In practical optical imaging systems, the lateral resolution is often defined by R=kλ/NA，where λ represents the illumination wavelength, NA denotes the numerical aperture of the imaging system, and k is the imaging factor related to multiple variables including illumination conditions, signal distortions, and sample characteristics. In the Abbe resolution limit, the imaging factor is 0.5, specifying the theoretical limit of the ultimate resolvable distance of a perfect imaging system. Due to unavoidable diffraction effects of light waves, the imaging factor k increases to 0.61, known as the Rayleigh diffraction limit, which provides a practical frontier that cannot be overcome with a conventional imaging system.
CDI, featuring a lensless geometry and a theoretically perfect transfer function, is considered to be the most promising imaging paradigm for achieving the Abbe resolution limit. Combined with innovative architectures and efficient algorithms, CDI continues to refresh the physical bandwidth limits of the imaging system. With these efforts, considerable critical issues, such as aberration, vignetting effect, depth-of-field and field-of-view constraints, coherence degradation, as well as system errors and artifacts, have indeed been addressed or significantly mitigated, enabling CDIs to easily approach or surpass the Rayleigh diffraction limit (kRayleigh = 0.61). Even more, certain advances have successfully pushed the imaging factor approaching the Abbe limit (kAbbe = 0.5). However, reported CDIs that approach the Abbe limited resolution are all achieved under low NA (< 0.6). In high NA (≥0.6) scenarios, the imaging factor falls short of the Abbe limit of 0.5. Surprisingly enough, up to now, no lensless CDI with an ultra-high NA (>0.8) has been reported. Limited by the low NA and poor imaging factor, the lateral resolution achieved so far has been restricted to 0.69 λ for real-world objects via CDIs.
In a new paper published in Light: Science & Applications, a team of scientists, led by Professors Shiyuan Liu and Honggang Gu from School of Mechanical Science and Engineering, Huazhong University of Science and Technology, China, have demonstrate the theoretical possibility of achieving perfect transfer functions in CDIs with various NAs and successfully push the imaging resolution to the Abbe diffraction limit. Their core innovation is a computational framework called 'rigorous Fraunhofer diffraction (RFD)', in which the rigorous Taylor expansion is adopted instead of the approximate McLaughlin-type binomial expansion commonly used in CDIs. It is the first time that the high-NA, resolution-limit CDI problem is solved once and for all in the Ewald sphere (ES) space by rigorous model-based computation. Especially in nearly 0.9NA, it has achieved a k = 0.501 imaging factor in ptychographic CDI, pushing the Abbe resolution diffraction limit for the first time in such ultra-high-NA scenarios. Leveraging this the ultra-high NA and the Abbe-limit k-factor, it demonstrates a record-high imaging resolution of 0.57 λ for CDIs. It also has been selected as the cover front as the cover front for the current issue.
