A novel optical surface testing method termed the grating-slit test is demonstrated to provide quantitative measurements and a large dynamic measurement range. Although it uses a grating and a slit, as in the traditional Ronchi test, the grating-slit test is different in that the grating is used as the object and the slit is located at the observation plane. This is an arrangement that appears not to have been previously discussed in the optical testing literature. The grating-slit test produces fringes in accordance with the transverse ray aberrations of an aberrated wavefront. By using a spatial light modulator as the incoherent sinusoidal intensity grating it is possible to modulate the grating and produce phase shifting to make a quantitative measurement. The method becomes feasible given the superior intensity grayscale ability and highly incoherent illumination of the spatial light modulator used. Since the grating is used as the object, there are no significant diffraction effects that usually limit the Ronchi test. A geometrical and a detailed physical analysis of the grating-slit test are presented that agree in the appropriate limit. In order to convert the measured transverse ray aberrations to the surface figure error, a surface slope sensitivity method is developed. This method uses a perturbation algorithm to reconstruct the surface figure error from the measured transverse ray aberration function by exact ray tracing. The algorithm takes into account the pupil distortion and maps the transverse ray aberration from the coordinate system of the observation plane to the coordinate system of the surface under test. A numerical simulation proves the validity of the algorithm. To demonstrate the dynamic range of the grating-slit testing method, two optical surfaces are measured. The first surface is a polished spherical mirror with 0.6 waves of aberration as measured with an interferometer. Using the concept of transverse ray aberration separation, the first surface is measured without a strict alignment requirement. The second surface is a concave ground optical surface with 275 waves of astigmatism. The measurements from the grating-slit test yield useable surface figure information that is in agreement with the results from other testing methods.

An on-axis, vibration insensitive, polarization Fizeau interferometer is realized through the use of a novel pixelated mask spatial carrier phase shifting technique in conjunction with a low coherence source and a polarization path matching mechanism. In this arrangement, coherence is used to effectively separate out the orthogonally polarized test and reference beam components for interference. With both the test and the reference beams on-axis, the common path cancellation advantages of the Fizeau interferometer are maintained. Microwave modulation of a high powered red laser diode is used to create a 15 mW laser source having a coherence length of 250 um with minimal sidelobe ringing. With a 15 mW source, the maximum camera shutter speed, used when measuring a 4% reflector, was 150 usec, resulting in very robust vibration insensitivity. Additionally, stray light interference is substantially reduced due to the source's short coherence, allowing the measurement of thin transparent optics. Experimental results show the performance of this new interferometer to be within the specifications of commercial phase shifting interferometers.This work starts with a basic review of interferometry, phase shifting, and polarization as a lead in to a description of the theory and operation of the pixelated mask spatial carrier phase shifting technique. An analysis of the standard Fizeau Interferometer is then given. This is followed by detailed theoretical discussion of the path matched vibration insensitive (PMVI) Fizeau, which includes a theoretical model of the effects of multiple beam return from the test surface when measuring high value reflectors. The coherence properties of laser diodes are then discussed, a theoretical model for the effects of high frequency drive current is derived, and experimental results are given. Finally, the performance of the PMVI Fizeau is experimentally analyzed, potential error sources discussed, and suggestions for improvements provided.

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.

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.

Cataract is a condition in the eye that if left untreated, could lead to blindness. One of the effective ways to treat cataract is the removal of the cataractous natural crystalline lens and implantation of an artificial lens called an intraocular lens(IOL). The designs of the IOLs have shown improvements over the years to further imitate natural human vision. A need for an objective testing and analysis tool for the latest IOLs grow with the advancements of the IOLs.In this dissertation, I present a system capable of objective test and analysis of the advanced IOLs. The system consists of-Model eye into which an IOL can be inserted to mimic conditions of the human eye.-Modulation Transfer Function measurement setup capable of through-focus test for depth of field studies and polychromatic test for study of effects of chromatization.-Use of Defocus Transfer Function to simulate depth of field characteristic of rotationally symmetric multifocal designs and extension of the function to polychromatic conditions.-Several target imaging experiments for comparison of stray light artifacts and simulation using a non-sequential ray trace package.

The LSST M1/M3 combines an 8.4 m primary mirror and a 5.1 m tertiary mirror on one glass substrate. The combined mirror was completed at the Richard F. Caris Mirror Lab at the University of Arizona in October 2014. Interferometric measurements show that both mirrors have surface accuracy better than 20 nm rms over their clear apertures, in near-simultaneous tests, and that both mirrors meet their stringent structure function specifications. Acceptance tests showed that the radii of curvature, conic constants, and alignment of the 2 optical axes are within the specified tolerances. The mirror figures are obtained by combining the lab measurements with a model of the telescope's active optics system that uses the 156 support actuators to bend the glass substrate. This correction affects both mirror surfaces simultaneously. We showed that both mirrors have excellent figures and meet their specifications with a single bending of the substrate and correction forces that are well within the allowed magnitude. The interferometers do not resolve some small surface features with high slope errors. We used a new instrument based on deflectometry to measure many of these features with sub-millimeter spatial resolution, and nanometer accuracy for small features, over 12.5 cm apertures. Mirror Lab and LSST staff created synthetic models of both mirrors by combining the interferometric maps and the small high-resolution maps, and used these to show the impact of the small features on images is acceptably small.

This dissertation presents the design of a miniature injection-molded objective lens for a fiber-optic confocal reflectance microscope. This is part of an effort to demonstrate the ability to fabricate low cost, high performance biomedical optics for high resolution in vivo imaging. Disposable endoscopic microscope objectives could help in vivo confocal microscopy technology mature to enable large-scale clinical screening and detection of early cancers and pre-cancerous lesions. This five lens plastic objective has been tested as a stand-alone optical system and has been coupled to a confocal microscope for in vivo imaging of cells and tissue. Changing the spacing and rotation of the individual optical elements can compensate for fabrication inaccuracies and improve performance. An optical-bench testing system was constructed to allow interactive alignment during testing. The modulation transfer function (MTF) of the miniature objective lens is determined using the slanted-edge method. A custom MATLAB program, edgeMTF, was written to collect, analyize, and record test data. An estimated Strehl ratio of 0.64 and an MTF value of 0.70, at the fiber-optic bundle Nyquist frequency, have been obtained. The main performance limitations of the miniature objective are mechanical alignment and flow-induced birefringence. Annealing and experimental injection molding runs were conducted in effort to reduce birefringence.

The Richard F. Caris Mirror Lab at the University of Arizona is responsible for production of the eight 8.4 m segments for the primary mirror of the Giant Magellan Telescope, including one spare off-axis segment. We report on the successful casting of Segment 4, the center segment. Prior to generating the optical surface of Segment 2, we carried out a major upgrade of our 8.4 m Large Optical Generator. The upgrade includes new hardware and software to improve accuracy, safety, reliability and ease of use. We are currently carrying out an upgrade of our 8.4 m polishing machine that includes improved orbital polishing capabilities. We added and modified several components of the optical tests during the manufacture of Segment 1, and we have continued to improve the systems in preparation for Segments 2-8. We completed two projects that were prior commitments before GMT Segment 2: casting and polishing the combined primary and tertiary mirrors for the LSST, and casting and generating a 6.5 m mirror for the Tokyo Atacama Observatory.

Edward H. Linfoot developed an integral expression for the irradiance in the image of a lens or mirror under the Foucault knife-edge test as a function of figure error. Samuel Katzoff developed a convenient method of inverting the linearized form of Linfoot's equation to express figure error in terms of the irradiance distribution in the image (Foucault pattern). This paper presents the results of an experimental study on a 20-centimeter-diameter f/5 spherical mirror to complement the analytical work of Linfoot and Katzoff. The results clearly affirm the practicability of the Foucault test to quantitative evaluation of figure errors of near-diffraction-limited optical elements via the Linfoot/Katzoff formulation. The evaluation was based on a comparison of Foucault-test figure error data with parallel data from independent scatterplate interferometer measurements. The results are particaularly significant in that they reveal the fallacy of the widespread regard of the Foucault test as limited to qualications for the field of optical testing, since the test is basically simple, its implementation for quantitative figure error analysis is straightforward, and the associated experiemntal data processing is much simpler than that of interferometric testing methods. The question of potential use in figure error sensing in the planned large orbital telescope seems particularly pertinent.

The ability to produce mirrors for large astronomical telescopes is limited by the accuracy of the systems used to test the surfaces of such mirrors. Typically the mirror surfaces are measured by comparing their actual shapes to a precision master, which may be created using combinations of mirrors, lenses, and holograms. The work presented here develops several optical testing techniques that do not rely on a large or expensive precision, master reference surface. In a sense these techniques provide absolute optical testing.The Giant Magellan Telescope (GMT) has been designed with a 350 m2 collecting area provided by a 25 m diameter primary mirror made out from seven circular independent mirror segments. These segments create an equivalent f/0.7 paraboloidal primary mirror consisting of a central segment and six outer segments. Each of the outer segments is 8.4 m in diameter and has an off-axis aspheric shape departing 14.5 mm from the best-fitting sphere. Much of the work in this dissertation is motivated by the need to measure the surfaces or such large mirrors accurately, without relying on a large or expensive precision reference surface.One method for absolute testing describing in this dissertation uses multiple measurements relative to a reference surface that is located in different positions with respect to the test surface of interest. The test measurements are performed with an algorithm that is based on the maximum likelihood (ML) method. Some methodologies for measuring large flat surfaces in the 2 m diameter range and for measuring the GMT primary mirror segments were specifically developed. For example, the optical figure of a 1.6-m flat mirror was determined to 2 nm rms accuracy using multiple 1-meter sub-aperture measurements. The optical figure of the reference surface used in the 1-meter sub-aperture measurements was also determined to the 2 nm level. The optical test methodology for a 1.7-m off axis parabola was evaluated by moving several times the mirror under test in relation to the test system. The result was a separation of errors in the optical test system to those errors from the mirror under test. This method proved to be accurate to 12nm rms.Another absolute measurement technique discussed in this dissertation utilizes the property of a paraboloidal surface of reflecting rays parallel to its optical axis, to its focal point. We have developed a scanning pentaprism technique that exploits this geometry to measure off-axis paraboloidal mirrors such as the GMT segments. This technique was demonstrated on a 1.7 m diameter prototype and proved to have a precision of about 50 nm rms.