6.2 Design algorithm
6.3.2 Measurement
The field generated by the fabricated surface profile was characterised experimen-tally. A fibre coupled Q-switched Nd:YAG laser (Minilite, Continuum, San Jose, CA, USA) was used to excite ultrasound from the fabricated sample. The pro-cess used to couple this laser is described in Appendix 1. The optical pulses had a wavelength of 1064 nm, a pulse length of 6 ns, pulse energies of ∼14 mJ, and an approximately Gaussian profile. Measurements of the acoustic field were made using the optical scanner described in Chapter 5.
A schematic of the set-up used is shown in Fig. 6.5. The fibre was attached to a circular tube with a length of 10 cm and a diameter of 2.5 cm. The natural diver-gence of the laser beam expanded the beam to 2.5 cm by the end of the tube. The surface profile was attached to a retaining ring which was connected to the other end of the tube. The front face of the surface profile was then immersed in water approx-imately 1 cm above the optical scanner. Signals were recorded over a 22.20×22.05 mm area using a step size of 0.15 mm. Four averages were taken at each position.
The 3-D wavefield was calculated from the experimental measurements using linear
Fabry-perot polymer film sensor and detection system
Water
Surface profile Sustaining ring
1.5 mm multimode optical fibre Q-switch YAG 1064nm
25 mm tube
Figure 6.5: Schematic of experimental set-up used for the characterisation of the acous-tic fields generated from the tailored optoacousacous-tic surface profiles. Figure reprinted from [180] under CC BY 4.0 License.
acoustic holography. Prior to this the data was band-pass filtered between 30 kHz and 6 MHz and was spatially up-sampled by a factor of 2. The filter was applied to remove low frequency noise introduced by the detection system and to limit the measurement data to the design bandwidth.
The experimental measurements were compared against a simulation carried out using the k-Wave toolbox. The simulation grid was 288×288×384 grid points with a spacing of 0.1 mm. The calculated hi j was up-sampled by a factor of 2 in (x, y) such that each position (i, j) was represented by 4 pixels, and then inserted as a source mask in the simulation. The medium for the simulation was inhomogeneous.
The backing material VeroClear was inserted as a region with a sound speed of 2495 m s-1and a density of 1190 kg m-3. The rest of the medium was set to a sound speed of 1500 m s-1 and a density of 1000 kg m-3. A bipolar pulse filtered at 6 MHz was used to represent the acoustic signal generated from the sample. The spatial profile
y-position (mm)
Figure 6.6: (a) Normalised peak pressure in the target plane of the surface in the simu-lation. (b) Normalised peak pressure in the target plane of the surface in the experimental data. Figure reprinted from [180] under CC BY 4.0 License.
of the laser was approximated by adding a 2-D Gaussian apodisation to the source.
This had a standard deviation of 5 mm.
6.3.3 Results
The peak pressure in the target plane of the surface for both the experimental data and the simulation may be seen in Fig. 6.6. In both cases, the numeral 7 has been clearly realised and the two show excellent agreement in the overall shape of the pattern, and in the low background pressure. The focal gain of the surface profile in the experimental data is 2. This gave pressures of approximately 60 kPa across the target pattern. The signal to noise ratio (SNR) in the target plane of the experimental data is 4.1. This was quantified by creating a mask encompassing the target pattern and calculating the ratio of the average peak pressure within the mask to outside it. The time window between the first and last occurrence of a peak across the target pattern was 2.6 µs. There are however noticeable differences in the amplitude
generated across the 7 in both datasets. As in previous Chapters, these are generated by variations in the apodisation of the sample in the experimental set-up compared to the simulation. However, in this case, this can’t be corrected via registration of the back-propagated pressure due to the complex shape of the source. In the future, pre-measurement of the apodisation Ai j in the experimental set-up for input into both the optimisation and the simulation would eliminate this variation.
6.4 Conclusion
This Chapter has demonstrated that complex patterned distributions of pressure can be generated with a single optical pulse by using tailored optoacoustic surface pro-files. An optimisation approach has been developed for the design of these profiles from an arbitrary set of input foci. This builds on the direct search approach re-ported in earlier Chapters, incorporating a new initialisation that ensures the surface is initialised in a smooth state that generates a high peak pressure across the target points. A modified version of this optimisation that allows for temporal control over the peak pressure has also been reported and numerically validated. This adjusts the cost function to reward increases in the pressure at the specified time points. This could also be applied to the algorithms described in Chapters 4 and 5. Finally, the design method has been experimentally validated and it has been shown that the calculated profiles can be fabricated using widely available, cheap, techniques such as 3-D printing.
Several factors determine the complexity of the acoustic fields that can be gen-erated and the focal gain and SNR that can be achieved with this method. The surface profile consists of a set of partial bowl transducers each centred on a target point and taking up a fraction of the aperture. The focal gain is therefore fundamen-tally limited by the aperture size, the centre frequency, and the total area occupied by the target pattern. However, the optimisation allows certain positions on the aperture to contribute to the peak pressure at multiple points, so the precise scaling varies with the distribution of target points and the bandwidth of the acoustic signal.
In addition to these factors, the performance also improves with smaller pixel size
and the sizes of features that can be realised in the pattern are diffraction limited.
There are several directions along which the work in this Chapter could be developed. First, the profiles could be combined with a modulated optical source for the generation of a narrowband spectra. This could enable the creation of op-toacoustic phase holograms by adapting the approach reported by Melde et al for single element piezoelectric transducers [17]. Second, the use of optimised nano-composite absorbers conjunction with the profiles could be investigated for in-creasing the achievable pressures. Chan et al [157] recently demonstrated that these composites can be spin-coated onto simple 3-D printed surfaces, however, the vi-ability of this method for more complex shapes needs to be established. Finally, different practical applications for the profiles could be explored. Focused laser generated transmitters are at present being investigated for use in cell cleaving and micro-bubble mediated drug delivery [92]. The method proposed in this Chap-ter would enable more precise shaping of the focus, or, for correction of medium-induced wavefront aberrations, improving the efficacy of these techniques.
Multi-frequency acoustic kinoforms
7.1 Introduction
The work in this thesis thus far has addressed the generation of arbitrary acous-tic fields using the opacous-tical generation of ultrasound. This modality has advantages namely, wide bandwidths, and ease of spatial modulation. However, at present, limitations on existing optical sources constrain the applications to which these methods can be applied. In this Chapter, the generation of arbitrary distributions of pressure using single element piezoelectric transducers is explored instead. This builds directly on work by Melde et al discussed in Sec. 2.4. Briefly, Melde de-veloped a new approach for generating complex, diffraction limited, acoustic fields from planar single element piezoelectric transducers [17]. This used 3-D printed surface profiles, dubbed acoustic kinoforms, that, when attached to the front face of a transducer, introduced a thickness dependent phase offset at each position due to variations in sound speed. These were used to map the output field of the trans-ducer onto different computer generated phase holograms, allowing the field to be diffracted onto different pre-determined acoustic fields.
This approach is extremely cheap to implement, foregoes the complicated driv-ing electronics required for 2-D arrays, and scales easily to MHz frequencies. How-ever, one drawback is that the acoustic field is fixed. Each kinoform is designed for a single driving frequency and target distribution (which can be multi-planar).
To overcome this limitation, multi-frequency kinoforms for which different target
distributions are encoded onto different frequencies could be used. The field at a particular depth could then be varied simply by altering the driving frequency of the transducer. This concept is illustrated by Fig. 7.1.
This Chapter investigates the design and properties of these multi-frequency kinoforms. In the next section, a modified direct search approach developed for the design of these kinoforms is introduced. This is then validated in Sec. 7.3 using two test cases, each designed to generate 3 target distributions at 3 distinct driving frequencies. Section 7.4 then reports a numerical investigation into the effect of different design parameters on the performance of these kinoforms. This is followed in Sec. 7.5 by the introduction of two extensions to the design algorithm improving its accuracy and flexibility. Finally, in Sec. 7.6 the conclusions of the work are presented along with future research directions.
The journal article in [184] has been modified and adapted to form parts of this chapter, with reprint permission under CC BY 4.0 License. The conference proceeding in [183]©IEEE 2017 has also been adapted.