Plane wave fronts in a collimated beam of light are distorted in their passage through a region of variable density, and as a result a variable phase distribution is produced in an exit plane which lies just beyond the disturbance and is perpendicular to the direction of propagation of the collimated beam (optical axis). This phase distribution, ordinarily invisible due to the tremendous rapidity of optical oscillations, can be converted to an intensity distribution in which the maxima and minima of intensity correspond to points in the exit plane where the optical path length differs from that in an undisturbed portion of this plane (free field) by an integral multiple of half a wavelength. This can be done in a conventional schlieren system by forming an image of the exit (object) plane with a convex lens (or parabolic mirror) and then inserting a small absorbing object or other appropriate modification in the focal plane in such a way as to block the central maximum of the Fraunhofer pattern due to the free field. Very little disturbance light is cut off in the process since this light is refracted and does not go through the focal point. The blocking of free-field light sets up a diffraction process which causes this light to spread into the bordering disturbance image. The resulting interference produces the intensity band system mentioned earlier.
If the disturbance is two-dimensional, with density-gradient vectors perpendicular to the optical axis, the measurement of the phase distribution is equivalent to a measurement of density, by virtue of the Dale-Gladstone law, µ- 1 = Kρ, where µ is the index of refraction, ρ is the density, K is a constant. Measurements which have heretofore required the use of a Mach-Zehnder interferometer can, therefore, be made in a conventional schlieren system. The possibility of duplicating interferometer fringe-field experiments has also been investigated.
EDWARD B. TEMPLE, "Quantitative Measurement of Gas Density by Means of Light Interference in a Schlieren System," J. Opt. Soc. Am. 47, 91-99 (1957)