Bayesian state estimators use both noisy measurement data and prior knowledge about the stochastic dynamics of a system to make an inference about the true value of the state. A Kalman filter applies Bayesian estimation for linear dynamics over discrete time steps to estimate a state over time. However, the Kalman filter assumes the state to be a normal (Gaussian) distribution, a light tailed distribution, and thus is inadequate for systems with heavy-tailed noise, or those with higher probability of data distributed towards the tails of the probability density function. Thus, the analytic and recursive Cauchy estimator was developed basing the (modeled) noises on the heavy-tailed Cauchy distribution. Because the amount of memory required for the Cauchy estimator grows indefinitely with each discrete time step, a sliding window approximation was implemented to ensure an estimator with a fixed amount of memory could be made at any given time step. This windowed Cauchy algorithm was tested on a nonlinear three-state model of a homing missile with radar measurement. When the algorithm was used to estimate the position, relative velocity, and target acceleration of the missile over time, it was found to significantly outperform the Kalman filter. Because larger window sizes require more computation and memory, different window sizes were tested against each other. Little significant decrease in estimation accuracy was measured at smaller window sizes, thus implying that the windowed Cauchy filter can practically be applied without excessive computational power.

Optics research and applications often require accurate and precise measurements of the power, time-of-flight, or spectral content of a laser. Examples of this include lidar, spectroscopy or supercontinuum (SC) generation, a nonlinear optical process in which a short pulse laser experiences extreme spectral broadening after passing through a material. Current data acquisition systems for spectral measurements operate at an acquisition rate of around 1 Hz using a monochromator, photodetector, and oscilloscope. High speed data acquisition systems must be implemented to accurately measure the spectral content of lasers operating at a repetition rate of 1 kHz. We created a mock-up experimental setup with a variable pulse length 656.6 nm diode laser to focus on automating the spectral data collection process. Communication with the oscilloscope and monochromator was accomplished by Python code. We produced an acquisition rate of around 50 Hz, the maximum frequency before the oscilloscope collected repeated values. We tested the data acquisition framework by first mapping the spectrum of the diode laser to determine its central wavelength and bandwidth. Then, we measured spectra consisting of multiple diffraction orders over a wide range of grating angles. Future steps will focus on implementing the automated data collection process in experiments in the mid-infrared spectral range.

Free Electron Light Sources (FEL) create intense bursts of x-rays that are millionths of a billionth of a second long, enabling unprecedented scientific discoveries: capturing the birth of chemical bonds, creating images of biological models, studying diseases, and much more. Access to FELs is limited, however, because there are few FELs in the world; current machines are very expensive (>$1B) and very long (>1km). This project aims to address both these challenges, and thus increase access, by further developing short-period undulators. The undulator is composed of alternating magnetic fields that transversely accelerate an electron beam as it travels, which generates the x-rays. Shortening the undulator period lowers the required electron beam energy to obtain a given photon wavelength, which in turn reduces the length and cost of the electron accelerator. Conventional undulators used in XFELs have period lengths around 3 cm; we designed undulators with periods of 3 and 6 mm, a 10x reduction, which would result in an accelerator length reduction of ~68%. Out of the three designs tested, simple, Halbach, and hybrid, the hybrid has the strongest field but also the highest likelihood of unacceptable field variation due to material inhomogeneities. To address this, we developed a novel method of shimming, or local magnetic field adjustment, that works within tight space constraints. Successful development of such strategies for short-period undulators has the potential to transform the field of light sources: democratizing access to discover the world on an atomic scale.

X-ray free-electron lasers (XFELs) produce short, high-energy pulses of X-ray radiation by wiggling a beam of relativistic electrons through a magnetic array called an undulator. While these distinctly powerful X-ray pulses enable unprecedented research in a broad range of fields, XFELs are large, cost billions of dollars, and are only able to serve a few experiments at time, resulting in severely limited facility access. So-called “short-period” undulators have the potential to reduce the cost and size of an XFEL; however, these tend to be drastically less efficient than undulators with longer periods. One way to target this inefficiency is by focusing the electron beam as it passes through the undulator. This increases the efficiency of the FEL process, leading to a shorter overall undulator length and higher photon beam power, but previous techniques employing permanent magnets are not tunable and difficult to manufacture and align. We propose using copper current sheets instead, which are both tunable and simple to install. In this experiment, we investigate the practicality of this design through simulation and modeling. Our results illustrate the optimum width of current sheet at 4.75 mm for our chosen gap height of 2.5 mm, creating a “good field” region 2.4 mm wide while maintaining a gradient of 0.25 T/m at a small current density of 1.92e7 A/m^2. The gradient could reasonably be increased by two or three orders of magnitude with larger currents, commensurate with desired gradient levels in upcoming FELs.

Securely identifying an electronic device can be extremely difficult. The majority of current solutions, such as RFIDs or printed barcodes are either too expensive to use at industrial scale, or too easy to spoof and therefore insecure. Due to these limitations, finding an alternative that fulfills both criteria is highly desired. Electromagnetic emissions have been proven to be unique enough to identify individual devices from one another, and add no extra cost to device manufacturing. However, it has yet to be shown that it is possible to identify devices at extended ranges, especially when such devices do not have wireless transceivers. We show that by analyzing the emanations for common features across device types while still retaining individuality, it is possible to recover enough data at range (>1 meter) to uniquely identify separate devices. Electromagnetic emissions from several devices in various states (idle, running programs) were obtained using a USRP Software-Defined Radio and GNURadio. This data was then processed in MATLAB to extract useful features that are both unique and consistent over time, for usage in feature based classification models. These features were then supplied to a Random Forest classifier to identify specific devices. Initial results from the model show that it is possible to identify devices at 1 meter of range with a success rate of 91%. Therefore, our feature-based model is able to determine not only the type of the device in range but also the exact individual device, demonstrating the feasibility of this method for secure identification.