FCPM is the abbreviation for Fluorescence Confocal Polarizing Microscopy, a very powerful technique to visualize the director field in three dimensions. It combines several microsope techniques: Optical polarizing microscopy, fluoresence microscopy and confocal microscopy. The most important features of this methods can be found below.

### Confocal Microscopy

Schematic working principle of a confocal microscope: Only light from the focal plane can pass the pinhole, light from other planes is blocked.

The confocal microscopy technique was invented in 1955 by Marvin Minsky. It offers to resolve images not only latteraly, but also axially and the basic principle remained unchanged since then: Light of a point-like light source (e.g. the aperture of a laser) is focused onto the sample using a high aperture objective. The reflected or re-emitted light is then collected by the same objective and focused on a pinhole, which is located in front of the light detector. With this setup, only light from the focal plane of the objective can pass the pinhole, while light coming from other planes will be filtered by the pinhole.
Confocal microscopy is a scanning probe technique, which requires a point by point measurement and does not give a direct image of the sample. The magnification is therefore determined by the scanning area, not by the magnification of objective. The resolution in confocal microscopy depends on the numerical aperture $NA$ and the magnification $m$ of the objective, the wavelength $\lambda$ of the light source and the diameter of $d$ of the pinhole. The maximum theoretical lateral resolution improves by the factor $1/\sqrt{2}$ compared to a conventional brightfield microscope.

### Fluorescence confocal polarizing microscopy

The benefits of optical polarizing microscopy and fluorescence confocal microscopy can be combined by adding polarizers to a fluorescence confocal microscope. As most LCs usually show suitable fluorescence, a small amount of dichroic dye is added to the LC. According to the guest-host mechanism the dye molecules orient parallel to the local director of the LC phase. If the orientation of the transition dipole moment $\vec{M}$ to the long axis of the dye molecule is known, the detection of fluorescence intensity between crossed polarizers allows a 3d-imaging of the director field distribution.
As can easily be shown, the detecable light intensity scales with the angle $\zeta$ between the excitation light and the transition dipole moment $\vec{M}$ over the relation

The high sensitivity of $I_{det}$ to the angle $\zeta$ allows the detection of even very small director field fluctuations. Four fundamental orientations of dye and excitation field are shown in the figure below. In cases where $\vec{M}$ is perpendicular to the plane of polarization of the exciting light, no fluorescence intensity can be detected. For parallel alignment of $\vec{M}$ and $\vec{E}$, the maximum fluorescence intensity can be detected. In the general case of arbitrary orientation of $\vec{M}$ and $\vec{E}$, the intensity scales by $\cos^4\left(\zeta\right)$:

Illustration of the angle dependent fluorescence response in FCPM measurements.

The following series of axially resolved FCPM-images shows the Fréedericksz-transition in a planar test cell $(d=10\mu m)$, as described in the section The electro-optic effect.

Experimental FCPM series of the Fréedericksz-transition. With increasing applied voltage the molecules rotate from planar (bright) to perpendicular (dark) and the FCPM images reveal the axial director field distribution.

<<previous back next>>