Introduction

Closely related to the method of interferometry are and that employ variation in refractive index with density (and hence, temperature and concentration) to map a thermal or a species concentration field. With some changes, the flow field can itself be mapped. While image formation in interferometry is based on changes in the the refractive index with respect to a reference domain, schlieren uses the transverse derivative for image formation. In shadowgraph, effectively the second derivative (and in effect the Laplacian ) is utilized. These two methods use only a single beam of light. They find applications in combustion problems and high-speed flows involving shocks where the gradients in the refractive index are large. The schlieren method relies on beam refraction towards zones of higher refractive index. The shadowgraph method uses the change in light intensity due to beam expansion to describe the thermal/concentration field.

Before describing the two methods in further detail, a comparison of interferometry (I), schlieren (Sch) and shadowgraph (Sgh) is first presented. The basis of this comparison will become clear when further details of the measurement procedures are described.

1. Interferometry relies on the changes in the refractive index in the physical region and hence the changes in the optical path length relative to a known (reference) region. Schlieren measures the small angle of deflection of the light beam as it emerges from the test section. Shadowgraph measures deflection as well as displacement of the light beam at the exit plane of the apparatus.

2. Displacement effects of the light beam are neglected in schlieren while displacement as well as deflection effects are neglected in interferometry. In effect, the light rays are taken to travel straight during interferometry.

3. Since large gradients will displace and deflect the light beams, interferometry is suitable for small gradients and shadowgraph for very large gradients. Schlieren fits well in the intermediate range.

4. In a broad sense, interferometry yields the refractive index field , schlieren - the gradient field and shadowgraph .
5. Since deflection and displacement calculations are more complicated than that of the optical path length, shadowgraph analysis is the most involved, schlieren is less so, and interferometry is the simplest of the three.
6. All the three methods yield a cumulative information of the refractive index field (or its gradients), integrated in the viewing direction, i.e. along the path of the light beam.
7. As will be seen in the text of this module, schlieren and shadowgraph methods require simpler optics than interferometry. Shadowgraph is the simplest of all. The price to be paid is in terms of the level (and complexity) of analysis.