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

Reflective Property of Parabolas

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...

Surface Area Calculations

Surface Area Calculations

Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...

Geometry of Hyperbolas

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 curve’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...

Centroid for the Paraboloid of Revolution

Centroid for the Paraboloid of Revolution

The paraboloid of revolution is an axially symmetric surface generated by rotating a parabola around its axis. This shape has several applications in mechanical engineering due to its advantageous structural properties, such as strength against stress concentration points and rotational symmetry.
The centroid for the paraboloid of revolution is the point where all the mass of the paraboloid is concentrated. This centroid is important for engineering applications, as it determines how forces are...

Gauss's Law: Spherical Symmetry

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 ρ0, 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 ρ1 and the bottom half has a uniform...

Design of Prismatic Beams for Bending

Design of Prismatic Beams for Bending

The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and stress...

You might also read

Related Articles

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

Sort by

Same author

Data of the Insect Biome Atlas: a metabarcoding survey of the terrestrial arthropods of Sweden and Madagascar.

Scientific data·2025

Same author

Wide volume versus helical acquisition using 320-detector row computed tomography for computed tomography urography in adults.

Diagnostic and interventional imaging·2018

Same author

A view from the outside in.

IEEE pulse·2014

Same author

What is biocompatibility?: a new definition based on the latest technology.

IEEE pulse·2014

Same author

Biocompatible medical devices: raise the bar for health care.

IEEE pulse·2014

Same author

Multifaceted biomaterials extend to multiple uses: new developments in biocompatibility.

IEEE pulse·2014

Search research articles

Related Experiment Video

Updated: Jun 15, 2026

Microfabrication of Implantable Optics Integrated in a Microstructured Imaging Window for Advanced In Vivo Imaging

Microfabrication of Implantable Optics Integrated in a Microstructured Imaging Window for Advanced In Vivo Imaging

Published on: April 11, 2025

Geometrical design for aspheric reflecting systems.

|March 11, 2010

Summary

New geometric design methods calculate aspheric surfaces for optical systems. These procedures correct optical path length (OPL) and offense against the sine condition (OCS), enabling novel telescope and microscope designs.

Area of Science:

Optical Engineering
Geometric Optics
Telescope Design

Background:

Designing optical systems with aspheric surfaces presents unique challenges.
Existing methods may not adequately address simultaneous correction of optical path length (OPL) and offense against the sine condition (OCS), especially for extreme focal ratios.

Purpose of the Study:

To present two novel geometric design procedures for calculating aspheric surfaces.
To enable the simultaneous correction of OPL and OCS for improved optical system performance.
To explore applications in advanced telescope and microscope objective designs.

Main Methods:

Development of a procedure for calculating individual reflecting surfaces to correct OPL.
Development of a procedure for jointly calculating pairs of surfaces to correct both OPL and OCS.

More Related Videos

Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging

Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging

Published on: September 8, 2017

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

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

Published on: April 8, 2019

Related Experiment Videos

Last Updated: Jun 15, 2026

Microfabrication of Implantable Optics Integrated in a Microstructured Imaging Window for Advanced In Vivo Imaging

Microfabrication of Implantable Optics Integrated in a Microstructured Imaging Window for Advanced In Vivo Imaging

Published on: April 11, 2025

Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging

Demonstration of a Hyperlens-integrated Microscope and Super-resolution Imaging

Published on: September 8, 2017

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

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

Published on: April 8, 2019

Application of these procedures to Arecibo-style telescopes, coma-correctors, and various aplanatic systems.

Main Results:

The proposed procedures are effective for calculating aspheric surfaces, even with extreme focal ratios.
Successful application to the design of Arecibo-style telescopes and their coma-correctors.
Emergence of new aplanatic designs for telescope and microscope objectives.

Conclusions:

The presented geometric design procedures offer a robust method for calculating aspheric surfaces.
These methods facilitate the creation of advanced optical systems with corrected OPL and OCS.
The findings pave the way for innovative designs in astronomical and microscopic instrumentation.