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 deff(f) rather than the geometrical sensitive element diameter dg. The objective of this work was to quantify average deff(f) for needle hydrophones as a function of dg and f. Estimates of effective radii aeff(f) = deff(f) / 2 were inferred from directivity measurements from 0.5 to 20 MHz on 16 needle hydrophones with dg = 2ag ranging from 75 to 1000 μm (139 hydrophone / frequency combinations). Effective sensitive element diameter deff(f) exceeded dg by over 100 % when λ > 4dg (where λ is the wavelength). For kag > 0.75 (where k=2π/λ), deff(f) was consistent with the "rigid piston" (RP) theory, reinforcing a previous report from our laboratories. However, for kag < 0.75, deff(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 dg = 75 μm at 1 MHz (kag = 0.16), the data imply that average deff = 505 μm. 2) For a needle hydrophone with dg = 400 μm at 500 kHz (common parameters for human transcranial neuromodulation; kag = 0.42), the data imply that average deff = 1215 μm.