Calibration method of the phase-shifting error for the topography measurement utilizing white light interferometric microscopy

Sequence of low coherence interferograms were captured during the vertical scanning of the interferometric microscope in the measurement procedure of the white light interferometric microscopy, and thus the topography of the surface under test was retrieved through determining the locations where the optical path difference (OPD) was zero in the envelope of the correlogram. The calculations of the topography for the micro-structures were composed of the vertical scanning interferometric (VSI) algorithm determining the coarse map and the phase-shifting interferometric (PSI) algorithm retrieving the fine map. Usually, the vertical scanning step was set as one eighth of the central wavelength, but the phase-shifting departures from π/2 inevitably due to the phase shifter error as well as the numerical aperture (NA) effect of the interferometric microscope. In this manuscript, the center-of-gravity solving of the visibility curves was adopted as VSI algorithm, and the 4M-frame method as well as the 7-frame method were both utilized as PSI algorithm respectively. The effect of the phase-shifting error on the topography measurement adopting the three above mentioned methods was discussed. Both theoretical derivations and simulation analysis demonstrate that the 7-frame method was insensitive to phase-shifting errors even under the low coherence illuminations. The fine phase error induced by phase-shifting error utilizing the 4M-frame method was by lucky coincides the form of the NA effect increasing the fringe spacing, and they were cancelled out during the transform from the fine phase to the topography. Therefore, adopting the center-of-gravity method as VSI algorithm and the 4M-frame method as the PSI algorithm, the phase-shifting errors arising from NA effect can be ignored, and the topography can be calibrated confronting the phase shifter error through measuring a certificated step standard in advance. A step height of 460 nm was measured utilizing the proposed method, and the topography demonstrate that it was both accurate and robustness.