Classification scheme and properties of schlieren techniques.

Spatial filtering techniques used to detect thin phase structures can be represented by a unique transfer function (phase-contrast function, PhCF). The PhCF is here formulated in terms of mathematical symmetry to define, analyze, and classify schlieren techniques (ST). It is shown that all ST can be identified by essentially the same PhCF. This latter function performs a passband Hilbert transformation under coherent illumination. It can also act as a differential filter provided that the illumination is noncoherent.