c). Briefly, light from a wavelength-tunable continuous-wave laser (TSL-550, Santec) was delivered via a fiber optic circulator to a collimator (F220APC-1550, Thorlabs). The resulting collimated beam was transmitted through a 5° axicon (AX255-C, Thorlabs), forming a Bessel beam. This beam was relayed at normal incidence to an FP sensor by a 4f system formed by two plano-convex lenses (LA1509-C-ML, Thorlabs). In these conditions, light reflected by the sensor propagated back through the system to the circulator, which delivered it to a photodiode connected to a custom-made transimpedance amplifier [11]. Amplified signals from the photodiode, encoding the reflected light intensity, were measured using an oscilloscope (PicoScope 6403D, Pico Technology).

For comparison, experiments were performed using an FP sensor interrogated using a conventional Gaussian beam with a waist (intensity full width at ${1/e}^2$ ) of 50 µm. A spatial intensity profile and angular spectrum were computed and plotted in Figs. 1(d) and 1(e), respectively. As expected, both are Gaussian distributed. In the angular spectrum case, the distribution contains polar angles ranging from 0° to about 1.1° (intensity full width at ${1/e}^2$ ). To interrogate the FP sensor with this beam, the system was adapted, as shown in Fig. 1(f). Briefly, light exiting the circulator was collimated by a different collimator (F280-APC, Thorlabs), then focused at normal incidence onto the FP sensor using a lens (LA1509-C-ML, Thorlabs). As before, the reflected light propagated back through the optical system to the photodiode via the circulator.

B. FP Ultrasound Sensor

To test the Bessel interrogation concept, an FP ultrasound sensor capable of attaining a high $Q$ -factor, free of confounding factors due to optical imperfections, was required. To meet this requirement, a custom FP sensor with a thick planar spacer layer formed of high-quality optical grade fused silica was fabricated. Compared to typical FP ultrasound sensors with thin-film polymer spacers [11], this conferred two main advantages. First, the thicker cavity allowed for a higher maximum $Q$ -factor. Second, the fused silica spacer afforded a high level of performance and confidence in a number of physical parameters including optical transparency [27], thickness uniformity [28], and surface smoothness [29]. A further property of the fused silica sensor was a lower compressibility. This led to a lower overall (ultrasonic) sensitivity. However, it did not limit our ability to fairly compare the different interrogation schemes.

To fabricate the FP sensor, a 500 µm thick fused silica layer was coated on both sides with 95% reflective dielectric mirrors. The mirrors were formed by alternating dielectric stacks of silicon dioxide ${\mathrm{S}\mathrm{i}\mathrm{O}}_2$ and zirconium dioxide ( ${\mathrm{Z}\mathrm{r}\mathrm{O}}_2$ ), with an optical thickness of a quarter of a chosen design wavelength of 1500 nm. To provide an acoustically matched backing layer, the sensor was affixed to a $2.5\mathrm{c}\mathrm{m}\times 2.5\mathrm{c}\mathrm{m}\times 2.5\mathrm{c}\mathrm{m}$ thick, anti-reflection coated-glass cube. For physical protection, the sensor was encapsulated in a 20 µm polyparachloroxylylene (PPXC) barrier layer [11].

C. Selection of the Sensor Bias Wavelength

Preparing the system for ultrasonic sensing required selecting an appropriate interrogation laser power and bias wavelength as described above. The bias wavelength was selected by measuring an ITF and choosing the wavelength that maximized the value of the function [12]:

where $d\mathrm{I}\mathrm{T}\mathrm{F}(\lambda )/d\lambda$ was the derivative of the normalized ITF, which is proportional to the change in reflected power per unit pressure per unit interrogation power. Meanwhile, the term $\mathrm{I}\mathrm{T}\mathrm{F}(\lambda )$ was the normalized value of the ITF, which is inversely proportional to the ultrasonic sensitivity because it determines the usable interrogation power without saturating the photodiode. To explain briefly, when making ultrasonic measurements, the interrogation power was chosen such that the power received by the photodiode was equal to a predetermined (high) value limited by the photodiode’s saturation point. In these conditions, a lower ITF value led to a higher interrogation laser power, thus a higher sensitivity.

A. On-Axis Sensitivity

To evaluate the relative on-axis ultrasonic sensitivity of the FP sensor interrogated using the Bessel scheme, ultrasonic waveforms obtained in response to a normally incident ultrasonic plane wave were compared to those obtained using a conventional Gaussian interrogation scheme.

First, measurements were made with the Gaussian scheme [Figs. 1(d)–1(f)]. Having set up the system, the sensor was insonified by an ultrasonic plane wave generated using a piezoelectric transducer (V380-SU, Olympus) with a central frequency of 3.5 MHz and a 67% bandwidth ( $-6\mathrm{d}\mathrm{B}$ ). The ultrasonic waves were coupled to the sensor using water. To provide a plane wave, the transducer was driven by a pulse provided by a pulser-receiver (DPR 300, Altana BYK). To ensure a signal well within the linear working range of the FP sensor, the driving signal from the pulser was attenuated with a 20 dB attenuator.

To calculate the bias wavelength, the ITF was measured by recording the reflectance of the FP sensor while sweeping the interrogation wavelength. The ITF was plotted in Fig. 2(a) labeled Gaussian. The ITF was asymmetric along the wavelength axis, with visibility around 0.5, a maximum gradient of approximately $40{\mathrm{n}\mathrm{m}}^{-1}$ , and a $Q$ -factor of $3\times {10}^4$ . Taking into account the thickness and mirror reflectivity of the sensor, the low visibility and asymmetry observed were an expected consequence of the Gaussian beam providing a poor match to the planar cavity modes [16,19].

Having measured the ITF, the sensor was biased as described in Section 2.C, and an ultrasonic measurement was made. The resulting waveform was plotted in Fig. 2(b) labeled Gaussian. The waveform contained a single bipolar pulse with the expected shape and time of arrival given the known characteristics and location of the transducer. The pulse had a peak amplitude of 0.59 V, and the FWHM of the positive peak was 115 ns. To examine the noise level, the measurement was repeated with the pulse-receiver switched off. The resulting waveform is plotted in Fig. 2(c). The root mean square (RMS) of the noise voltage was 1.9 mV for a 20 MHz bandwidth, indicating a signal-to-noise ratio (SNR) of 311.

The process was repeated using the Bessel beam interrogation scheme [Figs. 1(a)–1(c)]. As before, an ITF was measured and plotted in Fig. 2(a) labeled Bessel. Compared to the ITF obtained with a Gaussian beam, this ITF is more symmetric, with a higher visibility of 0.8, a higher peak derivative of approximately $72{\mathrm{n}\mathrm{m}}^{-1}$ , and a higher $Q$ -factor of $6\times {10}^4$ . These changes are in line with expectations, given the better mode matching between the Bessel beam and the planar FP cavity [30]. The ITF obtained with the Bessel beam also exhibited a high-frequency low-visibility ripple, likely parasitic interference due to an optical cavity being formed between the FP’s first mirror and the first surface (air–glass interface) of the glass backing.

As above, having obtained the ITF, the sensor was biased, and an acoustic waveform was measured and plotted in Fig. 2(b) labeled Bessel. Like before, the ultrasonic waveform contained the expected bipolar pulse with a similar shape. However, as expected, the bipolar pulse had a larger amplitude, with a peak value of 1.22 V, indicating an increase of approximately 2.1 times in the on-axis ultrasonic sensitivity. This increase was slightly larger than the increase in the optical sensitivity, due to the fact that the higher visibility enabled the use of a higher laser power without saturating the photodiode. The FWHM of the positive peak was 114 ns (similar to the value for the Gaussian scheme). To check the noise level, a noise-only measurement was made and processed as above and plotted in Fig. 2(c). The noise level was 2.1 mV, similar to the value obtained with the Gaussian beam system, indicating an SNR of 581.

B. Directivity

To examine the directivity of the FP ultrasound sensor interrogated with the Bessel and Gaussian schemes, the relative sensitivity as a function of the incident ultrasonic angle and frequency was measured for both the schemes.

The setup [Fig. 3(a)] was similar to the one described previously [31]. Briefly, ultrasonic waveforms were measured in response to broadband ultrasonic plane waves incident upon the FP sensor at a range of different angles [31]. The plane waves were provided by a laser ultrasound source comprising a 5 mm thick polymethyl methacrylate (PMMA) disk with a 4 cm diameter, coated with a thin ( $\approx 10\text{µ}\mathrm{m}$ thick) layer of black spray paint. The paint layer was irradiated by 4 ns pulses of light provided by a pulsed laser system (Photosonus X, EKSPLA) delivered via a multimode fiber with a diameter of 1.5 mm and a numerical aperture of 0.22. The wavelength of the laser light was 1064 nm, and the pulse repetition rate was 100 Hz. The absorption of the light in the paint layer resulted in the generation of a plane wave via the photoacoustic effect. It is estimated that the plane wave contained detectable frequency components ranging from below 1 MHz up to at least 40 MHz. To control the plane wave’s angle of incidence upon the FP sensor, the laser ultrasound source was mounted on a motorized rotation stage (PRM1/MZ8, Thorlabs), whose rotation was controlled using custom control software [32,33]. To ensure that the rotation point was co-incident with the interrogation point, the rotation stage was aligned such that the ultrasound wave arrived at the interrogation point at the same time, independent of the angle.

As before, measurements were first made using the Gaussian interrogation scheme [Figs. 1(d)–1(f)]. The angular range of the measurements was from $-{32}^{\circ }$ to 32° with a step size of 0.25°. At each step, 100 waveforms were acquired for averaging. To visualize the sensor’s response as a function of ultrasonic frequency, the averaged waveforms were Fourier transformed. The resulting frequency spectra were stacked together to form a 2D dataset, which is plotted in Fig. 3(b), hereafter referred to as a directivity map.

Broadly speaking, the directivity map appears consistent with previous directivity data obtained using FP sensors made of thick glass cavities [34]. The map is visually angularly symmetric, with regions of high or low sensitivity, and regions in which the response is relatively uniform as a function of angle, e.g., at $\pm {10}^{\circ }$ and $\le 8\mathrm{M}\mathrm{H}\mathrm{z}$ . Also evident, at certain angles, is a high sensitivity at all frequencies, e.g., at 15° and 27° [34].

The measurement was repeated using the Bessel interrogation scheme [Figs. 1(a)–1(c)]. The resulting directivity map was plotted in Fig. 3(c). As with the Gaussian scheme, the directivity map was angularly symmetric, with regions of relatively high and low sensitivity. Broadly speaking, the two maps look visually similar in terms of their spatial features.

To examine the data more closely, line profiles were extracted from the directivity maps at two orientations. First, a vertical line profile through the center was extracted, representing the frequency response at normal incidence. The resulting frequency responses were plotted in Fig. 3(d). The frequency responses are similar, both showing a smooth roll-off from low frequency to an apparent cut-off (around 10 MHz) as expected. Second, horizontal profiles were extracted at 1 and 5 MHz and plotted in Figs. 3(e) and 3(f). At 1 MHz, the angular responses of the two schemes were similar ( $<50\mathrm{\%}$ variation). However, at 5 MHz, the responses clearly differ. Specifically, although the response is similar at normal incidence, as the angle increases, the sensitivity afforded by the Gaussian scheme increasingly exceeds that of the Bessel scheme. Referring back to the 2D directivity maps and their associated colorbars, it is evident that there is a region of generally lower sensitivity in the Bessel case, in the higher angle, high-frequency region of the plot. In other words, the Bessel beam was more directional at higher ultrasonic frequencies.

C. Spatial Resolution in PAT Imaging

To evaluate the spatial resolution when performing PAT imaging, an experiment was designed to enable imaging of a resolution phantom using a single detection point on the FP sensor.

The setup was similar to the one described previously [15]. Briefly, as shown in Fig. 4(a), a pulsed laser was used to excite photoacoustic waves in a phantom, which was mechanically scanned along two dimensions parallel to the plane of the FP sensor. Translating the phantom in this way, while detecting photoacoustic waves at one fixed position defined by the interrogation point on the sensor, allowed for emulating the detection of the waves at different positions as in a traditional FP-based PAT system in which the interrogation beam is scanned across the sensor surface [11].

The phantom was made of seven synthetic hairs with a diameter of approximately 60 µm. The hairs were oriented along the $y$ axis, where the $z$ axis was the axis normal to the FP sensor, as illustrated in Fig. 4(a). To generate the photoacoustic waves, the hairs were illuminated with a 4 ns pulsed laser with a wavelength of 1064 nm generated by a 100 Hz Photosonus X (EKSPLA). To homogenize the fluence and serve as a coupling medium for the ultrasound waves, the phantom was submerged in a liquid solution with a scattering coefficient of around $10{\mathrm{c}\mathrm{m}}^{-1}$ . The solution was made by diluting 20% intralipid in water with a ratio of 5%. To translate the phantom, it was mounted on two motorized linear stages (PT1-Z8 and MTS25/M-8, Thorlabs). While the phantom was scanned along the $x$ axis, photoacoustic waveforms were measured every 25 µm across a total scan range of 2 cm. Meanwhile, the $y$ axis location was varied in steps of 500 µm across a total scan range of 1 cm. The measured photoacoustic waveforms were stacked together along $x$ and $y$ to form a photoacoustic time series dataset. Using this dataset, a PAT image was reconstructed using a time reversal algorithm [35], assuming a sound speed of $1480{\mathrm{m}\mathrm{s}}^{-1}$ (water at 20°C).

Imaging was first performed while using the Gaussian interrogation scheme. A cross-sectional slice through the resulting photoacoustic time series dataset is plotted in Fig. 4(b). As expected, seven parabolic wavefronts were visible, one for each of the hairs, along with seven negative V-shaped artifacts [one of which is highlighted by the arrow in Fig. 4(b)]. The corresponding PAT image is plotted in Fig. 4(d). As expected, all seven hairs were visible in the image, along with V-shaped artifacts.

The process was repeated using the Bessel interrogation scheme. The resulting photoacoustic time series dataset is plotted in Fig. 4(c). Again, seven parabolic ultrasound wavefronts were seen with accompanying V-shaped artifacts. The corresponding PAT image is plotted in Fig. 4(e). As before, the seven hairs were visible with the V-shaped artifacts. However, as compared to the image obtained using the Gaussian beam, the hairs appeared visually more blurred out in the $x$ direction.

To evaluate the spatial resolution, axial and lateral line profiles were taken through the center point of one of the hairs and plotted in Fig. 4(f). As expected, the profiles each contain a peak corresponding to the cross-section of the hair. The axial profiles were similar, with FWHMs of 80 µm and 112 µm for the Gaussian and Bessel schemes, respectively. However, the lateral profiles differed significantly, with the Bessel scheme yielding a significantly broader width (492 µm) compared to the Gaussian (112 µm). Beyond their widths, the Bessel scheme profiles have a lower peak intensity as compared to the Gaussian. Thus, in addition to the Bessel scheme providing a 4–5 times poorer lateral resolution, it also yielded lower image contrast (despite providing a higher on-axis ultrasonic sensitivity in Section 3.A).