Traditional optical imaging systems operate on a direct physical mapping mechanism, in which lightis refracted by optical lenses, is focused onto the sensor plane, thereby establishing a “point-to-point” mapping relationship between the object and the image plane. This process provides a uniform sampling and reproduction of the object’s radiation intensity in real space, offering a “what you see is what you get” imaging paradigm. In fact, the information obtained through conventional optical imaging is inherently constrained by various physical factors, including the diffraction limit, the discrete sampling of the detector, and the space–bandwidth product of the imaging system, making it difficult to achieve imaging performance that surpassescurrent systemic limits. By contrast, computational imaging reconceptualizes the imaging process as one of information transmission and reconstruction, where the object functions as the information source and the imaging system acts as the transmission channel. By introducing active optical encoding modulation at the front end and combining with physical model-based computational reconstruction at the back end, it enables the indirect perception and efficient reconstruction of object information. This paradigm, which deeply integrates optical modulation with algorithmic processing, is able to transcend the conventional restrictions of physical hardware, thereby greatly enhancing imaging performance and making it possible to achieve both a large field of view and high spatial resolution simultaneously. Such a computational imaging framework, which departs from reliance on imaging lenses, is particularly well suited to extreme ultraviolet and X-ray wavelengths, where it avoids the limitations imposed by low numerical aperture, highly complex, and costly reflective objective systems, and thus shows considerable potential for applications in fields such as semiconductor metrology.

The theoretical foundation of computational imaging redefines the traditional imaging paradigm by introducing a systematic “encoding–decoding” framework. At its core, the method involves actively modulating light with front-end optical elements, where distortions, blur, or scattering are deliberately introduced into the intermediate image so that high-dimensional information—such as polarization, phase, or spectral—is encoded into two-dimensional sensor. These encoded measurements are then reconstructed using accurate physical forward models together with advanced computational algorithms at the back end, which enable the recovery of high-quality images or additional information beyond the limits of conventionalimaging.

Fig.1 The framework of computational imaging

I. Scientific Issues and Methods

Focusing on the underlying characteristics of computational imaging, we have summarized and identified several fundamental scientific issues, including the existence and uniqueness of computational imaging solutions; the convergence and robustness of reconstruction algorithms; systematic error correction, traceability and accuracy assessment; noise suppression and signal-to-noise ratio enhancement; light field manipulation and multi-dimensional information multiplexing; high-throughput, high-resolution and high-dimensional information imaging. Leveraging modern numerical theory and optimization methods, combined with recent advances in machine learning, super-resolution imaging, and light field manipulation. Key research focuses include: rapid physical modelling approaches for spatio-temporal partially coherent imaging approximating complex experimental scenarios, near-field computation of light-sample interactions, and diffraction propagation with far-field computation; Inverse optimization algorithms based on Wigner gradient, subgradient, and Hessian regularized projection; Multi-dimensional information evaluation systems for cross-domain optimization (non-pixel domain) based on feature domains, wavelet domains, etc.; Error tracing for imaging systems, uncertainty assessment for quantitative phase measurement, and accuracy evaluation methods. Through the research, we can transcend the physical constraints of conventional computational imaging. By exploring and continually advancing computational imaging techniques, we can push beyond the spatio-temporal bandwidth limitations of existing systems (approaching atomic-level spatial resolution and femtosecond-level temporal resolution). This breakthrough provides novel principles, methodologies, and pathways for enabling online, non-destructive, and precise measurements in advanced manufacturing processes such as integrated circuit fabrication and atomic-level manufacturing.

II. Instrumentations and Applications

(1) Coherent Diffraction Imaging Microscope

Coherent diffraction imaging (CDI)microscopes is a lensless imaging technique that relies on phase retrieval algorithms. By processing a series of diffraction intensity patterns containing redundant information, it simultaneously reconstructs the amplitude and phase distributions of both the sample and probe, while offering a large field of view and high resolution. In response to the multidimensional requirements of nanoscale metrology and inspection, our research is directed towards developing new principles and algorithms for computational coherent diffraction imaging. We aim to establish advanced CDI microscopes in a range of configurations—including broadband, high-resolution, reflective, and transmissive setups—while addressing critical challenges such as the development of fast and robust reconstruction algorithms, together with the precise in-situ calibration of system parameters. Building on these advances, the instruments we develop will be applied to frontier fields such as biomedical research, novel optoelectronic materials, and device characterisation, where they will enable quantitative measurements of micro- and nanoscale structures and material properties.

Fig.2 Coherent diffraction computational imaging microscope: (a) Optical path diagram; (b) The prototype system

Fig. 3 Typical applications of ptychographic computational imaging microscopy: (a) USAF-1951 resolution target; (b) Characterization of micro/nano structures in multilayer OLED devices; (c) Biological cell imaging

(2) EUV Ptychography System

Extreme ultraviolet (EUV) ptychography combines EUV and soft X-ray illumination sources with ptychographic imaging principles to achieve nanoscale resolution in sample characterization. Widely used in advanced semiconductor manufacturing, this technique supports nanostructure metrology, defect inspection and material characterization in integrated circuits, offering sub-10 nm imaging resolution and atomic-scale detection sensitivity. EUV ptychography reconstructs high-resolution complex amplitude images of samples over a large field of view, providing rich measurement information including absorption, phase, structural anisotropy and three-dimensional morphology. The technique is particularly suited to applications such as defect inspection in EUV lithography masks, where phase defects and absorption-layer imperfections are critical, as well as nanoscale metrology and defect detection in patterned wafers, which often involve buried structures or interface doping. Beyond semiconductor applications, EUV ptychography enables the characterization of the structural and optical properties of emerging nanoscale and atomic-level materials, including quantum, topological, and low-dimensional systems.

Figure.4 Extreme ultraviolet ptychography system: (a) System optical path diagram; (b) Schematic of the system's three-dimensional structure; (c) SEM characterization results of the extreme ultraviolet mask prototype; (d) Extreme ultraviolet mask layered diffraction imaging results at the original wavelength

(3) Wavefront Detection Systems Based on Computational Imaging

In computational imaging-based wavefront sensing, sequences of diffraction fields modulated by diffractive elements are captured and reconstructed using algorithms such as ptychography. This allows the complex amplitude of the illumination probe to be determined. Incorporating light-field propagation models enables this approach to retrieve detailed wavefront information of the optical system. Thanks to its lensless architecture, computational wavefront sensing achieves diffraction-limited wavefront reconstruction, overcoming the spatial resolution constraints imposed by the complex, highly precise optical components required by conventional sensing techniques. The development of robust, low-complexity, high-dynamic-range and cost-effective systems, together with advances in phase unwrapping algorithms and spatial error calibration, enables the high-resolution, high-precision detection of wavefronts and multidimensional spatiotemporal light fields. Wavefront analysis can be extended to applications such as aberration detection and three-dimensional micro- and nanoscale structural metrology. Tailored measurement systems and algorithms are being developed for these applications. These include the measurement of surface profiles of optical components, the characterization of micro- and nanoscale devices, the detection of optical system aberrations, light-field sensing and the analysis of beam quality.

Figure.5 Computational imaging wavefront detection system: (a) Schematic of wavefront aberration measurement; (b) Three-dimensional spatial light field detection; (c) Three-dimensional topography measurement of micro-nano structures

(4) Ptychographic Mueller Matrix Imaging Polarimetry

Traditional Mueller matrix polarimeters are constrained by the imaging optics of objective lenses, which result in complex structures, high costs, and an inherent trade-off between imaging resolution and field of view. To address these limitations, we introduce polarization modulation into computational ptychographic imaging systems and propose a novel ptychographic Mueller matrix imaging technique, whereby computational imaging methods are employed to realise Mueller matrix measurements. By incorporating polarization modulation and demodulation before and after the interaction of light with the sample, we capture ptychographic diffraction fields under multiple polarization states, from which Mueller matrix images are reconstructed using advanced computational algorithms. Building on this approach, we have developed new instruments, including ptychographic Mueller matrix imaging polarimeters and Fourier ptychographic Mueller matrix imaging polarimeters. Our research is centered on critical technologies such as constructing forward physical models for vectorial ptychographic imaging, developing dedicated Mueller matrix reconstruction algorithms, calibrating system parameters, performing error quantification, and analyzing optical physical information. These advancements enable measurement applications for anisotropic samples, including biological tissues, low-dimensional materials, and novel optoelectronic devices. By harnessing the comprehensive polarization information encoded in Mueller matrices, we aim to uncover new optical phenomena and elucidate the underlying mechanisms in materials and micro- to nanostructures.

Fig.6 Ptychographic Mueller matrix imaging polarimeter: (a) System schematic; (b) Mueller matrix plot of USAF resolution target

Selected Papers：

1. L. Liu, J. Du, B. Zhuang, M. Gong, J. Liu, H. Gu, and S. Liu, "Pushing the resolution limit of coherent diffractive imaging," Light Sci. Appl. 14, 298 (2025). [Front Cover]

2. C. Chen, H. Gu, and S. Liu, "Ultra-simplified diffraction-based computational spectrometer," Light Sci. Appl. 13, 9 (2024). [Front Cover]

3. C. Chen, H. Gu, and S. Liu, "Ultra-broadband diffractive imaging with unknown probe spectrum," Light Sci. Appl. 13, 213 (2024).

4. L. Liu, B. Zhuang, J. Du, L. Zhong, M. Gong, H. Chen, Q. Zhang, J. Liu, H. Gu, and S. Liu, "Wavelet-domain autofocusing algorithm for lensless ptychographic imaging," Measurement 253, 117634 (2025).

5. C. Chen, Y. Zhou, Y. Wang, H. Xia, H. Gu, and S. Liu, "Enhancing Monochromatization for Broadband Coherent Diffractive Imaging," IEEE Trans. Instrum. Meas. 74, 5038509 (2025).

6. L. Liu, L. Zhong, M. Gong, J. Du, H. Gu, and S. Liu, "An Efficient and Robust Self-calibration Algorithm for Translation Position Errors in Ptychography," IEEE Trans. Instrum. Meas. 73, 4503712 (2024).

7. L. Liu, W. Li, M. Gong, L. Zhong, H. Gu, and S. Liu, "Resolution-Enhanced Lensless Ptychographic Microscope Based on Maximum-Likelihood High-Dynamic-Range Image Fusion," IEEE Trans. Instrum. Meas. 73, 4502711 (2024).

8. C. Chen, H. Gu, and S. Liu, "Noise-robust ptychography using dynamic sigmoid-remolding," Opt. Laser Technol. 172, 110510 (2024).

9. L. Liu, W. Li, L. Zhong, H. Gu, and S. Liu, "An adaptive noise-blind-separation algorithm for ptychography," Opt. Lasers Eng. 169, 107748 (2023).

10. C. Chen, J. Liu, J. Zhu, H. Gu, and S. Liu, "Resolution-enhanced reflection ptychography with axial distance calibration," Opt. Lasers Eng. 169, 107684 (2023).

11. M. Gong, L. Liu, J. Du, B. Zhuang, J. Liu, H. Gu, and S. Liu, "Ptychographic Mueller matrix imaging (PMMI): principle and proof-of-concept demonstration," Opt. Lett. 49, 6409-6412 (2024).

12. M. Gong, L. Liu, N. Li, Q. Zhang, J. Liu, H. Gu, and S. Liu, "Ptychographic Mueller matrix imaging: in-situ system calibration and evaluation," Opt. Lett. 50, 6137-6140 (2025).