DEVELOPMENT OF A VERSATILE HIGH SPEED NANOMETER LEVEL SCANNING MULTI-PROBE MICROSCOPE

The motivation for development of a multi-probe scanning microscope, presented in this dissertation, is to provide a versatile measurement tool mainly targeted for biological studies, especially on the mechanical and structural properties of an intracellular system. This instrument provides a real-time, three-dimensional (3D) scanning capability. It is capable of operating on feedback from multiple probes, and has an interface for confocal photo-detection of fluorescence-based and single molecule imaging sensitivity. The instrument platform is called a Scanning Multi-Probe Microscope (SMPM) and enables 45 microm by 45 microm by 10 microm navigation of specimen with simultaneous optical and mechanical probing with each probe location being adjustable for collocation or for probing with known probe separations. The 3D positioning stage where the specimen locates was designed to have nanometer resolution and repeatability at 10 Hz scan speed with either open loop or closed loop operating modes. The fine motion of the stage is comprises three orthogonal flexures driven by piezoelectric actuators via a lever linkage. The flexures design is able to scan in larger range especially in z axis and serial connection of the stages helps to minimize the coupling between x, y and z axes. Closed-loop control was realized by the capacitance gauges attached to a rectangular block mounted to the underside of the fine stage upon which the specimen is mounted. The stage's performance was studied theoretically and verified by experimental test. In a step response test and using a simple proportional and integral (PI) controller, standard deviations of 1.9 nm 1.8 nm and 0.41 nm in the x, y and z axes were observed after settling times of 5 ms and 20 ms for the x and y axes. Scanning and imaging of biological specimen and artifact grating are presented to demonstrate the system operation. For faster, short range scanning, novel ultra-fast fiber scanning system was integrated into the xyz fine stage to achieve a super precision dual scanning system. The initial design enables nanometer positioning resolution and runs at 100 Hz scan speed. Both scanning systems are capable of characterization using dimensional metrology tools. Additionally, because the high-bandwidth, ultra-fast scanning system operates through a novel optical attenuating lever, it is physically separate from the longer range scanner and thereby does not introduce additional positioning noise. The dual scanner provides a fine scanning mechanism at relatively low speed and large imaging area using the xyz stage, and focus on a smaller area of interested in a high speed by the ultra-fast scanner easily. Such functionality is beneficial for researchers to study intracellular dynamic motion which requires high speed imaging. Finally, two high end displacement sensor systems, a knife edge sensor and fiber interferometer, were demonstrated as sensing solutions for potential feedback tools to boost the precision and resolution performance of the SMPM

Image-Force-Stabilized Interfacial Dipole Layer Impedes Charge Injection into Disordered Organic Semiconductors

We show using three-dimensional kinetic Monte Carlo simulations that the injection of charge carriers from a metallic electrode into a disordered organic semiconductor is under nominally Ohmic injection conditions strongly impeded by the short-range Coulomb interactions between the charge carriers in the image-force-stabilized interfacial dipole layer. In contrast, master equation and conventional one-dimensional drift-diffusion simulations underestimate these Coulomb interactions due to their mean-field approximation, and are found not to reveal the effect. The simulations predict a reduction of the current density in organic semiconductor devices when the nominal injection barrier is taken very small or even negative, consistent with recent experimental results [Kotadiya et al., Nat. Mater. 17, 329 (2018)]. However, whereas in that work a modification of the energetic disorder near the interface is assumed, we find that the effect is already obtained after including charge-charge interactions beyond a one-dimensional and mean-field approximation. </p

Markov Inequalities for Polynomials with Restricted Coefficients

Essentially sharp Markov-type inequalities are known for various classes of polynomials with constraints including constraints of the coefficients of the polynomials. For and we introduce the class as the collection of all polynomials of the form , , , . In this paper, we prove essentially sharp Markov-type inequalities for polynomials from the classes on . Our main result shows that the Markov factor valid for all polynomials of degree at most on improves to for polynomials in the classes on .</p

Strong Converse Inequality for a Spherical Operator

<p/> <p>In the paper titled as "Jackson-type inequality on the sphere" (2004), Ditzian introduced a spherical nonconvolution operator <inline-formula> <graphic file="1029-242X-2011-434175-i1.gif"/></inline-formula>, which played an important role in the proof of the well-known Jackson inequality for spherical harmonics. In this paper, we give the lower bound of approximation by this operator. Namely, we prove that there are constants <inline-formula> <graphic file="1029-242X-2011-434175-i2.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2011-434175-i3.gif"/></inline-formula> such that <inline-formula> <graphic file="1029-242X-2011-434175-i4.gif"/></inline-formula> for any <inline-formula> <graphic file="1029-242X-2011-434175-i5.gif"/></inline-formula>th Lebesgue integrable or continuous function <inline-formula> <graphic file="1029-242X-2011-434175-i6.gif"/></inline-formula> defined on the sphere, where <inline-formula> <graphic file="1029-242X-2011-434175-i7.gif"/></inline-formula> is the <inline-formula> <graphic file="1029-242X-2011-434175-i8.gif"/></inline-formula>th modulus of smoothness of <inline-formula> <graphic file="1029-242X-2011-434175-i9.gif"/></inline-formula>.</p

Consensus-Based Sequential Estimation of Process Parameters via Industrial Wireless Sensor Networks

Process parameter estimation, to a large extent, determines the industrial production quality. However, limited sensors can be deployed in a traditional wired manner, which results in poor process parameter estimation in hostile environments. Industrial wireless sensor networks (IWSNs) are techniques that enrich sampling points by flexible sensor deployment and then purify the target by collaborative signal denoising. In this paper, the process industry scenario is concerned, where the workpiece is transferred on the belt and the parameter estimate is required before entering into the next process stage. To this end, a consensus-based sequential estimation (CSE) framework is proposed which utilizes the co-design of IWSN and parameter state estimation. First, a group-based network deployment strategy, together with a TDMA (Time division multiple access)-based scheduling scheme is provided to track and sample the moving workpiece. Then, by matching to the tailored IWSN, the sequential estimation algorithm, which is based on the consensus-based Kalman estimation, is developed, and the optimal estimator that minimizes the mean-square error (MSE) is derived under the uncertain wireless communications. Finally, a case study on temperature estimation during the hot milling process is provided. The results show that the estimation error can be reduced to less than 3 ∘ C within a limited time period, although the measurement error can be more than 100 ∘ C in existing systems with a single-point temperature sensor