Corresponding to the local hue value in the test image, the beam displacement due to an applied thermal/solutal gradient is obtained from the calibration curve. The beam displacement of the light beam at the position of the color filter due to the deflection of light beam passing through the test cell by an angle is given as:

(2)

In Equation (2), the sign on the right side is determined by the change in hue in the filter plane and is the focal length of the decollimator lens. The displacement field is related to the change in refractive index and hence the thermal or the concentration gradient. The gradient of the physical quantity is integrated from a known boundary condition to obtain the respective thermal and concentration fields. The analytical expressions involved in the data analysis procedure are described in the following paragraphs.

For Rayleigh-Benard convection experiments in air at constant pressure , the beam displacement is related to the temperature gradient as:

(3)

Here is the refractive index of the medium, is the density of fluid medium and is the length of the test cell in the direction of the light beam.