Advancements in the design, manufacturing and testing of optical systems have created the need for new functional representations for aspheric surfaces. The representations must define surfaces that can compensate for a high degree of wavefront asphericity and represent steeply sloped surfaces as the surface normal becomes perpendicular to the optical axis. As the standard asphere is explicitly defined, the range of surfaces that it can properly describe is limited. This work develops both a parametrically defined surface approach and an implicitly defined surface approach. Whereas the surface sag of an explicit surface is defined directly using one equation, the sag of a parametric surface is defined using at least two equations. The sag of an implicit surface is defined indirectly using a surface function. The utility of these novel approaches is demonstrated using examples of current interest. Specifically, a truncated parametric Taylor surface and an implicit xyz-polynomial surface are shown to be more general definitions that represent highly aspheric surfaces better the standard explicit asphere. Ray tracing and optimization strategies for parametric and implicit surface representations are discussed. Additionally, this work shows that a Fourier series is not a useful optical surface and introduces the explicit superconic surface, which is a redefinition of the standard superconic surface. Finally, we compare the surface types discussed for ray tracing speed, optimization complexity, and ability to represent highly aspheric surfaces.

The Optical Reference Profilometer is a new coordinate measurement machine (CMM) configuration that utilizes a special optical referencing frame to provide a highly stable and highly accurate surface measurement. This new referencing frame provides several mechanical advantages that make it possible to use lower precision mechanical components while still maintaining a high measurement accuracy. The Optical Reference Profilometer also provides a reduced measurement sensitivity to thermal variations of the system. With the addition a Super-Invar metering rod network, this CMM system is essentially thermally insensitive to temperature changes on the order of 1°C. This special feature makes the Optical Reference Profilometer functional at a high measurement accuracy level in an open lab environment. For the current dissertation work, two profilometer designs were built: a prototype and a second-generation system. A discussion of both systems will be given where the advantages of the optical reference frame design will be shown, This dissertation will end with a discussion of the overall system performance and plans for future work that would increase the overall system accuracy. The optical reference profilometer has proven to be a viable testing device. It provides a high accuracy surface measurement, 100nm peak-to-valley and 15nm rms for surface slopes up to 20 degrees, with simple mechanical structures while maintaining the versatility to measure a variety of surface shapes.

This dissertation is concerned with an image processing algorithm that performs image enhancement and restoration. Closed form maximum entropy filtering will be derived from its foundations in classical Wiener filtering and maximum entropy theory. Ad hoc variations of Wiener filtering will be introduced and discussed in terms of information density. The language of information density will be used to examine the entropy filter and its merits. These merits will be demonstrated through a series of numerical simulations of real and artificial astronomical objects. The results of these simulations will be shown to be a 7% to 50% improvement over the classical Wiener estimate. The closed form maximum entropy filter will be adapted to the blind deconvolution problem. A test pattern will be estimated to demonstrate the potential power of this adaptation.

In designing imaging optical systems, the primary task is to correct aberrations. Aberrations are deviations from perfect imagery. They depend on both the filed size and pupil position. When the Constant Optical Path Length (OPL) condition is satisfied, an optical system is free of all orders of spherical aberrations, which have zero field dependence. When the Abbe Sine condition is satisfied, all the aberrations with linear filed dependence are corrected. The Abbe Sine condition does not involve any off-axis ray properties, but it predicts the correction of off-axis aberrations. We go one step beyond the Constant OPL condition and the Abbe Sine condition. By using Hamilton's characteristic functions, we developed a set of criteria for correcting the aberrations with quadratic field dependence and all orders of pupil dependence. These criteria involve only properties of the rays originating from the on-axis object point as the Abbe Sine condition does. Using these criteria, we analyzed some known designs and obtained new information about these designs. We also developed an algorithm to implement the criteria in designing well-corrected novel optical systems. Even when the criteria are not exactly satisfied, we now have a way to predict the residual quadratic field-dependent aberrations without tracing rays from any off-axis object point. We extended the Hamiltonian treatment to bilateral systems and developed similar criteria for correcting the quadratic field-dependent aberrations for this type of system.

Channeled spectropolarimetry is a novel method of measuring the spectral dependence of the polarization state of light. Amplitude modulation is employed to encode all four Stokes component spectra into a single optical power spectrum. The encoding is performed with a simple arrangement of two thick birefringent retarders and a linear analyzer. No moving parts are required, and the system is able to acquire its data in a single detector array integration time. We report the results of an in-depth study of channeled spectropolarimetry. The mathematics of the amplitude modulation analogy are explored, providing a basic design procedure. The system's spectral resolution is described in terms of the space bandwidth product. The technique is then analyzed in the general context of linear operator theory, using both analytic and computational approaches to the singular value decomposition and pseudoinversion of the system's operator. This analysis highlights the importance of the choice of object space in constraining linear reconstructions of data from under-determined systems, and provides the underpinnings of the calibration and reconstruction techniques for a hardware prototype. Calibration of the prototype is approached as experimental estimation of the system's operator. Our basic method of reconstruction involves pseudoinversion of the operator while constraining object space to a truncated Fourier basis. Apodization is helpful in reducing the ringing of reconstructions of spectra which extend beyond the edges of the system's spectral range. Experimental results are presented, including comparisons between measurements taken with the channeled spectropolarimeter and a reference rotating compensator, fixed analyzer instrument. We have used measurements of the effects of stress birefringence on light propagated through material subject to time-varying stress to demonstrate time-resolved snapshot spectropolarimetry. Continuing efforts include the combination of channeled spectropolarimetry with computed tomography imaging spectrometry to realize a snapshot imaging spectropolarimeter.

The modes and beam characteristics of a Gaussian gain laser resonator are analyzed. Such a gain is typically associated with an end pumped solid state laser. The beam propagation method is used to find the eigenmodes. The eigenmodes are non Gaussian in appearance and differ greatly from the modes of the same cavity with a quadratic gain. It is found that the cavity geometry strongly influences mode formation around degenerate cavity geometries throughout a broad range of operational parameters. The beam propagation method is used to evolve the field through the resonator, resulting in computation of the nonorthogonal eigenmodes. This permits evaluation of the excess noise dependence on geometric cavity parameters such as length and focal length. It is shown that the beam quality M² and Petermann K factor are related and are anticorrelated at degeneracies. An explanation is given based on the self Fourier transforming properties of degenerate cavity locations. It is shown how the empty cavity properties of transverse mode degeneracies are not revealed with a quadratic gain, but are strikingly present with a Gaussian gain. A confocal cavity is studied in detail and found to have the property that forces K to unity even in the presence of strong gains and narrow pump widths. The interplay between the diffraction effects of a geometrically stable cavity and the Gaussian gain will be studied to reveal the nature and implications of the non-normal modes encountered.

The dissertation addresses advancements in null corrector design. The Rayces zero-index concept is validated and used to design null correctors in single pass. By using a doublet field lens in the standard Offner null corrector, the overall length and size of the null corrector are reduced. The Multi-Object Double Spectrograph (MODS) blue corrector study outlines the process associated with designing and producing a null corrector. A novel ghost image analysis technique is used to evaluate candidate MODS blue null corrector designs. Tolerance analysis is performed and manufacturing specifications are defined for the MODS blue null corrector. Several off-axis null corrector designs are investigated as potential solutions to test 8.4 m off-axis elements of a 25 m diameter parabola. The dissertation also addresses advancements in null corrector certification. Truncated-series solutions for diamond turned mirrors and computer generated hologram certifiers for aspheric surfaces that can be modeled in lens design code are derived. The truncated-series solutions are general and can be applied to most aspheric surfaces with only simple changes in coefficients. These equations are implemented in lens design code via the user defined surface (UDS). The process of implementing a UDS is outlined in the dissertation. Once a UDS is identified, a two-step design process is used to create the certifier. First, the corresponding Shack surface of the aspheric surface or surfaces under test must be defined. Second, a point source illuminates the mirrored Shack surface and a certifier is placed at, in, or outside the center of curvature of the Shack surface. Because the rays go back to a point source after reflection from the Shack surface, a standard merit function that minimizes RMS spot radius can be used to find the coefficients. Certifier surface solutions are presented at the center of curvature and inside the center of curvature of the Shack surface for a broad range of aspheric optics. The solution for a certifier outside of the center of curvature of a parabola's Shack surface is also provided.

This dissertation is devoted to the study of third-harmonic generation (THG) in push-pull chromophore-doped polymer films. This kind of films, with amorphous structure, exhibit null second harmonic generation but strong THG when pumped at the fundamental wavelengths within the telecommunication range (1.4-1.6 μm). It is demonstrated that at 1550 nm, micrometer-thick samples generate up to 17 muW of green light with an input power of 250 mW delivered by an optical parametric oscillator. This high conversion efficiency is achieved without the use of phase matching or cascading of quadratic nonlinear effects and it is due to high values of the third-order nonlinear susceptibility combined with weak film absorption at the third harmonic wavelength. The efficient THG process opens the doors to low cost and sensitive third-order optical autocorrelation and cross-correlation applications. So, in addition to the basic research performed about the characterization of the THG in push-pull chromophore-doped polymer films, two applications are demonstrated. The first is the complete diagnostic of femtosecond pulses by THG-Interferometric Autocorrelation and by THG Frequency-Resolved Optical Gating. The second is the THG-Cross-correlation Time-Gated Imaging of objects embedded in highly scattering conditions.

Crosstalk in the readout channel of a data storage system is obtained by a linear decomposition of the reflected field from the optical disk according to Babinet's principle. Crosstalk is the jitter introduced into the readout signal. Also, the formation of the exit pupil irradiance is described heuristically as the combination of fields in a three beam interferometer resulting from the Babinet decomposition of the reflected disk field. Three detector patterns result. The properties of the detector patterns are affected by media parameters. The media parameters are the reflectivity function of the disk and the depths of the tracking grooves. The detector patterns are also affected by the aberrations introduced into the read laser beam. This dissertation provides a complete description of crosstalk and the detection process in optical data storage systems.

The development of high power, high brightness semiconductor lasers is important for applications such as efficient pumping of fiber amplifiers and free space communication. The ability to couple directly into the core of a single-mode fiber can vastly increase the absorption of pump light. Further, the high mode-selectivity provided by unstable resonators accommodates single-mode operation to many times the threshold current level. The objective of this dissertation is to investigate a more efficient semiconductor-based unstable resonator design. The tapered unstable resonator laser consists of a single-mode ridge coupled to a tapered gain region. The ridge, aided by spoiling grooves, provides essential preparation of the fundamental mode, while the taper provides significant amplification and a large output mode. It is shown a laterally finite taper-side mirror (making the laser a "finite-aperture tapered unstable resonator laser") serves to significantly improve differential quantum efficiency. This results in the possibility for higher optical powers while still maintaining single-mode operation. Additionally, the advent of a detuned second order grating allows for a low divergent, quasicircular output beam emitted from the semiconductor surface, easing packaging tolerances, and making two dimensional integrated arrays possible. In this dissertation, theory, design, fabrication, and characterization are presented. Material theory is introduced, reviewing gain, carrier, and temperature effects on field propagation. Coupled-mode and coupled wave theory is reviewed to allow simulation of the passive grating. A numerical model is used to investigate laser design and optimization, and effects of finite-apertures are explored. A microfabrication method is introduced to create the FATURL in InAlGaAs/-InGaAsP/InP material emitting at about 1410 nm. Fabrication consists of photolithography, electron-beam lithography, wet etch and dry etching processes, metal and dielectric electron-beam evaporation, and rapid-thermal annealing. FATURLs are compared to infinite aperture TURLs, and show significant improvements in differential quantum efficiency (more than 40%) under pulsed-current operation. Far-field measurements show diffraction-limited divergence up to at least 2.3 x Ith, and spectral characteristics show good control over the longitudinal mode spectrum. Finally, several modifications to the laser design and fabrication are presented to improve laser performance.