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Related Concept Videos

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...
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.
Perpendicular-Axis Theorem01:16

Perpendicular-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...
Gauss's Law: Cylindrical Symmetry01:20

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,...
Law of Rational Indices01:29

Law of Rational Indices

The Law of rational indices is a fundamental principle in the field of crystallography. According to this law, the intercepts of a crystal face along the crystallographic axes (the three-dimensional axes along which a crystal is measured) can be expressed as either equivalent to the unit intercepts (a, b, c) or simple whole number multiples of them. These multiples are typically denoted as na, n'b, and n''c, where n, n', and n'' are simple whole numbers.To illustrate, consider a crystal with...
Polar Coordinates01:24

Polar Coordinates

The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ��), where r is the radial distance from a fixed...

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Related Experiment Video

Updated: May 21, 2026

Comparison of Agreement and Accuracy using Binocular Wavefront Optometer with Autorefractor and Phoropter
05:14

Comparison of Agreement and Accuracy using Binocular Wavefront Optometer with Autorefractor and Phoropter

Published on: September 16, 2025

[Relationships between refractive parameters: sphere, cylinder and axis].

O Touzeau1, T Gaujoux, J Bullet

  • 1Service 5, centre hospitalier national d'ophtalmologie des Quinze-Vingts, 28, rue de Charenton, 75012 Paris, France; Inserm, institut de la vision, 17, rue Moreau, 75012 Paris, France. touzeau@quinze-vingts.fr

Journal Francais D'Ophtalmologie
|June 8, 2012
PubMed
Summary
This summary is machine-generated.

Refractive astigmatism is largely independent of spherical refractive error, except in high ametropia. Fellow eyes show strong correlations in refractive parameters, unlike relationships between different refractive components.

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Comparison of Agreement and Accuracy using Binocular Wavefront Optometer with Autorefractor and Phoropter
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Comparison of Agreement and Accuracy using Binocular Wavefront Optometer with Autorefractor and Phoropter

Published on: September 16, 2025

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09:43

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy

Published on: August 13, 2019

Area of Science:

  • Ophthalmology
  • Optometry
  • Vision Science

Background:

  • Understanding refractive error relationships is crucial for diagnosing and managing visual impairments.
  • Fellow eye symmetry and refractive parameter correlations provide insights into ocular development and stability.

Purpose of the Study:

  • To investigate the interrelationships among refractive parameters (sphere, cylinder, axis) in a normal population.
  • To analyze the degree of symmetry and correlation between the fellow eyes' refractive parameters.

Main Methods:

  • Prospective data collection of subjective refraction and auto-refractometry from 500 patients.
  • Analysis of refraction data in a 3D dioptric coordinate system.
  • Quantification of WTR/ATR ratio and enantiomorphism using specific mathematical functions.

Main Results:

  • Spherical component showed minimal influence on refractive astigmatism, except in high ametropia. Higher cylinder was observed in eyes with spherical equivalents >4D.
  • Cylinder and age significantly influenced the WTR/ATR ratio and enantiomorphism, with younger individuals and higher cylinder correlating with WTR and enantiomorphic axes.
  • Strong correlations were found between fellow eyes for both cylinder (r=0.66) and spherical equivalent (r=0.96). Oblique axes were less enantiomorphic and associated with lower cylinder.
  • Gender had no significant impact on refraction, except for a slight relative hyperopia in females.

Conclusions:

  • Refractive astigmatism is largely independent of the spherical component, barring high spherical ametropia.
  • Cylinder moderately affects axis orientation (WTR/ATR ratio) and enantiomorphism.
  • Fellow eye refractive parameters exhibit significantly stronger relationships than inter-parameter relationships within a single eye.