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Related Concept Videos

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...
Transformation of Plane Stress01:18

Transformation of Plane Stress

Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's faces...
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...
Symmetry Elements in a Crystal01:27

Symmetry Elements in a Crystal

Crystal symmetry operations are isometric transformations that map objects onto indistinguishable copies while preserving distances, angles, and volumes. The simplest symmetry operation is translation, which shifts the entire infinite crystal lattice parallelly by a translation vector.Crystallographic rotations involve rotations by an angle of 2π/n around an axis without changing the positions of points on the axis. It is called the rotational axis of the symmetry, denoted by n. The combination...
Crystallographic Point Groups01:29

Crystallographic Point Groups

Crystallographic point groups represent the various symmetry operations that can occur within crystals. They are unique in that at least one point will always remain unchanged during these actions. For instance, consider the triclinic system. This system, devoid of any axis or plane of symmetry, aligns with the C1 and Ci point groups.where Cᵢ is characterized solely by a center of inversion.Contrastingly, the monoclinic system introduces an element of symmetry. This system with one plane and...
Structures of Solids02:22

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...

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Fabricating van der Waals Heterostructures with Precise Rotational Alignment
09:25

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Published on: July 5, 2019

Alignment of rotational prisms.

D L Sullivan

    Applied Optics
    |February 2, 2010
    PubMed
    Summary
    This summary is machine-generated.

    This study presents an analytical method to precisely align optical prisms, like Dove or Pechan prisms, by analyzing nutational boresight errors. Understanding these errors allows for accurate adjustments, improving optical system performance.

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    Area of Science:

    • Optical Engineering
    • Mechanical Engineering
    • Optics and Photonics

    Background:

    • Optical image rotation relies on prisms like Dove or Pechan prisms.
    • Improper alignment of these prisms causes system boresight nutation.
    • Quantifying this nutational error is crucial for optical system precision.

    Purpose of the Study:

    • Derive an analytical expression for optical element alignment.
    • Develop a description for nutational boresight error.
    • Establish methods for distinguishing and measuring specific misalignments.

    Main Methods:

    • Formulating an analytical expression for prism alignment.
    • Developing a mathematical description of nutational boresight error.
    • Analyzing unique nutation patterns to identify misalignments.

    Main Results:

    • An analytical expression for optical element alignment was derived.
    • Nutational boresight error was described analytically in terms of misalignments.
    • Unique nutation patterns were identified for diagnosing specific misalignments.

    Conclusions:

    • Proper alignment requires both lateral and angular adjustments.
    • The derived analytical description aids in precise optical prism alignment.
    • Specific procedures for alignment adjustment axes were developed.