Spatial distribution

Equation 2.17 shows that the spatial distribution of initial pressure depends on the optical fluence φ (r) incident on each point, as well as the optical absorption µ(r) and Gruneisen parameter Γ(r) at that location. It isn’t possible to arbitrarily control the fluence incident at each point across a volume, as the light reaching a point is non-linearly dependent on the optical absorption elsewhere in the medium. How-ever, it is possible to control the fluence across a planar absorber.

Two spatial distributions are most commonly reported in the literature: annular patterns, and diffraction gratings. Exciting an annular (or ring) shaped distribution creates an inward and outward propagating wave on the surface of a material. This inward propagating wave constructively interferes along the axis through the centre of the ring. This results in an increased signal amplitude and allows the optical en-ergy to be distributed across the surface to avoid ablation [70]. The field generated by a ring shaped initial pressure is shown in Fig. 2.9. In comparison, exciting a diffraction grating (or series of lines) allows the generated acoustic spectra to be controlled [98] and the directivity to be enhanced [99]. For a series of lines gener-ated on a planar surface, the acoustic signal measured, in the same plane, perpendic-ular to the grating consists of a set of acoustic pulses arriving with an even spacing

∆t determined by the sound speed and the line separation. The acoustic spectra therefore has peaks at f = _∆t¹ and its harmonics. Out of plane, the peak frequency varies, as the temporal spacing ∆t changes as a function of the detection angle. This variation can be described using the grating equation d sin θ = nλ [100], where λ is the wavelength of the peak frequency. This is demonstrated by Fig. 2.10, which shows the peak frequency recorded in a simulation of a diffraction grating pressure distribution as a function of detection angle.

Source Transverse slice Axial slice

Figure 2.9: Illustrative figure of using an annular source pattern. Constructive interference is generated at the ring’s centre and along the axis passing through it.

Angle

grating meas

Peak freq

Time

Pressure

Simulation Source

Figure 2.10: Illustrative figure of using a diffraction grating source pattern. The time series perpendicular to the array consists of a train of pulses. The repetition fre-quency of the pulses is determined by the grating spacing and the angle of the detection point to the array. These can be related using the grating equation.

In order to generate an annular pattern, a positive axicon lens with a conical surface can be used. Dixon et al [101] and Cielo et al [102] both used this approach then measured the peak amplitude of the resulting surface waves as a function of radial distance from the centre. Increases in the peak pressure by factors of 7.5 and 20, respectively, were measured at the focus. An alternative approach was reported by Wang et al [103, 104] who altered a laser cavity to generate optical pulses with a ring shaped profile. These pulses were made incident on an aluminium plate and the generated signal was measured on the far side. The presence of defects within the plate was found to result in conversion between different acoustic modes which could be identified in the generated signal.

To generate diffractions gratings, the most common method is the transient grating technique (TG). A single laser pulse is split in two, then made to interfere on the surface or interior of a sample. The interference of the two pulses creates a fringe pattern with a spacing determined by the angle between the two. This has been reported by both Cachier [105] and Maznev et al [106], and has been used to study transient changes in materials on femtosecond timescales [107]. An extension

to this method is to frequency shift one of the two laser pulses. In that case, a grating is generated which sweeps across the surface of the sample. This sweeping speed can be matched to the phase velocity of the excited frequency to further amplify the signal [108]. Diffraction gratings can also generated with a variety of optical elements. For example, using a cylindrical lens combined an optical diffraction grating [109], lenticular arrays (an array of cylindrical lenses) [100], and optical masks [110].

Arbitrary 2-D spatial distributions of pressure can be generated by using opti-cal holograms to control the incident fluence. As discussed in Sec. 2.1.4, hologra-phy can be used to manipulate patterns of optical intensity in 3-D by modulating the phase or amplitude of coherent light across a 2-D aperture. Holograms that generate a desired distribution of light can be calculated using the CGH algorithms described in Sec. 2.1.5. These can then either be physically fabricated using etching [111] or lithography [112] (among other techniques), or more commonly displayed on a spa-tial light modulator (SLM). SLM is a general term for devices able to dynamically modulate the phase, amplitude, or polarisation of an incident optical field. They come in various forms: electro and acoustic-optic modulators, digital micro-mirror devices (DMD), and liquid crystal (LC). Of these, the latter two are the most com-mon for this application. Both consist of arrays of microscopic pixels, in the former, mechanical mirrors that can switch ‘on’ or ‘off’ to modulate the amplitude, and in the latter, liquid crystal cells with an electronically variable refractive index which can modulate the phase. These have been employed in a number of works. For example, Zamiri et al utilised a LC SLM to generate an annular pattern for the de-tection of flaws [113], while Kalms et al used one to tailor the shape of the incident optical intensity to match the physical structure of a composite being tested [114].

Rather than modulate the incident fluence, it is also possible to pattern the ab-sorbing layer itself. In this case, the pressure distribution is controlled by differences in absorption µ(r) and photoacoustic efficiency Γ_α(r) over this layer. Stratoudaki et al have developed cheap optical transducers (CHOTs) which utilise this approach [115]. These are patterned absorbers that can be deposited onto samples for

re-mote inspection with a laser. They constrain the spectrum of the resulting acoustic waves allowing for narrowband detection, improving signal to noise (SNR). Both diffraction grating and Fresnel zone plate patterns have been manufactured using this approach, for application to surface [116, 117] and longitudinal acoustic waves [118], respectively. This was also reported much earlier by Von Gutfeld, who also used a zone plate pattern to focus 10 MHz waves off axis [119]. Compared to mod-ulation of the incident fluence, this approach is significantly easier to implement, and the cost is lower. The disadvantage is that dynamic variation of the generated pressure is not possible. The relative efficiency of the two methods depends on the light utilization efficiency of the SLM.