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$Interference and Diffraction$ 02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.

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Related Experiment Video

Updated: Jul 4, 2026

Single-Digit Nanometer Electron-Beam Lithography with an Aberration-Corrected Scanning Transmission Electron Microscope

Single-Digit Nanometer Electron-Beam Lithography with an Aberration-Corrected Scanning Transmission Electron Microscope

Published on: September 14, 2018

Contrast in four-beam-interference lithography.

Justin L Stay¹, Thomas K Gaylord

¹School of Electrical and Computer Engineering, Georgia Institute of Technology, 777 Atlantic Drive NW, Atlanta, Georgia 30332-0250, USA.

|July 3, 2008

Summary

This summary is machine-generated.

Four-beam interference patterns can replicate Bravais lattice symmetries. This study details contrast ranges, unity contrast conditions, and pattern types for cubic lattices, advancing optical crystallography.

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Area of Science:

Crystallography
Optics
Solid-state physics

Background:

Four linearly polarized, monochromatic plane waves can generate interference patterns.
These patterns can exhibit symmetries corresponding to all 14 Bravais lattices.
Previous work established the potential for Bravais lattice symmetry replication.

Purpose of the Study:

To determine the range of absolute contrasts in four-beam interference.
To identify conditions required for achieving unity absolute contrast.
To classify interference pattern types under uniform contrast conditions for specific lattices.

Main Methods:

Analysis of four-beam interference configurations.
Mathematical determination of absolute contrast values.
Investigation of conditions leading to uniform contrast.
Examination of resulting interference patterns for cubic Bravais lattices.

Main Results:

Defined the spectrum of achievable absolute contrasts for four-beam interference.
Established the specific conditions necessary for obtaining unity absolute contrast.
Characterized the interference patterns generated under uniform contrast for base-centered cubic, face-centered cubic, and simple cubic lattices.

Conclusions:

Four-beam interference offers a versatile method for generating patterns with crystallographic symmetries.
Contrast control is crucial for specific pattern generation and lattice replication.
The study provides a framework for understanding and predicting interference patterns in optical crystallography.