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

Reflective Property of Parabolas01:26

Reflective Property of Parabolas

A parabola is a basic type of conic section that results from the intersection of a plane with a double-napped cone in a direction parallel to one of the cone's sides. This U-shaped curve has a distinctive reflective property: all incoming rays parallel to its axis of symmetry are directed toward a single point, known as the focus. This property is widely utilized in optical and communication technologies that require precise signal concentration.In analytic geometry, a parabola is defined as...
Lines in Space01:29

Lines in Space

In three-dimensional analytic geometry, a line can be fully described using vector equations when both a point on the line and its direction are known. This approach has practical applications in fields such as engineering and surveying, where precise spatial modeling is essential. For instance, a laser beam from a surveying instrument directed across a construction site can be modeled mathematically as a line using vectors.Let the laser beam originate from a known point Pโ‚€, represented by the...
Geometry of Hyperbolas01:30

Geometry of Hyperbolas

A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curveโ€™s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
Spherical Coordinates01:23

Spherical Coordinates

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ฯ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ฯ1 and the bottom half has a uniform...
Triple Integrals in Spherical Coordinates01:27

Triple Integrals in Spherical Coordinates

Triple integrals in spherical coordinates provide an efficient method for evaluating volumes over regions with central symmetry, such as spheres. Instead of describing points by rectangular coordinates, spherical coordinates use three variables: ๐œŒ, ๐œƒ, and ๐œ‘. Here, ๐œŒ is the distance from the origin, ๐œƒ is the angle in the xy-plane measured from the positive x-axis, and ๐œ‘ is the angle measured downward from the positive z-axis.To derive the volume of a sphere, the solid region can be divided...

You might also read

Related Articles

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

Sort by
Same author

Leptin and adiponectin receptor expression in oesophageal cancer.

The British journal of surgeryยท2014
Same author

Changes in plasma amino acids during conditioning therapy prior to bone marrow transplantation: Their relevance to antioxidant status.

Amino acidsยท2013
Same author

Patterns of lymphatic drainage and lymph node involvement in esophageal cancer.

Abdominal imagingยท2012
Same author

Pro-inflammatory and tumour proliferative properties of excess visceral adipose tissue.

Cancer lettersยท2011
Same author

Metabolic syndrome and leptin are associated with adverse pathological features in male colorectal cancer patients.

Colorectal disease : the official journal of the Association of Coloproctology of Great Britain and Irelandยท2011
Same author

T lymphocyte activation in visceral adipose tissue of patients with oesophageal adenocarcinoma.

The British journal of surgeryยท2011

Related Experiment Video

Updated: Jul 7, 2026

A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
11:15

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

Published on: May 30, 2016

Imaging a point to a line with a single spherical mirror.

J M Howard, B D Stone

    Applied Optics
    |February 15, 2008
    PubMed
    Summary

    This study presents a design for single spherical mirror systems that create aberration-free line images from point sources. Ray density along the line image is analyzed for uniform and Gaussian beam profiles.

    Area of Science:

    • Optical engineering
    • Image formation optics

    Background:

    • Imaging point sources to line images is crucial in various optical applications.
    • Spherical mirrors are fundamental optical components, but achieving aberration-free line images presents challenges.

    Purpose of the Study:

    • To investigate methods for imaging a single point source to a line image.
    • To present a design study of single spherical mirror systems capable of forming aberration-free line images.

    Main Methods:

    • Derivation of an expression for ray density along the line image.
    • Analysis for both uniform and Gaussian beam profiles.
    • Illustration of resulting ray density profiles for single spherical mirror systems.

    Main Results:

    More Related Videos

    A Guide to Build a Highly Inclined Swept Tile Microscope for Extended Field-of-view Single-molecule Imaging
    08:13

    A Guide to Build a Highly Inclined Swept Tile Microscope for Extended Field-of-view Single-molecule Imaging

    Published on: April 8, 2019

    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
    06:25

    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

    Published on: February 12, 2014

    Related Experiment Videos

    Last Updated: Jul 7, 2026

    A Guide to Structured Illumination TIRF Microscopy at High Speed with Multiple Colors
    11:15

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

    Published on: May 30, 2016

    A Guide to Build a Highly Inclined Swept Tile Microscope for Extended Field-of-view Single-molecule Imaging
    08:13

    A Guide to Build a Highly Inclined Swept Tile Microscope for Extended Field-of-view Single-molecule Imaging

    Published on: April 8, 2019

    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform
    06:25

    Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

    Published on: February 12, 2014

  • A design methodology for single spherical mirror systems producing aberration-free line images is established.
  • Ray density expressions are derived, providing insights into image quality.
  • Ray density profiles are visualized across a broad spectrum of design parameters.

    • Conclusions:

    • Single spherical mirror systems can be designed to achieve aberration-free line image formation.
    • The derived ray density expressions are valuable for predicting and optimizing image performance.
    • The study offers a comprehensive understanding of system design and performance characteristics.