Shadowgraph

Shadowgraph Technique

Shadowgraph has been used for decades to visualize refractive index variations in transparent media. Recently Prof. D.S. Cannell (UCSB) has developed a theoretical treatment that allows to utilize it in a quantitative manner as a valid substitute of traditional static or dynamic light scattering to get the power spectra of sample fluctuations.

The basic optical set-up (fig.1) involves a few components and requires no alignment. First a light source generating a plane parallel beam is needed. This can be achieved utilizing a laser plus a spatial filter and a collimating lens at a focal distance from the filter. The beam then passes through the transparent sample and is captured by a collection lens and a sensor, which is usually a CCD or a CMOS camera.

Fig.1 Typical optical setup of a Shadowgraph apparatus

Shadowgraph can be explained in a simplified geometrical way saying that refractive index variations within the sample act as small lenses making the incoming beam converge or diverge thus giving rise to lighter or darker spots on a screen, at a distance z. At a deeper level, we can say that sufficiently large but weak fluctuations of the refractive index generate two scattered beams at opposite angles and these beams interfere on the screen plane with the much more intense trasmitted one, giving rise to a diffraction pattern. From statistical analysis of the intensity pattern one can then recover the power spectrum of the sample. The result of interference among the three beams depends both on the scattering angle and the distance between the scattering sample and the observation plane, then the sensitivity of the Shadowgraph displays a sinusoidal behavior. This is commonly referred to as Talbot effect.

Fig.2 and Fig.3 show two different application of Shadowgraph technique for fluids investigation. Fig.2 shows concentration fluctuations in a binary mixture observed from above, that is vertically, during a diffusive process. The darker and brighter patches here show different concentration values in the horizontal plane where diffusion takes place, because the sample is prepared in the initial condition of two fluids one above the other separated by a sharp horizontal interface that is eventually smoothed down by the diffusive process. Since diffusion is not homogeneous in the horizonthal plane, contrary to common believe, one can observe macroscopic fluctuations of the concentration. Statistic analysis of images like this allows providing information about the static power spectrum as well as the temporal correlation function of the sample, thus providing the same results as a standard static or dynamic light scattering apparatus. The dynamics can be obtained by means of the Differential Dynamic Algorithm.

Fig.2 Concentration non equilibrium fluctuations in a free diffusing sample.

Fig.3 shows the temperature profile of an air jet coming out from a pressurized vessel. The outcoming jet is colder than room temperature so we are able to visualize the temperature difference and detect the turbulent motion of air. The jet passes through a carbon fiber cloth and the dispersion effect can be detected by the Shadowgraph image.

Fig.3 Temperature profile of an air jet.