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Related Concept Videos

Level Curves and Contour Maps01:22

Level Curves and Contour Maps

Level curves and contour maps provide a way to visualize functions of two variables on a two-dimensional plane. A useful example is a topographic map, where curved lines represent locations that share the same elevation. In mathematics, these curves are called level curves or contour lines. Each contour line corresponds to points in the domain where the function has a constant value. For a function of two variables written as z = f(x,y), a level curve is defined by the equation f(x,y) = k,...
Deformations in a Transverse Cross Section01:21

Deformations in a Transverse Cross Section

When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...
Cylinders in Three-Dimensional Space01:28

Cylinders in Three-Dimensional Space

A cylindrical surface is generated when a two-dimensional profile curve is translated along a straight line in three-dimensional space. The translated copies of the curve form a surface composed of parallel rulings, each oriented in the same fixed direction. This construction allows many three-dimensional forms to be described using relatively simple planar equations.In Cartesian coordinates, a cylindrical surface is often recognized by an equation that omits one of the three variables. For...
Topographic Surveying and Contours01:29

Topographic Surveying and Contours

Topographic surveying is critical for documenting the Earth's surface, focusing on capturing elevations, slopes, and natural and man-made features. It is essential in construction planning, water resource management, and land-use analysis. The primary outcome of such surveys is a topographic map, which uses contour lines to visually represent the shape and slope of the terrain, providing valuable insights into the landscape's characteristics.Contour lines are fundamental to understanding the...
Parametric Surfaces01:30

Parametric Surfaces

A parametric surface in three-dimensional space is defined through a vector-valued function\begin{equation*}\mathbf{r}(u, v) = x(u, v)\mathbf{i} + y(u, v)\mathbf{j} + z(u, v)\mathbf{k}\end{equation*}where u and v are parameters within a specified domain D in the uv-plane. The functions x(u, v), y(u, v), and z(u, v) define the coordinates of points on the surface. As u and v vary over D, the position vector r(u, v) traces a continuous surface in space. This parametric representation is essential...
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Oriented Surfaces

A surface is called orientable if a consistent choice of unit normal vector can be made at every point on the surface. A thin soap film stretched across a wire loop provides a familiar example. The film separates the air on one side from the air on the other, so one side can be selected as positive and the opposite side as negative. Once this choice is made, a unit normal vector can be assigned smoothly across the entire surface.At each point on the soap film, a unit normal vector points...

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Related Experiment Video

Updated: Jun 17, 2026

Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects
10:16

Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects

Published on: February 8, 2014

Multiple-index holographic contouring.

J S Zelenka, J R Varner

    Applied Optics
    |January 15, 2010
    PubMed
    Summary

    A novel holographic contouring technique enhances depth measurement accuracy. This new multiple index method provides high-contrast contours for detecting subtle surface variations, improving upon existing systems.

    Area of Science:

    • Optics
    • Holography
    • Metrology

    Background:

    • Holographic contouring is crucial for non-contact surface measurement.
    • Existing methods face challenges in detecting small depth changes over large areas.

    Purpose of the Study:

    • To introduce a new multiple index technique for holographic contour generation.
    • To enable high-contrast contour fringes for precise depth change detection.
    • To compare the new technique with a multiple frequency system.

    Main Methods:

    • Development of an improved multiple index holographic technique.
    • Holographic contour generation using the new method.
    • Comparative analysis with a multiple frequency holographic system.

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    Technical Approach for Infrared Tracking for Soft Tissue Navigation with a Holographic Head-Mounted Display and Preclinical Validation

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    Related Experiment Videos

    Last Updated: Jun 17, 2026

    Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects
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    Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects

    Published on: February 8, 2014

    A MRI-Based Toolbox for Neurosurgical Planning in Nonhuman Primates
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    A MRI-Based Toolbox for Neurosurgical Planning in Nonhuman Primates

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    Main Results:

    • The new multiple index technique successfully generates high-contrast contours.
    • It effectively denotes small depth changes across large surfaces.
    • Experimental results demonstrate the technique's efficacy.

    Conclusions:

    • The presented multiple index technique offers a significant advancement in holographic contouring.
    • It provides superior performance for measuring small surface variations.
    • This method enhances the capability of holographic metrology.