Although William Wallace shouted this in the movie, “Braveheart,” as he died in the hopes to inspire others to join his fight against tyranny, our interest here at Boston Micromachines is related to “degrees of freedom” rather than individual rights. I chose this as a post because numerous times we have come across customers who miscalculate the minimum number of control points (re: actuators) needed to satisfy their wavefront control needs because the forget about this simple concept. Here’s an example:
A customer recently came to us insisting that they needed one of our advanced tip-tilt-piston devices over a continuous surface deformable mirror. Their reasoning was that with the same number of actuators, to correct for their wavefront, tipping and tilting the individual segments would give them more control than using the simple piston mechanism of our continuous device. This is true if you compare the number of segments (with three actuators) to the number of single actuators of a continuous DM. However, if you choose to use a tip-tilt-piston device over a continuous surface mirror, you actually need more actuators (if you work out the numbers, 1.8 times more) to achieve the same level of correction capability. This has been explained and presented very well by Claire Max at UC Santa Cruz. See the presentation materials here (Slide 47 goes over the equations).
If we step back from the equations and look for the basic concept behind this, it boils down to the ability to change the profile of the surface in many more ways using a continuous membrane as opposed to stiff, separate segments. Even more simply put: If you want to approximate a curvy line using only a few points (five, let’s say), would you prefer to use a slightly less curvy line, or a series of straight lines?
The figure below illustrates this concept.
So, the next time you’re considering wavefront control, keep this in mind before hitching your wagon to a particular architecture. THINK FREEDOM!!!!!