Determination of two-dimensional planar displacement by moiré fringes of concentric-circle gratings

Investigation of the moiré patterns of defected radial and circular gratings using the reciprocal vectors approach

In this work, for the first time to the best of our knowledge, an investigation on the moiré patterns of superimpositions of two radial or two circular gratings consisting of topological defects and their mutual superimpositions with each other, or with linear forked gratings or defected zone plates, is presented. For characterization of the resulting moiré patterns, we use the reciprocal vectors approach. In this approach, by considering local spatial frequencies for the superimposed structures, their reciprocal vectors are determined from the transmission function of the structures. The local reciprocal vector of the resulting moiré pattern at a given point is determined in terms of the local reciprocal vectors of the superimposed structures defined at the same point. In this approach, the topological singularities of the superimposed structures are described by the azimuthal component of the reciprocal vectors. This formulation is very simple, uniform, and comprehensive. In this work, we offer a detailed discussion on the different resulting moiré patterns for the above-mentioned superimpositions and some potential applications of the proposed superimpositions are introduced. In addition, different resulting moiré patterns are simulated.

Moiré fringe alignment using composite circular-line gratings for proximity lithography

We explore the feasibility of a controllable and easy-to-implement moiré-based composite circular-line gratings imaging scheme for optical alignment in proximity lithography. One circular grating and four line gratings located on both the mask alignment mark and wafer alignment mark are used to realize the coarse alignment and fine alignment respectively. The fundamental derivation of coarse alignment employing circular gratings and fine alignment employing line gratings are given. Any displacement of misalignment that occurs at the surface of two overlapped gratings can be sensed and determined through subsequent fringe phase analysis without the influence of the gap between the mask and the wafer or wafer process. The design and manufacture process of the alignment marks are presented. The experimental results validate and demonstrate the feasibility of the proposed approach.

Determination of small angular displacement by moiré fringes of matched radial-parallel gratings

We investigate the properties of the moiré fringes of matched radial-parallel (MRP) gratings that are useful for the fine visual indication of angular displacements. Moiré patterns formed by overlapping two different MRP gratings of angular pitches, P(theta) and P(theta)? (<P(theta)), can provide a simple fringe-counting method for determining both the angle and the direction of the relative angular displacement of the gratings within the accuracy of (P(theta)?/M(theta)), where M(theta) is the angular magnification for radial vernier fringes.