High-resolution, large field-of-view label-free imaging via aberration-corrected, closed-form complex field reconstruction
Abstract
Computational imaging methods empower modern microscopes to produce high-resolution, large field-of-view, aberration-free images. Fourier ptychographic microscopy can increase the space-bandwidth product of conventional microscopy, but its iterative reconstruction methods are prone to parameter selection and tend to fail under excessive aberrations. Spatial Kramers–Kronig methods can analytically reconstruct complex fields, but is limited by aberration or providing extended resolution enhancement. Here, we present APIC, a closed-form method that weds the strengths of both methods while using only NA-matching and darkfield measurements. We establish an analytical phase retrieval framework which demonstrates the feasibility of analytically reconstructing the complex field associated with darkfield measurements. APIC can retrieve complex aberrations of an imaging system with no additional hardware and avoids iterative algorithms, requiring no human-designed convergence metrics while always obtaining a closed-form complex field solution. We experimentally demonstrate that APIC gives correct reconstruction results where Fourier ptychographic microscopy fails when constrained to the same number of measurements. APIC achieves 2.8 times faster computation using image tile size of 256 (length-wise), is robust against aberrations compared to Fourier ptychographic microscopy, and capable of addressing aberrations whose maximal phase difference exceeds 3.8π when using a NA 0.25 objective in experiment.
Copyright and License
© The Author(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Acknowledgement
This research is supported by Heritage Medical Research Institute (HMRI) (Award number HMRI-15-09-01). The authors thank Dr. Jerome Mertz for the insightful discussion of this work.
Contributions
These authors contributed equally: Ruizhi Cao, Cheng Shen.
R.C. conceived the idea. R.C. conducted the theoretical analysis, conducted the simulations and wrote the reconstruction algorithm. C.S. built the experiment setup, wrote the hardware controlling code and performed the calibration of the system. R.C. and C.S. conducted the experiments. C.Y. supervised this project. All authors contributed to the preparation of the manuscript.
Data Availability
Part of the data that supports this study is available on GitHub (https://github.com/rzcao/APIC-analytical-complex-field-reconstruction). The complete data that support the plots within this paper and other findings of this study are available from the corresponding authors upon request. Source data are provided with this paper.
Code Availability
The reconstruction code that supports the plots within this paper and other findings of this study is available on Supplemetary Code 1 as well as GitHub (https://github.com/rzcao/APIC-analytical-complex-field-reconstruction) and the zenodo repository25.
Conflict of Interest
The authors (R.C., C.S., and C.Y.) declare the following competing interests: On 30 March 2023, the California Institute of Technology filed a provisional patent application for APIC, which covered the concept and implementation of the APIC system described here.
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Additional details
- PMCID
- PMC11148160
- California Institute of Technology
- Heritage Medical Research Institute HMRI-15-09-01
- Caltech groups
- Division of Biology and Biological Engineering (BBE), Heritage Medical Research Institute