Laser Schlieren

Image formation in a schlieren system is due to the deflection of light beam in a variable refractive index field towards regions that have a higher refractive index. In order to recover quantitative information from a schlieren image, one has to determine the cumulative angle of refraction of the light beam emerging from the test cell as a function of position in the plane. This plane is defined to be normal to the light beam, whose direction of propagation is along the coordinate.The path of the light beam in a medium whose index of refraction varies in the vertical direction can be analyzed using the principles of geometric or rays optics as follows:

Consider two wave fronts at times and as shown in Figure 5.3. At time the ray is at a position . After a interval , the light has moved a distance of times the velocity of light, which in general, is a function of , and the wave front or light beam has turned an angle . The local value of the speed of light is where is the velocity of light in vaccum and is the refractive index of the medium. Hence the distance that the light beam travels during time interval is

There is a gradient in the refractive index along the direction. The gradient in results in a bending the wave front due to refraction. The distance is given by

Let represent the blending angle at a fixed location . For a small increment in the angle, can be expressed as

In the limiting case

Hence the cumulative angle of the light beam at the exit of the test region will be given by

(2)

where the integration is performed over the entire length of the test region.