Quantitative Fourier analysis of schlieren masks: the transition from shadowgraph to schlieren

In a schlieren setup, a lens system forms an image of the refractive index fluctuations of a transparent sample onto a matrix detector while an intensity mask is positioned in the Fourier plane of a collecting lens to perform the required spatial filtering. In the absence of the mask, the resulting technique is that of a shadowgraph. The two methods provide different information about the refractive index of transparent fluids and can be used both for visualization purposes and scattering measurements. Here, we describe the effect of the intensity mask on the technique transfer function, i.e., its ability to detect different spatial frequencies and show how the special cases of shadowgraph, schlieren, and the transition between the two can be derived. We also present experimental data that agree well with our predictions.