## Inhomogeneous Lenses, II. Chromatic Paraxial Aberrations

JOSA, Vol. 61, Issue 6, pp. 777-783 (1971)

http://dx.doi.org/10.1364/JOSA.61.000777

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### Abstract

If the glasses constituting a symmetric optical system are inhomogeneous, any chromatic paraxial-aberration coefficient can be expressed as a sum of the usual surface contributions, together with a sum of integrals over each inhomogeneous medium. The explicit form of the various contributions to the chromatic paraxialaberration coefficients of the first and second chromatic degree are written down. Given the dependence of the refractive index on both wavelength and position, these formulas can be used to compute the chromatic paraxial-aberration coefficients. The effectiveness of the inhomogeneities as additional degrees of freedom for the control of chromatic aberrations is discussed. Some recent work on the dispersion of glasses is reported. This work supports the use of Buchdahl’s dispersion formula and color coordinate ω in the context of the chromatic aberrations of systems operating in the visible part of the spectrum.

**Citation**

P. J. SANDS, "Inhomogeneous Lenses, II. Chromatic Paraxial Aberrations," J. Opt. Soc. Am. **61**, 777-783 (1971)

http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-61-6-777

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### References

- P. J. Sands, J. Opt. Soc. Am. 60, 1436 (1970). Throughout the present paper, reference will be made to it as IL, an abbreviation of its title. References to equations in IL will be made by preceding the number of the equation concerned by IL; thus IL Eq. (8), etc.
- The notation used in the present paper is that of IL. Thus, in this case, x is the distance, parallel to the optical axis, from some reference plane and ξ is the square of the radial distance from the optical axis.
- D. T. Moore, thesis, University of Rochester, 1970.
- The total contribution by any single lens is the sum of the two surface contributions and the transfer contribution, i.e., the contribution due to transfer across the inhomogeneous medium. For a lens which is formally thin, the transfer contribution vanishes and the inhomogeneities will affect the total contribution of a thin lens if and only if they affect the surface contributions.
- The meaning of "chromatic degree" will become apparent in Sec. V.
- H. A. Buchdahl, Optical Aberration Coefficients (Dover, New York, 1969). Where necessary, the title of this monograph will be abbreviated to OAC and equations in OAC will be referenced by preceding the equation number by OAC.
- F. A. Jenkins and H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1957).

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