Related Experiment Video
Updated: Jun 6, 2026
05:46
Correction of Presbyopia by Monocular Bi-Aspheric Ablation Profile
Published on: September 20, 2024
Computationally directed axisymmetric aspheric figuring (after N. J. Brown)
Applied Optics
|November 25, 2010
Summary
This study presents computational algorithms for finishing axisymmetric optical surfaces, making complex calculations accessible for modern personal computers. These methods simplify optical finishing processes for engineers and researchers.
Area of Science:
- Optical engineering
- Computational science
- Surface finishing
Background:
- N. J. Brown's 1978 paper discussed computational problems in finishing axisymmetric optical surfaces.
- Advancements in computing power necessitate updated algorithms for optical surface finishing.
Purpose of the Study:
- To develop and present computational algorithms for finishing axisymmetric optical surfaces.
- To adapt existing methods for implementation on contemporary personal computers.
- To provide practical tools for optical engineers and researchers.
Main Methods:
- Algorithm development based on principles outlined by N. J. Brown.
- Adaptation of computational methods for personal computer implementation.
- Illustrative sample calculations to demonstrate algorithm utility.
Main Results:
- Successfully developed algorithms for computational problems in optical surface finishing.
- Demonstrated the feasibility of implementing these algorithms on personal computers.
- Provided practical examples showcasing the application of the developed algorithms.
Conclusions:
- The developed algorithms offer efficient solutions for axisymmetric optical surface finishing.
- Modern personal computers are capable of handling these computational tasks.
- The study facilitates the practical application of advanced optical finishing techniques.
Related Concept Videos
01:16Perpendicular-Axis Theorem
The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body.
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...
01:15Unsymmetric Bending - Angle of Neutral Axis
Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal centroidal axes. The...
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal centroidal axes. The...
01:16Eccentric Axial Loading in a Plane of Symmetry
Eccentric axial loading occurs when an axial load is applied away from the centroidal axis of a structural member. This scenario is common in engineering, where structural elements may not be directly aligned due to various design or functional requirements.
01:24Area Computation by the Alternative Coordinate Method
The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...
01:20Gauss'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,...
01:26Gauss'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...