DATA REDUCTION    

Principles of interferometry and the evaluation of interferograms for the determination of fringe temperature are discussed in the present section. It is shown that fringe in the infinite fringe setting are isotherms when the flow field is two-dimensional. More generally, fringes are isocontours of a path integral function of temperature.

Interferometry

In the infinite fringe setting, the optical path difference between the test and reference beam is zero in the absence of any thermal disturbance. Hence interference is constructive and a bright field-of-view is obtained. The image obtained is practically fringe-free, but may show imperfection associated with the spatial filter and the interferometer optics in the form of a single broad fringe. When non-isothermal condition prevail in the path of the test beam (i.e.,a candle flame) each ray of light undergoes a change of phase, depending on the extent of change of the refractive index of medium. Hence an optical path difference is established between the test and the reference beams, resulting in a fringe pattern. In the wedge fringe setting, the optical components are deliberately misaligned to produce a set of line fringes of any convenient spacing. In the presence of a thermal disturbance the fringes would be displaced towards regions of higher temperatures, thus producing a fringe pattern that resembles the temperature profile itself.

In the present discussion, attention is restricted to image patterns that from in the infinite fringe setting. Here, the test beam records information about the variation of the refractive index of the fluid. To make temperature measurement possible, the refractive index variation must be related to temperature. The relationship between the refractive index and temperature is established as follows. For transparent media, the Lorenz-Lorentz relationship holds.

(4)

For gases, the refractive index is closed to unity and the expression reduces to the Gladstone-Dale equation

(5)

where is density. Hence . For moderate changes in temperature, typically and nearly uniform bulk pressure, density varies linearly with temperature as

(6)

it follow that is also a constant, being purely a material property. Hence changes in temperature simultaneously result in changes in refractive index and from principles of wave optics, lead to changes in the phase of the wave. This is the origin of fringe formation in interformetric images.

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