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In this paper, we propose a systematic approach to design a four-componentzoom system with fixed spacing between focal points based on matrix optics.Since the more complex model the higher degree of freedom it has, the task ofdetermining the zoom trajectory is meaningful and challenging. The elements ofthe system matrix imply the working state of the optical system, and axialdisplacement equation for the desired zoom system are derived by restrictingspecific matrix elements. Properly selected trajectory of the particularcomponent described by means of a parametric function can make the model becomesolvable explicitly. Then the paraxial design problem is transformed into theoptimization of these parameters with regard to the merit functionsencompassing the primary aberration terms, compactness, smoothness of thetrajectories. We adopt Particle Swarm Optimization (PSO) algorithm to globallyoptimize the parameters to retrieve the optimum zoom trajectory in specificdesign criteria. The proposed method is demonstrated through two numericalexamples under different configurations. The simulation results demonstratethat our proposed method can be a practical and powerful tool for paraxialdesign of complex multi-group zoom optical systems.

Paraxial design of four-component zoom lens system with fixed distance between focal points by matrix optics