Abstract

We incorporate an algorithm for ray tracing in birefringent media into a full ray-tracing package based on the Mathematica software application. To validate the package, we compare the calculated and observed wave-front aberration introduced by an optical system that comprises lenses fabricated from birefringent material. Using the package, we calculate the influence of the lens shape factor on the aberrations associated with the e-ray polarization and show that it differs significantly from that of the o-ray polarization.

© 2000 Optical Society of America

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References

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1998

1993

1992

W. Fiala, “Multifocal intraocular lenses fabricated from media exhibiting tuned birefringence,” Optom. Vision Sci. 69, 329–332 (1992).
[CrossRef]

H. Shimomura, H. Kikuta, K. Iwata, “First-order aberration of a double focus lens made of a uniaxial crystal,” J. Opt. Soc. Am. A 9, 814–819 (1992).
[CrossRef]

1990

1986

1985

M. J. Downs, W. H. McGivern, H. J. Ferguson, “Optical system for measuring the profiles of super smooth surfaces,” Precis. Eng. 7, 211–215 (1985).
[CrossRef]

1982

J. A. Ghosh, A. K. Chakraborty, “High frequency enhancement using a birefringent lens,” Opt. Commun. 40, 329–331 (1982).
[CrossRef]

Chakraborty, A. K.

J. A. Ghosh, A. K. Chakraborty, “High frequency enhancement using a birefringent lens,” Opt. Commun. 40, 329–331 (1982).
[CrossRef]

Chipman, R. A.

Chou, C.

Downs, M. J.

M. J. Downs, W. H. McGivern, H. J. Ferguson, “Optical system for measuring the profiles of super smooth surfaces,” Precis. Eng. 7, 211–215 (1985).
[CrossRef]

Echarri, R. M.

Ferguson, H. J.

M. J. Downs, W. H. McGivern, H. J. Ferguson, “Optical system for measuring the profiles of super smooth surfaces,” Precis. Eng. 7, 211–215 (1985).
[CrossRef]

Fiala, W.

W. Fiala, “Multifocal intraocular lenses fabricated from media exhibiting tuned birefringence,” Optom. Vision Sci. 69, 329–332 (1992).
[CrossRef]

Ghosh, J. A.

J. A. Ghosh, A. K. Chakraborty, “High frequency enhancement using a birefringent lens,” Opt. Commun. 40, 329–331 (1982).
[CrossRef]

Hillman, L. W.

Huang, Y.

Iwata, K.

Khoo, I.

F. T. S. Yu, I. Khoo, Principles of Optical Engineering (Wiley, New York, 1990).

Kikuta, H.

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).

Kinnstatter, K.

Liang, Q.-T.

Lipson, H.

S. G. Lipson, H. Lipson, Optical Physics (Cambridge U. Press, Cambridge, 1969).

Lipson, S. G.

S. G. Lipson, H. Lipson, Optical Physics (Cambridge U. Press, Cambridge, 1969).

McClain, S. C.

McGivern, W. H.

M. J. Downs, W. H. McGivern, H. J. Ferguson, “Optical system for measuring the profiles of super smooth surfaces,” Precis. Eng. 7, 211–215 (1985).
[CrossRef]

Ojima, M.

Pedrotti, F. L.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics (Prentice-Hall, Englewood Cliffs, N.J., 1993).

Pedrotti, L. S.

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics (Prentice-Hall, Englewood Cliffs, N.J., 1993).

Shimomura, H.

Shyu, J.

Simon, M. C.

Welford, W. T.

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).

Yonezawa, S.

Yu, F. T. S.

F. T. S. Yu, I. Khoo, Principles of Optical Engineering (Wiley, New York, 1990).

Yuan, C.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Commun.

J. A. Ghosh, A. K. Chakraborty, “High frequency enhancement using a birefringent lens,” Opt. Commun. 40, 329–331 (1982).
[CrossRef]

Optom. Vision Sci.

W. Fiala, “Multifocal intraocular lenses fabricated from media exhibiting tuned birefringence,” Optom. Vision Sci. 69, 329–332 (1992).
[CrossRef]

Precis. Eng.

M. J. Downs, W. H. McGivern, H. J. Ferguson, “Optical system for measuring the profiles of super smooth surfaces,” Precis. Eng. 7, 211–215 (1985).
[CrossRef]

Other

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978).

W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, New York, 1974).

F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics (Prentice-Hall, Englewood Cliffs, N.J., 1993).

F. T. S. Yu, I. Khoo, Principles of Optical Engineering (Wiley, New York, 1990).

S. G. Lipson, H. Lipson, Optical Physics (Cambridge U. Press, Cambridge, 1969).

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Figures (8)

Fig. 1
Fig. 1

Diagram of a birefringent telescope that comprises two birefringent lenses with their optic axes perpendicular to each other.

Fig. 2
Fig. 2

Observed interferograms and modeled results for various lens separations in a telescope that comprises two birefringent lenses with perpendicular optic axes. From top to bottom: f e + f o - 1 mm, f e + f o - 0.5 mm, f e + f o , f e + f o + 0.5 mm, f e + f o + 1 mm.

Fig. 3
Fig. 3

Variation of spherical aberration of a calcite lens with focal lengths f o ≈ 90 mm and f e ≈ 120 mm with shape factor (SF) for the o ray (solid curve) and the e ray (dashed curve).

Fig. 4
Fig. 4

Variation of coma for a calcite lens with focal lengths f o ≈ 90 mm and f e ≈ 120 mm as a function of shape factor (SF). The solid line shows how coma varies for the o ray. The two dashed lines show how coma varies for the e ray when the incident ray bundle is parallel (short dashes) and perpendicular (long dashes) to the optic axis.

Fig. 5
Fig. 5

Variation of astigmatism with shape factor (SF) for the e ray in a calcite lens with focal lengths f o ≈ 90 mm and f e ≈ 120 mm. Solid curve, a lens of thickness 5 mm; dashed curve, a lens of thickness 4 mm.

Fig. 6
Fig. 6

Geometrical spot diagrams for calcite lenses with shape factor SF = -1 and focal lengths f o ≈ 90 mm and f e ≈ 120 mm at f/8. All spot diagrams are contained in squares of dimensions 100 µm by 100 µm. Δz represents the distance away from the circle of least confusion.

Fig. 7
Fig. 7

Geometrical spot diagrams for calcite lenses with shape factor SF = 0 and focal lengths f o ≈ 90 mm and f e ≈ 120 mm at f/8. All spot diagrams are contained in squares of dimensions 100 µm by 100 µm. Δz represents the distance away from the circle of least confusion.

Fig. 8
Fig. 8

Geometrical spot diagrams for calcite lenses with shape factor SF = +1 and focal lengths f o ≈ 90 mm and f e ≈ 120 mm at f/8. All spot diagrams are contained in squares of dimensions 100 µm by 100 µm. Δz represents the distance away from the circle of least confusion.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

niki×n=nrkr×n,
neff=nenone21-kr·z32+no2kr·z321/2.
niki×n=nenokr×nne21-kr·z32+no2kr·z321/2.
S=krue2+uo2-ue2kr·z3z3,
OPL=neffkrlS,
SF=rf+rbrf-rb,
C=i-oi+o,
ΔW=Ax2+y22+Byx2+y2+Cx2+3y2+Dx2+y2+Ey+Fx,
SF=-2no2-1no+2 C.
SF=-2no2-no-1no+1 C.

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