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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 33, Iss. 12 — Dec. 1, 1943
  • pp: 651–652

Gaussian Optics and Gaussian Brackets

M. HERZBERGER  »View Author Affiliations


JOSA, Vol. 33, Issue 12, pp. 651-652 (1943)
http://dx.doi.org/10.1364/JOSA.33.000651


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Abstract

Gauss invented an algorithm for certain arithmetical purposes, which has various applications in optical problems. For instance, it is sometimes of value to see how the focal length, magnification, and back focus of a lens system vary with the change of one of the construction elements (thickness, radius, or refractive index). It is sometimes very useful to have explicit expressions for these significant lens characteristics as functions of the construction elements. However, the usefulness of these Gaussian brackets is not limited to Gaussian optics. The image errors for finite rays in the new form recommended by the author can be expressed with their help.

Citation
M. HERZBERGER, "Gaussian Optics and Gaussian Brackets," J. Opt. Soc. Am. 33, 651-652 (1943)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-33-12-651


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References

  1. L. Euler, Institutiones Calculi Differentialis cum ieus usu in Analysi Finitonum de Doctrina Serierum (Imperial Academy of Science, Petrograd, 1755).
  2. C. F. Gauss, Disquistiones Arithmeticae (1801).
  3. M. Herzberger, Am. Math. Soc. 53, 218 (1942).
  4. M. Herzberger, Quart. App. Math. 1, 1 (1943).
  5. The methods developed here were first made public in a comment by the present author on a paper by S. Rosin and O. H. Clark [J. Opt. Soc. Am. 31, 198–201 (March, 1941)] presented at a meeting of this Society. In this paper, Rosin and Clark had given the data of Gaussian optics in explicit form, with the help of determinants.

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