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Related Concept Videos

Deflection of a Beam01:19

Deflection of a Beam

Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
Polar Coordinates: Problem Solving01:27

Polar Coordinates: Problem Solving

Directional radiation patterns are central to antenna analysis, as they illustrate how signal strength varies with direction. These patterns are often modeled using polar plots, where the radial distance from the origin represents signal intensity at a given angle. A commonly used idealized form is the four-lobed rose curve, which captures the concept of directional beams in a simplified mathematical form.The four-lobed rose curve, described by r = cos⁡(2θ), features four symmetric lobes, each...
Singularity Functions for Bending Moment01:18

Singularity Functions for Bending Moment

Singularity functions simplify the representation of bending moments in beams subjected to discontinuous loading, allowing the use of a single mathematical expression. For a supported beam AB, with uniform loading from its midpoint M to the right side end B, the approach involves conceptual 'cuts' at specific points to determine the bending moment in each segment. By cutting the beam at a point between A and M, the bending moment for the segment before reaching midpoint M is represented using a...
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...
Beams01:30

Beams

Beams are integral components of structural engineering and construction, designed to support loads applied at various points along their length. These long, straight members can be classified based on geometry, cross-section, support type, and equilibrium condition.
Based on geometry, beams can be straight, tapered, or curved. Straight beams are the most common type and have a constant cross-section throughout their length. Tapered beams, on the other hand, have a varying cross-section along...
Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and stress...

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Related Experiment Video

Updated: Jun 16, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Binary imagery and its application to beam shaping.

T W Barnard

    Applied Optics
    |January 30, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Binary images effectively represent continuous-tone images by leveraging spatial frequency. Decreasing element spacing improves image quality, with optimal results achieved when spacing is one-third the highest spatial frequency period.

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    Last Updated: Jun 16, 2026

    Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
    08:39

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    Published on: January 28, 2019

    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
    09:43

    Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping

    Published on: March 20, 2017

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
    12:14

    The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry

    Published on: August 12, 2013

    Area of Science:

    • Image processing
    • Optics
    • Digital imaging

    Background:

    • Continuous-tone images are often represented by binary images in digital systems.
    • Understanding the spatial frequency response is crucial for accurate image representation.

    Purpose of the Study:

    • To present a theory for binary image representation of continuous-tone images.
    • To quantitatively evaluate image errors in binary representations.
    • To apply binary image theory to the design of optical modulation masks.

    Main Methods:

    • Analysis of the spatial frequency response function of the viewer.
    • Development of an analytical formulation for quantitative error evaluation.
    • Generation of a binary Gaussian function for approximation.

    Main Results:

    • Binary images can effectively represent band-limited, continuous-tone images.
    • Image quality improves as binary element spacing decreases.
    • Optimal binary image representation is achieved when element spacing is approximately one-third the highest spatial frequency period.
    • A binary Gaussian function was generated with +/-0.5% approximation error.

    Conclusions:

    • Binary image theory provides a framework for understanding and optimizing image representation.
    • The findings have direct applications in designing transparency masks for spatial light modulation.
    • Digital image processing operations can benefit from these insights into binary image fidelity.