Extended depth-of-focus liquid-crystal-based lens with deterministic forward design based on frozen-wave synthesis.

An extended depth-of-focus (EDOF) lens is essential for overcoming the limited axial response of conventional optical systems, where high-quality imaging is confined to a narrow depth range. However, existing optimized approaches based on phase engineering or inverse design often suffer from limited physical interpretability and restricted control over the axial response. Here, we propose a forward-designed EDOF strategy based on the frozen-wave framework, in which the axial intensity distribution is directly prescribed through the coherent superposition of Bessel beams with different cone angles. The resulting point spread function (PSF) is rotationally symmetric and maintains an invariant transverse profile over an extended propagation range, enabling uniform axial resolution. The proposed design is implemented using a liquid-crystal (LC) platform, and PSF tests confirm stable performance over a large depth range. Image degradation caused by surrounding sidelobes can be effectively mitigated via deconvolution, leading to improved recovered quality. Furthermore, broadband measurements show consistent PSF behavior across different wavelengths, indicating wavelength-robust imaging performance. This work provides a deterministic and physically intuitive approach for EDOF imaging, with potential applications in compact machine-vision and inspection systems requiring enhanced depth tolerance.