The light is reflected off the surface of the water at the Brewster angle using a small mirror. The reflected beam is then sent through a series of lenses and the final image recorded using a CCD camera. The basic principle behind the Brewster angle micrscope is that the density of the monolayer and the tilt of the molecules relative to the polarization of the incoming beam change the index of refraction of the surface. This changes the Brewster angle and results in an intensity variation that is a function of density and tilts angle. This allows us to image both domains of constant tilt angle and density.
Many references exist on liquid crystals.
A review of pattern formation in liquid crystals is L. Kramer and W. Pesch, Annu. Rev. Fluid Mech. A review of spatio-temporal chaos is M. C. Cross and P. C. Hohenberg, Rev. Mod. For reviews of Langmuir monolayers, see H. Mohwald, Annu. For a review of phase transitions in monolayers, see C. M. Knobler and R. C. Desai, Annu.