Sequential tilt and tilted power of thin lenses

Optometry and Vision Science : Official Publication of the American Academy of Optometry
W F Harris

Abstract

The purposes of this article were, for any sequence of tilts applied to a thin lens, to calculate an equivalent turn and single tilt, to show how to use the equivalent turn and tilt to calculate the tilted power of the lens, and, given the desired tilted power, to calculate the power of the untilted lens necessary to compensate for the effects of tilt. The untilted lens may be stigmatic (spherical) or astigmatic (spherocylindrical). The analysis makes use of rotation matrices to represent rotation in space and previous work in third-order optics on oblique central refraction. Equations are presented for calculating the combination of turn and tilt that is equivalent to any sequence of tilts. They are specialized for the particular case of combinations of faceform and pantoscopic tilts and allow the decomposition of an arbitrary tilt into a combination of turn and pantoscopic and faceform tilts. The equations also lead to a procedure for calculating or compensating for the tilted power of a sequentially tilted thin lens. Previous work on the effect of tilt on thin lenses has been generalized to handle combinations of arbitrary tilts.

References

Jan 1, 1976·American Journal of Optometry and Physiological Optics·W F Long
Oct 1, 1974·American Journal of Optometry and Physiological Optics·K Nakayama
Oct 1, 1980·American Journal of Optometry and Physiological Optics·M P Keating
Apr 1, 1995·Optometry and Vision Science : Official Publication of the American Academy of Optometry·M P Keating
Jun 1, 1995·Vision Research·T Haslwanter
Oct 1, 1993·Optometry and Vision Science : Official Publication of the American Academy of Optometry·M P Keating
Feb 7, 2002·Optometry and Vision Science : Official Publication of the American Academy of Optometry·Ralf Blendowske
Aug 30, 2002·Optometry and Vision Science : Official Publication of the American Academy of Optometry·W F Harris
Oct 1, 1957·Journal of the Optical Society of America·G WESTHEIMER

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Citations

Dec 17, 2008·Ophthalmic & Physiological Optics : the Journal of the British College of Ophthalmic Opticians (Optometrists)·Ravi C BakarajuEric B Papas
Sep 15, 2006·Optometry and Vision Science : Official Publication of the American Academy of Optometry·W F Harris

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