This web page is made in support of the following two papers:
  1) L.Y. Beaulieu, Michel Godin, Olivier Laroche, Vincent Tabard-Cossa, 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 Tabard-Cossa, and Peter Grütter, A Complete Analysis of the Laser Beam Deflection Systems Used in Cantilever-Based 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 (xmax, zend). See figure 1. The following program produces zend, xmax, and g (where g is described in equations 4 and 8 of paper 2) for both end-moment and point-load 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: End-Moment:
  Because of the simplicity of the end-moment 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 end-moment 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: Point-Load:
 

The point load type deflection is more complicated then the end-moment 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.