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The Zwicky Transit Facility (ZTF) is a powerful time domain survey telescope with a large field of view of 47 deg 2 . We apply the synthetic tracking technique to integrate a ZTF’s deep drilling data set, which consists of 133 nominal 30 s exposure frames spanning about 1.5 hr, to search for slowly moving asteroids down to approximately 23rd magnitude. We found 1168 objects from searching 40 of the 64 CCD-quadrant subfields, each of which covers a field size of about 0.73 deg 2 . While most of the objects are in the core region of the asteroid belt, there are asteroids belonging to families of Trojan, Hilda, Hungaria, Phocaea, and near-Earth-asteroids. Such an approach is effective and productive for discovering new asteroids. Here we report the data processing and results as well as discuss a potential deep drilling operation mode using this approach for survey facilities.

Synthetic tracking technique uses multiple short exposure images to observe moving objects to prevent the objects from streaking in an individual frame. It integrates frames in post-processing, where the tracking of telescope at any desired rate can be simulated by shifting frames accordingly. Such an approach avoids trailing loss, thus improves detection sensitivity, especially for fast moving objects. It also yields accurate astrometry for moving objects independent of rate of motion with precision comparable to stellar astrometry. Using the Gaia DR2 catalog, we are able to demonstrate 10 mas level near-Earth-object (NEO) astrometry with the synthetic tracking technique. Accurate NEO astrometry allows us to determine NEO orbit more precisely. We discuss applications such as cataloging newly discovered NEOs with less measurements and/or from observation time windows covering shorter orbit arcs, better predicting the chance for a potentially hazardous asteroid to impact the Earth, measuring non-gravitational acceleration to infer physical properties of minor planets, and optical navigation for future spacecraft carrying optical communication lasers.

Near-Earth Object (NEO) initial orbit determination typically uses astrometric measurements during a close approach over a time window much shorter than the orbital period of the NEO. The initial orbit is only weakly determined with dominant uncertainties in the distance of the NEO from the Earth. Topocentric astrometric measurements allow us to estimate NEO distances using observed nonlinear motions of the NEOs relative to observers, which come from the relative orbital motion of the NEOs to the Earth plus the topocentric parallax (parallax) from the diversity of observatory locations relative to the Earth center. We calculate the ratio of the contributions to the nonlinear motion from the relative orbital motion and the parallax to be approximately (TΔ/(day au))2, where T is the arc length measured in days and Δ is the distance of close approach. The dominant nonlinear motion for ranging the NEO comes from the relative orbital motion of the NEO to the Earth center, due to mainly the differential solar gravitational acceleration, when TΔ ≳ 1 day au and the parallax when TΔ ≲ 1 day au. This is confirmed by simulation data and supported by observational data of real NEOs. In the regime TΔ ≲ 1 day au, the orbit determination uncertainties are inversely proportional to the amplitude of the parallax. Introducing diversities of hour angles and observatory latitudes (especially alternating between extreme values) into scheduled follow-up observations can improve the parallax amplitude, thus the orbit accuracy. Most of the newly discovered NEOs are in this regime, we recommend optimizing parallax by properly scheduling observations when the NEO is very close to the Earth and using synthetic tracking to improve astrometry accuracy for initial orbit determination.

Synthetic aperture LADAR (SAL) allows high resolution imaging of distant objects. Basic SAL image processing is based on fast Fourier transform (FFT) techniques originally developed for use in radar. These techniques can amplify noise and limit resolution. More advanced reconstruction techniques have been proposed for synthetic aperture radar (SAR), but have not been adapted for SAL. In addition, both conventional SAL and advanced SAR algorithms reconstruct the complex-valued reflection coefficient instead of the real-valued reflectance which leads to speckled images. In this paper, we present a model-based iterative reconstruction (MBIR) algorithm designed specifically for SAL. Rather than estimating the reflection coefficient, we propose estimating its variance which is equal to the reflectance, a function that more closely resembles conventional optical images. A Bayesian framework is used to find the maximum a posteriori (MAP) estimate for the reflectance using a Q-Generalized Gaussian Markov random field (QGGMRF) prior model. The QGGMRF is able to model complex correlations between neighboring pixels which promotes a smooth and more natural looking image. The expectation-maximization (EM) algorithm is used to derive a surrogate for the MAP cost function. Finally, the proposed MBIR algorithm is tested on both simulated and experimental data. Results show significant and consistent improvements over existing reconstruction techniques in terms of image contrast, speckle reduction, autofocus, and low signal-to-noise ratio performance.

Large or even medium sized asteroids impacting the Earth can cause damage on a global scale. Existing and planned concepts for finding near-Earth objects (NEOs) with diameter of 140 m or larger would take ~15-20 years of observation to find ~90% of them. This includes both ground and space based projects. For smaller NEOs (~50-70 m in diameter), the time scale is many decades. The reason it takes so long to detect these objects is because most of the NEOs have highly elliptical orbits that bring them into the inner solar system once per orbit. If these objects cross the Earth's orbit when the Earth is on the other side of the Sun, they will not be detected by facilities on or around the Earth. A constellation of MicroSats in orbit around the Sun can dramatically reduce the time needed to find 90% of NEOs ~100-140 m in diameter., 6 pages, 4 figures, 3 tables

The performance of optically coherent imaging systems can be limited by measurement and speckle noise. In this paper, we develop an image formation framework for computing the maximum a posteriori estimate of an object's reflectivity when imaged using coherent illumination and detection. The proposed approach allows for the use of Gaussian denoising algorithms (GDAs), without modification, to mitigate the exponentially distributed and signal-dependent noise that occurs in coherent imaging. Several GDAs are compared using both simulated and experimental data. The proposed framework is shown to be robust to noise and significantly reduce reconstruction error compared to the standard inversion technique.

An Inverse Synthetic Aperture LADAR (ISAL) system is capable of providing high resolution surface mapping of near Earth objects which is an ability that has gained significant interest for both exploration and hazard assessment. The use of an ISAL system over these long distances often presents the need to operate the optical system in photon-starved conditions. This leads to a necessity to understand the implications of photon and detector noise in the system. Here a Carrier-to-Noise Ratio is derived which is similar to other optical imaging CNR definitions. The CNR value is compared to the quality of experimentally captured images recovered using the Phase Gradient Autofocus technique both with and without the presence of atmospheric turbulence. A minimum return signal CNR for the PGA to work is observed.

High quality linear laser frequency chirp of high chirp rate is critical to many laser ranging applications. In this paper, we describe a cost-effective chirp linearization approach implemented on our Inverse synthetic Aperture LADAR (ISAL) imaging testbed. Our approach uses a COTS PZT for external cavity laser frequency tuning and a common self-heterodyne fiber interferometer as a frequency monitor, with a two-step hardware and software chirp linearization procedure to achieve high quality chirp. First, the nominal triangle waveform input to PZT drive is modified through an iterative process prior to ISAL imaging acquisition. Several waveforms with chirp rates between 1 and 4THz/s have been acquired with residual chirp rate error ~ +/-2% in usable region. This process generally needs to be done only once for a typical PZT that has excellent repeatability but poor linearity. The modified waveform is then used during ISAL imaging acquisition without active control while the imperfection in transmitted frequency is monitored. The received imaging data is resampled digitally based on frequency error calculated from the frequency monitor data, effectively reduce chirp nonlinearity to ~+/- 0.2% in chirp rate error. The measured system impulse response from return signal shows near designed range resolution of a few mm, demonstrating the effectiveness of this approach.

Here we expand on the current methods of characterizing small astronomical bodies, particularly asteroids, by viewing stellar occultation events. Stellar occultation has proven to be a viable method for determining the size of moons and asteroids; however, it comes with some limitations. In general the method does not consider or use all of the known diffraction effects that occur and thus provides a nominal radius--not a shape--of the occluder. We show that most stellar occultation events involving small near-Earth asteroids occur with low Fresnel numbers. This in effect renders the traditional methods useless to characterize the shape, because no sharp shadow exists. We show that using similar data collection to that of the traditional occultation method and inverting a Fresnel diffraction equation by a phase retrieval process can yield a complete reconstruction of the silhouette of the occluder. The effect of noise in the measurements is also discussed. A practical example applied to the asteroid 25143 Itokawa is shown.

Here, the possibility of a noniterative solution to the phase retrieval problem is explored. A new look is taken at the phase retrieval problem that reveals that knowledge of a diffraction pattern's frequency components is enough to recover the image without projective iterations. This occurs when the image is formed using Gaussian bases that give the convenience of a continuous Fourier transform existing in a compact form where square pixels do not. The Gaussian bases are appropriate when circular apertures are used to detect the diffraction pattern because of their optical transfer functions, as discussed briefly. An algorithm is derived that is capable of recovering an image formed by Gaussian bases from only the Fourier transform's modulus, without background constraints. A practical example is shown.

Here the effect of noisy measurement data is explored within the traditional phase retrieval problem with the goal of filtering the noise to obtain an estimate of the true data. The method proposed can be applied to most existing phase retrieval methods.

Here we focus on the stability and dynamic characteristics of a rectangular, liquid-filled vessel. The position vector of the center of gravity of the liquid volume is derived and used to express the equilibrium angles of the vessel. Analysis of the potential function determines the stability of these equilibria, and bifurcation diagrams are constructed to demonstrate the co-existence of several equilibrium configurations of the vessel. To validate the results, a vessel of rectangular cross section was built. The results of the experiments agree well with the theoretical predictions of stability. The dynamics of the unforced and forced systems with a threshold constraint is discussed in the context of the nonlinear Mathieu equation.

Here a modification to the hybrid input-output (HIO) method of phase retrieval is presented which aides in mitigating the negative effects of low signal-to-noise ratios (SNRs). Various type of interferometers measure diffraction patterns which are used to determine the Fourier transform modulus of an objective. Interferometry often suffers from very low SNRs making phase retrieval difficult because of the sensitivity of most phase retrieval algorithms to local minima. Here we analyze the effect of noise on the HIO method. The result is used as a rationale for the proposed modification to the HIO method. The algorithm presented here introduces a filtering scheme which removes much of the Fourier modulus noise. Examples are shown and the results are compared to the HIO method with and without the proposed modification. Comparisons are also made to other methods of filtering the Fourier modulus noise.