Eric Mason

Passive Synthetic Aperture Radar Imaging Using Low-Rank Matrix Recovery Methods

We present a novel image formation method for passive synthetic aperture radar (SAR) imaging. The method is an alternative to widely used time difference of arrival (TDOA) or correlation-based backprojection method. These methods work under the assumption that the scene is composed of a single or a few widely separated point targets. The new method overcomes this limitation and can reconstruct heterogeneous scenes with extended targets. We assume that the scene of interest is illuminated by a stationary transmitter of opportunity with known illumination direction, but unknown location. We consider two airborne receivers and correlate the fast-time bistatic measurements at each slow-time. This correlation process maps the tensor product of the scene reflectivity with itself to the correlated measurements. Since this tensor product is a rank-one positive semi-definite operator, the image formation lends itself to low-rank matrix recovery techniques. Taking into account additive noise in bistatic measurements, we formulate the estimation of the rank-one operator as a convex optimization with rank constrain. We present a gradient-descent based iterative reconstruction algorithm and analyze its computational complexity. Extensive numerical simulations show that the new method is superior to correlation-based backprojection in reconstructing extended and distributed targets with better geometric fidelity, sharper edges, and better noise suppression.

Passive synthetic aperture radar imaging based on low-rank matrix recovery

We present a novel image formation method for passive synthetic aperture radar (SAR) imaging. The method is an alternative to Time Difference of Arrival (TDOA) based backprojection method. The TDOA based backprojection works under the assumption that the scene is composed of a single or a few widely separated point targets. The new method overcomes this limitation and can reconstruct heterogenous scenes with extended targets. We assume that a scene of interest is illuminated by a stationary transmitter of opportunity with known illumination direction, but unknown location. We consider two airborne receivers collecting back-scattered data from the scene. We correlate the fast-time measurements from both receivers at each slow-time. The correlation process removes the transmitter dependency from the phase of the forward model under the small scene and far-field assumptions. We then define a linear model that maps the tensor product of the scene reflectivity with itself to the correlated measurements. The resulting inverse problem involves recovering a rank-one matrix from correlated measurements. We reconstruct the scene reflectivity by low-rank matrix recovery techniques. Numerical simulations show that the new method is superior to TDOA based backprojection for realistic SAR scenes.

A weakly-convex formulation for phaseless imaging

We consider the problem of reconstructing an object given magnitudes of linear measurements. We follow the ‘lifting’ approach, but unlike previous work which use convex relaxations of the unit rank constraint, we use a weakly-convex matrix penalty. We derive a convergent algorithm and show that it is computationally more feasible than those obtained under convex relaxations. We demonstrate numerically that when the signal to noise ratio is high, the proposed algorithm can achieve almost error-free reconstruction with fewer measurements than when convex relaxation is employed.

Deep learning for radar

Motivated by the recent advances in deep learning, we lay out a vision of how deep learning techniques can be used in radar. Specifically, our discussion focuses on the use of deep learning to advance the state-of-the-art in radar imaging. While deep learning can be directly applied to automatic target recognition (ATR), the relevance of these techniques in other radar problems is not obvious. We argue that deep learning can play a central role in advancing the state-of-the-art in a wide range of radar imaging problems, discuss the challenges associated with applying these methods, and the potential advancements that are expected. We lay out an approach to design a network architecture based on the specific structure of the synthetic aperture radar (SAR) imaging problem that augments learning with traditional SAR modelling. This framework allows for capture of the non-linearity of the SAR forward model. Furthermore, we demonstrate how this process can be used to learn and compensate for trajectory based phase error for the autofocus problem.

Moving target imaging using sparse and low-rank structure

In this paper we present a method for passive radar detection of ground moving targets using sparsely distributed apertures. We assume the scene is illuminated by a source of opportunity and measure the backscattered signal. We correlate measurements from two different receivers, then form a linear forward model that operates on a rank one, positive semi-definite (PSD) operator, formed by taking the tensor product of the phase-space reflectivity function with its self. Utilizing this structure, image formation and velocity estimation are defined in a constrained optimization framework. Additionally, image formation and velocity estimation are formulated as separate optimization problems, this results in computational savings. Position estimation is posed as a rank one PSD constrained least squares problem. Then, velocity estimation is performed as a cardinality constrained least squares problem, solved using a greedy algorithm. We demonstrate the performance of our method with numerical simulations, demonstrate improvement over back-projection imaging, and evaluate the effect of spatial diversity.

DUV light source sustainability achievements and next steps

Key sustainability opportunities have been executed in support of corporate initiatives to reduce the environmental footprint and decrease the running cost of DUV light sources. Previously, substantial neon savings were demonstrated over several years through optimized gas management technologies. Beyond this work, Cymer is developing the XLGR 100, a self-contained neon recycling system, to enable minimal gas consumption. The high efficiency results of the XLGR 100 in a production factory are validated in this paper. Cymer has also developed new light source modules with 33% longer life in an effort to reduce raw and associated resource consumption. In addition, a progress report is included regarding the improvements developed to reduce light source energy consumption.

Optimization Methods for Synthetic Aperture Radar Imaging

We review recent developments in Synthetic Aperture Radar (SAR) image formation from an optimization perspective. Majority of these methods can be viewed as constrained least squares problems exploiting sparsity. We reviewed analytic and large scale numerical optimization based approaches in both deterministic and Bayesian frameworks. These methods offer substantial improvements in image quality, suppression of noise and clutter. Analytic methods also have the advantage of computational efficiency.

Deep learning for SAR image formation

The recent success of deep learning has lead to growing interest in applying these methods to signal processing problems. This paper explores the applications of deep learning to synthetic aperture radar (SAR) image formation. We review deep learning from a perspective relevant to SAR image formation. Our objective is to address SAR image formation in the presence of uncertainties in the SAR forward model. We present a recurrent auto-encoder network architecture based on the iterative shrinkage thresholding algorithm (ISTA) that incorporates SAR modeling. We then present an off-line training method using stochastic gradient descent and discuss the challenges and key steps of learning. Lastly, we show experimentally that our method can be used to form focused images in the presence of phase uncertainties. We demonstrate that the resulting algorithm has faster convergence and decreased reconstruction error than that of ISTA.

Advances in DUV light source sustainability

Cymer continues to address several areas of sustainability within the semiconductor industry by reducing or eliminating consumption of power and specific types of gas (i.e. neon, helium) required by DUV light sources in order to function. Additionally, Cymer introduced a new recycling technology to reduce the dependence on production of raw gases. In this paper, those initiatives that reduce the operational cost, environmental footprint, and business continuity risk will be discussed. Cymer has increased the efficiency of its light sources through improvements that have resulted in energy output increase while maintaining the same or requiring less power consumption. For both KrF and ArF systems, there have been component [1], system, and architecture improvements [2] that allowed customers to increase energy efficiency and productivity. An example of module improvements is the latest MO chamber that helped reduce power consumption by ~15%. Future improvements aim to continue reducing the power consumption and cost of operation of the install base and new systems. The neon supply crisis in 2015 triggered an intensive effort by the lithography light source suppliers to find ways to minimize the use of neon, a main consumable of the light source used in DUV photolithography. Cymer delivered a multi-part support program to reduce natural resource usage, decrease overall cost of operation, and ensure that chipmaker’s business continuity risk is minimized. The methods used to minimize the use of neon for 248 nm and 193 nm photolithography that offered significant relief from supply constraints and reduction of business continuity risk for chipmakers were described in previous work [3]. In this paper, results from the program will be presented. In addition, techniques to capture the neon effluent and re-purify it within the semiconductor fabs have been pursued. For example, Cymer has developed and validated a neon recycling system for ArF light sources that resides within the chipmaker’s fab. Cymer has partnered with a global gas supplier to develop a system capable of capturing, recycling and delivering <90% of the total neon gas required by multiple ArF light sources through automated operation, including online analysis. In this paper, the neon recycle system performance as demonstrated by a quantitative analysis of facility-supplied gas versus the recycled neon in ArF light source performance will be discussed. Similarly, DUV light sources have historically used helium as a purge gas in the critical line narrowing module (LNM) to achieve stable wavelength and bandwidth control. Helium has a low coefficient of index of refraction change vs. temperature relative to nitrogen and provides efficient cooling and purging of critical optics in the LNM. Previous work demonstrated how helium consumption can be reduced and still achieve stable performance under all operating conditions [1]. In this paper, results of eliminating the use of helium will be described.

Enabling CoO improvement thru green initiatives

Chipmakers continued pressure to drive down costs while increasing utilization requires development in all areas. Cymer’s commitment to meeting customer’s needs includes developing solutions that enable higher productivity as well as lowering cost of lightsource operation. Improvements in system power efficiency and predictability were deployed to chipmakers’ in 2014 with release of our latest Master Oscillating gas chamber. In addition, Cymer has committed to reduced gas usage, completing development in methods to reduce Helium gas usage while maintaining superior bandwidth and wavelength stability. The latest developments in lowering cost of operations are paired with our advanced ETC controller in Cymer’s XLR 700ix product.