Critical needs of fringe-order accuracies in two-color holographic interferometry

Abstract

Two-color holographic interferometry is a promising technique for separating simultaneous concentration and temperature variations in solution for crystal-growth experiments on earth and in microgravity conditions in space. The ultimate success depends on two linearly independent fringe patterns due to the different wavelengths. With available practical lasers and typical crystal-growth experimental conditions the two interference fringe patterns (other than scale effects) may not be too different. The slight error in the measured fringe order can then yield large uncertainty in temperature and concentration determination. This aspect is analytically considered for the first time in this article. A simple cell (rectangular parallelpiped) is considered containing the fluid. For simplicyt, we assume a constant field along the object-wave-propagation direction in the cell. The two reconstructed fringe patterns are then represented in terms of temperature and concentration variations. Solving two equations theoretically yields the desired temperature and concentration. However, once the fringe-postition measurement error is introduced, error in the temperature and concentration results. These errors are analytically determined. A particular case of TGS (triglycine sulfate) aqueous solution with HeNe (λ=632.8 nm) and HeCd (λ=441.6 nm) lasers for holography is critically discussed. It is found that a high degree of accuracy in the fringe order is required in this particular case. To improve fringe-position measurements, special techniques such as electronic phase measurement or heterodyne detection may be necessary. The study provides the analytical guidelines for designing the experiments and critical needs of desired physical parameters.