This web page is made in support of the following two papers:  
1) L.Y. Beaulieu, Michel Godin, Olivier Laroche, Vincent TabardCossa, and Peter Grütter, Calibrating Laser Beam Deflection Systems for use in Atomic Force Microscopes and Cantilever Sensors. Applied Physics Letters, Accepted 2005  
2) L.Y. Beaulieu, Michel Godin, Olivier Laroche, Vincent TabardCossa, and Peter Grütter, A Complete Analysis of the Laser Beam Deflection Systems Used in CantileverBased Systems. To be Submitted.  
In these papers we introduced a
model that completely describes the way an optical beam detection system
interprets the deflection of a cantilever. In paper 1 we showed how a cantilever
based instrument can be calibrated such as to produce a known linear relationship
between the cantilever deflection and the signal measured by a position
sensitive photo detector (PSD). In paper 2 we presented the entire mathematical
formulism so that the reader may adapted the model to their own system.
In support of these publications we post software that the reader may
be free to use as they chose. 
1) Solving Equations 5 and 9 in Paper 2:  
In order to know the exact deflection of the lever it is necessary to know the coordinates of the end point of the lever (x_{max}, z_{end}). See figure 1. The following program produces z_{end}, x_{max}, and g (where g is described in equations 4 and 8 of paper 2) for both endmoment and pointload type deflections. Note this program solves equations 5 and 9 by brute force. Due to the small number of calculations, no attempts were made to optimize the program for speed. Press here to download this VB program. 
Figure 1

2) PSD Signal vs Cantilever Deflection: EndMoment:  
Because of the simplicity of the endmoment type
deflection, it is possible with little effort to use Excel to perform all
calculations. Press here
to download an excel worksheet for calculating the PSD signal versus cantilever
deflection for an endmoment type deflection. Note that in order to perform
these calculations, columns 2 and 3 (zDflec and xmax) must first be calculated
with the program above.

3) PSD Signal vs Cantilever Deflection: PointLoad:  
The point load type deflection is more complicated then the endmoment
type deflection. As a consequence we have written a Visual Basic program
that calculates the PSD signal versus cantilever deflection. The program
can also optimize the geometry by adjusting x to linearize the PSD signal versus cantilever deflection. Again,
no attempts have been made to optimize the program for speed. This program
performs all calculations by brute force and is totally devoid of computational
elegance. Press here
to download the VB program.
