Related Experiment Video
Updated: Jun 28, 2026
06:35
Basics of Multivariate Analysis in Neuroimaging Data
Published on: July 24, 2010
Partially correlated thin annular sources: the scalar case.
Franco Gori1, Massimo Santarsiero, Riccardo Borghi
1Dipartimento di Fisica, Universita degli studi Roma Tre, Rome, Italy. gori@uniroma3.it
Summary
This study introduces partially correlated thin annular sources for generating specialized light fields. Researchers developed a method to analyze these sources and predict how their light correlation properties evolve during propagation.
Area of Science:
- Optics and Photonics
- Classical Optics
- Fields and Waves
Background:
- Thin annular sources are crucial for creating diffraction-free and correlated light fields.
- Previous research focused on fully coherent or incoherent annular sources.
- Partially correlated sources offer a new avenue for light field synthesis.
Purpose of the Study:
- To develop a theoretical framework for thin annular sources with partial correlation.
- To analyze the modal expansion of fields generated by these sources.
- To investigate the propagation dynamics of correlation properties in radiated fields.
Main Methods:
- A scalar description of partially correlated thin annular sources was developed.
- The correlation function was assumed to depend only on the angular separation of points.
- Modal expansion of the radiated fields was derived.
Main Results:
- A straightforward method for finding the modal expansion of fields from partially correlated annular sources was established.
- The study demonstrates how correlation properties of the radiated fields evolve during free propagation.
- Examples and potential synthesis schemes for these sources were presented.
Conclusions:
- Partially correlated thin annular sources can be effectively described and analyzed.
- The theoretical framework allows for predicting the behavior of light fields generated by these sources.
- This work opens possibilities for novel applications in optical field synthesis.
More Related Videos
Related Concept Videos
01:28Scalar Notation
Scalar notation is a useful method for simplifying calculations involving vectors. When vectors are added or subtracted, their components can be added or subtracted separately using scalar notation. For instance, force, a vector quantity, can be broken down into its x and y components, called rectangular components, and then the magnitude and direction of these components can be determined using trigonometric functions.
Consider a man pulling a rope from a hook in the northeast direction. The...
Consider a man pulling a rope from a hook in the northeast direction. The...
01:21Couples: Scalar and Vector Formulation
One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel's rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment. To...
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel's rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment. To...
01:06Scalar and Vector Triple Products
Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the resultant is a vector. These rules of the scalar or vector product between two vectors can be applied to multiple vectors to obtain meaningful combinations. The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors.
The scalar triple product is the dot product of a vector with the cross product of two vectors.
01:05Relating Angular And Linear Quantities - II
In the case of circular motion, the linear tangential speed of a particle at a radius from the axis of rotation is related to the angular velocity by the relation:
01:22Scalar and Vectors
In mechanics, commonly used terms like force, speed, velocity, and work can be classified as either scalar or vector quantities. A scalar is a physical quantity that can be described by its magnitude alone and does not require any directional components. Examples of scalar quantities are mass, area, and length.
Scalar quantities with the same physical units can be added or subtracted according to the usual algebra rules for numbers. For example, a class ending 10 min earlier than 50 min lasts...
Scalar quantities with the same physical units can be added or subtracted according to the usual algebra rules for numbers. For example, a class ending 10 min earlier than 50 min lasts...
01:31Resultant Moment: Scalar Formulation
When multiple forces act on an object in two-dimensional space, the concept of the net moment can be used to understand the tendency of these forces to induce rotational motion about a fixed point. The scalar formulation of the resultant moment is a helpful tool in analyzing the equilibrium of structures subjected to multiple forces.
To determine the resultant moment, the moments caused by all the forces in a system in the x-y plane are considered. Positive moments are typically...
To determine the resultant moment, the moments caused by all the forces in a system in the x-y plane are considered. Positive moments are typically...