Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Fast Fourier Transform01:10

Fast Fourier Transform

1.3K
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
1.3K
Trigonometric Fourier series01:17

Trigonometric Fourier series

1.3K
Fourier series is a foundational mathematical technique that decomposes periodic functions into an infinite series of sinusoidal harmonics. This method enables the representation of complex periodic signals as sums of simple sine and cosine functions, facilitating their analysis and interpretation in various fields, including signal processing, acoustics, and electrical engineering.
The trigonometric Fourier series specifically expresses a periodic function with a defined period T using sine...
1.3K
Aliasing01:18

Aliasing

947
Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...
947
Exponential Fourier series01:24

Exponential Fourier series

1.2K
In audio signal processing, the exponential Fourier series plays a crucial role in sound synthesis, allowing complex sounds to be broken down into simpler sinusoidal components. This decomposition process is fundamental in analyzing and reconstructing musical notes and other audio signals. The exponential Fourier series expresses periodic signals as the sum of complex exponentials at both positive and negative harmonic frequencies, providing a powerful tool for signal analysis.
Euler's identity...
1.2K
IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

3.3K
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...
3.3K
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

7.3K
A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
7.3K

You might also read

Related Articles

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

Sort by
Same authorSame journal

Holographic generation of panoramic 3D scenes by concave ellipsoidal mirror reflection.

Optics letters·2026
Same author

Controlled generation of nonlinear dynamic signals in a perturbed photorefractive two-wave mixing process.

Optics express·2025
Same author

Triple-exposure holographic multiplexing for tunable vector-vortex beam generation using different reconstruction effects in azo-carbazole polymer films.

Optics letters·2025
Same author

Hyperboloidal mirror reflection for super-wide viewing zones in computer-generated holography.

Optics letters·2025
Same author

Photoconductive Dynamics of Photorefractive Poly((4-Diphenylamino)benzyl Acrylate)-Based Composites Sensitized by Perylene Bisimide.

Polymers·2025
Same author

Tailoring an arbitrary large vectorial structured light beam array utilizing the tensor theory of multiplexed polarization holograms.

Optics express·2024

Related Experiment Video

Updated: May 5, 2026

Quantifying Microorganisms at Low Concentrations Using Digital Holographic Microscopy DHM
07:27

Quantifying Microorganisms at Low Concentrations Using Digital Holographic Microscopy DHM

Published on: November 1, 2017

9.8K

Fast calculation method for computer-generated cylindrical holograms based on the three-dimensional Fourier spectrum.

Yusuke Sando, Daisuke Barada, Boaz Jessie Jackin

    Optics Letters
    |November 28, 2013
    PubMed
    Summary

    This study derives a rigorous diffraction formula for cylindrical surfaces, enabling efficient calculation of 3D object wavefronts using Fourier transforms and numerical simulations.

    More Related Videos

    Recording Ultra-Realistic Full-Color Analog Holograms for Use in a Moving Hologram Display
    09:04

    Recording Ultra-Realistic Full-Color Analog Holograms for Use in a Moving Hologram Display

    Published on: January 14, 2020

    9.3K
    Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization
    10:28

    Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization

    Published on: July 5, 2016

    9.5K

    Related Experiment Videos

    Last Updated: May 5, 2026

    Quantifying Microorganisms at Low Concentrations Using Digital Holographic Microscopy DHM
    07:27

    Quantifying Microorganisms at Low Concentrations Using Digital Holographic Microscopy DHM

    Published on: November 1, 2017

    9.8K
    Recording Ultra-Realistic Full-Color Analog Holograms for Use in a Moving Hologram Display
    09:04

    Recording Ultra-Realistic Full-Color Analog Holograms for Use in a Moving Hologram Display

    Published on: January 14, 2020

    9.3K
    Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization
    10:28

    Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization

    Published on: July 5, 2016

    9.5K

    Area of Science:

    • Optics and Photonics
    • Computational Electromagnetics
    • Wave Propagation

    Background:

    • Understanding the diffraction of three-dimensional (3D) objects is crucial for various optical applications.
    • Existing models often face challenges in accurately describing diffraction onto curved surfaces.
    • Fourier analysis provides a powerful framework for analyzing wave phenomena.

    Purpose of the Study:

    • To establish a rigorous diffraction formula for cylindrical surfaces.
    • To develop efficient computational methods for calculating diffracted wavefronts.
    • To demonstrate the practical application through numerical simulation and optical experiments.

    Main Methods:

    • Analysis of the relationship between a 3D object and its diffracted wavefront in 3D Fourier space.
    • Derivation of a rigorous diffraction formula specifically for cylindrical surfaces.
    • Application of one-dimensional (1D) convolution integrals and 1D inverse Fourier transforms for azimuthal and height spatial frequency directions.
    • Utilization of fast Fourier transforms (FFTs) for computational efficiency.
    • Numerical simulation of diffracted wavefronts on cylindrical surfaces.
    • Optical experiment demonstrating reconstruction from cylindrical holograms.

    Main Results:

    • A rigorous diffraction formula for cylindrical surfaces was successfully derived.
    • Efficient computational methods using 1D convolution and inverse Fourier transforms were established.
    • Numerical simulations accurately depicted diffracted wavefronts on cylindrical surfaces.
    • An optical experiment validated the theoretical framework through reconstruction from cylindrical holograms.

    Conclusions:

    • The derived diffraction formula provides an accurate and efficient method for analyzing wavefronts diffracted by cylindrical objects.
    • The combination of Fourier analysis and numerical simulations offers a powerful tool for optical reconstruction and design.
    • The demonstrated optical experiment confirms the practical applicability of the theoretical framework for cylindrical holography.