Contents I. Introduction
High-Quality envelope restoration and accurate central fringe position identification are critical for effective white-light interferometer (WLI) images. Some schemes and algorithms have previously been presented for these purposes [1]–[7]. These algorithms, performed in the spatial domain, suppress noise, recover the envelope, and find the central fringe position in different ways. However, all of these methods directly collect data from interferograms without preprocessing, and their results will inevitably include background noises. For images captured by a charge-coupled device (CCD) camera, degradation factors from several aspects may be present, forming a potential source of errors for envelope recovery and central fringe position identification when using general preprocessing techniques performed in the spatial domain. One such factor could be noise introduced by improper adjustment of the exposure time and/or gain of the CCD camera. Another important factor is minor optic imperfections or dust on the component surfaces of the bulky decoding system, which adds additional background noises to the fringe patterns. Generally, these patterns have different shapes, sizes, and intensity distributions. Their physical positions in every image will not change during the measurement. However, when fringes shift continuously across the CCD sensor array, these noise patterns will affect the intensity of the fringes in extremely complex ways, adding more uncertainties to the image quality and data fitting process, and contributing to the central fringe measurement errors. Unfortunately, it is difficult to remove these noise patterns by general image processing methods performed in the spatial domain such as vertical edge filter.
