Plane Fitting & Bow Artifacts

While flattening subtracts an n-th order polynomial from every trace and retrace, plane fitting subtracts one polynomial uniformly in the X- and Y-directions. The polynomials can be of different orders in the two orthogonal directions.

Plane fitting is a necessary complement to flattening. While flattening tends to literally flatten out the large wavelength structure, the purpose of plane fitting it to preserve large scale morphology. It is very useful imaging patterned or lithographed structures where it is precisely the large scale structure that is of interest.

The images are 100 μm scans of a smooth PMMA coated surface. In the top image a 1st order polynomial-- an offset and a tilt-- were removed in both the X- and Y-directions. The surface which is very smooth over a large lateral length. The image looks like a bowl which is a scanner artifact called a bow artifact. It is due to the trajectory scanned by a scanned tip scanner over large distances. The sample really doesn't look like this. Regardless of where one scanned one would obtain a similar image.

The bottom image has a 3rd order polynomial removed in the X- and Y- directions. This has removed the bow artifact. One now has a realistic representation of the surface where surface defects and some large wavelength features on the order of several 10's μm are visible.