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

Gradient Fields

Gradient Fields

A gradient field is a vector field derived from a scalar field. A scalar field assigns a single numerical value to every point in space, such as temperature, pressure, or electric potential. The gradient field describes how that value changes from point to point. It gives both the direction of the fastest increase and the rate of change in that direction.For a scalar field f(x, y), the gradient is written as\begin{equation*}\nabla f=\left\langle \jfrac{\partial f}{\partial x},\jfrac{\partial...

Angle Closure Glaucoma: Treatment

Angle Closure Glaucoma: Treatment

Angle-closure glaucoma, or closed-angle glaucoma, is an eye condition where the iris bulges out and blocks the iridocorneal angle, resulting in a buildup of aqueous humor and increased intraocular pressure. Immediate medical attention is necessary due to the sudden onset of symptoms. The treatment for angle-closure glaucoma includes short-term and long-term approaches. Short-term treatment involves using eye drops like pilocarpine to lower intraocular pressure by increasing aqueous humor...

Gradient Vectors and Their Applications

Gradient Vectors and Their Applications

Every point on a topographical map corresponds to a particular elevation, so the landscape can be modeled as a surface whose height depends on horizontal position. From any given location, a hiker may face infinitely many directions, but only one direction produces the fastest possible increase in elevation. This unique route is called the direction of steepest ascent, and in multivariable calculus, it is represented by the gradient vector of the elevation function.The gradient vector points...

Open Angle Glaucoma: Treatment

Open Angle Glaucoma: Treatment

In open-angle glaucoma, the iridocorneal angle remains open, but the trabecular meshwork becomes stiff, slowing down the outflow of aqueous humor. This causes a buildup of aqueous humor in the anterior chamber, leading to a sudden increase in intraocular pressure. The treatment for open-angle glaucoma focuses on reducing the elevated intraocular pressure by either decreasing the secretion of aqueous humor or increasing its outflow.
Drugs such as carbonic anhydrase inhibitors, α2- and...

Glaucoma: Overview

Glaucoma: Overview

Glaucoma is an eye condition characterized by increased intraocular pressure that damages the retina and optic nerve, leading to irreversible blindness if left untreated. The human eye has various components, including the cornea, iris, pupil, lens, and optic nerve. Aqueous humor is secreted by the epithelium of the ciliary body in the posterior chamber and flows through the trabecular meshwork and canal of Schlemm, maintaining normal intraocular pressure. The trabecular meshwork and the canal...

Significance of the Gradient Vector

Significance of the Gradient Vector

A surface defined by a function of two variables can be understood by examining how it changes along specific directions. When one variable is held constant, the surface reduces to a curve that reflects variation in the other variable. For example, fixing one variable and moving parallel to a coordinate axis produces a cross-sectional curve. The slope of this curve at a given point represents how the function changes in that particular direction, providing a measure of local steepness.By...

You might also read

Related Articles

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

Sort by

Same author

Gradient-index optics: introduction by the feature editors.

Applied optics·2010

Same author

Microoptics: introduction by the feature editors.

Applied optics·2010

Same author

Pseudoaxicon lenses.

Applied optics·2010

Same author

Rapid ray tracing in radial gradients.

Applied optics·2010

Same author

Gradient-index imaging optics today.

Applied optics·2010

Same author

Photographic gradient singlets.

Applied optics·2010

Search research articles

Related Experiment Video

Updated: Jun 12, 2026

Rotating the Intraocular Lens to Prevent Posterior Capsular Opacification in Cataract Surgeries

Rotating the Intraocular Lens to Prevent Posterior Capsular Opacification in Cataract Surgeries

Published on: July 7, 2023

Axicon gradient lenses.

|June 26, 2010

Summary

This summary is machine-generated.

Odd powers in radial gradient refractive index profiles can cause significant optical aberrations. Even standard optical elements like Wood lenses demonstrate how these aberrations arise, impacting optical system performance.

Related Experiment Videos

Last Updated: Jun 12, 2026

Rotating the Intraocular Lens to Prevent Posterior Capsular Opacification in Cataract Surgeries

Rotating the Intraocular Lens to Prevent Posterior Capsular Opacification in Cataract Surgeries

Published on: July 7, 2023

Area of Science:

Optics
Optical Engineering
Materials Science

Background:

Radial gradient refractive index (GRIN) profiles are typically modeled using even powers of radial distance (r).
Deviations from this standard representation can introduce unexpected optical phenomena.
Understanding these deviations is crucial for designing precise optical systems.

Purpose of the Study:

To investigate the impact of odd powers of r in radial gradient refractive index profiles.
To analyze the resulting optical aberrations caused by these non-standard profiles.
To illustrate the practical implications using a Wood lens as a case study.

Main Methods:

Theoretical analysis of refractive index profiles containing odd powers of r.
Aberration analysis based on the derived non-standard GRIN profiles.
Examination of the Wood lens as a specific example of a radial gradient lens.

Main Results:

The presence of odd powers of r in the radial gradient significantly affects the refractive index distribution.
These non-standard terms lead to serious and potentially detrimental optical aberrations.
The Wood lens, when analyzed with odd powers, exhibits these aberration characteristics.

Conclusions:

Odd powers in radial GRIN profiles are not merely theoretical artifacts but have tangible effects on optical performance.
Careful consideration of the refractive index profile is necessary to mitigate aberrations in optical design.
The Wood lens serves as a critical example highlighting the importance of accurate GRIN profile representation.