Practical method to determine the filter shape function used in the three-dimensional Fourier filtering method

The procedure to determine the appropriate filter shape function used in the three-dimensional Fourier filtering method (3D-FFM) is discussed from a practical point of view, so as to reduce the artificial contrast induced by the processing and to achieve a high signal-to-noise ratio. The effects of cutting off the high spatial frequency of the filter shape function and damping at low spatial frequency were investigated by using through-focus images of a gold (110) thin film. In addition, the effect of the width of the filtered area was discussed using through-focus images of a carbon nanotube. For reliable image processing, the filter shape function should be cut off beyond the information limit and attenuated with damping at low spatial frequency. Furthermore, the extraction area should include the distributed area of the relevant structural components appearing in the 3-D Fourier spectrum.