Design of Multiple Modulated Frequency Lock-In Amplifier for Tapping-Mode Atomic Force Microscopy Systems

Nonlinear contact between tip and sample in tapping mode atomic force microscopy (AFM) systems induces higher harmonics, which may be useful for extraction of some characteristics of the sample. In this paper, a new efficient method for implementing multichannel digital lock-in technique is presented, which is able to measure the amplitude and phase of multiple modulated frequency signals. In order to solve the two most important problems in AFM systems, which are resolution and cost, previous multichannel lock-in amplifier methods are investigated and an improved algorithm for amplitude and phase extraction using fast Fourier transform is developed. In addition, we propose a novel multichannel digital lock-in algorithm including an
$N$
-slow digital filter and a multichannel direct digital synthesis block for generating reference signals. We achieve optimal noise reduction using the appropriate decimation filters prior to harmonic extraction. This modification results in a significant hardware reduction in implementation compared with classical designs. Since the precision of the design is sensitive to the sampling frequency, we perform the suitable sampling rate conversion using fractional delay and decimation filters, which enhance the accuracy and noise resiliency of the designed architectures. Experimental results prove the efficiency of the proposed method in multiple modulated frequencies extraction. Also, FPGA implementation results show that the proposed architecture is superior to previous structures, especially in the aspect of area.