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

Discrete-time Fourier transform

Discrete-time Fourier transform

The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...

Fast Fourier Transform

Fast Fourier Transform

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...

Discrete Fourier Transform

Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...

Total Internal Reflection Fluorescence Microscopy

Total Internal Reflection Fluorescence Microscopy

Total internal reflection fluorescence microscopy or TIRF is an advanced microscopic technique used to visualize fluorophores in samples close to a solid surface with a higher refractive index, such as a glass coverslip. TIRF only allows fluorophores in proximity to the solid surface to be excited. When light from a medium with a lower refractive index (such as air) hits the glass coverslip at a critical angle, the light undergoes total internal reflection stead of passing through the glass.

Continuous -time Fourier Transform

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...

You might also read

Related Articles

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

Sort by

Same author

Extracting one-dimensional wavelet features with a diffractive optical inner-product transform.

Applied optics·2010

Same author

Single-element diffractive optical system for real-time processing of synthetic aperture radar data.

Applied optics·2010

Same author

Complex-valued Fresnel-transform sampling.

Applied optics·2010

Same author

Diffractive optical Hough transform implemented with phase singularities.

Applied optics·2010

Same author

Implementation of general point transforms with diffractive optics.

Applied optics·2010

Same author

Diffractive optical implementation of rotation transform performed by using phase singularities.

Applied optics·2010

Same journal

Multifunctional reconfigurable terahertz metasurface based on vanadium dioxide phase transition: achieving broadband absorption and efficient polarization conversion.

Applied optics·2026

Same journal

High-Q-factor electromagnetically induced transparency utilizing quasi-bound states in the continuum in an all-dielectric terahertz metasurface.

Applied optics·2026

Same journal

Automated stitching interferometry for high-precision metrology of X-ray mirrors.

Applied optics·2026

Same journal

Experimental demonstration of an approach to designing a metal-dielectric DBR resonant cavity structure.

Applied optics·2026

Same journal

High-precision wavefront reconstruction from a single-shot interferogram using a physics-driven hybrid feature calibration network.

Applied optics·2026

Same journal

Ultra-high-Q Fano resonance based on coupled topological corner states in Kagome photonic crystals.

Applied optics·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jun 6, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

Rotation- and scale-invariant feature extraction by a diffractive optical inner-product transform.

|November 19, 2010

Summary

This summary is machine-generated.

A novel diffractive optical element extracts rotation- and scale-invariant image features. This element uses basis functions derived from the Fourier-Mellin transform for image analysis.

More Related Videos

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

Published on: May 30, 2016

Related Experiment Videos

Last Updated: Jun 6, 2026

A Multimodal Wide-Field Fourier-Transform Raman Microscope

A Multimodal Wide-Field Fourier-Transform Raman Microscope

Published on: December 30, 2025

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors

Published on: May 30, 2016

Area of Science:

Optical engineering
Image processing

Background:

Feature extraction is crucial for image analysis.
Traditional methods struggle with rotation and scale variations.

Purpose of the Study:

To present a diffractive optical element (DOE) for rotation- and scale-invariant feature extraction.
To demonstrate the DOE's functionality using simulated image data.

Main Methods:

The DOE performs an inner product between an input image and specific basis functions.
These basis functions are derived from the Fourier-Mellin transform.
Simulations were conducted on scaled and rotated versions of input images.

Main Results:

The diffractive optical element successfully extracted invariant features from simulated images.
The method showed robustness against image scaling and rotation.
Performance was validated using two distinct input images.

Conclusions:

The developed diffractive optical element offers a robust solution for invariant feature extraction.
This technology has potential applications in computer vision and pattern recognition.
The Fourier-Mellin transform-based approach is effective for designing such optical elements.