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Related Concept Videos

Polar Coordinates: Problem Solving01:27

Polar Coordinates: Problem Solving

Directional radiation patterns are central to antenna analysis, as they illustrate how signal strength varies with direction. These patterns are often modeled using polar plots, where the radial distance from the origin represents signal intensity at a given angle. A commonly used idealized form is the four-lobed rose curve, which captures the concept of directional beams in a simplified mathematical form.The four-lobed rose curve, described by r = cos⁡(2θ), features four symmetric lobes, each...
Polar Coordinate System01:30

Polar Coordinate System

The polar coordinate system provides a natural way to describe points in the plane when distances and directions are more meaningful than horizontal and vertical displacements. It is especially useful for modeling non-rectangular regions such as circles and spirals, where symmetry about a center point is easier to express than it is in a rectangular grid. A familiar example is a ship’s plan position indicator, which marks detected targets as dots positioned relative to the ship at the display’s...
Graphs of Polar Equations01:17

Graphs of Polar Equations

The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
Polar Equations of Conics01:29

Polar Equations of Conics

A conic section can be defined in polar coordinates as the set of all points whose distance from a fixed point, known as the focus, bears a constant ratio to their distance from a fixed line, known as the directrix. This constant ratio is called the eccentricity. This definition unifies all types of conic sections—ellipses, parabolas, and hyperbolas—under a single framework. When the focus is positioned at the origin of the polar coordinate system, a single polar equation can describe any conic...
Integration Applied to Polar Coordinates to Find Areas01:15

Integration Applied to Polar Coordinates to Find Areas

A rotating lawn sprinkler with an uneven spray pattern produces a variable reach as it distributes water in different directions. This directional variation in spray distance can be effectively described using polar coordinates, where the distance from the center is represented as a function of the angle of rotation. The path traced by the spray then forms a polar curve, which captures the irregularities in the sprinkler’s reach across the full rotation.To calculate the total area watered by...
Polar and Cylindrical Coordinates01:22

Polar and Cylindrical Coordinates

The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Published on: September 5, 2019

Fundamental estimation bounds for polarimetric imagery.

Daniel A Lemaster1

  • 1Department of Electrical and Computer Engineering, Air Force Institute of Technology, 2950 Hobson Way, Wright-Patterson AFB, OH 45433, USA. daniel.lemaster@afit.edu

Optics Express
|August 6, 2008
PubMed
Summary

Accurate channel registration is vital for passive polarimetric imaging. This study uses the Cramer-Rao bound to define registration precision limits, aiding optimal channel design for better image estimation.

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Area of Science:

  • Optical Engineering
  • Image Processing
  • Remote Sensing

Background:

  • Effective use of passive polarimetric imagery requires precise channel-to-channel registration.
  • Registration errors can significantly degrade image quality and data interpretation.

Purpose of the Study:

  • To determine the theoretical limits of registration precision for passive polarimetric imagery.
  • To analyze the impact of misregistration on Stokes image estimation.
  • To establish criteria for preferring joint estimation over external registration correction.

Main Methods:

  • Application of the Cramer-Rao bound to quantify registration precision limits.
  • Analysis of factors including scene polarization diversity, channel noise, and translational errors.
  • In-depth exploration of misregistration effects on Stokes image estimation.

Main Results:

  • The Cramer-Rao bound provides a framework for understanding registration precision limits.
  • Misregistration effects on Stokes image estimation are quantified.
  • Conditions under which joint estimation is advantageous are identified.

Conclusions:

  • The Cramer-Rao bound is a valuable tool for optimizing passive polarimetric imaging systems.
  • Proposed optimum polarization channel arrangements can enhance registration accuracy.
  • Understanding registration limits is crucial for reliable polarimetric data exploitation.