Noise in optical measurements of cantilever deflections

Abstract

The optical beam deflection method using the knife edge detection technique is one of the simplest optical sensing methods. We investigate theoretically the limit to the resolution when sensing the displacements of a mechanical cantilever using the knife edge detection technique implemented with a quasimonochromatic thermal-like optical source. Simple formulas for the minimum detectable displacement of the cantilever’s front end are derived assuming all nonoptical noises negligible. It is shown that superluminiscent diodes can yield a minimum detectable displacement of the cantilever about 5 dBs above the shot noise for 1 mW of optical power. It is also shown that in many cases of practical interest the source induced noise is smaller than the thermal-vibration noise of the cantilever. Thus, in many cases, using an inexpensive thermal-like source with the knife edge detection technique can be as effective as using a high-coherence shot-noise limited source.