Observer based Q-control imaging methods for atomic force microscopy
AssigneeIowa State University Research Foundation, Inc.
InventorsMurti V. Salapaka, Deepak Ranjan Sahoo
Life of this patent
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Abstract
An observer based Q control method for a cantilever in an atomic force microscopy is provided that provides for a “dual” Q behavior such that a particular effective Q is achieved when a sample is present and another effective Q when a sample is absent. In the control method, the transfer function from dither input to photo-diode output is independent of the observer so that the cantilever effectively behaves like a spring-mass-damper system. The effective quality factor and stiffness of the cantilever can be changed by appropriately choosing the state feedback gain. The method provides sample-imaging using transient atomic force microscopy.
Claims13
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=[e1, e2, . . . , eM]T, and e is an error in an estimate of the output of an observer.
A method to perform transient imaging of a sample from detecting transient cantilever movement in an atomic force microscope using Q control, 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 estimated position and an estimate velocity of the tip;
- generating an innovation signal based upon the input dither signal, the tip deflection data, the estimated position and the estimated velocity, 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
- further comprising the step of adding the estimated position and the estimate velocity in a feedback loop to add to the input dither signal, thereby actively damping a quality factor (“Q”) of the cantilever.
A method to perform transient imaging of a sample from detecting transient cantilever movement in an atomic force microscope using Q control, 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 estimated position and an estimate velocity of the tip;
- generating an innovation signal based upon the input dither signal, the tip deflection data, the estimated position and the estimated velocity, 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
- further comprising the step of adding the estimated position and the estimate velocity in a feedback loop to add to the input dither signal, thereby actively enhancing a quality factor (“Q”) of the cantilever.
A method to perform transient imaging of a sample from detecting transient cantilever movement in an atomic force microscope using Q control, the cantilever having a tip, the method comprising the steps of:
- receiving an input dither signal and tip deflection data corresponding to the input signal;
- generating an estimated position and an estimate velocity of the tip;
- generating an innovation signal based upon the input dither signal, the tip deflection data, the estimated position and the estimated velocity, 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;
- wherein the step of generating an estimated position and an estimate velocity comprises the step of generating an estimated position and an estimate velocity using an observer;
- and
- wherein dynamics of the observer are given in accordance with:
- {circumflex over ({dot over (x)})}=A{circumflex over (x)}+Bu+L(y−C{circumflex over (x)});
- {circumflex over (x)}(0)={circumflex over (x)}0
- u=(g+F{circumflex over (x)})
- {circumflex over (p)}=C{circumflex over (x)}
- {circumflex over (ν)}=D{circumflex over (x)}
- where {circumflex over ({dot over (x)})} is the estimate dynamic state of the cantilever, L is the observer gain, F is the state feedback gain, g is the input dither signal, {circumflex over (p)} is the estimate position, A, B, C, and D are state matrices realized from the frequency response from a dither-piezo input to a photo-diode output, u is the dither-piezo input, y is the photo-diode output, and {circumflex over (ν)} is the estimated velocity.
Dependencies are inferred from the claim text.