Transport Of Intensity Equation Research Articles

Transport-of-intensity phase imaging using commercially available confocal microscope.

Confocal microscopy is an indispensable tool for biologists to observe samples and is useful for fluorescence imaging of living cells with high spatial resolution. Recently, phase information induced by the sample has been attracting attention because of its applicability such as the measurability of physical parameters and wavefront compensation. However, commercially available confocal microscopy has no phase imaging function. We reborn an off-the-shelf confocal microscope as a phase measurement microscope. This is a milestone in changing the perspective of researchers in this field. We would meet the demand of biologists if only they had measured the phase with their handheld microscopes. We proposed phase imaging based on the transport of intensity equation (TIE) in commercially available confocal microscopy. The proposed method requires no modification using a bright field imaging module of a commercially available confocal microscope. The feasibility of the proposed method is confirmed by evaluating the phase difference of a microlens array and living cells of the moss Physcomitrium patens and living mammalian cultured cells. In addition, multi-modal imaging of fluorescence and phase information is demonstrated. TIE-based quantitative phase imaging (QPI) using commercially available confocal microscopy is proposed. We evaluated the feasibility of the proposed method by measuring the microlens array, plant, and mammalian cultured cells. The experimental result indicates that QPI can be realized in commercially available confocal microscopy using the TIE technique. This method will be useful for measuring dry mass, viscosity, and temperature of cells and for correcting phase fluctuation to cancel aberration and scattering caused by an object in the future.

Transport of intensity phase retrieval in the presence of intensity variations and unknown boundary conditions

The so-called Transport of Intensity Equation (TIE) phase retrieval technique is widely applied in light, X-ray and electron optics to reconstruct, e.g., refractive indices, electric and magnetic fields in solids. Here, we present a largely improved TIE reconstruction algorithm, which properly considers intensity variations as well as unknown boundary conditions in a finite difference implementation of the Transport of Intensity partial differential equation. That largely removes reconstruction artifacts encountered in state-of-the-art Poisson solvers of the TIE, and hence significantly increases the applicability of the technique.

A Review: Phase Measurement Techniques Based on Metasurfaces

Phase carries crucial information about the light propagation process, and the visualization and quantitative measurement of phase have important applications, ranging from ultra-precision metrology to biomedical imaging. Traditional phase measurement techniques typically require large and complex optical systems, limiting their applicability in various scenarios. Optical metasurfaces, as flat optical elements, offer a novel approach to phase measurement by manipulating light at the nanoscale through light-matter interactions. Metasurfaces are advantageous due to their lightweight, multifunctional, and easy-to-integrate nature, providing new possibilities for simplifying traditional phase measurement methods. This review categorizes phase measurement techniques into quantitative and non-quantitative methods and reviews the advancements in metasurface-based phase measurement technologies. Detailed discussions are provided on several methods, including vortex phase contrast, holographic interferometry, shearing interferometry, the Transport of Intensity Equation (TIE), and wavefront sensing. The advantages and limitations of metasurfaces in phase measurement are highlighted, and future research directions are explored.

Quantitative analysis of phase retrieval with the transport of intensity equation under low-light conditions

Quantitative analysis of phase retrieval with the transport of intensity equation under low-light conditions

Utilizing quantitative phase microscopy to localize fluorescence in three dimensions via the transport of intensity equation.

We demonstrate the use of a novel, to the best of our knowledge, localization algorithm for digitally refocusing fluorescence images from a three-dimensional cell culture. Simultaneous phase and fluorescence intensity images are collected through a multimodal system that combines digital holography via quantitative phase microscopy (QPM) and fluorescence microscopy. Defocused fluorescence images are localized to a specific z-plane within the three-dimensional (3D) matrix using the transport of intensity equation (TIE) and depth-resolved information derived from the QPM measurements. This technique is applied to cells stained with different fluorescent tags suspended in 3D collagen hydrogel cultures. Experimental findings demonstrate the localization of defocused images, facilitating the analysis and comparison of cells within the hydrogel matrix. This method holds promise for comprehensive cellular imaging of fluorescence labeling in three-dimensional environments, enabling detailed investigations into cellular behavior and interactions.

Evolution of magnetization textures in Mn1.4PtSn under magnetic field

We have used Lorentz transmission electron microscopy (LTEM) and the transport of intensity equation (TIE) method to investigate the spin structures in the Mn1.4PtSn magnet, which exhibits D2d symmetry. The evolution of the spin structures under the external magnetic field was observed. In particular, a perpendicular field is able to modulate the striped domain widths and to induce the formation of anti-skyrmions and bubbles. While an in-plane magnetic field can control the state of these structures, the coexistence of different types of skyrmions suggests that the hysteresis properties of the magnet may affect the effectiveness of the field control.

Neural-field-assisted transport-of-intensity phase microscopy: partially coherent quantitative phase imaging under unknown defocus distance

The transport-of-intensity equation (TIE) enables quantitative phase imaging (QPI) under partially coherent illumination by measuring the through-focus intensities combined with a linearized inverse reconstruction algorithm. However, overcoming its sensitivity to imaging settings remains a challenging problem because of the difficulty in tuning the optical parameters of the imaging system accurately and because of the instability to long-time measurements. To address these limitations, we propose and experimentally validate a solution called neural-field-assisted transport-of-intensity phase microscopy (NFTPM) by introducing a tunable defocus parameter into neural field. Without weak object approximation, NFTPM incorporates the physical prior of partially coherent image formation to constrain the neural field and learns the continuous representation of phase object without the need for training. Simulation and experimental results of HeLa cells demonstrate that NFTPM can achieve accurate, partially coherent QPI under unknown defocus distances, providing new possibilities for extending applications in live cell biology.

Measurement of protein concentration in bacteria and small organelles under a light transmission microscope.

Protein concentration (PC) is an essential characteristic of cells and organelles; it determines the extent of macromolecular crowding effects and serves as a sensitive indicator of cellular health. A simple and direct way to quantify PC is provided by brightfield-based transport-of-intensity equation (TIE) imaging combined with volume measurements. However, since TIE is based on geometric optics, its applicability to micrometer-sized particles is not clear. Here, we show that TIE can be used on particles with sizes comparable to the wavelength. At the same time, we introduce a new ImageJ plugin that allows TIE image processing without resorting to advanced mathematical programs. To convert TIE data to PC, knowledge of particle volumes is essential. The volumes of bacteria or other isolated particles can be measured by displacement of an external absorbing dye ("transmission-through-dye" or TTD microscopy), and for spherical intracellular particles, volumes can be estimated from their diameters. We illustrate the use of TIE on Escherichia coli, mammalian nucleoli, and nucleolar fibrillar centers. The method is easy to use and achieves high spatial resolution.

An enhanced multimode phase imaging method based on the transport of intensity equation.

Label-free biological cell imaging relies on rapid multimode phase imaging of biological samples in natural settings. To improve image contrast, phase is encoded into intensity information using the differential interference contrast (DIC) and Zernike phase contrast (ZPC) techniques. To enable multimode contrast-enhanced observation of unstained specimens, this paper proposes an improved multimode phase imaging method based on the transport of intensity equation (TIE), which combines conventional microscopy with computational imaging. The ZPC imaging module based on adaptive aperture adjustment is applied when the quantitative phase results of biological samples have been obtained by solving the TIE. Simultaneously, a rotationally symmetric shear-based technique is used that can yield isotropic DIC. In this paper, we describe numerical simulation and optical experiments carried out to validate the accuracy and viability of this technology. The calculated Michelson contrast of the ZPC image in the resolution plate experiment increased from 0.196 to 0.394.

3D fluorescence imaging through a scattering medium using the transport of intensity equation and Fresnel ping-pong algorithm.

A three-dimensional (3D) fluorescent imaging method through a scattering medium has been presented. The proposed method combines digital phase conjugate reconstruction of the scattered light wave by the transport of intensity equation-based 3D fluorescent imaging to the position of scattering medium and followed phase retrieval method by Fresnel ping-pong algorithm. The effectiveness of the proposed method is experimentally verified by measuring the 3D distribution of fluorescent beads and tobacco-cultured cells through a thin diffuser. Compared to other methods, the reconstructed images show enhancement of the detailed structure of the objects blurred by the diffuser in a wide area. In the simulation, the proposed method is capable of recovering images degraded by scattering in the phase modulation range from 0 to 2π. The capability to identify the depth position is also presented.

Eagle-Eye Inspired Meta-Device for Phase Imaging.

The dual-focus vision observed in eagles' eyes is an intriguing phenomenon captivates scientists since a long time. Inspired by this natural occurrence, the authors' research introduces a novel bifocal meta-device incorporating a polarized camera capable of simultaneously capturing images for two different polarizations with slightly different focal distances. This innovative approach facilitates the concurrent acquisition of underfocused and overfocused images in a single snapshot, enabling the effective extraction of quantitative phase information from the object using the transport of intensity equation. Experimental demonstrations showcase the application of quantitative phase imaging to artificial objects and human embryonic kidney cells, particularly emphasizing the meta-device's relevance in dynamic scenarios such as laser-induced ablation in human embryonic kidney cells. Moreover, it provides a solution for the quantification during the dynamic process at the cellular level. Notably, the proposed eagle-eye inspired meta-device for phase imaging (EIMPI), due to its simplicity and compact nature, holds promise for significant applications in fields such as endoscopy and headsets, where a lightweight and compact setup is essential.

Monitoring the dynamics of cultured tobacco cells division by TIE-based 3D fluorescence microscopy with two-synchronized image sensors

The dynamic activity of the microtubule cytoskeleton is critical to cellular organization, including structural support, intracellular transport, and engagement in processes such as cell division and cell motility. In this work, we monitor the volumetric cell division process of tobacco BY-2 suspension cells including the dynamics of microtubule in a single-shot by using a 3D epi-fluorescence microscope based on the transport of intensity equation (3DFM-TIE) with two synchronized image sensors. The technique makes it possible to recognize and track cell mobility by examining the fluorescently tagged proteins and studying their behavior and dynamics during the cell division process. In light of experimental findings, the 3DFM-TIE system could be a favored option for live cell imaging and analysis because of its real-time 3D imaging capability and simple and compact optical design, and it has the potential to be employed in both basic and clinical investigations.

Quantitative phase imaging with a compact meta-microscope

Quantitative phase imaging (QPI) based on the transport-of-intensity equation (TIE) is a powerful technique in label-free microscopy. The image stack required for a successful TIE-QPI is traditionally obtained by translating the object or image plane, and the optical elements used in the conventional TIE-QPI systems are usually bulky and cumbersome. Stable and compact TIE-QPI methods capable of non-motion optical zooming can significantly facilitate applications that demand portability. Here, we propose a non-motion TIE-QPI method based on a dispersive metalens. The dispersive nature of the metalens is utilized to provide a spectral focal tuning. With fixed object and image planes, seven through-focus intensity images are captured by changing the illumination wavelength. The QPI performance is validated by retrieving the surface phase profiles of a microlens array and a phase resolution target, showing a high phase detection accuracy (deviation less than 0.03 wavelength). Subsequently, we established a compact meta-microscope by integrating the metalens with a commercially available CMOS image sensor, which shows good performance in microscopic imaging of unstained bio-samples. Our approach, based on the large-dispersive metalens, facilitates a compact and robust QPI system for optical metrology and label-free microscopy.

3D fluorescence imaging through scattering medium using transport of intensity equation and iterative phase retrieval.

In this paper, we have proposed a method of three-dimensional (3D) fluorescence imaging through a scattering medium. The proposed method combines the numerical digital phase conjugation propagation after measurement of the complex amplitude distribution of scattered light waves by the transport of intensity equation (TIE) with followed iterative phase retrieval to achieve 3D fluorescence imaging through a scattering medium. In the experiment, we present the quantitative evaluation of the depth position of fluorescent beads. In addition, for time-lapse measurement, cell division of tobacco-cultured cells was observed. Numerical results presented the effective range of the phase amount in the scattering medium. From these results, the proposed method is capable of recovering images degraded by a thin scattering phase object beyond a small phase change approximation.

Real-time phase retrieval in division of aperture microscopy with the transport of intensity equation.

The transport of intensity equation (TIE) allows to recover the phase of a microscopy sample from differently focused intensity measures along the axial direction of its optical field. In the present work, we propose a cost-effective technique for snapshot phase retrieval with TIE. The optics of a commercially available camera is replaced with a doublet system consisting of a microscope objective and a lenslet array with an extra lens mask attached to it. The system allows to obtain, in real-time and with no mechanical shift of either the sample or the sensor, the in-focus as well as a defocused image of the sample. From these two sub-aperture images, the intensity derivative term in TIE can then be approximated after image rectification. Phase is then retrieved for static as well as dynamic samples over the common view area. Validation experiments are presented.

TIE-GANs: single-shot quantitative phase imaging using transport of intensity equation with integration of GANs.

Artificial intelligence (AI) has become a prominent technology in computational imaging over the past decade. The expeditious and label-free characteristics of quantitative phase imaging (QPI) render it a promising contender for AI investigation. Though interferometric methodologies exhibit potential efficacy, their implementation involves complex experimental platforms and computationally intensive reconstruction procedures. Hence, non-interferometric methods, such as transport of intensity equation (TIE), are preferred over interferometric methods. TIE method, despite its effectiveness, is tedious as it requires the acquisition of many images at varying defocus planes. The proposed methodology holds the ability to generate a phase image utilizing a single intensity image using generative adversarial networks (GANs). We present a method called TIE-GANs to overcome the multi-shot scheme of conventional TIE. The present investigation employs the TIE as a QPI methodology, which necessitates reduced experimental and computational efforts. TIE is being used for the dataset preparation as well. The proposed method captures images from different defocus planes for training. Our approach uses an image-to-image translation technique to produce phase maps and is based on GANs. The main contribution of this work is the introduction of GANs with TIE (TIE:GANs) that can give better phase reconstruction results with shorter computation times. This is the first time the GANs is proposed for TIE phase retrieval. The characterization of the system was carried out with microbeads of size and structural similarity index (SSIM) for microbeads was found to be 0.98. We demonstrated the application of the proposed method with oral cells, which yielded a maximum SSIM value of 0.95. The key characteristics include mean squared error and peak-signal-to-noise ratio values of 140 and 26.42dB for oral cells and 100 and 28.10dB for microbeads. The proposed methodology holds the ability to generate a phase image utilizing a single intensity image. Our method is feasible for digital cytology because of its reported high value of SSIM. Our approach can handle defocused images in such a way that it can take intensity image from any defocus plane within the provided range and able to generate phase map.

Enhancing Contrast of Spatial Details in X-ray Phase-Contrast Imaging through Modified Fourier Filtering

In-line X-ray phase contrast imaging, which is simple to experiment with, provides significantly higher sensitivity, compared to conventional X-ray absorption imaging. The inversion of the relationship between recorded Fresnel diffraction intensity and the phase shift induced by the object is called phase retrieval. The transport of intensity equation (TIE), a simple method of phase retrieval, which is solved by the fast Fourier transform algorithm proposed by Paganin et al., has been widely adopted. However, the existing method suffers from excessive suppression of high-frequency information, resulting in loss of image details after phase retrieval, or insufficient detail contrast, leading to blurry images. Here, we present a straightforward extension of the two-distance FFT-TIE method by modifying the Fourier filter through the use of a five-point approximation to calculate the inverse Laplacian in a discrete manner. Additionally, we utilize a combination of continuous Fourier transform and a four-point approximation to compute the gradient operator. The method is evaluated by simulating samples with a shape similar to the resolution test map and by using a photograph of a dog for further evaluation. The algorithm that incorporates the modified gradient operator and the algorithm that solely utilizes the continuous Fourier transform for gradient computation were compared with the results obtained using the two-distance FFT-TIE method. The comparisons were conducted using the results obtained from two distances from the sample to the detector. The results show that this method improves the contrast of spatial details and reduces the suppression of high spatial frequencies compared to the two-distance FFT-TIE method. Furthermore, in the low-frequency domain, our algorithm does not lose much information compared to the original method, yielding consistent results. Furthermore, we conducted our experiments using carbon rods. The results show that both our method and the FFT-TIE method exhibit low-frequency distortion due to the requirement of close proximity between the absorption maps and the detector. However, upon closer inspection, our proposed method demonstrates superior accuracy in reproducing the finer details of the carbon rod fibers.

Flexible dynamic quantitative phase imaging based on division of focal plane polarization imaging technique.

This paper proposes a flexible and accurate dynamic quantitative phase imaging (QPI) method using single-shot transport of intensity equation (TIE) phase retrieval achieved by division of focal plane (DoFP) polarization imaging technique. By exploiting the polarization property of the liquid crystal spatial light modulator (LC-SLM), two intensity images of different defocus distances contained in orthogonal polarization directions can be generated simultaneously. Then, with the help of the DoFP polarization imaging, these images can be captured with single exposure, enabling accurate dynamic QPI by solving the TIE. In addition, our approach gains great flexibility in defocus distance adjustment by adjusting the pattern loaded on the LC-SLM. Experiments on microlens array, phase plate, and living human gastric cancer cells demonstrate the accuracy, flexibility, and dynamic measurement performance for various objects. The proposed method provides a simple, flexible, and accurate approach for real-time QPI without sacrificing the field of view.

Multi-particles detection in transformer oil based on lens-free digital holography and transport of intensity equation

Transformer oil quality plays an important role in health condition monitoring of a transformer. In order to better monitor the quality of transformer oil, a hybrid method combining lens-free digital holography and transport of intensity equation is proposed. We take a single-shot hologram of sample oil with a large field of view, and then reconstruct intensity images with different distances, which are necessary inputs of transport of intensity equation. After that, we can get relatively high-resolution image of oil. Via experiments, we compare the results from basic lens-free digital holography reconstruction and hybrid method reconstruction. The results show that, the hybrid method can effectively improve the image reconstruction accuracy and achieve a resolution of 2.67 μm across a large field-of-view of 60.35 mm2, which means that we can get high-resolution zoom-in oil image with more details and quantitative parameters in real time, which is a breakthrough for quick transformer oil testing.

Target-surface multiplexed quantitative dynamic phase microscopic imaging based on the transport-of-intensity equation.

Microscopic phase digital imaging based on the transport of intensity equation, known as TIE, is widely used in optical measurement and biomedical imaging since it can dispense with the dependence of traditional phase imaging systems on mechanical rotational scanning and interferometry devices. In this work, we provide a single exposure target-surface multiplexed phase reconstruction (SETMPR) structure based on TIE, which is remarkably easy to construct since it directly combines a conventional bright-field inverted microscope with a special image plane transmission structure that is capable of wavefront shaping and amplification. In practice, the SETMPR is able to achieve dynamic, non-interferometric, quantitative refractive index distribution of both static optical samples and dynamic biological samples in only one shot, meaning that the only limitation of measuring frequency is the frame rate. By comparing the measurement results of a microlens array and a grating with a standard instrument, the quantitative measurement capability and accuracy are demonstrated. Subsequently, both in situ static and long-term dynamic quantitative imaging of HT22 cells were performed, while automatic image segmentation was completed by introducing machine learning methods, which verified the application prospect of this work in dynamic observation of cellular in the biomedical field.