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Orthogonal Trajectories01:26

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Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
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Analyzing AC circuits in electrical systems is a fundamental aspect of electrical engineering. In these circuits, AC power is supplied from a distribution panel and wired to various household appliances in parallel. To perform a comprehensive analysis, electrical engineers use Kirchhoff's voltage and current laws, which are equally applicable in AC circuits as in DC circuits.
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Relative velocity is the velocity of an object as observed from a particular reference frame, or the velocity of one reference frame with respect to another reference frame. The concept of relative velocity can be used to describe motion in two dimensions. Consider a particle P and two reference frames S and S′. The position of the origin of S′ as measured in S is , the position of P as measured in S′ is , and the position of P as measured in S is , which can be evaluated by utilizing...
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A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. Due to its adaptability and capacity to withstand complex loads, the space truss is widely used in various construction projects.
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Related Experiment Video

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Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Ray tracing method in phase space for two-dimensional optical systems.

C Filosa, J H M Ten Thije Boonkkamp, W L IJzerman

    Applied Optics
    |May 4, 2016
    PubMed
    Summary

    A novel phase space ray tracing method enhances optical system accuracy and speed. This technique traces fewer rays, focusing on discontinuities for improved computational efficiency compared to traditional methods.

    Area of Science:

    • Optics and Photonics
    • Computational Physics

    Background:

    • Classical ray tracing calculates photometric variables for non-imaging optical systems.
    • Existing methods can be computationally intensive and lack optimal accuracy.

    Purpose of the Study:

    • To introduce a new ray tracing technique for improved accuracy and reduced computational time.
    • To apply the novel method to a two-dimensional TIR-collimator.

    Main Methods:

    • Utilizing phase space representation for the optical system's source and target.
    • Implementing a procedure to trace only rays near luminance discontinuities, disregarding smooth regions.
    • Focusing computations on rays within the meridional plane.

    Main Results:

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  • The phase space approach demonstrates superior speed and accuracy over Monte Carlo ray tracing.
  • Numerical simulations confirm the efficiency gains of the new method.
  • The phase space method exhibits convergence proportional to 1/N, surpassing Monte Carlo's 1/sqrt(N) convergence rate.

    • Conclusions:

    • The presented phase space ray tracing method offers significant advantages in accuracy and computational efficiency for non-imaging optical systems.
    • This technique provides a faster and more precise alternative to conventional ray tracing algorithms.
    • The method's ability to trace fewer, targeted rays leads to improved performance and faster convergence.