Computational Depth from Defocus via Active Quasi-random Pattern Projections

Depth information is one of the most fundamental cues in interpreting the geometric relationship of objects. It enables machines and robots to perceive the world in 3D and allows them to understand the environment far beyond 2D images. Recovering the depth information of the scene plays a crucial role in computer vision, and hence has a strong connection with many applications in the fields such as robotics, autonomous driving and computer-human interfacing. In this thesis, we proposed, designed, and built a comprehensive system for depth estimation from a single camera capture by leveraging the camera response to the defocus effect of the projected pattern. This approach is fundamentally driven by the concept of active depth from defocus (DfD) which recovers depth by analyzing the defocus effect of the projected pattern at different depth levels as appeared in the captured images. While current active DfD approaches are able to provide high accuracy, they rely on specialized setups to obtain images with different defocus levels, making it impractical for a simple and compact depth-sensing system with a small form factor. The main contribution of this thesis is the use of computational modelling techniques to characterize the camera defocus response of the projection pattern at different depth levels, a new approach in active DfD that enables rapid and accurate depth inference in the absence of complex hardware and extensive computing resources. Specifically, different statistical estimation methods are proposed to approximate the pixel intensity distribution of the projected pattern as measured by the camera sensor, a learning process that essentially summarizes the defocus effect to a handful of optimized, distinctive values. As a result, the blurring appearance of the projected pattern at each depth level is represented by depth features in a computational depth inference model. In the proposed framework, the scene is actively illuminated with a unique quasi-random projection pattern, and a conventional RGB camera is used to acquire an image of the scene. The depth map of the scene can then be recovered by studying the depth feature in the captured image of the blurred projection pattern using the proposed computational depth inference model. To verify the efficacy of the proposed depth estimation approach, quantitative and qualitative experiments are performed on test scenes with different structural characteristics. The results demonstrate that the proposed method can produce accurate depth reconstruction results with high fidelity and has strong potential as a cost effective and computationally efficient mean of generating depth maps

Analysis of and techniques for adaptive equalization for underwater acoustic communication

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2011Underwater wireless communication is quickly becoming a necessity for applications in ocean science, defense, and homeland security. Acoustics remains the only practical means of accomplishing long-range communication in the ocean. The acoustic communication channel is fraught with difficulties including limited available bandwidth, long delay-spread, time-variability, and Doppler spreading. These difficulties reduce the reliability of the communication system and make high data-rate communication challenging. Adaptive decision feedback equalization is a common method to compensate for distortions introduced by the underwater acoustic channel. Limited work has been done thus far to introduce the physics of the underwater channel into improving and better understanding the operation of a decision feedback equalizer. This thesis examines how to use physical models to improve the reliability and reduce the computational complexity of the decision feedback equalizer. The specific topics covered by this work are: how to handle channel estimation errors for the time varying channel, how to use angular constraints imposed by the environment into an array receiver, what happens when there is a mismatch between the true channel order and the estimated channel order, and why there is a performance difference between the direct adaptation and channel estimation based methods for computing the equalizer coefficients. For each of these topics, algorithms are provided that help create a more robust equalizer with lower computational complexity for the underwater channel.This work would not have been possible without support from the O ce of Naval Research, through a Special Research Award in Acoustics Graduate Fellowship (ONR Grant #N00014-09-1-0540), with additional support from ONR Grant #N00014-05- 10085 and ONR Grant #N00014-07-10184

Design, Analysis, And Optimization Of Diffractive Optical Elements Under High Numerical Aperture Focusing

The demand for high optical resolution has brought researchers to explore the use of beam shaping diffractive optical elements (DOEs) for improving performance of high numerical aperture (NA) optical systems. DOEs can be designed to modulate the amplitude, phase and/or polarization of a laser beam such that it focuses into a targeted irradiance distribution, or point spread function (PSF). The focused PSF can be reshaped in both the transverse focal plane and along the optical axis. Optical lithography, microscopy and direct laser writing are but a few of the many applications in which a properly designed DOE can significantly improve optical performance of the system. Designing DOEs for use in high-NA applications is complicated by electric field depolarization that occurs with tight focusing. The linear polarization of off-axis rays is tilted upon refraction towards the focal point, generating additional transverse and longitudinal polarization components. These additional field components contribute significantly to the shape of the PSF under tight focusing and cannot be neglected as in scalar diffraction theory. The PSF can be modeled more rigorously using the electromagnetic diffraction integrals derived by Wolf, which account for the full vector character of the field. In this work, optimization algorithms based on vector diffraction theory were developed for designing DOEs that reshape the PSF of a 1.4-NA objective lens. The optimization techniques include simple exhaustive search, iterative optimization (Method of Generalized Projections), and evolutionary computation (Particle Swarm Optimization). DOE designs were obtained that can reshape either the transverse PSF or the irradiance distribution along the optical axis. In one example of transverse beam shaping, all polarization components were simultaneously reshaped so their vector addition generates a focused flat-top square irradiance pattern. Other designs were obtained that can be used to narrow the axial irradiance distribution, giving a focused beam that is superresolved relative to the diffraction limit. In addition to theory, experimental studies were undertaken that include (1) fabricating an axially superresolving DOE, (2) incorporating the DOE into the optical setup, (3) imaging the focused PSF, and (4) measuring aberrations in the objective lens to study how these affect performance of the DOE

A Focusing Method in the Calibration Process of Image Sensors Based on IOFBs

A focusing procedure in the calibration process of image sensors based on Incoherent Optical Fiber Bundles (IOFBs) is described using the information extracted from fibers. These procedures differ from any other currently known focusing method due to the non spatial in-out correspondence between fibers, which produces a natural codification of the image to transmit. Focus measuring is essential prior to carrying out calibration in order to guarantee accurate processing and decoding. Four algorithms have been developed to estimate the focus measure; two methods based on mean grey level, and the other two based on variance. In this paper, a few simple focus measures are defined and compared. Some experimental results referred to the focus measure and the accuracy of the developed methods are discussed in order to demonstrate its effectiveness

Capacity and mutual information of wideband multipath fading channels

We investigate the capacity and mutual information of a broadband fading channel consisting of a finite number of time-varying paths. We show that the capacity of the channel in the wideband limit is the same as that of a wideband Gaussian channel with the same average received power. However, the input signals needed to achieve the capacity must be “peaky” in time or frequency. In particular, we show that if white-like signals are used instead (as is common in spread-spectrum systems), the mutual information is inversely proportional to the number of resolvable paths L˜ with energy spread out, and in fact approaches 0 as the number of paths gets large. This is true even when the paths are assumed to be tracked perfectly at the receiver. A critical parameter L˜crit is defined in terms of system parameters to delineate the threshold on L over which such overspreading phenomenon occurs

Detection and classification of vibrating objects in SAR images

The vibratory response of buildings and machines contains key information that can be exploited to infer their operating conditions and to diagnose failures. Furthermore, since vibration signatures observed from the exterior surfaces of structures are intrinsically linked to the type of machinery operating inside of them, the ability to monitor vibrations remotely can enable the detection and identification of the machinery. This dissertation focuses on developing novel techniques for the detection and M-ary classification of vibrating objects in SAR images. The work performed in this dissertation is conducted around three central claims. First, the non-linear transformation that the micro-Doppler return of a vibrating object suffers through SAR sensing does not destroy its information. Second, the instantaneous frequency (IF) of the SAR signal has sufficient information to characterize vibrating objects. Third, it is possible to develop a detection model that encompasses multiple scenarios including both mono-component and multi-component vibrating objects immersed in noise and clutter. In order to cement these claims, two different detection and classification methodologies are investigated. The first methodology is data-driven and utilizes features extracted with the help of the discrete fractional Fourier transform (DFRFT) to feed machine-learning algorithms (MLAs). Specifically, the DFRFT is applied to the IF of the slow-time SAR data, which is reconstructed using techniques of time-frequency analysis. The second methodology is model-based and employs a probabilistic model of the SAR slow-time signal, the Karhunen-Loève transform (KLT), and a likelihood-based decision function. The performance of the two proposed methodologies is characterized using simulated data as well as real SAR data. The suitability of SAR for sensing vibrations is demonstrated by showing that the separability of different classes of vibrating objects is preserved even after non-linear SAR processing Finally, the proposed algorithms are studied when the range-compressed phase-history data is contaminated with noise and clutter. The results show that the proposed methodologies yields reliable results for signal-to-noise ratios (SNRs) and signal-to-clutter ratios (SCRs) greater than -5 dB. This requirement is relaxed to SNRs and SCRs greater than -10 dB when the range-compressed phase-history data is pre-processed with the Hankel rank reduction (HRR) clutter-suppression technique