Optical phase measurement is crucial for various applications, including optical metrology, adaptive optics, and biomedical imaging. Current techniques broadly fall into two categories: interferometry-based methods, which offer high accuracy but require complex setups and are sensitive to environmental fluctuations; and computational phase retrieval methods, which are less sensitive but often require multiple measurements and constraints. Wavefront sensing techniques offer an alternative indirect approach, measuring the wavefront's propagation direction to retrieve the phase map. Shack-Hartmann wavefront sensors (SHWFS), while simple and stable, have been limited by the low sampling density and small acceptance angle of traditional lenslet arrays, typically around 100 per mm² and 1°, respectively, restricting their use to slowly varying wavefront structures. This research aims to overcome these limitations by utilizing a metasurface-enhanced SHWFS (meta SHWFS) to achieve high-resolution phase imaging of complex objects.

The paper reviews existing phase imaging techniques, highlighting the advantages and limitations of interferometry-based methods and computational phase retrieval approaches. It emphasizes the challenges of traditional SHWFS in achieving high spatial resolution and large acceptance angles due to limitations in lenslet array fabrication. The authors note existing work on metalens arrays, but highlight the absence of their use in single-shot phase imaging of complex structures.

The researchers designed a meta SHWFS utilizing an array of metalenses. The performance of the SHWFS is determined by three key parameters: maximum acceptance angle (θmax), number of resolvable angles (Ng), and sampling density (Ns). The metalens diameter is identified as the key parameter influencing sampling density. The optimum focal length of the metalenses was determined by considering spot localization errors at various signal-to-noise ratios (SNRs), aiming to maximize the ratio of maximum allowable displacement to resolution error (Δmax/Δres). A 100x100 metalens array with a lenslet diameter of 12.95 μm and a focal length of 30 μm was fabricated, achieving a high sampling density and large acceptance angle. The metalenses were designed using silicon nitride (SiN) rectangular cuboids arranged on a subwavelength lattice. The large angle calibration was performed by measuring focal spot displacements for varying incidence angles using a plane wave controlled by galvanometer mirrors. The capability of the meta SHWFS to track an incoherent light source was demonstrated using an LED. The influence of chromatic aberration and spatial coherence was discussed and addressed.

The meta SHWFS demonstrated a sampling density of 5963 per mm² and a maximum acceptance angle of ±8°. This represents a substantial improvement over traditional SHWFS, achieving 100 times better spatial resolution and 10 times larger phase gradient. The experimental results validated the uniform translation of focal spots within the large acceptance angle range. The meta SHWFS successfully performed single-shot 3D position tracking of an incoherent LED light source. The focusing efficiency of the metalenses was experimentally measured to be 47.7%. The high performance of the meta SHWFS allowed for phase imaging of complex patterns, including a confluent histopathologic tissue structure, showcasing its potential for high-resolution phase imaging applications.

The high sampling density and large acceptance angle achieved by the meta SHWFS significantly broaden its applicability in wavefront sensing and phase imaging. The successful single-shot phase imaging of complex structures demonstrates the superior capabilities of the meta SHWFS compared to traditional methods. The use of an incoherent light source expands the potential applications of the sensor. The detailed analysis of the parameters influencing the performance of the meta SHWFS provides guidelines for optimizing its design for specific applications. The high resolution and large angular field of view open possibilities in various fields, including biomedical imaging, astronomy, and optical metrology.

The developed meta SHWFS provides a significant advancement in wavefront sensing technology. Its high sampling density and large angular field of view overcome the limitations of traditional SHWFS, enabling high-resolution phase imaging of complex objects. Future research could focus on integrating additional optical functionalities of metasurfaces to enhance the sensor's capabilities further and explore applications in dynamic wavefront sensing and real-time imaging.

While the meta SHWFS shows excellent performance, some limitations exist. The focusing efficiency of the metalenses could be further improved. The impact of chromatic aberration was discussed and mitigated but could still be an area for optimization. Further investigation on the impact of noise in the signal processing and calibration procedures is needed. The current design operates at a specific wavelength, and extending its operational range to a broader spectrum could be valuable.