Reconstruction of continuous signals from a number of their discrete samples is central to digital signal processing. Digital devices can only process discrete data and thus processing the continuous signals requires discretization. After discretization, possibility of unique reconstruction of the source signals from their samples is crucial. The classical sampling theory provides bounds on the sampling rate for unique source reconstruction, known as the Nyquist sampling rate. Recently a new sampling scheme, Compressive Sensing (CS), has been formulated for sparse signals. CS is an active area of research in signal processing. It has revolutionized the classical sampling theorems and has provided a new scheme to sample and reconstruct sparse signals uniquely, below Nyquist sampling rates. A signal is called (approximately) sparse when a relatively large number of its elements are (approximately) equal to zero. For the class of sparse signals, sparsity can be viewed as prior information about the source signal. CS has found numerous applications and has improved some image acquisition devices. Interesting instances of CS can happen, when apart from sparsity, side information is available about the source signals. The side information can be about the source structure, distribution, etc. Such cases can be viewed as extensions of the classical CS. In such cases we are interested in incorporating the side information to either improve the quality of the source reconstruction or decrease the number of the required samples for accurate reconstruction. A general CS problem can be transformed to an equivalent optimization problem. In this thesis, a special case of CS with side information about the feasible region of the equivalent optimization problem is studied. It is shown that in such cases uniqueness and stability of the equivalent optimization problem still holds. Then, an efficient reconstruction method is proposed. To demonstrate the practical value of the proposed scheme, the algorithm is applied on two real world applications: image deblurring in optical imaging and surface reconstruction in the gradient field. Experimental results are provided to further investigate and confirm the effectiveness and usefulness of the proposed scheme.

Fabry-Pérot (FP) filters are widely used in telecommunications, lasers and spectroscopy to measure the wavelengths of light. The properties of a FP filter depend on the wavelength and incident angle of the light source, the thickness of the etalon and the refractive index of the material between the reflecting surfaces. In previous studies, the nematic liquid crystal (NLC) is employed as the medium of FP filters because of its simple structure and ease of modulation. The directors of the NLC could be rotated by applying an electric field. Due to the birefringence of the NLC, the optical characteristics of the device are polarization dependent. Blue phase liquid crystal (BPLC) is the phase between cholesteric phase and isotropic phase. It¡¦s an optically isotropic material can function as an active index-tuning material adopted in a FP filter, and the characteristics of the BPLC-based FP filter are polarization independent. By applying an electric field, the Kerr effect can be induced due to the local reorientation of liquid crystals in BP structure, leading to the effective index change of BPLC and the transmission peak shifts. Furthermore, the effective index of BPLC approaches the ordinary index of host LCs under increasing electric fields. In addition, the BPLC using polymer network construction can be stabilized in room temperature and improves the convenience of the device. According to the experimental results, the tunability of the BPLC-based FP filter is about 1nm/V. The measured response time of the BPLC-based FP filter is 1ms.

It is well known that thermally evaporated a-As2S3 thin films are prone to oxidation when exposed to an ambient environment. These As2O3 crystals are a major source of scattering loss in sub-micron optical integrated circuits. Magnetron sputtering a-As2S3 not only produces films that have optical properties closer to their equilibrium state, the as-deposited films also show no signs of photo-decomposed As2O3. The TM propagation loss of the as-deposited As2S3-on-Ti:LiNbO3 waveguide is 0.20 plus/minus 0.05 dB/cm, and it is the first low loss hybrid waveguide demonstration. Using the recipe developed for sputtering As2S3, a hybrid Mach-Zehnder interferometer has been fabricated. This allows us to measure the group index of the integrated As2S3 waveguide and use it in the study of the group velocity dispersion in the sputtered film, as both material dispersion and waveguide dispersion may be present in the system. The average group index of the integrated As2S3 waveguide is 2.36 plus/minus 0.01. On-chip optical amplification was achieved through thermal diffusion of erbium into X-cut LiNbO3. The net gain measured for a transverse magnetic propagation mode in an 11 μm wide Er:Ti:LiNbO3 waveguide amplifier is 2.3 dB plus/minus 0.1 dB, and its on-chip gain is 1.2 plus/minus 0.1 dB/cm. The internal gain measured for a transverse electric propagation in an 7 μm wide Er:Ti:LiNbO3 waveguide amplifier is 1.8 dB plus/minus 0.1 dB and is among the highest reported in the literature. These gains were obtained with two 1488 nm lasers at a combined pump power of 182mW. In order to increase further the on-chip gain, we have to improve the mode overlap between the pump and the signal. This can be done by doping erbium into As2S3 film using multi-layer magnetron sputtering. The Rutherford backscattering spectroscopy shows that the doping of Er:As2S3 film with 16 layers of erbium is homogeneous, and Raman spectroscopy confirms no significant amount of Er-S clusters in the sputtered film. The deposition method was used to fabricate an Er:As2S3 waveguide, and the presence of active erbium ions in the waveguide is evident from the green luminescence it emitted when it was pumped by 1488 nm diode laser.

Organic polymer materials have been broadly applied in optical storage, optical communication and optical signal process. It has been revealed that these organic materials have some superior characteristics such as larger electro-optical (EO) coefficients, broader bandwidth and shorter response time, which make it good for EO modulator application. In our study, the goal is to study the EO coefficient of novel polymer material to be used in low driving voltage EO modulator. During the experiment, the dependence of the second harmonic generation (SHG) intensity on doping concentration of DR1/PMMA was observed and a reasonable explanation of the nonlinear dependency was given. We measured the EO coefficient of a new material, ASF/PMMA, using a Mach-Zehnder interferometer. We also observed the relaxation process of SHG intensity of this new material, which was compared with that of DR1/PMMA. Under the same measurement condition, we found that the EO coefficient of ASF/PMMA (13.1 pm/V) is significantly larger than that of DR1/PMMA (3 pm/V). It is also found that relaxation time of ASF/PMMA and DR1/PMMA are 22 and 8.5 seconds, respectively. Because of the superior characteristics of this material, it is suitable to be used in EO modulator.

In the paper, the beam propagation method is used to analyze the characteristics and the applications of nonlinear optical waveguide structures. The nonlinear optical waveguide is a medium whose refractive index changes with the electric field intensity. Based on the mode theory, the propagating envelop of optical light waves in the three-layers nonlinear waveguide with the nonlinear cladding, the nonlinear substrate and the linear guiding film can be solved. Not only the dispersion relation curve is described, but also the affection of input power to the electric field distribution is observed. In the application of nonlinear optical waveguide structure, the three-layers nonlinear waveguide structure and the local nonlinear Mach-Zehnder waveguide interferometer structure will be discussed: In the three-layers nonlinear waveguide structure, by launching the symmetric and antisymmetric modes, various characteristics of spatial optical solitons will be observed. Based on the interaction property between spatial optical solitons, a new all-optical 1¡ÑN switching device will be proposed; In the local nonlinear Mach-Zehnder waveguide interferometer structure, by fixing the input signal power and changing the control power, output signal beam will show the switching property. Besides, by changing the local nonlinear distributions, the nonlinear Mach-Zehnder interferometer will show various logic functions. The numerical results show that the proposed structures could function as all-optical switch devices and all-optical logic gates.

New millimeter wave interferometric, multifunctional sensors have been studied for industrial sensing applications: displacement measurement, liquid-level gauging and velocimetry. Two types of configuration were investigated to implement the sensor: homodyne and double-channel homodyne. Both sensors were integrated on planar structure using MMIC (Microwave Monolithic Integrated Circuit) and MIC (Microwave Integrated Circuit) technology for light, compact, and low-cost design. The displacement measurement results employing homodyne configuration show that sub-millimeter resolution in the order of 0.05 mm is feasible without correcting the non-linear phase response of the quadrature mixer. The double-channel homodyne configuration is proposed to suppress the nonlinearity of the quadrature mixer and to estimate the effect of frequency stability of a microwave signal source without the help of additional test equipment, at the loss of a slight increase of circuit complexity. The digital quadrature mixer is constituted by a quadrature-sampling signal processing technique and takes an important role in the elimination of conventional quadrature mixer's nonlinear phase response. Also, in the same displacement measurement, the radar sensor with the double-channel homodyne configuration provided a better resolution of 0.01mm, the best-reported resolution to date in terms of wavelength in the millimeter wave range, than the sensor employing simple homodyne configuration. Short-term stability of a microwave signal source, which is an important issue in phase sensitive measurement, is also considered through phase noise spectrum obtained by FFT spectral estimator at Intermediate Frequency (IF). The developed sensors demonstrate that displacement sensing with micron resolution and accuracy and high-resolution low-velocity measurement are feasible using millimeter-wave interferometer, which is attractive not only for displacement and velocity measurement, but also for other industrial sensing applications requiring very fine resolution and accuracy.

This research represents the first effort to apply vertical cavity surface emitting lasers (VCSELs) to the monitoring of interferometric fiber optic sensors. Modulation of the drive current causes thermal tuning of the laser light frequency. Reflection of this frequency-modulated light from a fiber Fabry-Perot interferometer (FFPI) sensor produces fringe patterns which can be used to measure the optical path difference of the sensor. Spectral characteristics were measured for 850nm VCSELs to determine the combination of dc bias current, modulation current amplitude and modulation frequency for which single mode VCSEL operation and regular fringe patterns are achieved. The response characteristics of FFPI sensors were determined experimentally for square, triangular, saw-tooth waveforms at frequencies from 10kHz to 100kHz. The dependence of VCSEL frequency on the dc bias current was determined from spectral measurements to be ~165GHz/mA. An independent measurement of this quantity based on counting fringes from the FFPI sensor as the laser modulated was in good agreement with this value. The effect of optical feedback into the laser was also studied. By observing the fringe shift as the FFPI sensor was heated, a fractional change in optical length with temperature of 6.95 X 10-6/°C was determined in good agreement with previous measurements on a 1300nm single mode fiber. The performance of 850nm VCSEL/FFPI systems was compared with their counterparts using 1300nm distributed feedback (DFB) lasers. The results of these experiments show that the 850nm VCSEL/FFPI combination gives regular fringe patterns at much lower bias current and modulating current amplitudes than their 1300nm DFB/FFPI counterparts.

A large multi-aperture telescope has the potential to reach the diffraction limit corresponding to its baseline. To do so, Adaptive Optics (AO) and beam combination are critical to good performance. Operation as an interferometer is a complicated mode for the telescope. The system now has much tighter tolerances and is difficult to align. The alignment process needs to be planned in multiple steps, and tolerance and sensitivity analysis needs to be performed for each step. Alignment tools can be prepared based on the resolution found in the sensitivity analysis in each step. Random fluctuation is another critical factor that reduces system performance. If noise sources near the telescope are characterized and identified, image quality can be improved by post-image processing. Measuring the outer scale of atmosphere is also helpful for understanding the system performance. The fringe tracking method in the Large Binocular Telescope Interferometer (LBTI) system provides optical path difference (OPD) variation, and the power spectral density of the OPD variation is used to estimate the size of the outer scale. However, this method is limited by the baseline of the LBTI by 5√3 B, where B is the baseline, and by this equation the outer scale size which is able to be estimated should be more than 125 m. AO simulation can provide an understanding of new AO system concepts and parameter variations before they are applied to the real system. In this dissertation study, we simulated an LBTI system with structural vibration of 10 Hz and 20 Hz and with various amplitudes. From the simulation, we learned that the slower bandwidth of piston-correcting systems allows stars as faint as ~13the magnitude to be observed. If there is significant vibration on the structure, the increased bandwidth will limit the phasing stars to 10~11th magnitudes. This demonstrates the limits of the LBTI system regarding structural vibration. An alternative phasing sensor for the LBTI system, the pseudo phasing sensor, can be used for more than 1000 m of outer scale of atmosphere. If the direct phasing sensor embedded in the LBTI system cannot be used for a very faint star, the pseudo phasing sensor, which approximately estimates the phase difference by AO wavefront sensor, can be useful for atmospheric conditions with estimated outer scale of about 1000 m. The analyses in this dissertation provide a partial guide for developing large-scale telescopes and astronomical instruments.

High-precision optical systems are generally tested using interferometry, since it often is the only way to achieve the desired measurement precision and accuracy. Interferometers can generally measure a surface to an accuracy of one hundredth of a wave. In order to achieve an accuracy to the next order of magnitude, one thousandth of a wave, each error source in the measurement must be characterized and calibrated.Errors in interferometric measurements are classified into random errors and systematic errors. An approach to estimate random errors in the measurement is provided, based on the variation in the data. Systematic errors, such as retrace error, imaging distortion, and error due to diffraction effects, are also studied in this dissertation. Methods to estimate the first order geometric error and errors due to diffraction effects are presented.Interferometer phase modulation transfer function (MTF) is another intrinsic error. The phase MTF of an infrared interferometer is measured with a phase Siemens star, and a Wiener filter is designed to recover the middle spatial frequency information.Map registration is required when there are two maps tested in different systems and one of these two maps needs to be subtracted from the other. Incorrect mapping causes wavefront errors. A smoothing filter method is presented which can reduce the sensitivity to registration error and improve the overall measurement accuracy.Interferometric optical testing with computer-generated holograms (CGH) is widely used for measuring aspheric surfaces. The accuracy of the drawn pattern on a hologram decides the accuracy of the measurement. Uncertainties in the CGH manufacturing process introduce errors in holograms and then the generated wavefront. An optimal design of the CGH is provided which can reduce the sensitivity to fabrication errors and give good diffraction efficiency for both chrome-on-glass and phase etched CGHs.

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