KEYWORDS: Phase imaging, Holography, Contrast transfer function, Super resolution, Microscopy, Image resolution, Diffraction, Transmittance, Phase shifts, Near field diffraction
Quantitative phase imaging (QPI) has emerged as a powerful computational tool that enables imaging unla- belled specimens with high contrast. It finds applications in microscopy, refractive index mapping , biomedical imaging and surface measurement. Several techniques including interferometry, holography, iterative methods and Transport of Intensity Equation have been developed over the years for QPI. However, the spatial resolution of the retrieved phase images are limited by the diffraction limit of the imaging system. Prior work on Super resolution phase imaging has been primarily focused on holography based techniques which require illumination sources with high coherence , phase unwrapping and high experimental stability. In this work, we propose a propagation based super resolution phase imaging technique using Contrast Transfer Function(CTF) and structured illumination. An enhancement in resolution by two folds is demonstrated using numerical results.
Structured illumination (SI) phase imaging is an important strategy to achieve quantitative phase imaging via encoding phase-induced diffraction into modulation intensity signals through propagation. However, the nonlinear property of SI-based transfer function results in ill-posedness in phase imaging retrieval. Overlapping modulation spectrum usually leads to loss of high spatial frequency components. Recent studies show that such nonlinear inversion problems can be efficiently represented by deep neural networks, as have been demonstrated in phase retrieval via holography and Fourier ptychography techniques. Here we present a hierarchical synthesis network (HSNet) which uses multiple splitting networks to extract structural features of structured intensity images in various modulation frequency and synthesis network to produce high fidelity reconstruction. We show that the proposed framework retrieve clear and accurate phase profile with reduced computing requirements in simulation.
Transport of Intensity Equation (TIE) is a powerful computational tool for quantitative phase imaging using intensity only measurement. However, one drawback of TIE is that it does not include any parameters of the imaging system in the equation. To account for the effect of the imaging system on the retrieved phase, TIE is reformulated using Contrast Transfer Function (CTF) to analytically derive the distortion functions present in TIE. The distortion function attenuates the frequency components in the pass band resulting in a blurry phase image. For image restoration, signal parameters are estimated by minimizing a cost function for power spectrum and an optimal wiener filter is employed to deconvolve the distortion function. The proposed method is experimentally demonstrated through a visible enhancement in the phase images of human cheek cells obtained using a bright field microscope.
KEYWORDS: Image resolution, Signal to noise ratio, Phase imaging, Signal processing, Diffraction, Phase shift keying, Optical transfer functions, Modulation, Filtering (signal processing), Digital filtering
Transport of Intensity equation(TIE) is a non-interferometric method used for quantitative phase imaging. By reformulating the TIE using Contrast Transfer Function, it can be determined that the spatial resolution of the phase retrieved using TIE is limited by the product of imaging system transfer function and a sinc function. In this work, we apply the principles of structured illumination fluorescent microscopy to develop a TIE based super resolved phase imaging technique. The sinusoidal intensity pattern down modulates high frequency spectrum of the phase into the system pass band thereby providing a convenient approach to synthetically enlarge the numerical aperture of the system. Resolution enhancement by two folds is demonstrated using simulations.
Quantitative phase imaging (QPI) provides enhanced contrast for weakly absorbing specimens such as biological tissues under optical light and soft materials under X-ray. In this work, we develop a model-based phase retrieval framework by integrating the physics principles of phase imaging with the deep learning-based approach. Both measurements and the forward model are used as the inputs for a model-based neural network. The features of the object and the regularization weight of the established priors are learned by minimizing the difference between the network output to the ground truth during the training process. This method is tested on phase imaging of handwriting digital patterns and biological cells in a simulation of propagation-based TIE (transport of intensity equation) phase retrieval. We achieve enhanced accuracy for the phase retrieval compared to non-model based end-to-end neural networks and reduce the computation cost compared to traditional model-based iterative reconstruction algorithms.
Porous structures are widely found in natural and engineered material systems. To study the defect initialization and damage evolution in the complex 3D network structures, we explore advanced X-ray phase tomography to provide holistic and high-resolution 3D data. A pipeline of deep learning-based phase retrieval, computer vision, and damage identification algorithms are implemented to extract various types of damage for large volumetric tomography data. We first obtain high-quality phase tomography reconstruction from noisy and insufficient CT acquisition. Based on a hybrid approach using both model-based feature filtering and data-driven machine learning, we then identifies the defects and damaged regions from the background of porous structures. This method is applied to an in-situ X-ray tomography measurement on a natural cellular material; the accurate and comprehensive defects detection reveals insight into 3D damage evolution modes for porous material systems.
Structured-illumination (SI) is used for quantitative phase retrieval for improved contrast and sensitivity. However, the nonlinear nature of SI-based phase retrieval process, such as the spatial frequency biases and mixture of different spatial frequency components, usually leads to phase aberrations, in particular in the high spatial frequency components. Recent studies show that nonlinear inversion problems can be efficiently represented by deep neural networks in an end-to-end framework. In this study, we present a deep learning framework for SI-based quantitative phase imaging via the Conditional Generative Adversarial Network (cGANs). A series of structured images paired with the corresponding ground truth of phase images are used to train two competing networks of generator and discriminator. We demonstrate that the GAN-based approach produces sharp and accurate phase image and the structured illumination pattern simultaneously based on our simulation.
X-ray computed tomography has been recently applied to capture the dynamic behaviors of complex material systems in 4D. The dynamic 3D acquisition, however, usually leads to insufficient data acquisition with low-dose X-ray radiation and limited-angle projections. A high-fidelity CT reconstruction is challenging based on the severely limited acquisition. While prior constraint, such as local smoothness, can improve the quality of reconstructions, a more general reconstruction strategy to include structural features on a range of different scales proves to yield better reconstruction results and are more adaptive to complex structured materials. In this work, we develop the hierarchical synthesis network to establish structural priors for sparse-view CT reconstruction, which achieves high-fidelity with an improved computation efficiency. We found that the established knowledge of structural priors on each different scale can be independently transferred to sparse-view CT reconstruction under different conditions, enabling the transfer of non-local features into the reconstruction of a phase tomography application.
We present a hierarchical imaging reconstruction algorithm for a 3D phase tomography based on the densely extracted features on a multi-band pyramid of convolutional network. By implementing a layer-wise hierarchical machine learning network and combine different bands of information for the imaging retrieval, a more efficient and adaptive learning strategy is established to enable an accurate reconstruction with fewer training data and improved accuracy. In addition, the distinction of intensity and spectral bands in the feature training process enables bias correction for reconstruction under varied conditions. In particular, we demonstrate a robust imaging reconstruction for a sparse-view phase tomography application, where spectrally biased phase diffraction and intensity-biased photon noise are both successfully corrected for.
We present a high-temporal resolution 4D-XCT with feature-based iterative reconstruction method(FBIR) by imposing feature priors in the reconstruction process. The 4D reconstruction is acquired through an iterative minimization of the cost function which is obtained by combining the forward model and multiple structural featurebased priors. The scheme is applied to the study of the mechanical response of a porous structure (sea urchin spines), which achieves high temporal resolution and demonstrates robustness against noise, limited views and motion induced blurring.
A one-shot multi-directional ultra-small angle X-ray scattering imaging successfully resolves the fiber orientation of a wood sample. This 2D structured illumination enables the retrieval of scattering signals in multiple directions simultaneously.
Robust phase retrieval is obtained by using structured illumination with the Transport of Intensity Equation (SI-TIE). By imposing a proportional relationship between the attenuation coefficient and the refractive index (known as the phase-absorption duality), we are allowed to reformulate the SI-TIE propagation equation to probably address both the transmission and diffraction signals using only a single shot of intensity measurement. The correlation between the phase and attenuation fixes the low frequency instability, resulting in robust phase imaging with enhanced sensitivity.
We observe efficient forward stimulated Brillouin scattering (FSBS) in a standard 2-km highly-nonlinear optical
fiber (NHLF), where we see multiple resonance peaks between 425 MHz to 1.1 GHz. The most efficient acousto-optical
coupling appears for the 20th radially-guided acoustic mode at 933.8 MHz, which has maximum spatial
overlapping with the tightly confined optical mode in the NHLF fiber. A large gain coefficient of 34.7 W-1 is
obtained at this resonance when pumped with a 8 mW continuous-wave (cw) beam at 1550 nm, and an enhanced
gain of 57.6 is obtained by using a pulsed pump beam at 80 mW. Interference between the FSBS process and
the Kerr effect is observed to enhance the resonance and cause asymmetric profile for the observed resonances.
We study the slow light effect via stimulated Brillouin scattering (SBS) using broadly-tunable frequency-swept sources,
such as that used in optical coherence tomography. Slow light can be achieved, in principle, over the entire transparency
window of the optical fiber (many 100's of nm at telecommunication wavelengths). We demonstrate a SBS slow light
delay of more than 1 ns over a wide bandwidth at 1.55 μm using a 2-km-long highly nonlinear fiber with a source sweep
rate of 20 MHz/μs and a delay of 10 ns using a 10-m-long photonic crystal fiber with a sweep rate of 400 MHz/μs. We
also find that, for a given sweep rate R, there is an optimum value of fiber length L to obtain the largest delay.
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