Precise estimation of the surface profile of an object is a critical task in many industrial applications. It can be achieved by a variety of methods, including contact methods such as stylus-based profile measurement and noncontact optical methods that fall into interferometric techniques, focus detection, and fringe projection methods, to name a few. The authors of this paper describe a profile measuring technique that falls under the method of optical fringe projection.

Surface profiles can be measured with subnanometer resolution easily with these techniques, but when it comes to fast acquisition of surface information, nothing beats light! Optical methods are way ahead in accuracy and speed in this regard. When using interferometric methods to retrieve the surface profile of objects, one ends up obtaining the height information in terms of fringe shifts or wavefront distortions, related to what is called phase information.

In certain applications the phase is related to a physical quantity, e.g., in astronomy it relates to the object phase and its bispectrum phase, in MRI it is associated with the degree of magnetic field inhomogeneities in the water–fat separation, and in optics it corresponds to wavefront distortions. The correct phase information can lead to a quantitative and accurate measurement of these physical quantities. Most often, absolute phase is wrapped into the interval [-π, +π], leading to an ambiguity problem. Phase unwrapping is a mathematical technique used to solve this problem and therefore obtain the absolute phase from the wrapped phase data. Many algorithms have been developed to address the phase-unwrapping problem. The work of Jiang et al. proposes a method to overcome the burden on the speed of calculations for such a problem.

The authors propose an efficient and fast unsupervised algorithm to acquire the true phase from the wrapped one, based on “clustering driven noise residue filtering.” The filter is based on the idea that most of the residues (discontinuities in the phase that appear when integration around a path consisting of 2x2 pixels has a value other than zero) are present in areas surrounding noisy wrapped phases. For tightly packed fringes, this method divides the correct and noisy phase into filtering windows having similar values and uses a filter-driven, path-independent phase-unwrapping method that results in a noise-free surface profile. This method of obtaining true phase from noisy data is efficient and faster than the previously used algorithms for applications such as surface profile measurement, in which the aim is to obtain good quality maps of an object with subnanometer resolution in height measurements. The current approach is going to be extremely advantageous for applications in which noncontact, quick, and automated inspection of solid surfaces is required, such as industrial inspections and manufacturing environments.

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