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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.

IR Frequency Region: Fingerprint Region

IR Frequency Region: Fingerprint Region

IR spectra are divided into two main regions: the diagnostic region and the fingerprint region. The diagnostic region of the spectrum lies above 1500 cm−1. The absorptions resulting from single-bond vibrations of the N–H, C–H, and O–H stretch at higher wavenumbers and appear on the left side of the spectrum. The stretching absorptions of the C≡C and C≡N occur between 2100–2300 cm−1. In contrast, those arising from stretching absorptions of the C=O, C=N, and C=C occur between 1600–1850 cm−1.
The...

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to the...

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single stretching vibration...

IR Spectroscopy: Molecular Vibration Overview

IR Spectroscopy: Molecular Vibration Overview

When Infrared (IR) radiation passes through a covalently bonded molecule, the bonds transition from lower to higher vibrational levels. The fundamental vibrational motions that result in infrared absorption can be classified as stretching or bending vibrations.
Stretching vibrations are vibrational motions that occur along the bond line, changing the bond length or distance between two bonded atoms. They are further distinguished as symmetric or asymmetric. In symmetric stretching, the...

Phase Contrast and Differential Interference Contrast Microscopy

Phase Contrast and Differential Interference Contrast Microscopy

Phase-Contrast Microscopes
In-phase-contrast microscopes, interference between light directly passing through a cell and light refracted by cellular components is used to create high-contrast, high-resolution images without staining. It is the oldest and simplest type of microscope that creates an image by altering the wavelengths of light rays passing through the specimen. Altered wavelength paths are created using an annular stop in the condenser. The annular stop produces a hollow cone of...

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Related Experiment Video

Updated: Jul 7, 2026

Micro/Nano-scale Strain Distribution Measurement from Sampling Moiré Fringes

Micro/Nano-scale Strain Distribution Measurement from Sampling Moiré Fringes

Published on: May 23, 2017

Measurement range analysis in moiré evaluation Fizeau interferometry.

B V Dorrío, C López, A F Doval

|June 1, 1997

Summary

This study introduces a method for evaluating Fizeau interferograms using phase-stepping algorithms. It determines the measurement range for height surface derivatives, verified with spherical surface measurements.

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Area of Science:

Optical Metrology
Surface Metrology
Interferometry

Background:

Fizeau interferograms are crucial for surface analysis.
Two-beam phase-stepping algorithms require specific intensity profiles.
Existing methods may have limitations in measurement range.

Purpose of the Study:

To evaluate Fizeau interferograms using phase-stepping algorithms.
To determine the measurement range of this evaluation method based on height surface derivatives.
To validate the method by measuring a spherical surface.

Main Methods:

Obtaining sinusoidal intensity profiles by low-pass filtering moiré patterns.
Superposing Fizeau interferograms onto a Ronchi grid.
Modulating phase via in-plane grid displacement using a motorized stage.
Calculating the measurement range as a function of the maximum derivative of height surfaces.

Main Results:

The study successfully calculated the measurement range for the Fizeau interferogram evaluation method.
Experimental verification using a spherical surface in various configurations confirmed the calculated range.
The relationship between measurement range and surface height derivatives was established.

Conclusions:

The proposed method effectively evaluates Fizeau interferograms for surface analysis.
The determined measurement range provides critical parameters for practical applications.
The findings are validated through experimental measurements of a spherical surface.