Latent-wavefront Fourier ptychography for stained tissue microscopy

Fourier ptychographic microscopy (FPM) is a promising technique for achieving high-resolution and large field-of-view imaging, which is particularly suitable for pathological applications, such as imaging hematoxylin and eosin (H&E) stained tissues with high space-bandwidth and reduced artifacts. However, current FPM implementations require either precise system calibration and high-quality raw data, or significant computational loads due to iterative algorithms, which limits the practicality of FPM in routine pathological examinations. In this work, latent wavefront denoting the unobservable exiting wave at the surface of the sensor is introduced. A latent wavefront physical model optimized with variational expectation maximization (VEM) is proposed to tackle the inverse problem of FPM. The VEM-FPM alternates between solving a non-convex optimization problem as the main task for the latent wavefront in the spatial domain and merging together their Fourier spectrum in the Fourier plane as an intermediate product by solving a convex closed-formed Fourier space optimization. The VEM-FPM approach enables a stitching-free, full-field reconstruction for Fourier ptychography over a 5.3 mm ×5.3 mm field of view, using a 2.5× objective with a numerical aperture (NA) of 0.08. The synthetic aperture achieves a resolution equivalent to 0.53 NA at 532 nm wavelength. The execution speed of VEM-FPM is twice as fast as that of state-of-the-art feature-domain methods while maintaining comparable reconstruction quality.