Rather than measuring aberrations at several locations across the field to quantify the alignment of an optical system, we show how a simple measurement of the pupil mapping can be used to measure the off-axis performance of the system. This method uses the Abbe sine condition to relate the mapping between the entrance and the exit pupils, where the violations of the generalized sine condition are used to determine the pupil mapping error. From this pupil mapping, the linearly field-dependent aberrations can be calculated. One of the advantages to this method is that all of the test equipment can be aligned to the center of the field while making measurements of the off-axis performance, which reduces the uncertainty of the measurement. This advantage is particularly evident with systems or sub-systems that have large inherent aberrations where off-axis alignment tolerances are very tight. Additionally, in the Sine Condition Test (SCTest), the test equipment can be designed to compensate for the native Siedel coma in the system. This makes it more straightforward to measure the linearly field dependence of the aberrations. By reducing or removing coma, the measurement uncertainty is further reduced. This work begins by explaining the background of the Abbe sine condition, derivation of the pupil mapping error, and an overview of linearly field-dependent astigmatism that arises from misalignment. Next, the general method of implementation is discussed, and expanded further by exploring the two different source options: a point source with a grating or a flat-panel display. Experimental results from proof of concept systems are shown for both cases. Next, this dissertation explains how the SCTest can be implemented on more complex systems. Last, this dissertation shows how the linear aberrations, along with constant field-dependent aberrations, can be used to align a system. Here, the application of the alignment version of the SCTest on a three mirror anastigmat (TMA) is discussed. Using simulation, this dissertation then investigates the behavior of the alignment SCTest for various levels of mirror misalignment, mirror fabrication errors, and misalignment of the test equipment. All of these tests show that the alignment SCTest can successfully align an optical system.

Interferometry with computer generated holograms (CGH) has evolved to be a standard technology for optical testing and metrology. By controlling the phase of the diffracted light, CGHs are capable of generating reference wavefronts of any desired shape, which allows using of interferometers for measuring complex aspheric surfaces. Fabrication errors in CGHs, however, cause phase errors in the diffracted wavefront, which directly affects the accuracy and validity of the interferometric measurements. Therefore, CGH fabrication errors must be either calibrated or budgeted. This dissertation is a continuation and expansion of the analysis and calibration of the wavefront errors caused by CGH in optical testing. I will focus on two types of error: encoding error and etching variation induced errors. In Topic one, the analysis of wavefront error introduced by encoding the CGH is discussed. The fabrication of CGH by e-beam or laser writing machine specifically requires using polygon segments to approximate the continuously smooth fringe pattern of an ideal CGH. Wavefront phase errors introduced in this process depend on the size of the polygon segments and the shape of the fringes. We propose a method for estimating the wavefront error and its spatial frequency, allowing optimization of the polygon sizes for required measurement accuracy. This method is validated with both computer simulation and direct measurements from an interferometer. In Topics two, we present a new device, the Diffractive Optics Calibrator (DOC), for measuring etching parameters, such as duty-cycle and etching depth, for CGH. The system scans the CGH with a collimated laser beam, and collects the far field diffraction pattern with a CCD array. The relative intensities of the various orders of diffraction are used to fit the phase shift from etching and the duty cycle of the binary pattern. The system is capable of measuring variations that cause 1 nm peak-to-valley (P-V) phase errors. The device will be used primarily for quality control of the CGHs. DOC is also capable of generating an induced phase error map for calibration. Such calibration is essential for measuring freeform aspheric surfaces with 1 nm root-mean-square (RMS) accuracy.

This dissertation aims to investigate two different applications in optics using maximum-likelihood (ML) estimation. The first application of ML estimation is used in optical metrology. For this application, an innovative iterative search method called the synthetic phase-shifting (SPS) algorithm is proposed. This search algorithm is used for estimation of a wavefront that is described by a finite set of Zernike Fringe (ZF) polynomials. In this work, we estimate the ZF coefficient, or parameter values of the wavefront using a single interferogram obtained from a point-diffraction interferometer (PDI). In order to find the estimates, we first calculate the squared-difference between the measured and simulated interferograms. Under certain assumptions, this squared-difference image can be treated as an interferogram showing the phase difference between the true wavefront deviation and simulated wavefront deviation. The wavefront deviation is defined as the difference between the reference and the test wavefronts. We calculate the phase difference using a traditional phase-shifting technique without physical phase-shifters. We present a detailed forward model for the PDI interferogram, including the effect of the nite size of a detector pixel. The algorithm was validated with computational studies and its performance and constraints are discussed. A prototype PDI was built and the algorithm was also experimentally validated. A large wavefront deviation was successfully estimated without using null optics or physical phase-shifters. The experimental result shows that the proposed algorithm has great potential to provide an accurate tool for non-null testing. The second application of ML estimation is used in nuclear medical imaging. A high-resolution positron tomography scanner called BazookaPET is proposed. We have designed and developed a novel proof-of-concept detector element for a PET system called BazookaPET. In order to complete the PET configuration, at least two detector elements are required to detect positron-electron annihilation events. Each detector element of the BazookaPET has two independent data-acquisition channels. One of the detector channels is a 4 x 4 silicon photomultiplier (SiPM) array referred to as the SiPM-side. The SiPM-side is directly coupled to an optical window of the scintillator with optical grease. The other channel is a CCD-based gamma camera with an imaging intensifier called the Bazooka-side. Instead of coupling by direct contact like the SiPM-side, an F/1.4 lens pair is used for optical coupling. The scintillation light from the opposite optical window to the SiPM-side is imaged by the F/1.4 lens to the Bazooka-side. Using these two separate channels, we can potentially obtain high energy, temporal and spatial resolution data by associating the data outputs via several ML estimation steps. We present the concept of the system and the prototype detector element. In this work, we focus on characterizing individual detector channels, and initial experimental calibration results are shown along with preliminary performance-evaluation results. We also address the limitations and the challenges of associating the outputs of the two detector channels.

When designing a lens, cost and manufacturing concerns are extremely challenging, especially with radical optical designs. The tolerance process is the bridge between design and manufacturing. Three techniques which improve the interaction between lens design and engineers are successfully shown in this thesis along with implementation of these techniques. First, a method to accurately model optomechanical components within lens design is developed and implemented. Yield improvements are shown to increase by approximately 3% by modeling optomechanical components. Second, a method utilizing aberration theory is applied to discover potential tolerance sensitivity of an optical system through the design process. The use of aberration theory gives an engineer ways to compensate for errors. Third, a method using tolerance grade mapping is applied to error values of an optical system. This mapping creates a simplified comparison method between individual tolerances and lens designs.

Classical field curvature theory emphasizes the Petzval theorem, which models field curvature aberration to the 4th order. However, modern lens designs use aspheric surfaces. These surfaces strongly induce higher order field curvature aberration which is not accounted for Petzval field curvature. This dissertation focuses on developing higher order field curvature theories that are applied to highly aspheric designs. Three new theories to control field curvature aberration are discussed. Theory 1: an aspheric surface that is close to the image and has two aspheric terms sharply reduces field curvature by 85%. Theory 2: an aspheric surface that is farther from the image plane induces astigmatism to balance Petzval field curvature. Theory 3: oblique spherical aberration can be induced to balance Petzval field curvature. All three theories are applied to real design examples including the following lenses: cellular phone, wide angle, fast photographic, and zoom lenses. All of the analyses results are consistent with the theories. Moreover, two types of novel aspheric surfaces are proposed to control field curvature. Neither of the surfaces are polynomial-type surfaces. Examples show that the novel aspheric surfaces are equivalent to even aspheric surfaces with two aspheric coefficients in terms of field curvature correction. The study on field curvature correction using aspheric surfaces provides an alternative method to use when aspheres are accessible. Overall, this dissertation advances the theory of field curvature aberration, and it is particularly valuable to evaluate highly aspheric designs when Petzval theory is inapplicable.

Geosynchronous (GEO) satellites are essential for modern communication networks. If communication to a GEO satellite is lost and a malfunction occurs upon orbit insertion such as a solar panel not deploying there is no direct way to observe it from Earth. Due to the GEO orbit distance of ~36,000 km from Earth's surface, the Rayleigh criteria dictates that a 14 m telescope is required to conventionally image a satellite with spatial resolution down to 1 m using visible light. Furthermore, a telescope larger than 30 m is required under ideal conditions to obtain spatial resolution down to 0.4 m. This dissertation evaluates a method for obtaining high spatial resolution images of GEO satellites from an Earth based system by measuring the irradiance distribution on the ground resulting from the occultation of the satellite passing in front of a star. The representative size of a GEO satellite combined with the orbital distance results in the ground shadow being consistent with a Fresnel diffraction pattern when observed at visible wavelengths. A measurement of the ground shadow irradiance is used as an amplitude constraint in a Gerchberg-Saxton phase retrieval algorithm that produces a reconstruction of the satellite's 2D transmission function which is analogous to a reverse contrast image of the satellite. The advantage of shadow imaging is that a terrestrial based redundant set of linearly distributed inexpensive small telescopes, each coupled to high speed detectors, is a more effective resolved imaging system for GEO satellites than a very large telescope under ideal conditions. Modeling and simulation efforts indicate sub-meter spatial resolution can be readily achieved using collection apertures of less than 1 meter in diameter. A mathematical basis is established for the treatment of the physical phenomena involved in the shadow imaging process. This includes the source star brightness and angular extent, and the diffraction of starlight from the satellite. Atmospheric effects including signal attenuation, refraction/dispersion, and turbulence are also applied to the model. The light collection and physical measurement process using highly sensitive geiger-mode avalanche photo-diode (GM-APD) detectors is described in detail. A simulation of the end-to-end shadow imaging process is constructed and then utilized to quantify the spatial resolution limits based on source star, environmental, observational, collection, measurement, and image reconstruction parameters.

As techniques for manufacturing and metrology advance, optical systems are being designed with more complexity than ever before. Given these prescriptions, alignment and calibration can be a limiting factor in their final performance. Computer generated holograms (CGHs) have several unique properties that make them powerful tools for meeting these demanding tolerances. This work will present three novel methods for alignment and calibration of optical systems using computer generated holograms. Alignment methods using CGHs require that the optical wavefront created by the CGH be related to a mechanical datum to locate it space. An overview of existing methods is provided as background, then two new alignment methods are discussed in detail. In the first method, the CGH contact Ball Alignment Tool (CBAT) is used to align a ball or sphere mounted retroreflector (SMR) to a Fresnel zone plate pattern with micron level accuracy. The ball is bonded directly onto the CGH substrate and provides permanent, accurate registration between the optical wavefront and a mechanical reference to locate the CGH in space. A prototype CBAT was built and used to align and bond an SMR to a CGH. In the second method, CGH references are used to align axi-symmetric optics in four degrees of freedom with low uncertainty and real time feedback. The CGHs create simultaneous 3D optical references where the zero order reflection sets tilt and the first diffracted order sets centration. The flexibility of the CGH design can be used to accommodate a wide variety of optical systems and maximize sensitivity to misalignments. A 2-CGH prototype system was aligned multiplied times and the alignment uncertainty was quantified and compared to an error model. Finally, an enhanced calibration method is presented. It uses multiple perturbed measurements of a master sphere to improve the calibration of CGH-based Fizeau interferometers ultimately measuring aspheric test surfaces. The improvement in the calibration is a function of the interferometer error and the aspheric departure of the desired test surface. This calibration is most effective at reducing coma and trefoil from figure error or misalignments of the interferometer components. The enhanced calibration can reduce overall measurement uncertainty or allow the budgeted error contribution from another source to be increased. A single set of sphere measurements can be used to calculate calibration maps for closely related aspheres, including segmented primary mirrors for telescopes. A parametric model is developed and compared to the simulated calibration of a case study interferometer.

Dose as a result of radiation exposure is the notion generally used to disclose the imparted energy in a volume of tissue to a potential biological effect. The basic unit defined by the international system of units (SI system) is the radiation absorbed dose, which is expressed as the mean imparted energy in a mass element of the tissue known as "gray" (Gy) or J/kg. The procedure for ascertaining the absorbed dose is complicated since it involves the radiation transport of numerous types of charged particles and coupled photon interactions. The most precise method is to perform a full 3D Monte Carlo simulation of the radiation transport. There are various Monte Carlo toolkits that have tool compartments for dose calculations and measurements. The dose studies in this thesis were performed using the GEANT4 Application for Emission Tomography (GATE) software (Janet al., 2011) GATE simulation toolkit has been used extensively in the medical imaging community, due to the fact that it uses the full capabilities of GEANT4. It also utilizes an easy to-learn GATE macro language, which is more accessible than learning the GEANT4/C++ programming language. This work combines GATE with digital phantoms generated using the NCAT (NURBS-based cardiac-torso phantom) toolkit (Segars et al., 2004) to allow efficient and effective estimation of 3D radiation dose maps. The GATE simulation tool has developed into a beneficial tool for Monte Carlo simulations involving both radiotherapy and imaging experiments. This work will present an overview of absorbed dose of common radionuclides used in nuclear medicine and serve as a guide to a user who is setting up a GATE simulation for a PET and SPECT study.

Shown is the design of the Smartphone Oral Cancer Detection System (SOCeeDS). The SOCeeDS attaches to a smartphone and utilizes its embedded imaging optics and sensors to capture images of the oral cavity to detect oral cancer. Violet illumination sources excite the oral tissues to induce fluorescence. Images are captured with the smartphone’s onboard camera. Areas where the tissues of the oral cavity are darkened signify an absence of fluorescence signal, indicating breakdown in tissue structure brought by precancerous or cancerous conditions. With this data the patient can seek further testing and diagnosis as needed. Proliferation of this device will allow communities with limited access to healthcare professionals a tool to detect cancer in its early stages, increasing the likelihood of cancer reversal.

Optical resonators are structures that allow light to circulate and store energy for a duration of time. This work primarily looks at the fabrication, characterization, and application of whispering gallery mode microresonators and the analysis of organic photonic crystal-like structures and simulation of their resonant effects. Whispering gallery mode (WGM) microresonators are a class of cylindrically symmetric optical resonator which light circulates around the equator of the structure. These resonators are named after acoustic whispering galleries, where a whisper can be heard anywhere along the perimeter of a circular room. These optical structures are known for their ultra high Q-factor and their low mode volume. Q-factor describes the photon lifetime in the cavity and is responsible for the energy buildup within the cavity and sharp spectral characteristics of WGM resonators. The energy buildup is ideal for non-linear optics and the sharp spectral features are beneficial for sensing applications. Characterization of microbubble resonators is done by coupling light from a tunable laser source via tapered optical fiber into the cavity. The fabrication of quality tapered optical fiber on the order of 1-2 μm is critical to working on WGM resonators. The measurement of Q-factors up to 2x10⁸ and mode spectra are possible with these resonators and experimental techniques. This work focuses on microdisk and microbubble WGM resonators. The microdisk resonators are fabricated by femtosecond laser micromachining. The micromachined resonators are fabricated by ablating rotating optical fiber to generate the disk shape and then heated to reflow the surface to improve optical quality. These resonators have a spares mode spectrum and display a Q factor as high as 2x10⁶. The microbubble resonators are hollow microresonators fabricated by heating a pressurized capillary tube which forms a bubble in the area exposed to heat. These have a wall thickness of 2-5 μm and a diameter of 200-400 μm. Applications in pressure sensing and two-photon fluorescence of dye in microbubble resonators is explored. Photonic crystals can have engineered resonant properties by tuning photonic band gaps and introducing defects to create cavities in the photonic structure. In this work, a natural photonic crystal structure is analyzed in the form of diatoms. Diatoms are a type of phytoplankton which are identified by unique ornamentation of each species silica shell, called a frustule. The frustule is composed of a quasi-periodic lattice of pores which closely resembles manmade photonic crystals. The diatom frustules are analyzed using image processing techniques to determine pore-to-pore spacing and identify defects in the quasi-periodic structure which may contribute to optical filtering and photonic band gap effects. The data gathered is used to simulate light propagation through the diatom structure at different incident angles and with different material properties and to verify data gathered experimentally.