Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...

Gain

Gain

Gain and phase shift are properties of linear circuits that describe the effect a circuit has on a sinusoidal input voltage or current. The circuit's behavior that contains reactive elements will depend on the frequency of the input sinusoid. As a result, it is observed that the gain and phase shift will all be frequency functions.
Gain:
Suppose Vin is the input and Vout is the output signal to a circuit.

Interference: Path Lengths

Interference: Path Lengths

Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...

The Phase Rule

The Phase Rule

The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...

Time and frequency -Domain Interpretation of Phase-lead Control

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...

NMR Spectrometers: Resolution and Error Correction

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Binding and Functional Folding (BFF): A Physiological Framework for Studying Biomolecular Interactions and Allostery.

Journal of molecular biology·2022

Same author

High-numerical-aperture cryogenic light microscopy for increased precision of superresolution reconstructions.

Proceedings of the National Academy of Sciences of the United States of America·2017

Same author

Imaging enzyme kinetics at atomic resolution.

IUCrJ·2016

Same author

Computing spatial information from Fourier coefficient distributions.

The Journal of membrane biology·2011

Same author

3D reconstruction from electron micrographs a personal account of its development.

Methods in enzymology·2010

Same author

Bacterial flagellum: visualizing the complete machine in situ.

Current biology : CB·2006

Same journal

Report of the Executive Committee for 2006.

Acta crystallographica. Section A, Foundations of crystallography·2020

Same journal

Spin line groups.

Acta crystallographica. Section A, Foundations of crystallography·2013

Same journal

Distribution rules of systematic absences on the Conway topograph and their application to powder auto-indexing.

Acta crystallographica. Section A, Foundations of crystallography·2013

Same journal

Platonic solids generate their four-dimensional analogues.

Acta crystallographica. Section A, Foundations of crystallography·2013

Same journal

C70, C80, C90 and carbon nanotubes by breaking of the icosahedral symmetry of C60.

Acta crystallographica. Section A, Foundations of crystallography·2013

Same journal

Comparative study of X-ray charge-density data on CoSb3.

Acta crystallographica. Section A, Foundations of crystallography·2013

See all related articles

Search research articles

Related Experiment Video

Updated: Jul 7, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Why phase errors affect the electron function more than amplitude errors.

Eaton Lattman¹, David DeRosier

¹Thomas C. Jenkins Department of Biophysics, the Johns Hopkins University, Baltimore, MD 21218, USA.

Acta Crystallographica. Section A, Foundations of Crystallography

|February 21, 2008

Summary

This summary is machine-generated.

Amplitude swapping in structure factor analysis alters images by convolution. Swapped phases result in images that do not resemble the original structure, as detailed quantitatively.

More Related Videos

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Published on: May 27, 2021

Related Experiment Videos

Last Updated: Jul 7, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Neutron Spin Echo Spectroscopy as a Unique Probe for Lipid Membrane Dynamics and Membrane-Protein Interactions

Published on: May 27, 2021

Area of Science:

Crystallography and Structural Analysis
Image Processing in Science

Background:

Structure factors (F) are crucial for determining atomic arrangements in crystalline structures.
Amplitude swapping is a technique to modify structure factors, potentially altering the resulting image representation.

Purpose of the Study:

To quantitatively describe the effects of amplitude swapping on structure factors and their corresponding images.
To analyze the impact of phase differences on image reconstruction after amplitude swapping.

Main Methods:

Structure factors (Fexp(iα)) are multiplied by a factor (G/F) to achieve amplitude swapping.
The corresponding image (f) is convolved with the Fourier transform of the swapping factor (k).
Phase differences (Δα) are introduced, and the image is convolved with the Fourier transform of the phase difference (l).

Main Results:

Amplitude swapping, when combined with a convolution kernel (k) with a large origin peak, results in an image (f * k) that approximates the original image (f).
Swapped phases, however, lead to convolution with a kernel (l) lacking a strong origin peak, producing an image (f * l) that does not resemble the original.
The study provides quantitative measures to support these observations.

Conclusions:

Amplitude swapping preserves image resemblance when the convolution kernel has a dominant central peak.
Phase randomization or significant phase differences after swapping lead to image distortions that do not resemble the original structure.
The mathematical framework presented offers a way to understand and predict these effects in structural analysis.