Optics express
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We present a theoretical method for analyzing the first-order optics of stabilized zoom lenses with two focal-length-variable elements. The zoom equations are established through the use of the Gaussian brackets method. This is done because the optical power of the focal-length-variable elements varies during the zooming process. ⋯ This process leads to an increase in the zoom ratio of the zoom system. The results show successful four-group stabilized zoom lens designs with 2:1 and 5:1 zoom ratios, using two deformable mirrors as focal-length-variable elements. This system, with the inherent characteristics of a steepest gradient, could miniaturize zoom systems.