## Third-Order Aberrations of Inhomogeneous Lenses

JOSA, Vol. 60, Issue 11, pp. 1436-1443 (1970)

http://dx.doi.org/10.1364/JOSA.60.001436

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### Abstract

Various organizations in the United States and abroad are experimenting with techniques for manufacturing glass with a continuously varying refractive index. Use of such glasses in lens design would provide valuable additional degrees of freedom for the control of aberrations. This paper presents formulas by means of which the third-order (monochromatic) aberration coefficients of a symmetric system may be computed when the lenses are manufactured from glasses with continuously varying refractive indices. Each coefficient is expressed as a sum of contributions by each surface separating two distinct media and a sum of integrals over each inhomogeneous medium. The surface contribution consists of the usual contribution based on the assumption that the media are homogeneous, and an additional term that takes into account the variation of the index along the surface.

**Citation**

P. J. SANDS, "Third-Order Aberrations of Inhomogeneous Lenses," J. Opt. Soc. Am. **60**, 1436-1443 (1970)

http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-60-11-1436

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### References

- A. D. Pearson, W. G. French, and E. G. Rawson, Appl. Phys. Letters 15, 76 (1969).
- R. W. Wood, Physical Optics, 2nd ed. (Macmillan, New York, 1911) gives a fascinating account of an experimental verification of the focusing properties of cylindrical slabs of media whose refractive index depends only on the distance from the axis of the cylinder.
- An optical system is said to be symmetric if it has an axis of rotational symmetry (the optical axis) and is invariant under reflections in any plane containing the optical axis.
- E. W. Marchand, J. Opt. Soc. Am. 60, 1 (1970).
- For example, see E. G. Rawson, D. R. Herriott, and J. McKenna, Appl. Opt. 9, 753 (1970).
- H. A. Buchdahl, Optical Aberration Coefficients (Dover, New York, 1969). Throughout this paper a knowledge of the content of Appendix F of this text will be presupposed, as is some familiarity with the manner in which the contributions by a single surface to the aberrations of a (homogeneous) system may be derived from the quasi-invariant Λ. Repeated reference will be made to Optical Aberration Coefficients and the title of this will be abbreviated to OAC, and Appendix F of OAC to OACF.
- H. A. Buchdahl, An Introduction to Hamiltonian Optics (Cambridge University Press, New York, 1970), Sec. 19.

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