High-quality reconstruction of coherent modulation imaging using weak cascade modulators

Resolution enhancement with highly curved illumination in ptychography

By deducing a formula to compute a sample from recorded diffraction intensity directly and analytically, the relationship among the highest reachable resolution of the ptychographic iterative engine (PIE), its illumination angle, and its collection angle was discussed analytically. Curved illumination was then proposed to realize the resolution enhancement for PIE, and a corresponding computing algorithm was proposed to avoid an undersampling effect without increasing the size of the computing matrix, thus realizing speedy high-resolution PIE imaging with a simple experimental setup. While theoretical analysis was carried out, the feasibility of this proposed method was verified both numerically and experimentally.

Coherent modulation imaging using a physics-driven neural network

Coherent modulation imaging (CMI) is a lessness diffraction imaging technique, which uses an iterative algorithm to reconstruct a complex field from a single intensity diffraction pattern. Deep learning as a powerful optimization method can be used to solve highly ill-conditioned problems, including complex field phase retrieval. In this study, a physics-driven neural network for CMI is developed, termed CMINet, to reconstruct the complex-valued object from a single diffraction pattern. The developed approach optimizes the network's weights by a customized physical-model-based loss function, instead of using any ground truth of the reconstructed object for training beforehand. Simulation experiment results show that the developed CMINet has a high reconstruction quality with less noise and robustness to physical parameters. Besides, a trained CMINet can be used to reconstruct a dynamic process with a fast speed instead of iterations frame-by-frame. The biological experiment results show that CMINet can reconstruct high-quality amplitude and phase images with more sharp details, which is practical for biological imaging applications.

Physics-enhanced neural network for phase retrieval from two diffraction patterns

In this work, we propose a physics-enhanced two-to-one Y-neural network (two inputs and one output) for phase retrieval of complex wavefronts from two diffraction patterns. The learnable parameters of the Y-net are optimized by minimizing a hybrid loss function, which evaluates the root-mean-square error and normalized Pearson correlated coefficient on the two diffraction planes. An angular spectrum method network is designed for self-supervised training on the Y-net. Amplitudes and phases of wavefronts diffracted by a USAF-1951 resolution target, a phase grating of 200 lp/mm, and a skeletal muscle cell were retrieved using a Y-net with 100 learning iterations. Fast reconstructions could be realized without constraints or a priori knowledge of the samples.

Surface metrology by multiple-wavelength coherent modulation imaging

With the rapid progress of advanced manufacturing, three-dimensional metrology techniques that are able to achieve nanometer spatial resolution and to capture fast dynamics are highly desired, for which a snapshot ability and a common-light-path setup are required. Commonly used off-axis holography and phase-shifting interferometry are short in fulfilling those requirements. We studied the suitability and performance of the coherent modulation imaging (CMI) method for metrology applications. Both transparent and reflective samples are measured in visible light experiments. Thanks to its ability to retrieve separate wavefronts at different wavelengths from a single measurement, CMI allows for attaining an enlarged range of measurement free from phase wrapping by utilizing the concept of synthetic wavelength. The CMI method fulfills well the requirements for advanced metrology and can be implemented at any wavelength. We expect it would be a powerful addition to the pool of advanced metrology tools.

Three-dimensional phase and intensity reconstruction from coherent modulation imaging measurements

Coherent modulation imaging is a lensless imaging technique, where a complex-valued image can be recovered from a single diffraction pattern using the iterative algorithm. Although mostly applied in two dimensions, it can be tomographically combined to produce three-dimensional (3D) images. Here we present a 3D reconstruction procedure for the sample's phase and intensity from coherent modulation imaging measurements. Pre-processing methods to remove illumination probe, inherent ambiguities in phase reconstruction results, and intensity fluctuation are given. With the projections extracted by our method, standard tomographic reconstruction frameworks can be used to recover accurate quantitative 3D phase and intensity images. Numerical simulations and optical experiments validate our method.

Spatiotemporal coherent modulation imaging for dynamic quantitative phase and amplitude microscopy

The single-shot capability of coherent modulation imaging (CMI) makes it have great potential in the investigation of dynamic processes. Its main disadvantage is the relatively low signal-to-noise ratio (SNR) which affects the spatial resolution and reconstruction accuracy. Here, we propose the improvement of a general spatiotemporal CMI method for imaging of dynamic processes. By making use of the redundant information in time-series reconstructions, the spatiotemporal CMI can achieve robust and fast reconstruction with higher SNR and spatial resolution. The method is validated by numerical simulations and optical experiments. We combine the CMI module with an optical microscope to achieve quantitative phase and amplitude reconstruction of dynamic biological processes. With the reconstructed complex field, we also demonstrate the 3D digital refocusing ability of the CMI microscope. With further development, we expect the spatiotemporal CMI method can be applied to study a range of dynamic phenomena.

Coherent modulation imaging using unknown modulators

Coherent modulation imaging (CMI) is an effective lensless diffraction imaging method with fast algorithmic convergence and high robustness to data defects. In the reported algorithms for CMI, one important requirement is that the modulator function need to be known a priori; and an additional step for the modulator characterization is required to be carried out in advance by other methods, such as ptychography, which could be cumbersome in practice. Here, we propose an improved algorithm that allows for the transmission function of a completely unknown modulator to be recovered during the same iterative process of image reconstruction. We have verified the method in both simulations and optical experiments. This improvement would turn CMI into a more practical and standalone technique for broader applications in biology and materials science.

Enhancing Multi-Distance Phase Retrieval via Unequal Interval Measurements

In the conventional methods of multi-distance phase retrieval, the diffraction intensity patterns are recorded at equal intervals, which can induce slow convergence or stagnation in the subsequent reconstruction process. To solve this problem, a measurement method with unequal intervals is proposed in this paper. The interval spacings between adjacent measurement planes are decreased gradually. A large gap accelerates retrieval progress, and a short span helps to recover detailed information. The proposed approach makes full use of the available measured dataset and simultaneously generates variations in diversity amplitude, which is a crucial issue for the techniques of multi-image phase retrieval. Both computational simulations and experiments are performed. The results demonstrate that this method can improve the convergence speed by 2 to 3 times and enhance the quality of reconstruction results in comparison to that of the conventional methods.