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In the site survey of a four-sided traverse, internal angles are essential to ensure geometric accuracy. The survey revealed that the sum of the measured internal angles was 359 degrees and 48 minutes, which is 12 minutes less than the expected 360 degrees. This discrepancy signals an error likely arising from measurement inaccuracies during the fieldwork.To rectify this error, the adjustment process involved distributing the 12-minute shortfall equally across the four internal angles. By...
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On ray tracing for sharp changing media.

Jorge A Ramos Oliveira1, Arturo Baltazar1, Mario Castelán1

  • 1Robótica y Manufactura Avanzada, CINVESTAV, Ramos Arizpe, Coahuila 25900, Mexico.

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Summary
This summary is machine-generated.

This study presents an enhanced numerical algorithm for ray tracing, combining two classical methods. The new approach effectively handles both sharp and gradual changes in refractive index for improved imaging and inversion techniques.

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Area of Science:

  • Computational physics
  • Optics
  • Numerical analysis

Background:

  • Ray tracing is crucial for modern imaging and inversion.
  • Existing algorithms suit either sharp or gradual material property changes.
  • A unified approach is needed for diverse media.

Purpose of the Study:

  • To introduce an enhanced numerical ray tracing algorithm.
  • To address limitations of current methods in varied media.
  • To demonstrate applicability to initial-value problems.

Main Methods:

  • Combining two classical ray tracing implementations.
  • Solving ordinary differential equations with initial-value conditions.
  • Utilizing the shooting method for ray path computation.

Main Results:

  • The enhanced algorithm effectively traces rays in media with sharp refractive index changes.
  • The algorithm also performs well in media with gradual refractive index variations.
  • Demonstrated successful application of ray path computation.

Conclusions:

  • The proposed enhanced ray tracing algorithm offers versatility.
  • It is suitable for media with both abrupt and smooth property variations.
  • This method advances numerical techniques in optical modeling.