Designing interferometers within a single optical beam

Abstract

Interferometry provides highly sensitive access to optical phase and is central to much of modern metrology and phase imaging methods. Conventional implementations, however, often face trade-offs between mechanical stability and experimental or computational complexity. Here, we present a general framework for designing custom interferometers within a single optical beam by exploiting structured light. This approach yields compact, robust common-path configurations that bypass the need for complex post-processing and can easily be integrated into existing setups. We demonstrate the versatility of this concept by designing a range of interferometers, each tailored by the structured mode, and implement them through active and passive modal conversion optics, proving its adaptability to different experimental requirements. To showcase the practical utility of our framework, we apply it to quantitative phase imaging over a variety of physical samples, showing excellent agreement with atomic force microscopy benchmarks. Furthermore, we emphasise the flexibility of our structured light interferometers by mapping phase objects to a choice of either amplitude or polarisation, the latter providing a direct route toward real-time phase-retrieval. This cost-effective approach offers a practical, high-throughput solution for phase-sensitive metrology across fields such as fundamental physics, biology, and material science.