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Mankei Tsang
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The theory of semiparametric estimation offers an elegant way of computing the Cramer-Rao bound for a parameter of interest in the midst of infinitely many nuisance parameters. Here I apply the theory to the problem of moment estimation for incoherent imaging under the effects of diffraction and photon shot noise. Using a Hilbert-space formalism designed for Poisson processes, I derive exact semiparametric Cramer-Rao bounds and efficient estimators for both direct imaging and a quantum-inspired measurement method called spatial-mode demultiplexing (SPADE). The results establish the superiority of SPADE even when little prior information about the object is available.
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The scattering of multispectral incoherent light is a common and unfavorable signal scrambling in natural scenes. However, the blurred light spot due to scattering still holds lots of information remaining to be explored. Former methods failed to recover the polarized hyperspectral information from scattered incoherent light or relied on additional dispersion elements. Here we put forward the transmission matrix (TM) approach for extended objects under incoherent illumination by speculating the unknown TM through experimentally calibrated or digitally emulated ways. Employing a fiber bundle as a powerful imaging and dispersion element, we recover the spatial information in 252 polarized-spectral channels from a single speckle, thus achieving single-shot, high-resolution, broadband hyperspectral imaging for two polarization states with the cheap, compact, fiber-bundle-only system. Based on the scattering principle itself, our method not only greatly improves the robustness of the TM approach to retrieve the input spectral information, but also reveals the feasibility to explore the polarized spatio-spectral information from blurry speckles only with the help of simple optical setups.
Ghost imaging is usually based on optoelectronic process and eletronic computing. We here propose a new ghost imaging scheme, which avoids any optoelectronic or electronic process. Instead, the proposed scheme exploits all-optical correlation via the light-light interaction and the vision persistence effect to generate images observed by naked eyes. To realize high contrast naked-eye ghost imaging, a special pattern-scanning architecture on a low-speed light-modulation disk is designed, which also enables high-resolution imaging with lower-order Hadamard vectors and boosts the imaging speed. With this approach, we realize high-contrast real-time ghost imaging for moving colored objects.
In a previous paper [M. Tsang, Phys. Rev. A 99, 012305 (2019)], I proposed a quantum limit to the estimation of object moments in subdiffraction incoherent optical imaging. In this sequel, I prove the quantum limit rigorously by infinite-dimensional analysis. A key to the proof is the choice of an unfavorable parametric submodel to give a bound for the semiparametric problem. By generalizing the quantum limit for a larger class of moments, I also prove that the measurement method of spatial-mode demultiplexing (SPADE) with just one or two modes is able to achieve the quantum limit. For comparison, I derive a classical bound for direct imaging using the parametric-submodel approach, which suggests that direct imaging is substantially inferior.
Incoherent Fourier ptychography (IFP) is a newly developed super-resolution method, where accurate knowledge of translation positions is essential for image reconstruction.To release this limitation, we propose a preprocessing algorithm capable of extracting translation positions of the structure light directly from raw images of IFP, termed translation position extracting (TPE). TPE mainly involves two steps. First, the speckle parts mixed in the acquired intensities, in which the illumination motion is encoded, are isolated by intensity averaging and division. Then the cross-correlations of the speckle dataset are computed to determine the shift positions. TPE-IFP improves the previous IFP by removal of the requirement for prior knowledge of translation positions. Its effectiveness is demonstrated by obtaining high-quality super-resolution images in absence of location information in both simulations and experiments. By further relaxing the practical conditions, the proposed TPE may accelerate the applications of IFP. What is more, as a preprocessing approach, TPE might also contribute to the estimation of pattern positions for the similar speckle-based imaging.
Surface acoustic wave (SAW) is utilized in diverse fields ranging from physics, engineering, to biology, for transducing, sensing and processing various signals. Optical imaging of SAW provides valuable information since the amplitude and the phase of the displacement field can be measured locally with the resolution limited by the spot size of the optical beam. So far, optical imaging techniques rely on modulation of optical path, phase, or diffraction associated with SAW. Here, we report experiments showing that SAW can be imaged with an optical polarimetry. Since the amount of polarization rotation can be straightforwardly calibrated when polarimeters work in the shot-noise-limited regime, the polarimetric imaging of SAW is beneficial for quantitative studies of SAW-based technologies.
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