Fig. 1: Concept of angular ptychographic imaging with closed-form method (APIC) and comparison between the reconstruction process of APIC and Fourier ptychographic microscopy (FPM).

a Setup of APIC. The LEDs whose illumination angle matches up with the numerical aperture (NA) of the objective are lit sequentially to obtain the NA-matching measurements. Then, the LEDs whose illumination angle is larger than the objective’s receiving angle are successively lit for the darkfield measurements. b Reconstruction process of APIC. Once the aberration is extracted, it is used to correct aberration in the image-wise field reconstruction. The aberration-corrected spectrums are then stitched together and serves as a prior knowledge in the spectrum extension. Using darkfield measurements, the spectrum is furtherly extended to obtain a high-resolution, aberration-free reconstruction. c Reconstruction process of Fourier ptychographic microscopy (FPM). FPM iteratively updates the spectrum and the aberration to minimize the differences in the measurement and reconstruction output. This iterative process is terminated upon convergence to obtain the spectrum and coherent transfer function (CTF) estimate. Pupil in the figure denotes the reconstructed aberrations.