The applicability of extrapolation to the present study can be justified on the basis of two factors: First, the concentration level away from the growing crystal, corresponding to the supersaturated solution is practically constant. This is confirmed in the recorded schlieren images where the changes in the intensity are found to be localized in the vicinity of the growing crystal alone. These images are discussed in the subsequent sections.  Secondly, the information content of schlieren images decrease with the geometric path length of the light beam within the beaker, as indicated by the integration limits in Equation 3 (Lecture 26). The diminishing chord length of the beaker towards the edges shows that the measurement procedure de-emphasizes concentration variation occurring towards the sides of the beaker. Specifically, the chord length is zero at the extremities of the beaker. The approximation involved in extrapolating concentration outside the measurement volume is thus expected to be less serious in predicting the concentration field closer to the center of the beaker and hence the crystal location. Further justification can be based on the fact that concentration is continuously distributed in the fluid volume. 

In the present work, a tenth order polynomial has been used to extrapolate the concentration distribution, starting with the portion covered by the optical windows. Polynomials of order 5 to 10 produced practically identical results. The limiting values of concentration in the far field, and the necessity of maintaining slope-continuity in the concentration distribution at every point have been enforced. An independent check on the accuracy of the experiment, data analysis and extrapolation is the conservation of solutal mass in each of the projections. Mass balance was found to be better than 0.01% in all the experiments analyzed using tomography. Minor imbalances are subsequently rectified by normalizing the data-set. To account for changes in the integration length along the direction of the laser beam, the extrapolated data is multiplied by the local chord length as one proceeds from the center towards the periphery of the growth chamber. This projection data is used for tomographic reconstruction of the concentration field over a horizontal plane of the solution. The above approach has been successfully tested in the context of numerically simulated buoyancy-driven convection and is discussed in the section Validation of Reconstruction Procedure With Simulated Data.