High-fidelity pixel-super-resolved complex field reconstruction via adaptive smoothing.

In this Letter, we propose a new, to the best of our knowledge, lensless on-chip holographic microscopy platform, which can acquire sub-pixel-shifting holograms through centimeter (cm)-level lateral translations. An LED light source is used to illuminate the sample, and two orthogonally tilted step-structure glass plates are inserted into the optical path. By merely displacing the glass plates under cm-level precision, a series of holograms with sub-pixel displacements can be obtained. Combined with our improved pixel super-resolution (PSR) algorithm, high-quality PSR phase imaging can be achieved. Tests on the high-resolution USAF1951 target demonstrate that the system can achieve a half-width resolution of 870 nm by a camera with a pixel size of 1.67 µm. Additionally, imaging experiments were conducted on phase-type sinusoidal gratings, yeasts, red blood cells, and lilium ovary sections, respectively. The results show that the system can achieve large field-of-view, high-resolution phase imaging under low-cost hardware conditions and holds promise for its applications in biology and medicine.

In-line digital holography (DH) and lensless microscopy are 3D imaging techniques used to reconstruct the volume of micro-objects in many fields. However, their performances are limited by the pixel size of the sensor. Recently, various pixel super-resolution algorithms for digital holography have been proposed. A hologram with improved resolution was produced from a stack of laterally shifted holograms, resulting in better resolved reconstruction than a single low-resolution hologram. Algorithms for super-resolved reconstructions based on inverse problems approaches have already been shown to improve the 3D reconstruction of opaque spheres. Maximum a posteriori (MAP) approaches have also been shown capable of reconstructing the object field more accurately and more efficiently and to extend the usual field-of-view. Here we propose an inverse problem formulation for DH pixel super-resolution and an algorithm that alternates registration and reconstruction steps. The method is described in detail and used to reconstruct synthetic and experimental holograms of sparse 2D objects. We show that our approach improves both the shift estimation and reconstruction quality. Moreover, the reconstructed field-of-view can be expanded by up to a factor 3, thus making it possible to multiply the analyzed area 9 fold.

The imaging quality of in-line digital holography is challenged by the twin-image and aliasing effects because sensors only respond to intensity and pixels are of finite size. As a result, phase retrieval and pixel superresolution techniques serve as the two essential ingredients for high-fidelity holographic imaging. In this work, we combine the two within a unified algorithmic framework. Pixel super-resolution phase retrieval is recast as an optimization problem and is solved via gradient descent-based algorithms. Regularization techniques and Nesterov’s momentum are introduced to further speed up data acquisition and iterative reconstruction. The proposed algorithms are verified through a proof-of-concept lensless on-chip microscope. We demonstrate experimentally the capability of pixel super-resolution phase retrieval techniques in revealing the subpixel and quantitative phase information of complex biological samples.

High-throughput sectioning and optical imaging of tissue samples using traditional immunohistochemical techniques can be costly and inaccessible in resource-limited areas. We demonstrate three-dimensional (3D) imaging and phenotyping in optically transparent tissue using lens-free holographic on-chip microscopy as a low-cost, simple, and high-throughput alternative to conventional approaches. The tissue sample is passively cleared using a simplified CLARITY method and stained using 3,3'-diaminobenzidine to target cells of interest, enabling bright-field optical imaging and 3D sectioning of thick samples. The lens-free computational microscope uses pixel super-resolution and multi-height phase recovery algorithms to digitally refocus throughout the cleared tissue and obtain a 3D stack of complex-valued images of the sample, containing both phase and amplitude information. We optimized the tissue-clearing and imaging system by finding the optimal illumination wavelength, tissue thickness, sample preparation parameters, and the number of heights of the lens-free image acquisition and implemented a sparsity-based denoising algorithm to maximize the imaging volume and minimize the amount of the acquired data while also preserving the contrast-to-noise ratio of the reconstructed images. As a proof of concept, we achieved 3D imaging of neurons in a 200-μm-thick cleared mouse brain tissue over a wide field of view of 20.5 mm2. The lens-free microscope also achieved more than an order-of-magnitude reduction in raw data compared to a conventional scanning optical microscope imaging the same sample volume. Being low cost, simple, high-throughput, and data-efficient, we believe that this CLARITY-enabled computational tissue imaging technique could find numerous applications in biomedical diagnosis and research in low-resource settings.

A challenge in biological imaging is to capture high-resolution images at fast frame rates in live cells. The “instant structured illumination microscope” (iSIM) is a system designed for this purpose. Similarly to standard structured illumination microscopy (SIM), an iSIM provides a twofold improvement over widefield microscopy, in x, y and z, but also allows much faster image acquisition, with real-time display of super-resolution images.The assembly of an iSIM is reasonably complex, involving the combination and alignment of many optical components, including three micro-optics arrays (two lenslet arrays and an array of pinholes, all with a pitch of 222μm) and a double-sided scanning mirror. In addition, a number of electronic components must be correctly controlled. Construction of the system is therefore not trivial, but is highly desirable, particularly for live-cell imaging.We report, and provide instructions for, the construction of an iSIM, including minor modifications to a previous design in both hardware and software. The final instrument allows us to rapidly acquire fluorescence images at rates faster than 100fps, with approximately twofold improvement in resolution in both x–y and z; sub-diffractive biological features have an apparent size (full width at half maximum) of 145nm (lateral) and 320nm (axial), using a 1.49 NA objective and 488nm excitation.

Design and calibration of spreading equipment for agricultural materials are critically important but is facing some limitations in time and costs. Lack of personnel and environmental constraints, as well as equipment features present challenges in the calibration process and results. The major objective of this project was to introduce and investigate the feasibility of integration of automated electrical equipment into this calibration process in order to optimize the overall procedure in terms of cost, time and precision as an ultimate goal. Specific objectives focused on optical techniques as well as novel accelerometer technology. A photo based method in detection of collected grains based on counting of particles was investigated. Results from tests with three different grain particles showed that the sensor could be used in applications up to 20gr of collected materials in one pass. The sensor could detect multiple particles’ passage at the same time, but was unable to go further than a certain sample weight of 20, 30 and 60 grams for ammonium sulfate, rice and urea respectively while maintaining acceptable precision. In this regard, physical characteristics of the mentioned granular particles were also investigated to better address the importance of physical uniformity in this sensing system. A novel set of sensing plates based on accelerometer technology were introduced and the practicality of the sensors was tested using the standard setup for measurement of spreading patterns. A comparison between the outputs of a set of identical accelerometer plates showed a close estimate of the trend which could be achieved in the same deposition using the traditional dry calibration process. Moreover, the introduced sensor was highly flexible and could be adjusted in various ways in order to better match the application demands. In this regard, the proposed sensor was also tested at 10 and 20 degree angles with respect to the horizon and the results indicated almost twofold improvement in resolution from 595mV/g to 955mV/g at 10 and 20 degrees respectively. This novel accelerometer based technique may be practical for improved automation of calibration techniques.

As an expansion of coherent diffraction imaging, ptychographic iterative engine (PIE) not only inherits advantages such as ultra-high resolution and compact optical system, but also expands the field of view in quantitative imaging, thus PIE is widely used in short wavelength imaging such as X-ray and electron beam imaging, and then extended to visible light field. However, PIE requires coherent illumination for both phase and amplitude retrieval, while traditional X-ray or electron beam sources often cannot satisfy this strict coherent condition, which leads to poor-quality information retrieval with low signal-to-noise ratio. Though several proposed methods such as multiple wavelength and multi-mode algorithms can eliminate incoherency influence to some extent, various details such as quantitative spectrum of illuminating source should be obtained before information retrieval, which complicates computing procedures. In addition, it is hard to acquire the spectrum of the illuminating source in most cases. In order to acquire high-quality information based on PIE with partially coherent illumination, a newly designed enhanced phase retrieval method for weakly scattering samples in PIE with partially coherent illumination is presented in this paper, in which only the bright field of the diffraction patterns is used in the iterative procedures mimicking the coherent cases especially for weakly scattering samples without any prior illuminating details. The bright field area can be regarded as purely coherent diffraction patterns composed of a strengthened zeroth order beam and a weakened diffracted beam. While the dark-field area generated by interference of diffracted beams cannot satisfy the requirement for coherence, therefore, dark-field diffraction patterns should be excluded in sample information extraction and only the bright field is used for phase retrieval via iterative process. Compared with the proposed multiple wavelength and multi-mode algorithms, the proposed method can simplify sample reconstructing procedures due to needing no prior knowledge. Moreover, in order to enhance the information of weakly scattering samples in retrieval, high order iteration method is also introduced in the paper. Since the bright field can be regarded as purely coherent diffraction patterns composed of a strengthened zeroth order beam and a weakened diffracted beam. For weakly scattering sample, the weakened diffracted beam is much lower than zeroth order beam, thus it is difficult to acquire high-contrast information with classical PIE algorithms. Introducing high order iterative tactic, the contrast of weakly scattering sample is obviously improved and the details of weakly scattering sample can be retrieved clearly. Both theoretical analysis and numerical simulations are illustrated in detail, proving the robustness and availability of the designed method: high-contrast phase information can be obtained with the proposed method, while traditional phase retrieval algorithm almost loses all details of the sample. In order to mimic the real experimental situation, a 30 dB white noise is added into the simulation, the details of weakly scattering sample phase information can also be retrieved clearly by using the bright field of the diffraction patterns with high order iteration method. With the newly designed enhanced phase retrieval method for weakly scattering samples with partially coherent illumination, sample retrieval via PIE can not only use ordinary X-ray source or electron beam as illumination source, thereby avoiding the dependence on complete coherent source, but also obviously improve the retrieval quality of the sample characteristics, which widely expands the application fields of the PIE.

This paper presents the Pixel Super Resolution with Axial Scanning (PSR-AS) technique to enhance the resolution of Lensless Digital In-line Holographic Microscopy (LDHM). By utilizing multiple holograms captured at different axial distances, PSR allows for the recovery of high-resolution information, improving the image clarity and information content. Experimental results demonstrate a twofold lateral resolution enhancement, achieving the resolution of 1.23 μm in amplitude imaging and significantly augmenting phase reconstruction quality. The integration of PSR-AS into LDHM systems leads to notable reductions in noise and artifacts, offering a promising approach for high-resolution imaging in applications such as biomedical diagnostics and environmental monitoring. Full Text: PDF References Y. Park, C. Depeursinge, and G. Popescu, "Quantitative phase imaging in biomedicine," Nature Photon, 12(10), 578 (2018). CrossRef D. Gabor, "A New Microscopic Principle," Nature, 161(4098), 777 (1948). CrossRef K. Matsushima and T. Shimobaba, "Band-Limited Angular Spectrum Method for Numerical Simulation of Free-Space Propagation in Far and Near Fields," Opt. Express, 17(22), 19662 (2009). CrossRef Y. Wu and A. Ozcan, "Lensless digital holographic microscopy and its applications in biomedicine and environmental monitoring," Methods, 136, 4 (2018). CrossRef J. Zhang, J. Sun, Q. Chen, and C. Zuo, "Resolution Analysis in a Lens-Free On-Chip Digital Holographic Microscope," IEEE Transactions on Computational Imaging, 6, 697 (2020). CrossRef Gerchberg, R. W.. “A practical algorithm for the determination of phase from image and diffraction plane pictures.” Optik 35, 237 (1972). CrossRef H. Lee, J. Kim, J. Kim, P. Jeon, S. A. Lee, and D. Kim, "Noniterative sub-pixel shifting super-resolution lensless digital holography," Opt. Express,29(19), 29996 (2021). CrossRef A. Greenbaum and A. Ozcan, "Maskless imaging of dense samples using pixel super-resolution based multi-height lensfree on-chip microscopy," Opt. Express, 20(3), 3129 (2012). CrossRef J. Zhang, J. Sun, Q. Chen, J. Li, and C. Zuo, "Adaptive pixel-super-resolved lensfree in-line digital holography for wide-field on-chip microscopy," Sci Rep, 7(1), 11777 (2017). CrossRef L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Physica D: Nonlinear Phenomena, 60(1), 259 (1992). CrossRef

Phase retrieval with prior information can be cast as a nonsmooth and nonconvex optimization problem. To decouple the signal and measurement variables, we introduce an auxiliary variable and reformulate it as an optimization with an equality constraint. We then solve the reformulated problem by graph projection splitting (GPS), where the two proximity subproblems and the graph projection step can be solved efficiently. With slight modification, we also propose a robust graph projection splitting (RGPS) method to stabilize the iteration for noisy measurements. Contrary to intuition, RGPS outperforms GPS with fewer iterations to locate a satisfying solution even for noiseless case. Based on the connection between GPS and Douglas–Rachford iteration, under mild conditions on the sampling vectors, we analyze the fixed point sets and provide the local convergence of GPS and RGPS applied to noiseless phase retrieval without prior information. For noisy case, we provide the error bound of the reconstruction. Compared to other existing methods, thanks for the splitting approach, GPS and RGPS can efficiently solve phase retrieval with prior information regularization for general sampling vectors which are not necessarily isometric. For Gaussian phase retrieval, compared to existing gradient flow approaches, numerical results show that GPS and RGPS are much less sensitive to the initialization. Thus they markedly improve the phase transition in noiseless case and reconstruction in the presence of noise respectively. GPS shows sharpest phase transition among existing methods including RGPS, while it needs more iterations than RGPS when the number of measurement is large enough. RGPS outperforms GPS in terms of stability for noisy measurements. When applying RGPS to more general non-Gaussian measurements with prior information, such as support, sparsity and TV minimization, RGPS either outperforms state-of-the-art solvers or can be combined with state-of-the-art solvers to improve their reconstruction quality.

L&T bags EPC contract for NTPC's CO2-to-methanol demo plant

It is well-known that experimental or numerical backpropagation of waves generated by a point-source/-scatterer will refocus on a diffraction-limited spot with a size not smaller than half the wavelength. More recently, however, super-resolution techniques have been introduced that apparently can overcome this fundamental physical limit. This paper provides a framework of understanding and analysing both diffraction-limited imaging as well as super resolution. The resolution analysis presented in the first part of this paper unifies the different ideas of backpropagation and resolution known from the literature and provides an improved platform to understand the cause of diffraction-limited imaging. It is demonstrated that the monochromatic resolution function consists of both causal and non-causal parts even for ideal acquisition geometries. This is caused by the inherent properties of backpropagation not including the evanescent field contributions. As a consequence, only a diffraction-limited focus can be obtained unless there are ideal acquisition surfaces and an infinite source-frequency band. In the literature various attempts have been made to obtain images resolved beyond the classical diffraction limit, e.g., super resolution. The main direction of research has been to exploit the evanescent field components. However, this approach is not practical in case of seismic imaging in general since the evanescent waves are so weak – because of attenuation, they are masked by the noise. Alternatively, improvement of the image resolution of point like targets beyond the diffraction limit can apparently be obtained employing concepts adapted from conventional statistical multiple signal classification (MUSIC). The basis of this approach is the decomposition of the measurements into two orthogonal domains: signal and noise (nil) spaces. On comparison with Kirchhoff prestack migration this technique is showed to give superior results for monochromatic data. However, in case of random noise the super- resolution power breaks down when employing monochromatic data and a limited acquisition aperture. For such cases it also seems that when the source-receiver lay out is less correlated, the use of a frequency band may restore the super-resolution capability of the method.

Structured illumination microscopy (SIM) is a widely used super resolution imaging technique that can down-modulate a sample's high-frequency information into objective recordable frequencies to enhance the resolution below the diffraction limit. However, classical SIM image reconstruction methods often generate poor results under low illumination conditions, which are required for reducing photobleaching and phototoxicity in cell imaging experiments. Although denoising methods or auxiliary items improved SIM image reconstruction in low signal level situations, they still suffer from decreased reconstruction quality and significant background artifacts, inevitably limiting their practical applications. In order to improve the reconstruction quality, second-order optimized regularized SIM (sorSIM) is designed specifically for image reconstruction in low signal level situations. In sorSIM, a second-order regularization term is introduced to suppress noise effect, and the penalty factor in this term is selected to optimize the resolution enhancement and noise resistance. Compared to classical SIM image reconstruction algorithms as well as to those previously used in low illumination cases, the proposed sorSIM provides images with enhanced resolution and fewer background artifacts. Therefore, sorSIM can be a potential tool for high-quality and rapid super resolution imaging, especially for low signal images.

Transfer orthogonal sparsifying transform learning for phase retrieval

The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete Fourier transforms due to their high computational efficiency. However, the mathematics underpinning these algorithms is typically formulated using continuous mathematics, which can result in a loss of spatial resolution in the reconstructed images. Herein we investigate how phase retrieval algorithms for propagation-based phase-contrast X-ray imaging can be rederived using discrete mathematics and result in more precise retrieval for single- and multi-material objects and for spectral image decomposition. We validate this theory through experimental measurements of spatial resolution using computed tomography (CT) reconstructions of plastic phantoms and biological tissues, using detectors with a range of imaging system point spread functions (PSFs). We demonstrate that if the PSF substantially suppresses high spatial frequencies, the potential improvement from utilising the discrete derivation is limited. However, with detectors characterised by a single pixel PSF (e.g. direct, photon-counting X-ray detectors), a significant improvement in spatial resolution can be obtained, demonstrated here at up to 17%.

In the Multi-intensities phase retrieval processing, the measurement uncertainty of the defocus distance undermines its measurement accuracy. In this paper, using a general phase retrieval experimental arrangement, we propose an adaptive autofocusing nonlinear optimization phase retrieval algorithm based on the extended Nijboer-Zernike (ENZ) theory. This method concurrently accomplishes correction of defocusing position error and the wavefront measurement requiring without additional facility. The numerical experiments show that the proposed method accuracy searching for the optimal defocusing position is superior to 10 μm among different measurement planes. The numerical experiments show that the wavefront measurement accuracy with the proposed method is superior to λ/100 , RMSE.