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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 52, Iss. 4 — Apr. 1, 1962
  • pp: 376–383

Four-Component Optically Compensated Varifocal System

LEONARD BERGSTEIN and LLOYD MOTZ  »View Author Affiliations


JOSA, Vol. 52, Issue 4, pp. 376-383 (1962)
http://dx.doi.org/10.1364/JOSA.52.000376


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Abstract

The general theory of optically compensated varifocal systems is applied to the case of a four-component system consisting of four alternate stationary and movable components. The second and fourth components, counting from the object side, are interconnected and displaced in unison to change the over-all focal length of the system. An iteration method for the solution of the varifocal equations is developed which enables the determination of the Gaussian parameters of the system for any predetermined focal range in a matter of minutes (without the use of computers). Using this method, explicit expressions are found for the approximate values of the parameters of the optimum four-component systems as functions of the focal range. A numerical example is given to illustrate the iteration method.

Citation
LEONARD BERGSTEIN and LLOYD MOTZ, "Four-Component Optically Compensated Varifocal System," J. Opt. Soc. Am. 52, 376-383 (1962)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-52-4-376


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References

  1. L. Bergstein and L. Motz, J. Opt. Soc. Am. 52, 353 (1962).
  2. L. Bergstein and L. Motz, J. Opt. Soc. Am. 52, 363 (1962).
  3. L. Bergstein, J. Opt. Soc. Am. 48, 154 (1958).
  4. The "relative focal range" R is defined as the ratio of maximum to minimum over-all focal lengths of the system, i.e., [equation], For any required focal range R two lens types are possible. Either a lens system can be chosen which will have the maximum focal length when the movable components are in the extreme front position or a system can be chosen which will have its maximum focal length when the movable components are in the rear position. We refer to the first system as the P system and the latter as the N system. We define the "focal ratio" [equation] For the P system r=R, whereas for the N system r=1/R. We also introduce the normalized range [equation] where the positive sign applies to the P system, the negative sign to the N system. We note that 1<R<∞, 0<r<∞, and -1<r<+1.
  5. In reference 3 it is shown that under optimum conditions the maximum value of the image-plane deviation of a four-component system with full compensation at both ends of the operating range is approximately 4/3 times the maximum value of the image-plane deviation obtained when full compensation at both ends of the operating range is not required. The difference in the level of the two maximum values is thus small.
  6. The choice between the two optimum systems is governed by a number of considerations [L. Bergstein, J. Opt. Soc. Am. 48, 154 (1958)]. (The PNP system is generally preferable.)

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