Inferring Physical Parameters from Images of Vibrating Carbon Nanotubes.

We describe a hidden parameter inferencing algorithm for deducing the length, width, and vibration profile from images of thermally excited single-wall carbon nanotubes. With accurate estimates of these parameters, the Young's modulus can be deduced. The algorithm is sensitive to shot noise in the image, primarily because of the low nanotube image contrast. Noise causes the nanotube length and width to be overestimated, and the vibration amplitude to be underestimated. After correcting for shot noise, we infer an average value of the Young's modulus of <Y> = 1.20 +/- 0.20 TPa, which is larger than the currently accepted value for graphite.