Abstract

The use of a continuously varying index of refraction provides new degrees of freedom in the design of lens systems. By use of the third-order aberration theory developed by Sands, the effectiveness of these new degrees of freedom in correcting third-order aberrations is determined. After the theory is cast into a form suitable for a computer, two major designs are done. The first is a singlet with an axial gradient that is corrected for third-order spherical and chromatic aberrations and has no third-order distortion. A radial gradient is used in a singlet to correct all third-order monochromatic aberrations except Petzval curvature of field. The results of the study indicate that axial gradients have the same effect as aspheric surfaces for third-order aberrations. The study also shows that radial gradients are more effective in aberration correction than axial gradients and have a greater potential in lens design.

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  1. R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1968), pp. 269–302.
  2. H. A. Buchdahl, Optical Aberration Coefficients (Dover, New York, 1968), pp. 305–310.
  3. H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. P., Cambridge, England, 1970).
  4. L. Montagnino, J. Opt. Soc. Am. 58, 1667 (1968).
  5. E. W. Marchand, J. Opt. Soc. Am. 60, 1 (1970).
  6. P. J. Sands, J. Opt. Soc. Am. 60, 1436 (1970).
  7. The optical axis is assumed to be in the positive x direction.
  8. E. G. Rawson, D. R. Herriott, and J. McKenna, Appl. Opt. 9, 753 (1970).
  9. The S and T are normalized coordinates in their respective planes. For a discussion of the S and T, see Ref. 6 and Ref. 2.
  10. R. W. Wood, Physical Optics (Macmillan, New York, 1905), pp. 71–77.
  11. D. T. Moore, thesis, University of Rochester, 1970.
  12. The ΔX is the difference of X between one surface and the next. ΔX=Xj+1-Xj.

Buchdahl, H. A.

H. A. Buchdahl, Optical Aberration Coefficients (Dover, New York, 1968), pp. 305–310.

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. P., Cambridge, England, 1970).

Herriott, D. R.

E. G. Rawson, D. R. Herriott, and J. McKenna, Appl. Opt. 9, 753 (1970).

Luneburg, R. K.

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1968), pp. 269–302.

Marchand, E. W.

E. W. Marchand, J. Opt. Soc. Am. 60, 1 (1970).

McKenna, J.

E. G. Rawson, D. R. Herriott, and J. McKenna, Appl. Opt. 9, 753 (1970).

Montagnino, L.

L. Montagnino, J. Opt. Soc. Am. 58, 1667 (1968).

Moore, D. T.

D. T. Moore, thesis, University of Rochester, 1970.

Rawson, E. G.

E. G. Rawson, D. R. Herriott, and J. McKenna, Appl. Opt. 9, 753 (1970).

Sands, P. J.

P. J. Sands, J. Opt. Soc. Am. 60, 1436 (1970).

Wood, R. W.

R. W. Wood, Physical Optics (Macmillan, New York, 1905), pp. 71–77.

Other (12)

R. K. Luneburg, Mathematical Theory of Optics (University of California Press, Berkeley, 1968), pp. 269–302.

H. A. Buchdahl, Optical Aberration Coefficients (Dover, New York, 1968), pp. 305–310.

H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge U. P., Cambridge, England, 1970).

L. Montagnino, J. Opt. Soc. Am. 58, 1667 (1968).

E. W. Marchand, J. Opt. Soc. Am. 60, 1 (1970).

P. J. Sands, J. Opt. Soc. Am. 60, 1436 (1970).

The optical axis is assumed to be in the positive x direction.

E. G. Rawson, D. R. Herriott, and J. McKenna, Appl. Opt. 9, 753 (1970).

The S and T are normalized coordinates in their respective planes. For a discussion of the S and T, see Ref. 6 and Ref. 2.

R. W. Wood, Physical Optics (Macmillan, New York, 1905), pp. 71–77.

D. T. Moore, thesis, University of Rochester, 1970.

The ΔX is the difference of X between one surface and the next. ΔX=Xj+1-Xj.

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