Strategy for faster blind reconstruction of tip geometry for scanned probe microscopy

In scanned probe microscopy, it is necessary to know the tip's geometry in order to correct image distortions due to its finite size. Heretofore, methods have focused upon determining the tip shape by erosion of a 'tip characterizer' of known geometry from its image. Three dimensional knowledge of the characterizer with uncertainties small at the size scale of the tip is a prerequisite for this method. The necessary accuracy is often difficult to meet in practice, particularly for characterizers with relief on the order of a micrometer such as are required to measure tips for use with microlithographic specimens A recently proposed alternative, blind reconstruction, permits estimation of the tip shape even with an unknown tip characterizer. The method relies upon the fact that tips which are too blunt are inconsistent with observed image features. For each pixel on a measured image, one may determine a corresponding outer bound on the tip shape. The actual tip must be consistent with the bounds determined for all image points. For well-chosen characterizers, blind reconstruction provides a good estimate of the tip geometry. Although this method eliminates the need for separate calibration of the tip characterizer, it is more computationally intensive than reconstruction by erosion. Blind reconstruction is reviewed, and a strategy for decreasing the computation time is discussed. A factor of three or more may be saved for typical images in an exact calculation, while an additional factor of ten or more may be saved by restoring to approximate methods.