In a general setting, the material density will depend on pressure, temperature, and species concentration. Interferometric measurements of temperature are possible when pressure and concentration are either fully known, or, purely constant.

Consider a beam of light moving through a gaseous medium of varying temperature and of total length . is also equal to the geometric path length traversed by the light beam. The optical path length traversed by the light beam in the -direction, corrected for changes in the light speed is

Here, is the speed of light in vacuum, and , the refractive index is defined as

The integral is greater than since (except in absolute vacuum where ). The applicable coordinate system is shown in Figure 4.5.

Let beam 1 propagate through a region of variable density and hence refractive index, ₁ and beam 2 through a region constant density (and ₂). Then, the difference in path lengths between 1 and 2 can be calculated as