Uncertainty-Aware Fourier Ptychography
also called Differentiable FPM

Light: Science & Applications 14, 236 (2025)

Abstract

Fourier ptychography (FP) delivers wide field-of-view, high-resolution imaging, but its reliance on precise numerical forward models makes it vulnerable to physical uncertainties such as misalignment, optical aberrations, and data quality limitations. Conventional methods correct these issues separately – calibration for misalignment, pupil/probe recovery for aberrations, exposure or HDR techniques for data quality – and cannot address them jointly. We introduce Uncertainty-Aware FP (UA-FP), a fully differentiable framework that treats deterministic uncertainties (misalignment and optical aberrations) as optimizable parameters, while using differentiable optimization with domain-specific priors to handle stochastic uncertainties (noise and data quality limitations). UA-FP achieves superior reconstruction quality under challenging conditions, remaining robust with reduced sub-spectrum overlap and even low-bit sensor data, and extends FP’s use as a measurement tool for settings where precise alignment and calibration are impractical.

Reconstruction comparisons

The same measurements are reconstructed with Uncertainty-Aware Fourier Ptychography (UA-FP) and the ptychographic iterative engine (PIE). Both solvers upsample the measurements four times and recover the pupil as a fourth-order Zernike expansion (Noll indices 3 to 14; piston and tilt are held at zero). UA-FP runs 500 iterations and also optimizes the LED-array pose; PIE runs 30 sweeps over the LEDs (50 for the low-quality target) with the nominal geometry. Each figure is the solver’s own summary: reconstructed amplitude, unwrapped phase, log-magnitude object spectrum, recovered pupil phase and its Zernike coefficients, the loss curve, and the LED array. UA-FP’s bottom row shows the optimized array against the nominal one and the recovered translation and rotation over the iterations. Click a figure to enlarge it.

Blood smear

Data source: public Fourier ptychography dataset by Pengming Song and Guoan Zheng (University of Connecticut), bloodsmear_green. 2×/0.1 NA objective, 532 nm LED, 15 × 15 LED array.

UA-FP
PIE

Low-quality USAF resolution target

Data source: our own visible-light measurement, recorded as 8-bit frames. 532 nm LED, 0.1 NA / 4× objective, 15 × 15 LED array.

UA-FP
PIE

Blood cells

Data source: our own visible-light Fourier ptychography rig. 533 nm LED, 0.14 NA objective, 15 × 15 LED array (185 of the 225 positions recorded).

UA-FP
PIE

The code and data are not publicly available at this time. If you have data you would like reconstructed, please contact nichen.optics@gmail.com.

Bibtex

@article{Chen2025LSA,
  author     = {Ni Chen and Yang Wu and Chao Tan and Liangcai Cao and Jun Wang and Edmund Y. Lam},
  doi        = {10.1038/s41377-025-01915-w},
  ifactor    = LSA,
  journal    = {Light: Science \& Applications},
  month      = {7},
  number     = {1},
  pages      = {236},
  title      = {{Uncertainty-Aware Fourier Ptychography}},
  volume     = {14},
  year       = {2025},
}

Uncertainty-Aware Fourier Ptychography also called Differentiable FPM