Quantitative phase imaging, i.e., measuring the map of pathlength shifts due to the specimen of interest, has been developing rapidly over the past decade. The main methods and exciting applications to biomedicine will be reviewed.

Quantitative phase imaging in biomedicine

Quantitative X-ray ultra-small angle scattering retrieval with structured illumination for microvessel characterization

The past decade has witnessed transformative applications of deep learning in various computational imaging, sensing and microscopy tasks. Due to the supervised learning schemes employed, these methods mostly depend on large-scale, diverse, and labeled training data. The acquisition and preparation of such training image datasets are often laborious and costly, also leading to biased estimation and limited generalization to new sample types. Here, we report a self-supervised learning model, termed GedankenNet, that eliminates the need for labeled or experimental training data, and demonstrate its effectiveness and superior generalization on hologram reconstruction tasks. Without prior knowledge about the sample types to be imaged, the self-supervised learning model was trained using a physics-consistency loss and artificial random images that are synthetically generated without any experiments or resemblance to real-world samples. After its self-supervised training, GedankenNet successfully generalized to experimental holograms of various unseen biological samples, reconstructing the phase and amplitude images of different types of objects using experimentally acquired test holograms. Without access to experimental data or knowledge of real samples of interest or their spatial features, GedankenNet's self-supervised learning achieved complex-valued image reconstructions that are consistent with the Maxwell's equations, and its output inference and object solutions accurately represent the wave propagation in free-space. GedankenNet framework also exhibits resilience to random, unknown perturbations in the physical forward model, including changes in the hologram distances, pixel size and illumination wavelength. This self-supervised learning of image reconstruction tasks creates new opportunities for various inverse problems in holography, microscopy and computational imaging fields.

GedankenNet: Self-supervised learning of hologram reconstruction using physics consistency

We demonstrate a superresolution phase imaging method based on structure illumination. Phase variations beyond the diffraction limit is coupled to multiple orders of harmonics of the structure illumination generated by a 2D Ag dot array.

Superresolution phase retrieval from non-sinusoidal structure illumination

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.

Learning a model-based neural network for quantitative phase imaging based on the transport of intensity

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.

Hierarchical synthesis Network: a frequency extraction technique for structured illumination-based phase retrieval

Non-interferometric quantitative phase imaging based on Transport of Intensity Equation (TIE) has been widely used in bio-medical imaging. However, analytic TIE phase retrieval is prone to low-spatial frequency noise amplification, which is caused by the illposedness of inversion at the origin of the spectrum. There are also retrieval ambiguities resulting from the lack of sensitivity to the curl component of the Poynting vector occurring with strong absorption. Here, we establish a physics-informed neural network (PINN) to address these issues, by integrating the forward and inverse physics models into a cascaded deep neural network. We demonstrate that the proposed PINN is efficiently trained using a small set of sample data, enabling the conversion of noise-corrupted 2-shot TIE phase retrievals to high quality phase images under partially coherent LED illumination. The efficacy of the proposed approach is demonstrated by both simulation using a standard image database and experiment using human buccal epitehlial cells. In particular, high image quality (SSIM = 0.919) is achieved experimentally using a reduced size of labeled data (140 image pairs). We discuss the robustness of the proposed approach against insufficient training data, and demonstrate that the parallel architecture of PINN is efficient for transfer learning.

Physics-informed neural network for phase imaging based on transport of intensity equation.

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.

High resolution phase imaging with transport of intensity equation and sinusoidal illumination

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.

Transport of intensity phase imaging with Wiener deconvolution for enhanced visibility

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.

Sibi Chakravarthy Shanmugavel

Papers

Hierarchical synthesis Network: a frequency extraction technique for structured illumination-based phase retrieval

Physics-informed neural network for phase imaging based on transport of intensity equation.

High resolution phase imaging with transport of intensity equation and sinusoidal illumination

Transport of intensity phase imaging with Wiener deconvolution for enhanced visibility

Contrast transfer function with sinusoidal illumination for super resolved phase imaging