All-reflective imaging systems that are asymmetrical and eccentric have the advantage of providing more degrees of freedom to improve image quality. A disadvantage of these asymmetrical imaging systems is that they suffer from asymmetric mapping. This asymmetric mapping manifests itself mainly in the presence of keystone distortion and anamorphism. Due to the increase in degrees of freedom, the complexity of such systems escalates; thus, the designer is confronted with the difficult task of determining optimal starting points. This work addresses several first-order aspects of the design and characterisation of asymmetrical, all-reflective, aspherical, eccentric imaging systems. In contrast to the work of Stone and Forbes, which is based upon the theory of Hamiltonian optics and includes both the first- and second-order considerations, this work is based upon the theory of collineation. Because of the inherent simplicity of the collinear mapping, which is a projective transformation, we are able to present a simple but certainly not naive way of designing and characterising such asymmetrical all-reflective imaging systems. The simplicity of this proposition has the advantage that we can gain insights into asymmetrical mapping behaviour. Specifically, we apply the collinear mapping model on all-reflective asymmetrical imaging systems resulting in the description of how the mapping between conjugate planes may be described. First we will define keystone distortion and anamorphism. Then we will introduce and investigate the significance of the Cardinal points and planes, the Scheimpflug condition and the horizon planes and show how they are applied in the designing of imaging systems that are free of both keystone distortion and anamorphism. Having established a first-order layout of the optical system, we will then develop a process for converting the first-order layouts into imaging systems consisting of real aspheric surfaces.

Computer-generated holograms (CGHs) use diffraction to create wavefronts of light with desired amplitude and phase variations. The amplitude control is well known. But the sensitivity of phase, which is most important for some applications, such as interferometry, is less known. This dissertation studies phase errors resulted from design and fabrication limitations of CGHs. Fabrication uncertainties of CGHs are primarily responsible for the degradation of the quality of wavefronts generated by CGHs. In this dissertation, the binary linear diffraction model is introduced to study wavefront phase errors caused by substrate figure errors, pattern distortion, grating duty-cycle and etching depth errors. Wavefront sensitivity functions derived from diffraction model provide analytical solutions to estimate phase deviations due to duty-cycle or phase depth variations. The results of the wavefront sensitivity analysis also enable us to identify hologram structures that are the most sensitive, as well as the least sensitive to fabrication uncertainties. Experiments were conducted to validate the diffraction model. Example error budgets for common CGH optical testing configurations are demonstrated. In addition, a graphical representation of the diffraction fields is introduced. It provides an intuitive way for diffraction wavefront analysis and explains phase discontinuous observed in the diffraction model. Scalar diffraction models are commonly used in CGH analysis and modeling due to their computational simplicity compared with rigorous diffraction models. The validity of the scalar diffraction models becomes unclear when they are used to analyze diffractive elements with wavelength-scaled features. This dissertation discusses the validity of the scalar diffraction models with giving emphasis to wavefront phase. Fourier modal method (FMM) derived from rigorous diffraction theory is used to study a binary zone plate. The result of this analysis is compared with experimental data, This study shows that polarization sensitivities of the hologram are almost negligible for the chrome-on-glass zone plate with a minimum ring spacing of 2lambda. This result implies that scalar diffraction models may still be sufficient for modeling the phase from holograms with wavelength-scaled diffraction features for the case studied in this dissertation.

Amplitude stellar interferometry systems are often limited by signal-to-noise ratio. When the limiting noise is photon noise it is possible to increase the signal-to-noise ratio simply by increasing the observation time. When the source signal is extremely faint, the source signal may be overwhelmed by noises associated with the detection system. In these cases it is not possible to get an acceptable signal-to-noise ratio by increasing the observation time. It is for these faint object observations that the achromatic Michelson stellar interferometer (AMSI) is proposed. The AMSI uses N sub-systems, each sub-system being of the same design as a conventional Michelson stellar interferometer (MSI). The light from these N sub-systems is combined in such a way so as to produce a single set of "white light" fringes. By increasing the signal by a factor of N, the AMSI produces a significant increase in signal-to-noise ratio. This dissertation first presents the theory behind the conventional MSI. Results are given from tolerancing the conventional MSI. The tolerancing is performed both with a computer model and with parallel analytical calculations. A chart which summarizes the tolerance results is presented near the end of Chapter 4. The theory behind the AMSI is stated along with the limitations of this method. A method for extending the AMSI through spectral multiplexing is also given. Tolerancing of the AMSI is also performed, again using both a computer model and parallel calculations. The AMSI is found to provide an increase in detectability of faint sources provided that it can be supplied with an adequate fringe-locking system or used in a space-based environment.

In this work we present a non-iterative technique for computing the steady-state optical properties of nonlinear multilayers and we examine nonlinear multilayer designs for optical limiters. Optical limiters are filters with intensity-dependent transmission designed to curtail the transmission of incident light above a threshold irradiance value in order to protect optical sensors from damage due to intense light. Thin film multilayers composed of nonlinear materials exhibiting an intensity-dependent refractive index are used as the basis for optical limiter designs in order to enhance the nonlinear filter response by magnifying the electric field in the nonlinear materials through interference effects. The nonlinear multilayer designs considered in this work are based on linear optical interference filter designs which are selected for their spectral properties and electric field distributions. Quarter wave stacks and cavity filters are examined for their suitability as sensor protectors and their manufacturability. The underlying non-iterative technique used to calculate the optical response of these filters derives from recognizing that the multi-valued calculation of output irradiance as a function of incident irradiance may be turned into a single-valued calculation of incident irradiance as a function of output irradiance. Finally, the benefits and drawbacks of using nonlinear multilayer for optical limiting are examined and future research directions are proposed.

The work reported in this dissertation represents an investigation into some aspects of resonant and nonresonant light-matter interaction as experienced by femtosecond optical pulses. We look at the role of plasma generation via multi-photon ionization in the arrest of the 2-D collapse of femtosecond pulses governed by the nonlinear Schrodinger equation. First we studied the exciting new area of anomalous long-distance propagation of femtosecond optical pulses in the atmosphere. Our simulations do not support the existence of a stable pulse propagating through the air, but rather a dynamical picture involving several collapse events emerges. This investigation led us to consider the question of the role of pressure on the pulse propagation in gases. The pressure dependence of the collapse in Argon is discussed next, and we make the connection between the results obtained in crystals on one hand, and low-density gases on the other. An interesting behavior is observed for pressures at which the Kerr nonlinearity and plasma-induced defocusing are of the same order. Next, we investigate second harmonic generation of femtosecond pulses at the boundary of a nonlinear medium using the full vector Maxwell equations and simple phenomenological constitutive relations. We observe the initial pulse to split in time into two ultrashort pulses in the case of phase-mismatch. This phenomenon should be readily measured experimentally. The effect of low-frequency material dispersion and a possibility of "one-hump" pulsed solution is discussed. Finally, in the last chapter we investigate the resonant coupling of light to a semiconductor which is sensitive to the field polarization, using a many-body model for electronic structure. Pump-probe type experiments with copropagating, cross-polarized beams are considered, and we demonstrate theoretically the existence of an oscillating signal at twice the optical frequency in the probe transmission measurements. Our results show that the change of the interaction among the carriers leads to a phase shift of the oscillation pattern. We also know that such interaction depends on the intensity of light: The Coulomb screening is changed. Thus the phase shift contains information about the microscopic interaction among the carriers.

In any zoom lens, by virtue of the differential motions of lens groups, individual zoom groups experience both conjugate and pupil shifts during zooming. When using a modular design approach, in which lens groups are designed independently, one has to take into account the dynamic aberration matching among lens groups. Deliberate aberration can be introduced to zoom groups to produce an overall compensatory effect over the zoom range. Similarly perfect pupil matching among zoom groups cannot be maintained for a continuum of zoom positions. With the deliberate introduction of pupil aberration on the group level, compensatory effects can be obtained and a more desirable pupil match can be achieved, resulting in better stability of system image performance over the zoom range. The investigation presents a systematic explanation of how intrinsic lens group aberration contents can affect the overall aberrational behavior of mechanically compensated zoom systems. Particularly, the investigation centers around the explicit use of lens group pupil spherical aberration in controlling residual aberrations in zoom lenses. The study explores its capability in controlling the variation of distortion, which is often the dominant residual aberration in zoom systems. Different techniques for implementing explicit pupil spherical aberration control are also explored. The method employed in the study involves the use of black box lens modules. Lens groups are represented by mathematical constructs instead of actual constructional parameters in which individual lens group aberration contents can be manipulated directly. Instead of attempting to model the zoom lens problem analytically, actual ray trace results and well proven facts in aberration theory are relied upon. The method is to use ray trace experiments to substantiate the empirical arguments. Several zoom lens configurations are selected and converted into lens module equivalents. The optimum intrinsic lens group aberration contents are found using global optimization techniques. The aberration behavioral trends are then gathered and the connections between optimum lens group aberration contents and system aberrational behavior are observed. Conclusions are drawn based on the observations and well established results in aberration theory.

The properties of fiber Bragg gratings are investigated theoretically and experimentally. The effects of experimental parameters on grating characteristics are modeled for both uniform and non-uniform gratings. Particular emphasis is placed on the formation of fiber Bragg gratings tilted at 45 degrees with respect to the fiber axis in single mode fibers. In this case, light is coupled out of the fiber in a surface normal manner. Several fabrication methods for producing tilted fiber gratings are explored and characterized. The most efficient gratings are obtained with a prism coupling technique. Experimental tilted grating performance is shown to be in good agreement with the predictions of a two-dimensional coupled mode theory. Fiber gratings are also used to demonstrate an Er/Nd co-doped fiber laser. This dual wavelength laser is formed with a common cavity and common gain medium.

A novel imaging ellipsometer has been developed; the phase shifting interferometric imaging ellipsometer (PSIIE) is the first ellipsometer to use phase-shifting interferometry for data acquisition. The only moving part in the system is a solid state PZT. The PSIIE uses a polarization interferometer, followed by a Wollaston prism, to obtain simultaneously, samples of the S and P polarization component interferograms. Interferogram. phase yields the ellipsometric parameter, Δ, while the fringe modulation yields the tangent of the ellipsometric parameter Ψ. The instrument can perform multiple wavelength and multiple angle-of-incidence ellipsometry over the entire visible range with the addition of a tunable laser source. Repeatability of the prototype instrument approaches 0.15° for the measurement of Δ, and 0.4° for Ψ. Absolute accuracies are 1° for Δ and Ψ. Calculations indicate that hardware and software improvements would achieve a precision and absolute accuracy below 0.1°.

Volume holographic data storage uses the superposition of image holograms in a suitable medium to pursue large storage capacity and high readout rates. The holographic method of structuring the medium with data, and subsequent readout of those data structures, relies on an optical system with two distinct paths. The object path is typically a 4F system relaying a high space-bandwidth-product object to an image plane with the storage medium placed near the Fourier plane. Optical system parallelism, measured by space-bandwidth-produce, promotes both storage capacity and readout rate. The reference path is typically a relay with the field stop placed near the center of the storage material. We will consider how the properties of the object path optical system affect the storage capacity and readout rate. We will demonstrate that the object beam 4F system can be optimized for the particular requirements of volume holographic storage, and that relatively simple optical systems can provide high parallelism. We will also consider the optical parallelism possible for standard optical disk storage, and how these results compare to volume holographic storage. Finally, we will consider how the optical system of the reference path affects the storage capacity. We find that modifications to the reference beam, or apodization, can substantially mitigate the effects of interpage crosstalk, a fundamental noise source in volume holographic storage.

When a bar code symbol is passed over a scanner, it is struck across by a fast moving laser beam. The laser light is scattered by the bar code. The total scattered power is modulated by the reflectivity of the bars and spaces in the symbol. A fraction of the scattered light is collected and focused onto a photodetector that converts the light variation into an electronic signal. The electronic signal is then digitized for analysis by a computer. The scanning and detection process can be modeled by a convolution of the laser beam profile and the bar code reflectivity function. The switching between states in the digitized bar code signal, which represents transitions from a space to a bar or vice versa, is determined by a zero-crossing point in the second derivative of the analog signal. The laser profile acts like a smoothing function. It blurs the analog electronic signal. If the width of the laser profile is less than the minimum width of bars and spaces in the bar code reflectivity function, the transition point is not affected by the location of its neighboring edges. If the laser profile is wider than the minimum width in the bar code, the transition point can be shifted due to the locations of its neighboring edges. The behavior of the shift of transition is analyzed here for all cases in a UPC symbol. It is found that the amount of shift in the transition point is almost the same for several different cases within the depth of field of the scanner. The knowledge of the behavior of transition point shift can be used to accurately compensate printing errors in an over-printed bar code. The modulation transfer function (MTF) of bar code scanning is the Fourier transform of the marginal function of the scanning laser beam. The MTF through focus for a scanning system is presented. By using an aperture with central obscuration in the laser focusing system, the high frequency resolution of bar code scanning can be enhanced and the depth of field of the scanner can be extended.