Patent ID: 7627438

Claim:
A method to perform high-speed high resolution imaging of a sample from detecting transient cantilever movement in an atomic force microscope, the cantilever having a tip, the method comprising the steps of: receiving an input dither signal and tip deflection data corresponding to the input dither signal; generating an innovation signal based upon the input dither signal and tip deflection data, the innovation signal having a dynamic profile of unknown arrival time and unknown magnitude with additive white noise; computing maximum likelihood estimates of the arrival time and magnitude using a likelihood ratio test; deriving an image of the sample using the maximum likelihood estimates of the arrival time and magnitude; and wherein the likelihood ratio test is in accordance with r ⁡ ( M ) = e _ T ⁢ e _ T V where V is a covariance matrix, ē=[e 1 , e 2 , . . . , e M ] T , and e is an error in an estimate of the output of an observer.