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The sine-squared law is shown to describe changes in spherical power which either minimize the blur or maximize the visibility of gratings oriented at various angles to the principal meridians of an astigmatic eye. These results help justify the use of the sine-squared law in applications such as meridional refraction. This derivation and its interpretation(More)
  • M P Keating
  • American journal of optometry and physiological…
  • 1981
A single 4 X 4 system matrix is used to represent the para-axial properties of optical systems consisting of separated obliquely crossed spherocylindrical lenses. The 4 X 4 system matrix is a generalization and combination of the 2 X 2 Gaussian system matrix for spherical optical systems, and the 2 X 2 dioptric power matrix for a single spherocylindrical(More)
  • M P Keating
  • American journal of optometry and physiological…
  • 1981
The 4 x 4 system matrix is applied to corrected astigmatic systems including a schematic eye in which each surface is astigmatic at a different axis. In addition to representing the eye, the 4 x 4 system generates 2 x 2 magnification matrices which describe the meridional magnifications that occur in the presence of astigmatism including the magnifications(More)
  • M P Keating
  • American journal of optometry and physiological…
  • 1986
There is much confusion about whether or not dioptric power exists in an off-axis meridian of a spherocylindrical lens. One source of this confusion is an overly simplified definition of dioptric power. This paper proposes the conditions that a good definition of dioptric power should meet. Under these conditions, dioptric power does exist in an off-axis(More)
  • M P Keating
  • American journal of optometry and physiological…
  • 1981
An effective dioptric power matrix is defined. The effective dioptric power matrix can be calculated directly from the lens dioptric power matrix, its trace, and its determinant, without using the sphere, cylinder, and axis parameters of the lens. This greatly simplifies any calculations in which dioptric power matrices are obtained in intermediate steps,(More)
  • M P Keating
  • American journal of optometry and physiological…
  • 1980
Dr. W. F. Long pointed out that calculations of decentration in spherocylindrical lenses, as well as calculations of combinations of obliquely crossed spherocylindrical lenses, are considerably simplified by the use of matrix methods. In the obliquely crossed lens problem, Long used eigenvalue techniques to obtain the sphere, cylinder, and axis of the(More)
  • M P Keating
  • Optometry and vision science : official…
  • 1995
Thin lens equations, accurate to third order, are presented for the effective spherocylindrical parameters for oblique central refraction (OCR) through spherocylindrical lenses with both faceform and pantoscopic tilt. The equations can also be used to find the parameters of a lens that compensates for the tilts. Accuracy of the equations was checked by(More)
  • M P Keating
  • Optometry and vision science : official…
  • 1997
BACKGROUND When thickness or separation is taken into account, the dioptric power of systems with obliquely crossed toric surfaces (OCTS), including some corrected and uncorrected human eyes, can be represented by a four-dimensional vector space, provided that an arbitrary 2 x 2 asymmetric matrix is the equivalent power matrix of some optical system. The(More)