Formulation of the rotational transformation of wave fields and their application to digital holography

Kyoji Matsushima1

  • 1Department of Electrical and Electronic Engineering, Kansai University, Suita, Osaka, Japan. matsu@kansai-u.ac.jp

Applied Optics
|July 3, 2008
PubMed

Related Concept Videos

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...
Vector Transformation in Rotating Coordinate Systems01:16

Vector Transformation in Rotating Coordinate Systems

Consider a vector rotating about an axis with an angular velocity, such that its tip sweeps a circular path.
Properties of Fourier Transform II01:24

Properties of Fourier Transform II

The Fourier Transform (FT) is an essential mathematical tool in signal processing, transforming a time-domain signal into its frequency-domain representation. This transformation elucidates the relationship between time and frequency domains through several properties, each revealing unique aspects of signal behavior.
The Frequency Shifting property of Fourier Transforms highlights that a shift in the frequency domain corresponds to a phase shift in the time domain. Mathematically, if x(t) has...
Equations of Wave Motion01:02

Equations of Wave Motion

Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
Electromagnetic Wave Equation01:24

Electromagnetic Wave Equation

Maxwell's equations for electromagnetic fields are related to source charges, either static or moving. These fields act on a test charge, whose trajectory can thus be determined using suitable boundary conditions. The objective of electromagnetism is thus theoretically complete.
However, although electric and magnetic fields were first introduced as mathematical constructs to simplify the description of mutual forces between charges, a natural question emerges from Maxwell's equations: What...
Transformation of Plane Strain01:12

Transformation of Plane Strain

When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...