Transport Of Intensity Equation Method Research Articles

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.

Accurate decoding of data pages in an amplitude- and phase-modulated signal beam detected by the single-shot transport of intensity equation method with convolutional neural network-based classifiers

We propose an accurate method for the classification and decoding of data pages in complex-amplitude-modulated signal beams detected via the transport of the intensity equation (TIE) method using simple classifiers with a convolutional neural network (CNN) for holographic data storage (HDS). The classifiers allow a single-shot TIE method using two cameras to detect the complex-amplitude-modulated signal beam in HDS. Although the phase distribution detected using the single-shot TIE method tends to be superimposed with strong phase noise, we demonstrate experimentally that the CNN-based classifiers can classify/decode data pages in the complex-amplitude-modulated signal beam accurately without phase noise removal.

Correction to: Generation of amplitude- and phase-modulated signal beam with a phase-only spatial light modulator and its detection by the transport of intensity equation method for holographic data storage

Correction to: Generation of amplitude- and phase-modulated signal beam with a phase-only spatial light modulator and its detection by the transport of intensity equation method for holographic data storage

Generation of amplitude- and phase-modulated signal beam with a phase-only spatial light modulator and its detection by the transport of intensity equation method for holographic data storage

Generation of amplitude- and phase-modulated signal beam with a phase-only spatial light modulator and its detection by the transport of intensity equation method for holographic data storage

Binocular phase retrieval based on the transport of intensity equation under multiwavelength illumination

In view of the limitation that the transport of intensity equation method can only be used at a single wavelength, we propose a binocular phase retrieval algorithm based on multiwavelength illumination. First, we solve for the corresponding single-phase results at different wavelengths and then calculate the surface height of the object by combining the obtained synthetic wavelengths and synthetic phases, in order to reconstruct the initial phase results at different wavelengths. To solve the problem of amplification of traditional noise and surface profile noise in the phase diagram in the phase synthesis step, we introduce a step-by-step noise reduction method that can reduce the noise in the initial phase results to the level for a single wavelength and finally obtain the corresponding high-precision phase results at different wavelengths. The intensity images collected by the proposed dual-microscope system verify the correctness and effectiveness of the algorithm.

Comparison of common-path off-axis digital holography and transport of intensity equation in quantitative phase measurement

The quantitative phase imaging methods based on digital holography (DH) and transport of intensity equation (TIE) are both popular high-resolution computational imaging techniques with broad applications. In contrast, the results of TIE often lack reliability, while those of DH are always regarded as the standard for phase measurements. Is DH more reliable and accurate than TIE in all cases? Here, we fully compare and analysis some common factors of conventional FFT-based TIE method and common-path off-axis DH method in quantitative phase measurements, such as the grayscale of recorded image (or hologram), effective measurement area, temporal stability, noise and the focal plane offset. By measuring some standard (microlens array and cake structure) and unknown samples (HT22 cells and fiber microstructure), the effects of different factors can be clearly quantified and illustrated. As a result, the DH method mainly suffers from the serious coherent noise and poor temporal stability, and the TIE method has a huge error when several factors are not selected properly, which explains its unreliability. Comparatively speaking, the TIE method can achieve better results with appropriate parameters.

Solving the twin image problem in in-line holography by using multiple defocused intensity images reconstructed from a single hologram

Phase recovery from a hologram measurement is at the heart of coherent imaging techniques and online holography. In-line holography suffers from a blurred background problem that results from double images formed during hologram reconstruction. This so-called double image problem, inherent to the in-line geometry of the holographic experimental setup, limits the quality of the information (shape or refractive index of the object) obtained by reconstruction algorithms using a single hologram. We propose here a numerical reconstruction method combining the angular spectrum method (ASM) and the transport of intensity equation method using Gaussian process regression (GP-TIE) to solve this problem. In our approach, a single in-line hologram is used to recover the phase image free of any perturbation due to the presence of the double image.

Parallel Mode Differential Phase Contrast in Transmission Electron Microscopy, I: Theory and Analysis

In Part I of this diptych, we outline the parallel mode of differential phase contrast (TEM-DPC), which uses real-space distortion of Fresnel images arising from electrostatic or magnetostatic fields to quantify the phase gradient of samples with some degree of structural contrast. We present an analysis methodology and the associated software tools for the TEM-DPC method and, using them together with numerical simulations, compare the technique to the widely used method of phase recovery based on the transport-of-intensity equation (TIE), thereby highlighting the relative advantages and limitations of each. The TEM-DPC technique is particularly suitable for in situ studies of samples with significant structural contrast and, as such, complements the TIE method since structural contrast usually hinders the latter, but is an essential feature that enables the former. In Part II of this work, we apply the theory and methodology presented to the analysis of experimental data to gain insight into two-dimensional magnetic phase transitions.

Pebrine diagnosis using quantitative phase imaging and machine learning.

Pebrine is the most dreaded infectious disease of the silkworm and has devastated sericulture in Europe during the 18th century. Thereafter, if it is detected, the crop is burned to prevent further dissemination. The conventional microscopic examination of moth's body fluid is erroneous and it exacerbates on Metarhizium anisopliae (MA) contaminated test samples. This is due to the resemblance of pebrine and MA spores in the microscopic examination. Therefore, this study aims to demonstrate an efficient pebrine detection technique. In the proposed method, a motorised brightfield microscope is custom-made to acquire focused and defocused images of test spores. These images are used to produce quantitative phase images of the spores by the transport of intensity equation method. The phase images' histogram of oriented gradients feature is used by a machine learning classifier to categorise the spores. This system classified 92 pebrine and 185 MA spores with an accuracy of 97% at 0.04 seconds/spore. The duration taken for image acquisition is 2.5minutes per sample (10 fields of view covering an area of 302×260 μm2 ). The proposed method shows reliable results in pebrine diagnosis and would be an efficient alternative for current approaches.

High Capacity Steganography via Optical Phase-Encoding and Transport of Intensity Equation

A high capacity steganography based on optical phase-encoding and transport of intensity equation (TIE) is proposed. The secret image is phase-encoded and then attached a real-valued host image to form a complex light field, which diffracts a short distance and generate a slightly different complex amplitude. Its intensity is recorded and the corresponding amplitude is calculated as the stegoimage. For extraction, the secret image could be reconstructed near perfectly by using the TIE method. It is well known that the capacity and the imperceptibility are two fundamental but contrary attributes in any a steganography scheme. However, in this work, the high capacity could be attained while the imperceptibility is well preserved based on the phase-encoding and TIE method. As the steganography is applied mainly on the digital media which are transmitted through the Internet, the optical experiments are not essential in this situation, and we only provide the simulation results to verify the validity and feasibility of our method.

Transport of intensity equation method and its applications.

A phase retrieval technique based on a transport of intensity equation (TIE) is one of the defocus series reconstruction techniques in microscopy. Since it does not require any dedicated devices like a biprism, and only three defocus images are enough to retrieve phase information, it has been applied to observe magnetic fields, magnetic domains, electrostatic potentials and strains. It is also used to improve image resolution by correcting spherical aberration. This technique is simple and easy to use, but some artifacts often appear in the retrieved phase map. One should pay careful attention to the experimental conditions and the algorithms and boundary conditions used to solve the TIE. This paper reviews the principle of the TIE method, the algorithms used to solve it and application results in materials science.

Transport of intensity equation method based on edge detection and duty ratio fusion

The non-interferometric phase recovery method which is based on the transport of intensity equation is an important phase acquisition technique in microscopy imaging. In the actual operational process of this technology, at least three intensity images are needed to solve the equation. In the image acquisition process, the selection of the focused image is very important, but it is usually determined by subjective methods, thus causing inaccurate positioning of the in-focus, which further affects the precision of phase recovery result. A phase recovery algorithm based on edge detection and duty ratio is proposed. Firstly, a series of ‘subjectively determined focused images’ collected by the microscope are edge-extracted to obtain corresponding edge information points. Then the real in-focus position is found by calculating the duty ratio, and the corresponding defocused images are selected according to the position of the focused image. Finally, the high-precision phase recovery result is obtained by using these images of the accurate position to solve the equation. The algorithm does not require complex operations such as hardware modifications and can be applied to both discrete and continuous sample distributions. The experimental results effectively prove that the algorithm can accurately find the in-focus position, which improves the accuracy of phase recovery compared with the traditional method that is subjectively determined in-focus image position.

Single-shot common-path transport of intensity equation method with Greek-ladder sieves

Phase recovery based on the transport of intensity equation (TIE) is a promising method for quantitative phase imaging, which is useful for the observation of dynamic objects. This study proposes a single-shot common-path TIE method with Greek-ladder sieves to reconstruct the phase distribution of small transmissive objects. A Greek-ladder sieve was designed to simultaneously capture bi-planar images at a single recording plane; thus, the phase distribution is quantitatively retrieved using a single-shot measurement of the intensity. A 120 µm diameter Greek-ladder sieve was designed to operate at a wavelength of 13.5 nm, and its feasibility was verified in the optical region experimentally. With the advantages of operating in real time and reducing the effects of vibration, this method can be potentially applied for various imaging and detection techniques, especially for biological imaging and wave front detection.

Detection method for the complex amplitude of a signal beam with intensity and phase modulation using the transport of intensity equation for holographic data storage.

Holographic data storage (HDS), in which both the amplitude and the phase of a signal beam are modulated, has been extensively studied with the goal of increasing its storage capacity. To detect such modulation during data retrieval, it is necessary to acquire the complex amplitude of the signal beam. In this study, we focus on the transport of intensity equation (TIE) method, which allows us to detect the phase distribution of the light wave quantitatively without using interferometry, contributing to miniaturization of the optical system and improvement of the vibration tolerance of HDS. We discuss the conditions of the modulation phase distribution of the signal beam required for accurate phase detection and propose a method to estimate and eliminate the noise that frequently appears in the phase distribution detected by the TIE method.

Digital field of view correction combined dual-view transport of intensity equation method for real-time quantitative imaging

Dual-view transport of intensity equation (TIE) method is an ideal way for quantitative live cell imaging as it has advantages such as real-time imaging, multimode observations, compact setup, and large field of view (FoV). However, due to the image recorder installation error, the inevitable FoV mismatch between the captured under- and over-focus intensities reduces the accuracy in both amplitude and phase retrievals. Here, to eliminate this undesired FoV mismatch, the phase correlation-based digital FoV correction is adopted to recognize and compensate the rotation, scale, and translation between the under- and over-focus images. Both the numerical simulations as well as the experiments in standard sample detection and quantitative live cell imaging prove that the digital FoV correction combined dual-view TIE method can maintain the consistence of the dual FoVs, thus guaranteeing the high-accurate amplitude and phase computations, proving the proposed method is a promising quantitative live cell imaging tool in various applications such as biological observations and medical diagnostics.

Numerical tilting compensation in microscopy based on wavefront sensing using transport of intensity equation method

Wide-field microscopy is commonly used for sample observations in biological research and medical diagnosis. However, the tilting error induced by the oblique location of the image recorder or the sample, as well as the inclination of the optical path often deteriorates the imaging quality. In order to eliminate the tilting in microscopy, a numerical tilting compensation technique based on wavefront sensing using transport of intensity equation method is proposed in this paper. Both the provided numerical simulations and practical experiments prove that the proposed technique not only accurately determines the tilting angle with simple setup and procedures, but also compensates the tilting error for imaging quality improvement even in the large tilting cases. Considering its simple systems and operations, as well as image quality improvement capability, it is believed the proposed method can be applied for tilting compensation in the optical microscopy.

Artifacts in magnetic spirals retrieved by transport of intensity equation (TIE)

The artifacts in the magnetic structures reconstructed from Lorentz transmission electron microscopy (LTEM) images with TIE method have been analyzed in detail. The processing for the simulated images of Bloch and Neel spirals indicated that the improper parameters in TIE may overestimate the high frequency information and induce some false features in the retrieved images. The specimen tilting will further complicate the analysis of the images because the LTEM image contrast is not the result of the magnetization distribution within the specimen but the integral projection pattern of the magnetic induction filling the entire space including the specimen.

Rapid in-focus corrections on quantitative amplitude and phase imaging using transport of intensity equation method.

Transport of intensity equation (TIE) method can acquire sample phase distributions with high speed and accuracy, offering another perspective for cellular observations and measurements. However, caused by incorrect focal plane determination, blurs and halos are induced, decreasing resolution and accuracy in both retrieved amplitude and phase information. In order to obtain high-accurate sample details, we propose TIE based in-focus correction technique for quantitative amplitude and phase imaging, which can locate focal plane and then retrieve both in-focus intensity and phase distributions combining with numerical wavefront extraction and propagation as well as physical image recorder translation. Certified by both numerical simulations and practical measurements, it is believed the proposed method not only captures high-accurate in-focus sample information, but also provides a potential way for fast autofocusing in microscopic system.

Smartphone based hand-held quantitative phase microscope using the transport of intensity equation method.

In order to realize high contrast imaging with portable devices for potential mobile healthcare, we demonstrate a hand-held smartphone based quantitative phase microscope using the transport of intensity equation method. With a cost-effective illumination source and compact microscope system, multi-focal images of samples can be captured by the smartphone's camera via manual focusing. Phase retrieval is performed using a self-developed Android application, which calculates sample phases from multi-plane intensities via solving the Poisson equation. We test the portable microscope using a random phase plate with known phases, and to further demonstrate its performance, a red blood cell smear, a Pap smear and monocot root and broad bean epidermis sections are also successfully imaged. Considering its advantages as an accurate, high-contrast, cost-effective and field-portable device, the smartphone based hand-held quantitative phase microscope is a promising tool which can be adopted in the future in remote healthcare and medical diagnosis.

In-focus quantitative intensity and phase imaging with the numerical focusing transport of intensity equation method

Microscopy combined with the transport of intensity equation is capable of retrieving both intensity and phase distributions of samples from both in-focus and defocus intensities. However, during measurements, the focal plane is often decided artificially and the improper choice may induce errors in quantitative intensity and phase retrieval. In order to obtain accurate in-focus information, quantitative intensity and phase imaging with the numerical focusing transport of intensity equation method combined with cellular duty ratio criterion and numerical wavefront propagation is introduced in this paper. Both numerical simulations and experimental measurements are provided proving this designed method can increase both retrieved in-focus intensity and phase accuracy and reduce dependence of focal plane determination in transport of intensity equation measurements. It is believed that the proposed method can be potentially applied in various fields as in-focus compensation for quantitative phase imaging and automatic focal plane determination, etc.