Moiré fringes of higher-order harmonics versus higher-order moiré patterns

Area of Science:

• Physics
• Materials Science
• Optics

Background:

• Moiré patterns arise from the superposition of periodic or quasi-periodic structures.
• Understanding combinational spatial frequencies is crucial for analyzing complex interference patterns.

Purpose of the Study:

• To develop a simple and comprehensive approach for classifying combinational spatial frequencies in superimposed structures.
• To analyze the formation of different moiré patterns, including defected ones, and their characteristics.

Main Methods:

• Utilizing reciprocal vectors to represent spectral components of structures.
• Introducing a reciprocal vectors equation for combinational frequencies.
• Classifying moiré patterns into four categories: conventional, higher-order harmonics, higher-order, and pseudo-moiré patterns.

Main Results:

• A classification scheme for moiré patterns based on combinational frequencies is established.
• Conditions for the simultaneous formation of moiré patterns with different harmonics are investigated.
• The dependency of defect number and sign in moiré fringes on grating defects and harmonics is derived and verified.

Conclusions:

• The proposed reciprocal vectors equation provides a unified framework for classifying moiré patterns.
• The analysis clarifies the distinction between higher-order harmonic moiré fringes and higher-order moiré patterns.
• The study offers insights into defect formation in moiré patterns, with implications for optical vortex interference analysis.