Ray tracing through the fluid medium: Importance of the higher-order effects

In order to assess the importance of higher-order optical effects in shadowgraph imaging, the extent of the bending of rays is estimated by tracing the passage of rays through the fluid phase. In order to be able to do this, the shadowgraph images of the growth process recorded at different stages of growth are analyzed as follows: The Poisson equation governing the shadowgraph process is solved numerically to yield a depth-averaged refractive index value for each node point of the grid. The refractive index information is then used to determine the deflection of the ray at the exit plane of the growth chamber by solving the coupled ordinary differential equations (ODEs) governing the passage of light ray through the region of disturbance. The solution of these equation yields the two orthogonal components of the deflection of the ray and its gradient at the exit plane of the test cell. For the Poisson equation to be applicable for shadowgraph analysis, the ray deflections should be small.

Considering the length of the growth chamber containing the fluid as D and the screen to be at a distance behind the test section, the displacements of a light ray on the screen with respect to its entry position are given by Equations 27 and 28. A computer code for solving the coupled ODEs has been written and validated against analytical examples.

Correction factor for refraction at the glass-air interface

In order to perform laser shadowgraphic and interferometric imaging of the crystal growth process, two different growth chambers were fabricated. The crystal growth process referred here is described in detail in lectures 27-33. The growth chambers have optical windows for the entry and exit of the laser beam. The cavity is enclosed between the windows for the entry and exit of the laser beam. The cavity enclosed between the windows was filled with the KDP solution. During the process of crystal growth the KDP solution is a medium of varying refractive index, leading to the bending of the rays as the laser beam traverses through the solution. At the exit from the growth chamber, the light ray encounters two different interfaces, namely KDP-solution and glass, followed by glass and air. Thus, the light ray emerges at an angle different from the angle at which it is incident on the solution and glass interface. The refractive indices of the KDP solution, the quartz window and the air around result in a scale factor which must be taken into account to get the correct emergent angle of ray. The optical path of the light ray through the two interfaces is shown in Figure 5.10.

Figure 5.10: Optical Path of the light ray passing from the growth chamber into the air.