# A new directional acoustic lens: V-groove lens

Abstract: A new directional acoustic lens is introduced. The geometry is very similar to the line-focus lens except the lens cavity, which is shaped as a groove with flat-bottom V cross section. The slanted planar edges of the groove are inclined in order to generate waves incident on the object surface at a critical angle. Hence, the edges of the groove act like two wedge transducers facing each other. The cross section of the lens is the same as that of the Lamb Wave Lens. Therefore, it enjoys the same sensitivity to surface wave excitations. On the other hand, since the cross section remains the same along one of the lateral directions, it has directional properties very similar to that of the Line Focus Beam Lens. The waves normally incident on the object surface generated from the flat-bottom interfere with those at the critical angle, giving rise to a V(Z) effect. Calculated responses of the lens are presented for silicon (001) surface as a function of crystal orientation. The calculated curves are compared with measurement results. The leaky wave velocities are extracted from the measurement results using the conventional FFT algorithm. A new model based algorithm is proposed for extracting the velocity information from V(Z) data

## Summary (2 min read)

### Introduction

- The accuracy depends on the number of oscillations in the pattern.
- For high velocity materials the period is large, and thus there will be a limited number of oscillations, resulting in a low measurement accuracy.
- Lamb wave lens combines the V ( 2 ) effect with its higher efficiency of leaky wave excitation.
- First, the geometry of the V-groove lens is described and design considerations are discussed.
- Experimental results are presented and compared with the theory.

### V-Groove Lens

- V-groove lens differs from the line-focus-beam lens in the way the refracting element of the lens is fabricated.
- Essentially, the relationship between the LFB lens and the conventional lens is the same as the relationship between Vgroove lens and the Lamb wave lens [2] .
- Symmetrical sides of the groove causes a refraction, and hence two symmetrical beams insonify the object surface at the same incidence angle.
- Which encounter leaky wave modes on the object surface, with the reference beam resulting from the specular reflection of the normally incident beam produces the V(2).
- A good match between median direction of the refracted beam and the critical angle for the object improves the measurement accuracy.

### Simulations and Experiments

- Simulating the performance of a lens involves propagation of acoustic waves between the transducer and the refracting element.
- The wave front is then reflected from object surface upon propagation in liquid.
- While the circular symmetry of the Lamb lens allows the use of fast Hankel transform for propagation purposes, propagation problem in V-groove lens requires the more costly two dimensional FFT.
- Water temperature was stable within 0.2 degrees.
- The V ( 2 ) simulations are repeated along varying directions for the same surface of silicon.

### Leaky wave velocity extraction

- The conventional procedure A simple model is selected to reduce the computational complexity of the search process.
- The first term is due to the flat central portion of the V-groove lens and its phase is assumed to change linearly with the defocus distance.
- Since leaky waves are assumed to decay exponentially [7], the amplitude of the third term is exponentially dependent on the defocus distance.
- The parameters of the third term -among them is the leaky wave velocity of the objectis subsequently determined from the measured V ( 2 ) data on the object.
- Fig. 3 shows the measured squared difference data together with the results of the simple model whose parameters are optimized to best fit the data.

### Si

- The velocity estimates obtained from the same experimental data using model fitting method is depicted in Fig. 5 .
- The model assumes a single leaky wave excitation.
- It can be observed that the agreement between the extracted values and the calculations are significantly better, when there is no pseudo surface wave excitation.
- Obviously, in the presence of pseudo surface waves, a single model order can not match the inherent complexity of the data.
- Hence, the estimated velocity value falls somewhere between the two modes.

### Conclusions

- The proposed V-groove lens is proved to be a powerful tool for measuring leaky velocities with a good directional sensitivity.
- Since its excitation angle is fixed, a given V-groove lens can only be used for a limited range of velocities.
- Hence, a more accurate characterization is possible.
- The traditional approach is to use a FFT based spectral algorithm to find the velocities.
- The model makes use of all available physical and geometrical data with some unknown parameters.

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