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 frequencydependent 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, and 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.