**1. Introduction**

Calibration of surfaces by optical instruments such as interferometers is a necessary step in many applications in engineering and science. The merit of using optical instruments over stylus instruments is that the optical instruments do not physically contact the surface under test and hence protect the surface from damage. In recent years, automatically controlled interferometers were engineered and provided with computer-aided technologies. A combination of moving parts controlled by various computer techniques and sophisticated electronics, and wave front fitting techniques were used to ensure precision and reliability.

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

However, all two-beam interferometers suffer from the fact that they produce cos2 intensity distributions. This fact makes two-beam interferometers unpopular to characterize strongly curved surfaces and steep edges because of the too high density of fringes which makes the feature too complex to measure. Multiple-beam interferometers are used to characterize these surfaces successfully thanks to the very sharp fringes. In this chapter, we present new frontiers in both two- and multiple-beam interferometers carried out by the author. As modern interferometers use a laser as the light source, spurious and speckle noises arise in the fringe pattern. Numerical techniques should be applied to the fringe pattern to suppress these spurious and speckle noises. In Section 2, limitations of optical instruments including optical aberrations and denoising and effect of noise on phase unwrapping are explained. In Section 3, fundamentals of interferometry with focus on two- and multiple-beam interferometers and their capabilities in testing film thickness, curvatures of strongly curved surfaces, and parallelism of a standard optical flat are described. It is worth mentioning that the in-line configuration of interferometry can feature finer sample spatial details compared with the offaxis configuration. However, using in-line configuration requires the time-sequent phaseshifting (PS) process to eliminate both zero-order and the twin image. Single-shot parallel phase-shifting technique is proposed for real-time measurement. In Section 4, single-shot parallel four-step phase-shifting Fizeau interferometer for three-dimensional (3-D) surface micro-topography measurement is explained. Section 5 gives concluding discussions and remarks.
