arXiv subjects

Amit Ashok

Publications and source records attributed to Amit Ashok.

16 recordsLinked to original sources

arXiv2026

Attaining Fundamental Limits of Multiparameter Incoherent Optical Imaging Using Joint-Detection Quantum Measurements

Resolving extended incoherent objects below the diffraction limit poses an application-rich imaging challenge whose solution may enable a new generation of observational instruments and capabilities. In this work, we invoke a practical model for general imaging by approximating an arbitrary extended incoherent object as a finite grid of thermal point emitters parameterized by their brightnesses. We derive the quantum Fisher information matrix (QFIM) for simultaneous brightness estimation and show that the symmetric logarithmic derivatives weakly commute, indicating that the Helstrom bound furnishes the ultimate quantum limit on the estimation error for incoherent imaging. Furthermore, for deeply sub-diffraction scenes, we find numerical evidence of a gap between the Nagaoka-Hayashi (NH) bound and the Helstrom bound. This gap reveals that separable measurements, though more experimentally accessible, are insufficient to reach the quantum limit, and points to the prospective advantage of joint measurements acting on multiple state copies. Additionally, we show that spatial mode-demultiplexing (SPADE) often saturates the NH bound solidifying its status as a near-optimal separable measurement strategy that significantly outperforms direct imaging. Finally, we articulate two joint detection receivers implemented with bona fide quantum resources that asymptotically achieve the Helstrom bound.

quant-ph↗

arXiv2025

Fundamental Limits to Phase and Amplitude Estimation in the High-Strehl Regime

Context: Ground-based telescopes are susceptible to seeing, an atmospheric phenomenon that reduces the resolving power of large observatories to that of a home telescope. Compensating these effects is therefore critical to realizing the potential of upcoming extremely large telescopes, a challenging task that requires precise wavefront control. Ultimately, this precision is limited by one's wavefront sensor (WFS) and its capacity to accurately encode phase and amplitude aberrations. Aims: Our attention is on photon noise-limited wavefront sensing in the high-Strehl regime. In particular, we seek fundamental limits to phase and amplitude estimation in addition to a WFS that saturate these bounds. Methods: Information theory is employed for deriving minimum-achievable residual errors, as stipulated by a metric called the Holevo Cramer-Rao bound. Holevo's bound is closely related to another metric called the quantum Cramer-Rao bound, which has already been applied to phase estimation on nearly-corrected wavefronts. Results: We present a WFS that can perfectly extract and phase shift a telescope's piston mode. We show how this phase can be used to tune the apparatus' sensitivity to phase and amplitude, and provide a closed-form expression for the optimal phase shift. For circular apertures, this implementation saturates the fundamental limits, but it can be easily modified to work with arbitrary pupils. Moreover, our proposal uses optics that are manufactureable today and is readily achromatized with geometric phase shifters.

astro-ph.IM↗

arXiv2025

Zernike Mode Sorting with Vortex Phase Filters: Perfect Coronagraphs and Ideal Wavefront Sensors

Spatial mode sorting has come to prominence as an optical processing modality capable of saturating fundamental limits to numerous sensing tasks including wavefront sensing, coronagraphy, and superresolution imaging. But despite their promising theoretical advantages, contemporary mode sorters often feature large crosstalk, high loss, or sort modes that are poorly adapted to conventional imaging systems (e.g., Hermite- and Laguerre-Gauss). Here, we introduce an alternative architecture that sorts spatial modes natural to circularly symmetric apertures: Zernike polynomials. Using conventional optics hardware and even-order vortex phase plates, we show how to assemble a series of vortex phase filters that can in principle separate the various Zernike polynomials losslessly and without crosstalk. This idea is demonstrated via application to wavefront sensing and coronagraphy, where we propose an optical system that saturates the quantum sensitivity limits to both tasks. We expect our work to prove useful for high-contrast imaging of extrasolar planets, improving both wavefront control and coronagraph performance.

physics.optics↗

arXiv2024

Experimental Demonstration of a Quantum-Optimal Coronagraph Using Spatial Mode Sorters

Deep sub-diffraction exoplanet discovery currently lies beyond the reach of state-of-the-art direct imaging coronagraphs, which typically have an inner working angle larger than the diffraction scale. We present an experimental demonstration of a direct imaging coronagraph design capable of achieving the quantum limits of exoplanet detection and localization below the Rayleigh diffraction limit. Our benchtop implementation performs a forward and inverse pass through a free-space programmable spatial mode sorter configured to isolate photons in a point spread function (PSF)-adapted mode basis. During the forward pass, the fundamental mode is rejected, effectively eliminating light from an on-axis point-like star. On the inverse pass, the remaining modes are coherently recombined to form an image of a faint companion. Our experimental system is shown localizing an artificial exoplanet at sub-diffraction distances from its host star under a 1000:1 star-planet contrast.

astro-ph.IM↗

arXiv2024

Towards quantum-enhanced long-baseline optical/near-IR interferometry

Microarcsecond resolutions afforded by an optical-NIR array with kilometer-baselines would enable breakthrough science. However significant technology barriers exist in transporting weakly coherent photon states over these distances: primarily photon loss and phase errors. Quantum telescopy, using entangled states to link spatially separated apertures, offers a possible solution to the loss of photons. We report on an initiative launched by NSF NOIRLab in collaboration with the Center for Quantum Networks and Arizona Quantum Initiative at the University of Arizona, Tucson, to explore these concepts further. A brief description of the quantum concepts and a possible technology roadmap towards a quantum-enhanced very long baseline optical-NIR interferometric array is presented. An on-sky demonstration of measuring spatial coherence of photons with apertures linked through the simplest Gottesman protocol over short baselines and with limited phase fluctuations is envisaged as the first step.

astro-ph.IM↗

arXiv2024

Towards the Quantum Limits of Phase Retrieval

We consider the problem of determining the spatial phase profile of a single-mode electromagnetic field. Our attention is on input states that are a statistical mixture of displaced and squeezed number states, a superset of Gaussian states. In particular, we derive the quantum Fisher information matrix (QFIM) for estimating the expansion coefficients of the wavefront in an orthonormal basis, finding that it is diagonal. Moreover, we show that a measurement saturating the QFIM always exists, and point to an adaptive strategy capable of implementing it. We then construct the optimal measurements for three particular states: mixtures of photon number, coherent, and single-mode squeezed vacuum states. Sensitivity of the measurements to nuisance parameters is explored.

physics.optics↗

arXiv2024

Quantum Limits of Exoplanet Detection and Localization

Discovering exoplanets in orbit around distant stars via direct imaging is fundamentally impeded by the combined effect of optical diffraction and photon shot noise under extreme star-planet contrast. Coronagraphs strive to increase the signal-to-noise ratio of exoplanet signatures by optically suppressing light from the host star while preserving light from the exoplanet. However, it is unclear whether direct imaging coronagraphs constitute an optimal strategy for attaining fundamental limits relevant to exoplanet discovery. In this work, we first review the quantum information limits of exoplanet detection and localization characterized by (1) the quantum Chernoff exponent for symmetric hypothesis testing, (2) the quantum relative entropy for asymmetric hypothesis testing, and (3) the quantum Fisher information matrix for multiparameter estimation. We demonstrate that coronagraphs designed to completely suppress light in the fundamental mode of the telescope - while perfectly transmitting higher-order orthogonal modes - indeed achieve these limits in the regime of high star-planet contrasts. Furthermore, we formulate coronagraphs as quantum channels, thus generalizing the classical framework of coronography to the quantum setting. Using this framework, we compare the information-theoretic performance of leading coronagraph designs against the quantum limits. Our analysis indicates that quantum-optimal coronagraphs offer enhanced information efficiency in the sub-diffraction regime compared to leading coronagraph designs and may significantly expand the domain of accessible exoplanets.

quant-ph↗

arXiv2022

Quantum Multi-Parameter Adaptive Bayesian Estimation and Application to Super-Resolution Imaging

In Bayesian estimation theory, the estimator ${\hat θ} = E[θ|l]$ attains the minimum mean squared error (MMSE) for estimating a scalar parameter of interest $θ$ from the observation of $l$ through a noisy channel $P_{l|θ}$, given a prior $P_θ$ on $θ$. In quantum sensing tasks, the user gets $ρ_θ$, the quantum state that encodes $θ$. They choose a measurement, a positive-operator valued measure (POVM) $Π_l$, which induces the channel $P_{l|θ} = {\rm Tr}(ρ_θΠ_l)$ to the measurement outcome $l$, on which the aforesaid classical MMSE estimator is employed. Personick found the optimum POVM $Π_l$ that minimizes the MMSE over all possible measurements, and that MMSE. This result from 1971 is less-widely known than the quantum Fisher information (QFI), which lower bounds the variance of an unbiased estimator over all measurements, when $P_θ$ is unavailable. For multi-parameter estimation, i.e., when $θ$ is a vector, in Fisher quantum estimation theory, the inverse of the QFI matrix provides an operator lower bound to the covariance of an unbiased estimator. However, there has been little work on quantifying quantum limits and measurement designs, for multi-parameter quantum estimation in the {\em Bayesian} setting. In this paper, we build upon Personick's result to construct a Bayesian adaptive measurement scheme for multi-parameter estimation when $N$ copies of $ρ_θ$ are available. We illustrate an application to localizing a cluster of point emitters in a highly sub-Rayleigh angular field-of-view, an important problem in fluorescence microscopy and astronomy. Our algorithm translates to a multi-spatial-mode transformation prior to a photon-detection array, with electro-optic feedback to adapt the mode sorter. We show that this receiver performs far superior to quantum-noise-limited focal-plane direct imaging.

physics.data-an↗

arXiv2021

Invertibility of Multi-Energy X-ray Transform

Purpose: The goal is to provide a sufficient condition on the invertibility of a multi-energy (ME) X-ray transform. The energy-dependent X-ray attenuation profiles can be represented by a set of coefficients using the Alvarez-Macovski (AM) method. An ME X-ray transform is a mapping from $N$ AM coefficients to $N$ noise-free energy-weighted measurements, where $N\geq2$. Methods: We apply a general invertibility theorem which tests whether the Jacobian of the mapping $J(\mathbf A)$ has zero values over the support of the mapping. The Jacobian of an arbitrary ME X-ray transform is an integration over all spectral measurements. A sufficient condition of $J(\mathbf A)\neq0$ for all $\mathbf A$ is that the integrand of $J(\mathbf A)$ is $\geq0$ (or $\leq0$) everywhere. Note that the trivial case of the integrand equals to zero everywhere is ignored. With symmetry, we simplified the integrand of the Jacobian into three factors that are determined by the total attenuation, the basis functions, and the energy-weighting functions, respectively. The factor related to total attenuation is always positive, hence the invertibility of the X-ray transform can be determined by testing the signs of the other two factors. Furthermore, we use the Cramer-Rao lower bound (CRLB) to characterize the noise-induced estimation uncertainty and provide a maximum-likelihood (ML) estimator. Conclusions: We have provided a framework to study the invertibility of an arbitrary ME X-ray transform and proved the global invertibility for four types of systems.

physics.med-ph↗

arXiv2021

Bounds on mutual information of mixture data for classification tasks

The data for many classification problems, such as pattern and speech recognition, follow mixture distributions. To quantify the optimum performance for classification tasks, the Shannon mutual information is a natural information-theoretic metric, as it is directly related to the probability of error. The mutual information between mixture data and the class label does not have an analytical expression, nor any efficient computational algorithms. We introduce a variational upper bound, a lower bound, and three estimators, all employing pair-wise divergences between mixture components. We compare the new bounds and estimators with Monte Carlo stochastic sampling and bounds derived from entropy bounds. To conclude, we evaluate the performance of the bounds and estimators through numerical simulations.

eess.SP↗

arXiv2020

X-ray measurement model incorporating energy-correlated material variability and its application in information-theoretic system analysis

Extending our prior work, we propose a multi-energy X-ray measurement model incorporating material variability with energy correlations to enable the analysis and exploration of the performance of X-ray imaging and sensing systems. Based on this measurement model, we provide analytical expressions for bounds on the probability of error, $P_e$, to quantify the performance limits of an X-ray measurement system for binary classification task. We analyze the performance of a prototypical X-ray measurement system to demonstrate the utility of our proposed material variability measurement model.

eess.SP↗

arXiv2019

Approaching Quantum Limited Super-Resolution Imaging without Prior Knowledge of the Object Location

A recently identified class of receivers which demultiplex an optical field into a set of orthogonal spatial modes prior to detection can surpass canonical diffraction limits on spatial resolution for simple incoherent imaging tasks. However, these mode-sorting receivers tend to exhibit high sensitivity to contextual nuisance parameters (e.g., the centroid of a clustered or extended object), raising questions on their viability in realistic imaging scenarios where little or no prior information about the scene is available. We propose a multi-stage passive imaging strategy which segments the total recording time between different physical measurements to build up the required prior information for near quantum-optimal imaging performance at sub-Rayleigh length scales. We show via Monte Carlo simulations that an adaptive two-stage scheme which dynamically allocates the total recording time between a traditional direct detection measurement and a binary mode-sorting receiver outperforms idealized direct detection alone for simple estimation tasks when no prior knowledge of the object centroid is available, achieving one to two orders of magnitude improvement in mean squared error. Our scheme can be generalized for more sophisticated imaging tasks with multiple parameters and minimal prior information.

quant-ph↗

arXiv2018

Attaining the quantum limit of super resolution in imaging an object's length via pre-detection spatial mode sorting

Recent work considered the ultimate (quantum) limit of the precision of estimating the distance between two point objects. It was shown that the performance gap between the quantum limit and that of ideal continuum image-plane direct detection is the largest for highly sub-Rayleigh separation of the objects, and that a pre-detection mode sorting could attain the quantum limit. Here we extend this to a more general problem of estimating the length of an incoherently radiating extended (line) object. We find, as expected by the Rayleigh criterion, the Fisher information (FI) per integrated photon vanishes in the limit of small length for ideal image plane direct detection. Conversely, for a Hermite-Gaussian (HG) pre-detection mode sorter, this normalized FI does not decrease with decreasing object length, similar to the two point object case. However, unlike in the two-object problem, the FI per photon of both detection strategies gradually decreases as the object length greatly exceeds the Rayleigh limit, due to the relative inefficiency of information provided by photons emanating from near the center of the object about its length. We evaluate the quantum Fisher information per unit integrated photons and find that the HG mode sorter exactly achieves this limit at all values of the object length. Further, a simple binary mode sorter maintains the advantage of the full mode sorter at highly sub-Rayleigh length. In addition to this FI analysis, we quantify improvement in terms of the actual mean squared error of the length estimate. Finally, we consider the effect of imperfect mode sorting, and show that the performance improvement over direct detection is robust over a range of sub-Rayleigh lengths.

physics.optics↗

arXiv2017

Convolutional Neural Networks for Non-iterative Reconstruction of Compressively Sensed Images

Traditional algorithms for compressive sensing recovery are computationally expensive and are ineffective at low measurement rates. In this work, we propose a data driven non-iterative algorithm to overcome the shortcomings of earlier iterative algorithms. Our solution, ReconNet, is a deep neural network, whose parameters are learned end-to-end to map block-wise compressive measurements of the scene to the desired image blocks. Reconstruction of an image becomes a simple forward pass through the network and can be done in real-time. We show empirically that our algorithm yields reconstructions with higher PSNRs compared to iterative algorithms at low measurement rates and in presence of measurement noise. We also propose a variant of ReconNet which uses adversarial loss in order to further improve reconstruction quality. We discuss how adding a fully connected layer to the existing ReconNet architecture allows for jointly learning the measurement matrix and the reconstruction algorithm in a single network. Experiments on real data obtained from a block compressive imager show that our networks are robust to unseen sensor noise. Finally, through an experiment in object tracking, we show that even at very low measurement rates, reconstructions using our algorithm possess rich semantic content that can be used for high level inference.

cs.CV↗

arXiv2017

Fundamental limit of resolving two point sources limited by an arbitrary point spread function

Estimating the angular separation between two incoherently radiating monochromatic point sources is a canonical toy problem to quantify spatial resolution in imaging. In recent work, Tsang {\em et al.} showed, using a Fisher Information analysis, that Rayleigh's resolution limit is just an artifact of the conventional wisdom of intensity measurement in the image plane. They showed that the optimal sensitivity of estimating the angle is only a function of the total photons collected during the camera's integration time but entirely independent of the angular separation itself no matter how small it is, and found the information-optimal mode basis, intensity detection in which achieves the aforesaid performance. We extend the above analysis, which was done for a Gaussian point spread function (PSF) to a hard-aperture pupil proving the information optimality of image-plane sinc-Bessel modes, and generalize the result further to an arbitrary PSF. We obtain new counterintuitive insights on energy vs. information content in spatial modes, and extend the Fisher Information analysis to exact calculations of minimum mean squared error, both for Gaussian and hard aperture pupils.

physics.optics↗

arXiv2016

ReconNet: Non-Iterative Reconstruction of Images from Compressively Sensed Random Measurements

The goal of this paper is to present a non-iterative and more importantly an extremely fast algorithm to reconstruct images from compressively sensed (CS) random measurements. To this end, we propose a novel convolutional neural network (CNN) architecture which takes in CS measurements of an image as input and outputs an intermediate reconstruction. We call this network, ReconNet. The intermediate reconstruction is fed into an off-the-shelf denoiser to obtain the final reconstructed image. On a standard dataset of images we show significant improvements in reconstruction results (both in terms of PSNR and time complexity) over state-of-the-art iterative CS reconstruction algorithms at various measurement rates. Further, through qualitative experiments on real data collected using our block single pixel camera (SPC), we show that our network is highly robust to sensor noise and can recover visually better quality images than competitive algorithms at extremely low sensing rates of 0.1 and 0.04. To demonstrate that our algorithm can recover semantically informative images even at a low measurement rate of 0.01, we present a very robust proof of concept real-time visual tracking application.

cs.CV↗