Regularization mechanism in blind tip reconstruction procedure

In quantitative investigations of mechanical and chemical surface parameters using atomic force microscopy (AFM) techniques the determination of the probe radius and shape is required. To the most favorable methods of the microprobe characterization belongs the blind tip reconstruction method (BTR). The BTR similar to many other inverse problems is sensitive to noise and needs the so-called regularization mechanism. In this article we describe and investigate two the most popular regularization schemes, which were proposed in Villarubia et al. (1997) [30] and Tian et al. (2008) [31]. We have shown that the procedure described in Tian et al. (2008) [31] enables very effective probe shape reconstruction if we know the statistics of noise present in the AFM system. The increase of effectiveness with relation to the procedure described in Villarubia (1997) [30] is so significant that makes it possible to reconstruct probes with much larger resolution. We have also noticed the fact, that probes reconstructed by means of the procedure presented in Tian et al. (2008) [31] have flat apexes for AFM images with low signal to noise ratio (SNR). We propose procedure, which can improve the probe apex reconstruction. It uses the AFM image to estimate the initial shape of the reconstructed probe. This shape may be further improved by the BTR algorithm. We have shown that it is possible only for the procedure described in Tian et al. (2008) [31].