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Stigmatic optical systems.

W F Harris1

  • 1Optometric Science Research Group, Department of Optometry, Rand Afrikaans University, Johannesburg, South Africa. wfh@na.rau.ac.za

Optometry and Vision Science : Official Publication of the American Academy of Optometry
|December 14, 2004
PubMed
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A system is defined as stigmatic if every point object maps to a point image. This study identifies conditions for stigmatic and astigmatic optical systems, finding that matrix properties, not just refractive power, determine optical clarity.

Area of Science:

  • Optical Physics
  • Geometrical Optics

Background:

  • Thin lens systems are considered astigmatic if their cylinder is non-zero.
  • The definition of astigmatism in thick optical systems, such as the human eye, is less clear.
  • A clear definition is needed to distinguish between stigmatic and astigmatic systems.

Purpose of the Study:

  • To define stigmatic and astigmatic optical systems based on point object-image mapping.
  • To determine the conditions on ray transference for a system to be stigmatic or astigmatic.
  • To investigate if stigmatic refraction is sufficient for a system to be stigmatic.

Main Methods:

  • The study focuses on linear optics and ray transference.
  • A system is defined as stigmatic if every point object maps to a point image.

Related Experiment Videos

  • A system is astigmatic if at least one point object maps to a non-point image.

    • Main Results:

    • A system is stigmatic if and only if all its 2x2 submatrices are scalar multiples of a common orthogonal matrix.
    • Stigmatic refraction is not a sufficient condition for a system to be stigmatic.
    • An eye can be astigmatic even with stigmatic refraction.

    Conclusions:

    • The optical character of a system is determined by its ray transference.
    • The mathematical properties of the ray transference matrix define whether a system is stigmatic or astigmatic.
    • The human eye's astigmatism is not solely dependent on its refractive power.