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

Poisson Probability Distribution

Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...

Applications of Integration to Probability Density Functions

Applications of Integration to Probability Density Functions

Continuous probability distributions are used to model random variables that can take on any real value within a specified range. These variables do not take on isolated or countable values but rather exist on a continuum. For example, the height of an individual can be measured with increasing precision—such as 163.5 or 165.25 centimeters—demonstrating that height is a continuous random variable.The behavior of such variables is described using a probability density function (PDF), which...

Probability Distributions

Probability Distributions

The probability of a random variable x is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...

Probability Histograms

Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.

Poisson's And Laplace's Equation

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.

Probability in Statistics

Probability in Statistics

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...

You might also read

Related Articles

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

Sort by

Same author

Real-time optical image subtraction and edge enhancement using ferroelectric liquid-crystal devices based on speckle modulation.

Applied optics·2010

Same author

Color modulation properties of a liquid-crystal device.

Applied optics·2010

Same author

Image subtraction using polarization modulation of liquid-crystal television.

Applied optics·2010

Same author

Accuracy of peak detection in speckle clipping correlation.

Applied optics·2010

Same author

Frequency dependence of modal noise in multimode optical fibers.

Applied optics·2010

Same author

Intensity clipping correlation of speckle patterns.

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 12, 2026

Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells

Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells

Published on: September 16, 2020

Joint probability density function of partially developed speckle patterns.

|June 10, 2010

Summary

This summary is machine-generated.

This study derives the theoretical form of the joint probability density function (PDF) for partially developed speckle patterns. The findings reveal the joint PDF can be represented by an infinite series involving modified Bessel functions.

More Related Videos

Live Cell Imaging of F-actin Dynamics via Fluorescent Speckle Microscopy (FSM)

Live Cell Imaging of F-actin Dynamics via Fluorescent Speckle Microscopy (FSM)

Published on: August 5, 2009

Applying Permanent, Robust Stenciled Patterns of Fine Particles to Elastomeric Surfaces

Applying Permanent, Robust Stenciled Patterns of Fine Particles to Elastomeric Surfaces

Published on: July 8, 2025

Related Experiment Videos

Last Updated: Jun 12, 2026

Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells

Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells

Published on: September 16, 2020

Live Cell Imaging of F-actin Dynamics via Fluorescent Speckle Microscopy (FSM)

Live Cell Imaging of F-actin Dynamics via Fluorescent Speckle Microscopy (FSM)

Published on: August 5, 2009

Applying Permanent, Robust Stenciled Patterns of Fine Particles to Elastomeric Surfaces

Applying Permanent, Robust Stenciled Patterns of Fine Particles to Elastomeric Surfaces

Published on: July 8, 2025

Area of Science:

Optics and Photonics
Statistical Optics
Probability Theory

Background:

Speckle patterns are crucial in optical metrology and imaging.
Understanding the statistical properties of speckle is essential for accurate analysis.
Partially developed speckle patterns present unique statistical challenges.

Purpose of the Study:

To theoretically derive the joint probability density function (PDF) for partially developed speckle patterns.
To provide a mathematical framework for analyzing the statistical behavior of these patterns.
To establish a foundation for advanced speckle metrology techniques.

Main Methods:

The study assumes circular statistics for partially developed speckle patterns.
A theoretical derivation of the joint PDF was performed based on this assumption.
The derived PDF is expressed using mathematical functions.

Main Results:

The theoretical form of the joint PDF for partially developed speckle patterns was successfully derived.
The joint PDF is shown to be representable by an infinite series.
This series consists of products of modified Bessel functions of the first kind.

Conclusions:

The derived joint PDF provides a comprehensive statistical description of partially developed speckle patterns.
The representation using modified Bessel functions offers a practical tool for further analysis.
This work contributes to a deeper understanding of speckle statistics in optical applications.