Measurements of acoustic pressure in the non-linear range in water using quantitative schlieren

The schlieren method, based on Raman-Nath scattering by ultrasonic waves, is extended to pressures up to 8.8×10⁶ Pa (about 5 KW/cm² for 4 MHz CW waves) by capturing up to the 16^th order diffraction harmonics in water. Given the high spatial resolution (~100 μm); this kind of measurement is not possible with conventional hydrophones. Working under partially applicable Raman-Nath regime (thin grating, Q≈0.016≪2π but 0<ν<2000), the theoretical description fails beyond the first few orders. However, we demonstrate that an empirical calibration is possible as long as plane waves are used and the short interaction length is maintained. Examples of beams and measurements are presented and compared with the basic theory