Optical simulation and imaging performance evaluation on the influencing parameters of the Alvarez lenses

Optical varifocal systems have extensive applications such as consumer electronics, defense equipment, industrial monitoring, and medical devices. Traditional varifocal methods typically involve multiple lenses and mechanical components. The lenses often move along the optical axis using motors to achieve the varifocal ability. This configuration introduces some limitations, such as more structural complexity, larger size, slower varifocal speed, and higher production cost. Different from the traditional varifocal lenses, Alvarez lenses comprise two symmetrically arranged freeform surface phase plates moving perpendicular to the optical axis. The Alvarez lenses achieve a wide varifocal range through small lateral displacement offering a compact design and a large varifocal range. Besides the parameter of lateral displacement, the varifocal range and the imaging performance of the Alvarez lenses are influenced by other parameters. This paper aims to explore and analyze how different parameters impact the imaging performance of Alvarez lenses. The analysis focuses on the two parameters, i.e., the vector height modulation coefficient(A), the tilt of the freeform surface (D), air gaps, and installation errors. Parameter A controls the height difference between peaks and valleys of the freeform surface and directly affects the varifocal capability of the Alvarez lenses. Through the optical simulation of the Alvarez lens via OpticStudio software, we found that a decrease in the value of parameter A helps to reduce the rate of performance degradation. However, the smaller value of the parameter A necessitates a larger lateral displacement to achieve equivalent changes in focal length. The increase in displacement results in higher power consumption and a slower response time. Thus, selecting an optimal A value and refining D are crucial to enhancing the Alvarez lenses's overall performance. To identify the optimized parameters, we simulated five different sets of the parameter of A, i.e., 0.125 mm^-2, 0.100 mm^-2, 0.075 mm^-2, 0.050 mm^-2, and 0.025 mm^-2. Comprehensive evaluations, including ray-tracing spot diagrams, Strehl ratio measurements, wavefront PV values, MTF curves, and image simulations under different parameters of A are carried out. The simulated result indicated that the value of A 0.075 mm^-2 offers the balance between image clarity and system responsiveness. Further analysis is carried out to study the effect parameters of air gaps and installation errors on imaging performance. The impact of misalignments along the y- and z-axes on the Alvarez lenses's capabilities are studied, determining that a D value of -0.175 is optimal for minimizing such adverse effects. The results show that the optimized Alvarez lens design outperforms the original in all key evaluation metrics. At identical tuning points, the Alvarez lenses with the optimized parameters demonstrate a significant reduction in both ray aberrations and wavefront PV values, accompanied by a notable increase in the Strehl ratio. Additionally, the MTF curve of the Alvarez lenses with the optimized parameters closely approaches the diffraction limit, underscoring its superior imaging performance. This study successfully identifies the key parameters that affect the performance of Alvarez lenses and proposes an optimized design. The Alvarez lenses can achieve enhanced imaging quality by balancing parameter A and refining parameter D. These findings provide valuable insights for the future development of compact and high-performance optical varifocal systems.