Manipulations of Wavefront Propagation: Useful Methods and Applications for Interferometric Measurements and Scanning.

Phase measurements obtained by high-coherence interferometry are restricted by the 2π ambiguity, to height differences smaller than λ/2. A further restriction in most interferometric systems is for focusing the system on the measured object. We present two methods that overcome these restrictions. In the first method, different segments of a measured wavefront are digitally propagated and focused locally after measurement. The divergent distances, by which the diverse segments of the wavefront are propagated in order to achieve a focused image, provide enough information so as to resolve the 2π ambiguity. The second method employs an interferogram obtained by a spectrum constituting a small number of wavelengths. The magnitude of the interferogram's modulations is utilized to resolve the 2π ambiguity. Such methods of wavefront propagation enable several applications such as focusing and resolving the 2π ambiguity, as described in the article.

Wavefront reconstruction by spatial-phase-shift imaging interferometry.

Common-path imaging interferometers offer some advantages over other interferometers, such as insensitivity to vibrations and the ability to be attached to any optical system to analyze an imaged wavefront. We introduce the spatial-phase-shift imaging interferometry technique for surface measurements and wavefront analysis in which different parts of the wavefront undergo certain manipulations in a certain plane along the optical axis. These manipulations replace the reference-beam phase shifting of existing interferometry methods. We present the mathematical algorithm for reconstructing the wavefront from the interference patterns and detail the optical considerations for implementing the optical system. We implemented the spatial phase shift into a working system and used it to measure a variety of objects. Measurement results and comparison with other measurement methods indicate that this approach improves measurement accuracy with respect to existing quantitative phase-measurement methods.

Spatial phase-shift interferometry--a wavefront analysis technique for three-dimensional topometry.

We describe a new wavefront analysis method, in which certain wavefront manipulations are applied to a spatially defined area in a certain plane along the optical axis. These manipulations replace the reference-beam phase shifting of existing methods, making this method a spatial phase-shift interferometry method. We demonstrate the system's dependence on a defined spatial Airy number, which is the ratio of the characteristic dimension of the manipulated area and the Airy disk diameter of the optical system. We analytically obtain the resulting intensity data of the optical setup and develop various methods to accurately reconstruct the inspected wavefront out of the data. These reconstructions largely involve global techniques, in which the entire wavefront's pattern affects the reconstruction of the wavefront in any given position. The method's noise sensitivity is analyzed, and actual reconstruction results are presented.