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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: 363–370

Three-Component Optically Compensated Varifocal System

LEONARD BERGSTEIN and LLOYD MOTZ  »View Author Affiliations

JOSA, Vol. 52, Issue 4, pp. 363-370 (1962)

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The general theory of optically compensated varifocal systems is applied to a three-component system composed of two movable components placed on either side of a fixed component. The two movable components are displaced in unison to change the over-all focal length of the system. The three-component system is analyzed in detail and an iteration method for the solution of the varifocal equations is developed which enables us to determine the Gaussian parameters of the system for any predetermined focal range in a matter of a few minutes (without the use of computers). Using this method, explicit expressions are found for the approximate values of the parameters of the optimum three-component systems as functions of the focal range. A numerical example is given to illustrate the iteration method.

LEONARD BERGSTEIN and LLOYD MOTZ, "Three-Component Optically Compensated Varifocal System," J. Opt. Soc. Am. 52, 363-370 (1962)

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  1. L. Bergstein and L. Motz, J. Opt. Soc. Am. 52, 353 (1962).
  2. L. Bergstein, J. Opt. Soc. Am. 48, 154 (1958).
  3. The operating range of focal lengths of the system is determined by the "relative focal range" R defined as the ratio of maximum to minimum over-all focal lengths, i.e., [Equation]. It was already pointed out1,2 that for any required focal range R two lens types are possible. Either a lens system can be chosen which has the maximum focal length when the movable components are in the front position, or a system can be chosen which has its maximum focal length when the movable components are in the rear position. We refer to the first system as the P system; the latter is referred to as the N system. We define the "focal ratio" [Equation]. For the P system r = R, whereas r = 1/R for the N system. 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 1.0<R<∞, 0<r<∞, and -1.0<τ<+1.0.
  4. For τ=0, Eq. (16) reduces to b2y(z)=z(z-z2)(z-1.0).
  5. The choice between the two optimum systems is governed by a number of considerations.2 (The PNP system is generally preferable.)

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