Method of controlling frequency modulated-atomic force microscope

1. A method executed by a controller for controlling a frequency modulation (FM) atomic force microscope (AFM) comprising a cantilever having a resonant frequency and an excitation system configured to oscillate the cantilever in response to a drive signal, the method comprising:

initially determining latency of the excitation system; receiving a deflection signal indicating a deflection of a tip of the cantilever;

mixing the deflection signal with a first sine signal generated and output by a phase lock loop (PLL), based on a frequency response and the resonant frequency of the cantilever, to provide a mixed input signal input to the PLL;

measuring a frequency shift of a frequency response of the cantilever in response to the drive signal;

determining spurious phase of the cantilever based on the determined latency, the resonant frequency of the cantilever, and the measured frequency shift of the frequency response of the cantilever in response to the drive signal;

generating and outputting a second sine signal from the PLL as a sine drive signal having a phase that is advanced by the determined spurious phase to preemptively compensate for subsequent spurious phase of the cantilever; and

driving the excitation system using the sine drive signal with an adjusted amplitude as the drive signal.

2. The method of claim 1 , wherein the PLL tracks only phase changes arising from shifts of the frequency response of the cantilever.

3. The method of claim 1 , wherein the spurious phase of the cantilever is a difference in phase between an actual phase of the cantilever and a desired phase of about −90 degrees.

4. The method of claim 1 , further comprising:

determining a spurious response of the excitation system driven by the amplitude adjusted second sine signal; and

equalizing the determined spurious response.

5. The method of claim 4 , wherein determining the spurious response of the excitation system comprises dividing a frequency response of the excitation system by the frequency response of the cantilever.

6. The method of claim 4 , wherein equalizing the determined spurious response comprises filtering the amplitude adjusted second sine signal with an inverse of the determined spurious response.

7. The method of claim 4 , wherein equalizing the determined spurious response comprises:

fitting a line with a line coefficient to the absolute value of an inverse of the determined spurious response; and

adjusting the amplitude of the second sine signal based on the line coefficient and the frequency shift of the frequency response of the cantilever.

8. The method of claim 7 , wherein adjusting the amplitude of the second sine signal comprises multiplying the amplitude of the second sine signal by the sum of one and the product of the line coefficient and the frequency shift of the frequency response of the cantilever.

9. The method of claim 1 , wherein determining the latency of the excitation system comprises:

measuring the frequency response of the cantilever when not in contact with a sample surface; and

fitting the measured frequency response with a mathematical model of the cantilever and additional time delay.

10. The method of claim 1 , wherein the spurious phase of the cantilever is calculated in real time.

11. A method of controlling a frequency modulation (FM) atomic force microscope (AFM) comprising a cantilever having a resonant frequency and an excitation system configured to oscillate the cantilever in response to a drive signal, the method comprising:

initially determining a latency response of the excitation system;

receiving a deflection signal indicating a deflection of a tip of the cantilever;

mixing the deflection signal with a second sine signal generated and output by a phase lock loop (PLL) to provide a mixed input signal input to the PLL;

measuring a frequency shift of a frequency response of the cantilever in response to the mixed input signal;

generating a first sine signal based on the frequency response and the resonant frequency of the cantilever, wherein the second sine signal is generated by delaying the first sine signal by a delay time that corresponds to the determined latency response of the excitation system;

outputting the first sine signal from the PLL as a sine drive signal; and

driving the excitation system using the sine drive signal with an adjusted amplitude as the drive signal.

12. The method of claim 11 , further comprising:

determining a spurious response of the excitation system driven by the drive signal; and

equalizing the determined spurious response.

13. The method of claim 12 , further comprising:

determining the frequency response of the cantilever via a thermal tune, the thermal tune comprising fitting deflection noise density to a mathematical model of the cantilever.

14. The method of claim 12 , wherein equalizing the determined spurious response comprises filtering the drive signal with an inverse of the determined spurious response.

15. The method of claim 12 , wherein equalizing the determined spurious response comprises:

fitting a line with a line coefficient to the absolute value of an inverse of the determined spurious response; and

adjusting an amplitude of the first sine signal based on the line coefficient and the frequency shift of the frequency response of the cantilever.

16. The method of claim 15 , wherein adjusting the amplitude of the first sine signal comprises multiplying the amplitude of the first sine signal by the sum of one and the product of the line coefficient and the frequency shift of the frequency response of the cantilever.

17. The method of claim 11 , wherein delaying the first sine signal is implemented using one of a first-in-first out (FIFO) latch or a fractional delay filter.