Imaging with low-dose light is of importance in various fields, especially when minimizing radiation-induced damage onto samples is desirable. The raw image captured at the detector plane is then predominantly a Poisson random process with Gaussian noise added due to the quantum nature of photo-electric conversion. Under such noisy conditions, highly ill-posed problems such as phase retrieval from raw intensity measurements become prone to strong artifacts in the reconstructions; a situation that deep neural networks (DNNs) have already been shown to be useful at improving. Here, we demonstrate that random phase modulation on the optical field, also known as coherent modulation imaging (CMI), in conjunction with the phase extraction neural network (PhENN) and a Gerchberg-Saxton-Fienup (GSF) approximant, further improves resilience to noise of the phase-from-intensity imaging problem. We offer design guidelines for implementing the CMI hardware with the proposed computational reconstruction scheme and quantify reconstruction improvement as function of photon count.

Phase extraction neural network (PhENN) with coherent modulation imaging (CMI) for phase retrieval at low photon counts

We report that disordered media made of randomly distributed nanoparticles can be used to overcome the diffraction limit of a conventional imaging system. By developing a method to extract the original image information from the multiple scattering induced by the turbid media, we dramatically increase a numerical aperture of the imaging system. As a result, the resolution is enhanced by more than 5 times over the diffraction limit, and the field of view is extended over the physical area of the camera. Our technique lays the foundation to use a turbid medium as a far-field superlens.

Overcoming the Diffraction Limit Using Multiple Light Scattering in a Highly Disordered Medium

For photonic devices, structural disorder and light scattering have long been considered annoying and detrimental features that were best avoided or minimized. This review shows that disorder and complexity can be harnessed for photonic device applications. Compared to ordered systems, disordered systems provide much more possibilities and diverse optical responses. They have been used to create physical unclonable functions for secret key generation, and more recently for random projection, high-dimensional matrix multiplication, and reservoir computing. Incorporating structural disorder enables novel devices with unique functionalities as well as multi-functionality. A random system can function as an optical lens, a spectrometer, a polarimeter, and a radio frequency receiver. It is also employed for optical pulse measurement and full-field recovery. Multi-functional disordered photonic devices have been developed for hyperspectral imaging, spatial, and spectral polarimetry. In addition to passive devices, structural disorder has been incorporated to active devices. One prominent example is the random laser, which enables speckle-free imaging, super-resolution spectroscopy, broad tunability of high-power fiber laser, and suppression of lasing instabilities. Disordered devices have low fabrication costs, and their combination with advanced computational techniques may lead to a paradigm shift in photonics and optical engineering. 

Harnessing disorder for photonic device applications

Wavelength-dependent speckle multiplexing for imaging through opacity

We introduce a single-frame diffractive imaging method called randomized probe imaging (RPI). In RPI, a sample is illuminated by a structured probe field containing speckles smaller than the sample's typical feature size. Quantitative amplitude and phase images are then reconstructed from the resulting far-field diffraction pattern. The experimental geometry of RPI is straightforward to implement, requires no near-field optics, and is applicable to extended samples. When the resulting data are analyzed with a complimentary algorithm, reliable reconstructions which are robust to missing data are achieved. To realize these benefits, a resolution limit associated with the numerical aperture of the probe-forming optics is imposed. RPI therefore offers an attractive modality for quantitative X-ray phase imaging when temporal resolution and reliability are critical but spatial resolution in the tens of nanometers is sufficient. We discuss the method, introduce a reconstruction algorithm, and present two proof-of-concept experiments: one using visible light, and one using soft X-rays.

Single-frame far-field diffractive imaging with randomized illumination.

We report coherent imaging of objects behind opaque scattering media with only one piece of the power spectrum pattern. We solve the unique solution and improve algorithm speed for the inverse problem. Based on the proposed scattering-disturbance model, with only one piece of the Fourier transform power spectrum pattern under coherent illumination, we successfully reconstruct clear images of the objects fully hidden by an opaque diffuser. The experimental results demonstrate the feasibility of the reconstruction method and the scattering-disturbance model. Our method makes it possible to carry out snapshot coherent imaging of the objects obscured by scattering media, which extends the methodology of x-ray crystallography to visible-light scattering imaging for underwater and living biomedical imaging.

Single-shot coherent power-spectrum imaging of objects hidden by opaque scattering media.

With only one piece of the power-spectrum pattern, the single-shot coherent power-spectrum imaging can provide a clear object image for real-time applications even if the object is hidden by opaque scattering media, in which the feedback coefficient β value for the reconstruction with least retrievals and fastest speed has to be pre-estimated through time-consuming iterative loops. Here we report a method for estimating the optimal β value from the captured raw power-spectrum images adaptively to optimize the single-shot coherent power-spectrum imaging for practical exposure conditions. The results demonstrate that, based on exposure level analysis of the captured raw power-spectrum images even of underexposure, moderate exposure, and overexposure cases, the β value could be quickly determined with a compact expression for the algorithm to achieve clear reconstruction output efficiently. The proposed method helps to push ahead of the coherent diffractive imaging devices for real-time imaging through turbid mediums in Artificial Intelligence (AI), driving assistance, and flight assistance applications.

Mengzhu Li

Papers

Single-shot coherent power-spectrum imaging of objects hidden by opaque scattering media.

Optimizing Single-Shot Coherent Power-Spectrum Scattering Imaging Adaptively by Tuning Feedback Coefficient for Practical Exposure Conditions

Measurements of the Normal Incidence Sound Absorption Coefficient for Non-standard Sized Absorbers in Impedance Tubes