Precise simultaneous control of both angular and spatial light-field distributions remains a longstanding challenge in optical design, often requiring complex multi-element configurations. In this work, we propose a compact single-lens solution that achieves unified angular-spatial modulation through the co-optimization of double freeform surfaces. The problem is formulated as an extended caustic design that enforces prescribed irradiance patterns on two distinct receptive planes, where the dual-plane constraint implicitly defines the directional characteristics of the light field while preserving spatial accuracy. This framework eliminates the need for auxiliary optical components while delivering performance comparable to that of conventional multi-lens systems. Comprehensive numerical simulations verify the method's effectiveness, demonstrating accurate and stable control of both angular and spatial light-field properties. The proposed approach establishes a practical foundation for compact, high-performance optical systems and provides a promising route toward integrated angular-spatial light-field engineering.

翻译：对光场角分布与空间分布的同时精确调控一直是光学设计领域的长期挑战，通常需要复杂的多元件构型。本研究提出一种紧凑型单透镜解决方案，通过双自由曲面的协同优化实现角-空联合调制。该问题被建模为扩展焦散设计，要求在两个不同接收平面上形成指定的辐照度分布，其中双平面约束在保持空间精度的同时隐含定义了光场的方向特性。该框架无需辅助光学元件，即可实现与传统多透镜系统相媲美的性能。全面数值仿真验证了该方法的有效性，证明其能精确稳定地控制光场的角度与空间特性。所提方案为紧凑型高性能光学系统奠定了实用基础，并为集成化角-空光场工程开辟了可行路径。