polysaccharides\citep{rief97a}.
An AFM\index{AFM} uses a sharp tip integrated at the end of a
-cantilever to interact with the sample. Cantilever bending is
-measured by a laser reflected off the cantilever and incident on a
-position sensitive photodetector (\cref{fig:afm-schematic}). When the
-bending force constant of the cantilever is known\citep{levy02}, the
-force applied to the sample can be calculated using Hooke's law
-(\cref{eq:sawsim:hooke}).
-
-\begin{figure}
- \asyinclude{figures/schematic/afm}%
- \caption{Operating principle for an Atomic Force
- Microscope\index{AFM}. A sharp tip integrated at the end of a
- cantilever interacts with the sample. Cantilever bending is
- measured by a laser reflected off the cantilever and incident on a
- position sensitive photodetector.\label{fig:afm-schematic}}
-\end{figure}
+cantilever to interact with the sample\cite{binnig86}. Cantilever
+bending is measured by a laser reflected off the cantilever and
+incident on a position sensitive photodetector\cite{meyer88}
+(\cref{fig:afm-schematic}). When the bending force constant of the
+cantilever is known\citep{levy02}, the force applied to the sample can
+be calculated using Hooke's law (\cref{eq:sawsim:hooke}).
The substrate is mounted on a three dimensional piezoelectric actuator
so that the tip may be positioned on the surface with sub-nanometer
vertical (\cref{fig:piezo-schematic}).
\begin{figure}
- \asyinclude{figures/schematic/piezo}%
- \caption{Schematic of a tubular piezoelectric actuator. In our AFM,
- the substrate is mounted on the top end of the tube, and the
- bottom end is fixed to the microscope body. This allows the piezo
- to control the relative position between the substrate and the AFM
- cantilever. The electrodes are placed so radial electric fields
- can be easily generated. These radial fields will cause the piezo
- to expand or contract axially. The $z$ voltage causes the tube to
- expand and contract uniformly in the axial direction. The $x$ and
- $y$ voltages cause expansion on one side of the tube, and
- contraction (because of the reversed polarity) on the other side
- of the tube. This tilts the tube, shifting the sample
- horizontally.\label{fig:piezo-schematic}}
+ \begin{center}
+ \subfloat[][]{\label{fig:afm-schematic}
+ \asyinclude{figures/schematic/afm}}
+ \hspace{.25in}%
+ \subfloat[][]{\label{fig:piezo-schematic}
+ \asyinclude{figures/schematic/piezo}}
+ \caption{\subref{fig:afm-schematic} Operating principle for an
+ Atomic Force Microscope\index{AFM}. A sharp tip integrated at
+ the end of a cantilever interacts with the sample. Cantilever
+ bending is measured by a laser reflected off the cantilever and
+ incident on a position sensitive photodetector.
+ \subref{fig:piezo-schematic} Schematic of a tubular
+ piezoelectric actuator. In our AFM, the substrate is mounted on
+ the top end of the tube, and the bottom end is fixed to the
+ microscope body. This allows the piezo to control the relative
+ position between the substrate and the AFM cantilever. The
+ electrodes are placed so radial electric fields can be easily
+ generated. These radial fields will cause the piezo to expand
+ or contract axially. The $z$ voltage causes the tube to expand
+ and contract uniformly in the axial direction. The $x$ and $y$
+ voltages cause expansion on one side of the tube, and
+ contraction (because of the reversed polarity) on the other side
+ of the tube. This tilts the tube, shifting the sample
+ horizontally.\label{fig:afm-schematic-and-piezo}}
+ \end{center}
\end{figure}
% really, AFM can do this ;)