# Laser beam deflection calculations

I would like to use laser beam deflection to measure a small movement (100s nm) in a cantilever system as shown in the diagram, but I am unsure of the calculations. This may be something simple to do and I am making it more complicated in my head.

I would like to be able to calculate how the movement of the laser point on the detector/screen (PSD in the diagram) relates to the displacements I expect of the cantilever. So I can work out a rough set up and to where to place the equipment to achieve sufficient sensitivity.

Any advice or help would be appreciated, whether calculations or setup as this is not an area I am not familiar with.

• Is your cantilever such that you are guaranteed a nice specular reflection? That might complicate the actual experiment greatly. Aug 17 '18 at 14:47
• My cantilever should have a mirror finish across the entire length.
– Dave
Aug 26 '18 at 12:11

The change in $D$ will be negligible (unless the angle of incidence is very small) because the deflection is very small. The angle of incidence of the light onto the cantilever mirror equals the angle of reflection. It appears that your cantilever is tilted relative to the laser beam and the screen, so you need to do your trigonometry in 3D. In your calculation, just assume that D does not change and that the mirror tilts by a small angle. However, the angle of tilt as a function of the distance the cantilever is deflected actually will depend on the structure of the cantilever. If I were handed this problem as a homework assignment, I would ask for more specifics about the cantilever -- or would state in my answer that I'm assuming a specific structure (e.g., a uniform rectangular cross section "diving board").