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Interference and Diffraction02:18

Interference and Diffraction

Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
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When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...
Transformations of Functions III01:20

Transformations of Functions III

Transformations modify the graphical representation of a function without changing its fundamental form. One common transformation is reflection, which flips the graph across a designated axis. When the vertical coordinates of all points are multiplied by the negative one, the entire graph is mirrored over the horizontal axis. This transformation reverses the vertical orientation of peaks and troughs, akin to signal inversion in electrical systems, where a waveform is flipped, but the timing of...

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Related Experiment Video

Updated: Jul 7, 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

Image structure from mirrors with print-through undulations: theoretical analysis.

J W Harris, G Catalan, E Atad-Ettedgui

    Applied Optics
    |July 1, 1997
    PubMed
    Summary
    This summary is machine-generated.

    Periodic hexagonal mirror surface undulations create a phase grating, diffracting light into satellite images. This analysis details the impact of surface amplitude and random variations on image intensity and structure.

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    Last Updated: Jul 7, 2026

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    Published on: December 11, 2014

    Area of Science:

    • Optics
    • Surface Metrology
    • Diffraction Physics

    Background:

    • Periodic hexagonal patterns on mirror surfaces can arise from manufacturing processes like polishing honeycomb mirrors.
    • These surface undulations function as a two-dimensional phase grating when illuminated by light.

    Purpose of the Study:

    • To analyze the image structure generated by periodic hexagonal mirror surface undulations.
    • To quantify the effects of surface amplitude, periodicity, and random variations on diffraction patterns.

    Main Methods:

    • Theoretical analysis of diffraction from a two-dimensional phase grating.
    • Modeling the point spread function (PSF) and satellite image characteristics.

    Main Results:

    • Uniform undulations (amplitude H, period L) decrease central PSF intensity and diffract power into a hexagonal array of satellite images.
    • First-order satellites have intensities proportional to (H/lambda)^2, with intensities decreasing for higher orders.
    • Random surface bump amplitudes lead to reduced diffracted order intensity and a grasslike structure in the image plane.
    • Polychromatic light results in radially elongated satellite images with intensity decreasing as 1/lambda^4.

    Conclusions:

    • Hexagonal surface undulations significantly alter image formation through diffraction.
    • The characteristics of diffracted satellite images are directly related to the amplitude and statistical distribution of surface irregularities.
    • Understanding these diffraction effects is crucial for optical systems employing such mirrors.