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

Polar Curves

Polar Curves

The spirograph is a versatile tool for visualizing the relationship between geometry and mathematical representation. In particular, it demonstrates how polar coordinates offer an alternative framework for describing curves in comparison to Cartesian coordinates. Instead of specifying a point by its horizontal and vertical displacements (x, y), polar coordinates use a radius r, the distance from the origin, and an angle θ, measured counterclockwise from the polar axis. This system is...

Angle of Twist: Problem Solving

Angle of Twist: Problem Solving

An electric motor applies a torque of 700 N·m to an aluminum shaft, triggering a stable rotation. Two pulleys, B and C, are subjected to torques of 300 N·m and 400 N·m, respectively. The modulus of rigidity is provided as 25 GPa. With the knowledge of the length and diameter of each segment, the twist angle between the two pulleys can be computed. First, a section cut is made between pulleys B and C, and the cut cross-section is analyzed using a free-body diagram. Given that the torque exerted...

Space Curves

Space Curves

A space curve describes the path followed by a particle moving through three-dimensional space. Unlike plane curves, which are confined to two coordinates, space curves require three coordinate functions. If t is a parameter, the position of the particle is represented by the vector function\begin{equation*}\mathbf{r}(t)=\langle x(t),y(t),z(t)\rangle,\end{equation*}where x(t), y(t), and z(t) are differentiable functions of t. As t varies over an interval, the endpoints of the position vectors...

Torsion in Vector Calculus

Torsion in Vector Calculus

A toy train ascending a winding track that curves and tilts offers an intuitive view of torsion, a key geometric concept in the study of space curves. While curvature measures how sharply a path bends, torsion captures how the path twists out of the plane of bending. This twisting behavior is crucial in understanding three-dimensional motion and is precisely described using the Frenet–Serret framework.At each point along a space curve, the Frenet–Serret frame consists of three orthogonal unit...

Gauss's Law: Cylindrical Symmetry

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...

Gauss's Law: Planar Symmetry

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...

You might also read

Related Articles

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

Sort by

Same author

Intrinsic Value-Aligned Policy Optimization for Offline-to-Online Reinforcement Learning.

IEEE transactions on neural networks and learning systems·2026

Same author

Platelet-Type Phosphofructokinase Drives Immune Checkpoint Coexpression and Metabolic Pathway Activation in Liver Cancer: The Cancer Genome Atlas-Based and Experimental Validation.

Clinical and translational gastroenterology·2026

Same author

Albuvirtide-based regimens for advanced- stage HIV and <i>Talaromyces marneffei</i> co-infection: A longitudinal case series.

International journal of STD & AIDS·2026

Same author

Individual and neighborhood socioeconomic inequality and the risk of dementia: A 14-year follow-up study.

Alzheimer's & dementia : the journal of the Alzheimer's Association·2026

Same author

Screening of Lactic Acid Bacteria Tolerant to Antimicrobial Substances and Their Effects on the Quality of <i>Cyperus esculentus</i> Silage.

Microorganisms·2025

Same author

Fatal Mpox Coinfection in Advanced AIDS: A Case Report.

Infection and drug resistance·2025

Search research articles

Related Experiment Video

Updated: Jun 21, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Figuring technology of nonaxisymmetric errors with a spiral path.

Changjun Jiao¹, Shengyi Li, Xuhui Xie

¹National University of Defense Technology, DeYa, Changsha, Hunan Province 410073, China. kdjcj@vip.sina.com

|August 4, 2009

Summary

This study introduces a novel figuring technology for precision mirror fabrication. It uses a spiral path and a modified algorithm to correct nonaxisymmetric errors, enabling inexpensive manufacturing.

More Related Videos

Operation of the Collaborative Composite Manufacturing (CCM) System

Operation of the Collaborative Composite Manufacturing (CCM) System

Published on: October 1, 2019

Related Experiment Videos

Last Updated: Jun 21, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Operation of the Collaborative Composite Manufacturing (CCM) System

Operation of the Collaborative Composite Manufacturing (CCM) System

Published on: October 1, 2019

Area of Science:

Optics and Materials Science
Precision Engineering

Background:

Nonaxisymmetric errors pose challenges in precision mirror fabrication.
Existing methods for correcting these errors can be complex and costly.

Purpose of the Study:

To present a novel figuring technology for correcting nonaxisymmetric errors in precision optics.
To develop an efficient and cost-effective method for fabricating precision mirrors.

Main Methods:

A finite-field nonlinear model based on a removal function approximation.
A modified Richardson-Lucy iterative algorithm for deconvoluting dwell time.
A velocity realization method for implementing dwell time on a spiral path.

Main Results:

The proposed figuring technology effectively addresses nonaxisymmetric errors.
Simulations validate the accuracy and efficacy of the developed algorithms.
The method demonstrates potential for inexpensive fabrication of precision mirrors.

Conclusions:

The presented figuring technology offers a novel approach to precision mirror manufacturing.
This method provides a cost-effective solution for producing high-precision optical components.
Further research can explore scaling this technology for various applications.