Schlieren imaging with fractional Fourier transform to visualise ultrasonic fields

Schlieren imaging is widely used to visualise local density modulations in optically transparent media, for example to make fluid flow or ultrasonic waves visible. In common schlieren setups, spatial filtering is applied. This is accomplished by a 2 f -arrangement consisting of two lenses, where f is the focal length of the used lenses. Between the lenses, a spatial filter is positioned. The filter requires precise adjustment to obtain images showing the ultrasonic waves. In this paper a method is described to visualise ultrasonic fields that does not require spatial filtering. To accomplish this, a focussing macro lens is used. The observed effects are in accordance with the theory of the fractional Fourier transform.