Problems

1. Discuss fringe formation in a Mach-Zehnder interferometer when the test section is a region of non-isothermal fluid. Examine the effect of using a reference cell that maintains the fluid at the lowest temperature, average temperature, and the highest temperature. Compare infinite and wedge fringe settings.

2. Examine refraction errors during interferometry as a function of the length of the apparatus and the temperature gradient. Evaluate these errors numerically for assumed values of lengths and temperature differences. Would refraction errors be grater in liquids as compared to gases? Discuss removal of refraction errors from interferometric data.

3. A layer of common salt starts to dissolve in water contained in a circular beaker. It is required to image concentration field (and its gradients) as a function of time. It is proposed that Mach-Zehnder interferometry be used for this purpose. Develop the optical configurations required for this purpose and the steps involved in image analysis. Sketch expected images when the reference chamber is filled with (a) pure water and (b) saturated salt solution in water.

4. Discuss image processing techniques available for improving the intensity distribution in interferograms. Develop computer programs for methods such as Fourier filtering, contrast improvement, edge detection and histogram equalization. These programs can be applied to synthetic (analytically generated) interferograms created by suitably defined intensity functions.