Schlieren

Schlieren Technique

Schlieren has been used for decades to visualize refractive index variations in transparent media. Recently Dr. D. Brogioli and I utilized it in a quantitative manner as a valid substitute of traditional static and dynamic light scattering to get the power spectra of sample fluctuations (see our 2006 Applied Optics paper).

The basic optical set-up (Fig.1) is similar to that of a Shadowgaph involving a few components. 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. At the focal point of the collection lens an intensity mask is positioned to cover half of the Fourier plane.

Fig.1 Typical optical setup of a Schlieren apparatus

Schlieren can be explained similarly to the Shadowgraph saying that for sufficiently large but weak fluctuations of the refractive index, two scattered beams are generated from the sample at opposite angles, but one of the two is suppressed by the intensity mask in the Fourier plane of the collection lens and thus only one scattered beam interferes with the transmitted one on the screen plane giving rise to a diffraction pattern. From statistical analysis of the intensity pattern one can then recover the power spectrum of the sample in a more direct way than in the Shadowgraph case because the result of interference among the two beams does not depend on the scattering angle or the distance between the scattering sample and the observation plane. Consequently the sensitivity of the Schlieren displays a flat behavior.

If the intensity mask is not positioned exactely in the center of the Fourier plane of the system, then we get a technique which is a Shadowgraph for certain wave vectors and a Schlieren for other ones. The behavior is visible in Fig.2 where different power spectra are shown for different distanced d of the blade from the optical axis. A complete analysis of this behavior is reported in our 2011 Applied Optics paper.

Fig.2 2D-power spectra with diffeent positions of the intensity mask:

a) d=10 microns = Schlieren, b) d=50 microns,

c) d=120 microns, d) d=1000 microns = Shadowgraph