  Temperature controlled Polarization Modulation Near-Field Scanning Optical
Microscopy (PM-NSOM) measurements of a single supported $L_{\beta^{\prime}}$
1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipid bilayer are presented.
The effective retardance ($\Delta S = \frac{2 \pi (n_e-n_o)t}{\lambda}$), where
$t$ is the thickness of the bilayer and $\lambda$ is the wavelength of light
used and the direction of the projection of the acyl chains ($\theta $) were
measured simultaneously. From $\Delta S$ the birefringence ($n_e-n_o$) of the
bilayer was determined. A change of $\Delta S$ $\sim$ (3.8 $\pm$ 0.3)~mrad at
the transition temperature $T_m \sim$ 41$^{\circ}$C between the gel
$L_{\beta^{\prime}}$ to liquid disorder $L_{\alpha}$ was observed in a single
planar bilayer. This agrees well with previous values of ($n_e-n_o$) in the
$L_{\beta^{\prime}}$ phase and translates to an assumed $\langle \phi \rangle $
$\sim$ 32$^{\circ}$ when T $<T_m$ and 0$^{\circ}$ when T $>T_m$. Evidence of
supper heating and supper cooling are presented, along with a discussion of the
behavior that occurs around $T_m$.
