Optical Measurement of Ultrasonic Fourier Transforms

This paper presents a framework for a highperformance ultrasonic Fourier transform. By virtue of the properties of ultrasonic wave propagation, the Fourier transform of a transducer pattern can be retrieved from the wave diffraction pattern at the far-field. The computational complexity of an ultrasonic Fourier transform can be approximated by O(N), taking advantage of the fact that the field from each of the pixels is propagated and added in parallel. In the paper, we demonstrate this principle with a single CMOS compatible aluminum nitride transducer pixel on a silicon substrate. The transducer is driven by a pulsed gigahertz electric signal. The displacement of the backside silicon is detected by an optical UHF-120 vibrometer. The measured displacement pattern in the far field of a square transducer is compared to the predicted ultrasonic field distribution and the analytical Fourier transform.