The use of splines to analyze scanning tunneling microscopy data

Scanning tunneling microscopy (STM) requires a two‐dimensional (2D) image displaying technique for its interpretation. The flexibility and global approximation properties of splines, characteristic of a solid data reduction method as known from cubic spline interpolation, is called for. Splines were used to implement 2D representation, deconvolution, and Fourier transform routines with still a good performance in case of noisy measured functions. The implementation was done on a small computer system (8086/8087 processor) with a reasonable execution time. The underlying mathematics of 2D spline‐based routines will be shown and tests on STM‐like images will be given to show the performance. A reduction of 25–100 in memory of stored data is achieved using splines if these routines are used while scanning a surface as in STM.