Quantitative Analysis

The quantitative analysis tools allow you to analyze the measured intermodulation spectral data at each pixel in a variety of ways. Each spectrum is a frequency-domain representation of the tip motion at that pixel, and from this motion we are interested in learning about the forces of interaction between the tip and surface. In dynamic AFM there are several forces giving rise to the cantilever motion: The tip-surface force, cantilever bending forces, viscous drag force on the cantilever body, inertial force due to acceleration of the cantilever mass, and the drive force that we apply by shaking of the cantilever base. To properly separate out the tip-surface force from all other contributions we require three things: A good Calibration of the cantilever, and a good measurement of the cantilevers free motion when it is far away from the surface, and if you wish to compensate for background forces, a good measurement of the cantilevers just-lifted motion (see Measure just lifted).

Calibration is performed at the outset of ImAFM™ and the free motion is measured during Setup, before scanning. It is easy to lift well clear of the surface and re-do either of these at any time during the session. We recommend that you check the calibration occasionally, to see if the results are consistent with previous measurements. After each re-calibration you also need to re-do Setup and make a new measuremnet of the just-lifted response. The most recently measured or Current calibration data, free motion spectrum and lift motion spectrum are stored with each scan file. These measurements are an important part of the analysis of the scan data and they can be viewed using the Data Tree.

The focuses in this chapter is on how to use the software to perform different methods of analysis. References are given to the scientific literature where the fundamental physics and mathematics of the force reconstruction methods are explained in detail.

Inspecting single pixels

The intermodulation spectra at individual pixels can be analyzed by selecting the data with the Pixel inspector tool, which puts the data in to the Data Tree, allowing you to examine it in the following panels:

Analyzing lines and surfaces

At one pixel we can analyze data and make a curve of force or interaction energies as a function of cantilever deflection or oscillation amplitude. These curves can be parametrized, for example by fitting the data to a particular model of the interaction force. It is often very interesting to plot how the parameters change along a linear transect of the image. This type of analysis can be made in real time with the Line inspector tool. You can also run analysis of all pixels in a scan file to produce a color map image of each parameter. This later analysis is time consuming and it can be run in a batch processing mode. The creation of these different types of parameter plots and maps are described in the following sections:

Special Modes

The intermodulaiton measurement concept can be applied to the many different modes of AFM and several special modes are under development. At present the following modes are available.