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Cardinal and anti-cardinal points, equalities and chromatic dependence.

Tanya Evans1, William F Harris1

  • 1Department of Optometry, University of Johannesburg, Johannesburg, South Africa.

Ophthalmic & Physiological Optics : the Journal of the British College of Ophthalmic Opticians (Optometrists)
|March 28, 2017
PubMed
Summary

This study introduces anti-cardinal points and extends Pascal's ring to visualize relationships among cardinal and anti-cardinal points in Gaussian systems. The findings highlight frequency-dependent shifts, impacting optical definitions.

Keywords:
Pascal's ringanti-cardinal pointscardinal pointschromatic dependenceequalities

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Area of Science:

  • Optics
  • Gaussian optics
  • Geometric optics

Background:

  • Cardinal points are fundamental for ray tracing in Gaussian optical systems.
  • Anti-cardinal points, including anti-principal and anti-nodal points, represent an expanded set of special points within these systems.
  • Understanding the relationships between these points is crucial for accurate optical analysis.

Purpose of the Study:

  • To derive relationships and equalities between the six familiar cardinal points and the four anti-cardinal points.
  • To utilize Pascal's ring as a visual tool for illustrating these relationships and their dependencies.
  • To investigate the frequency dependence of these special points in optical systems.

Main Methods:

  • Application of Gaussian optics principles and the transference T.
  • Derivation of equations for locating cardinal and anti-cardinal points.
  • Extension of Pascal's ring to incorporate anti-cardinal points and illustrate frequency-dependent shifts.

Main Results:

  • Established equalities among cardinal and anti-cardinal points.
  • Demonstrated frequency dependence for focal and anti-cardinal points in reduced and multi-surface eye models.
  • Identified specific points (principal, nodal) that remain frequency-independent in certain models.

Conclusions:

  • Pascal's ring and its extension offer novel, visual methods for understanding complex point relationships in optics.
  • The frequency dependence of certain cardinal and anti-cardinal points has significant implications for defining optical aberrations.
  • Careful consideration is needed when defining optical concepts reliant on frequency-dependent cardinal points.