Spatial Resolution Limits for Needle Hydrophones from 0.5 to 20 MHz with Implications for Transcranial Ultrasound.

Hydrophone spatial resolution and spatial averaging effects are determined by the frequency-dependent effective sensitive element diameter d_eff(f) rather than the geometrical sensitive element diameter d_g. The objective of this work was to quantify average d_eff(f) for needle hydrophones as a function of d_g and f. Estimates of effective radii a_eff(f) = d_eff(f) / 2 were inferred from directivity measurements from 0.5 to 20 MHz on 16 needle hydrophones with d_g = 2a_g ranging from 75 to 1000 μm (139 hydrophone / frequency combinations). Effective sensitive element diameter d_eff(f) exceeded d_g by over 100 % when λ > 4d_g (where λ is the wavelength). For ka_g > 0.75 (where k=2π/λ), d_eff(f) was consistent with the "rigid piston" (RP) theory, reinforcing a previous report from our laboratories. However, for ka_g < 0.75, d_eff(f) showed noticeable deviations from RP theory and fell between predictions from RP theory and predictions for an unbaffled (UB) circular piston. Examples: 1) For a needle hydrophone with d_g = 75 μm at 1 MHz (ka_g = 0.16), the data imply that average d_eff = 505 μm. 2) For a needle hydrophone with d_g = 400 μm at 500 kHz (common parameters for human transcranial neuromodulation; ka_g = 0.42), the data imply that average d_eff = 1215 μm.