By Leitz Wetzlar Leica
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Extra info for Diffraction and Image Formation
It is important to recognize that the cantilever interacts with the surface of the sample by forces acting on its tip which is located at a distance δ from its free end. The laser beam, in contrast, is incident at a particular point across the cantilever, not necessarily at its free end. The position of the laser spot on the cantilever depends on the particular AFM model and cantilever make. Therefore, for a proper interpretation of the bending of a given cantilever, one has to know both its deflection, generated by the tip–sample forces, and its slope at a particular point from which the beam of the laser is deflected.
28) Note the strong dependence of k xT on the thickness and length of the cantilever and on the value of δ. The ratio of the angular and linear spring constants, ξ xT ( x ), is ξ xT ( x ) = k θx ( x) T k xT . 29) Inserting Eqs. 24) and (28) into Eq. 29) gives ξ xT ( x ) = log L L− x L − δ − δ log L δ . 5. The linear spring constant, k xT , is depicted in the figure. 6 shows the displacement of the triangular cantilever, δxT ( x ), as a function of the distance x from its base for Fx = 10 (solid line), 20 (dashed line), and 30 nN (dotted line).
This function is used by the software of the AFM to calibrate the tip–sample force using the specifications of the particular cantilever in use.