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.

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.

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.

Optics has the inherent advantages of parallelism and wide bandwidths in processing information. However, the need to interface with electronics creates a bottleneck that eliminates many of these advantages. The proposed research explores novel optical devices and techniques to overcome some of these bottlenecks. To address parallelism issues we take a specific example of a content-addressable memory that can recognize images. Image recognition is an important task that in principle can be done rapidly using the natural parallelism of optics. However in practice, when presented with incomplete or erroneous information, image recognition often fails to give the correct answer. To address this problem we examine a scheme based on free-space interconnects implemented with diffractive optics. For bandwidth issues, we study possible ways to eliminate the electronic conversion bottleneck by exploring all-optical buffer memories and all-optical processing elements. For buffer memories we examine the specific example of slow light delay lines. Although this is currently a popular research topic, there are fundamental issues of the delay-time-bandwidth product that must be solved before slow light delay lines can find practical applications. For all-optical processing we examine the feasibility of constructing circuit elements that operate directly at optical frequencies to perform simple processing tasks. Here we concentrate on the simplest element, a sub-wavelength optical wire, along with a grating coupler to interface with conventional optical elements such as lenses and fibers. Even such a simple element as a wire has numerous potential applications. In conclusion, information processing by all-optical devices are demonstrated with an associative memory using diffractive optics, an all-optical delay line using room temperature slow light in photorefractive crystals, and a subwavelength optical circuit by surface plasmon effects.

The problem of zero order diffraction (ZOD) in the computer generated hologram (CGH) is a commonly reported issue in employing computer generated hologram (CGH) systems. Failing to remove the zero order diffraction in either far-field or near-field region limits the display region or even worse, can destroy the reconstructed image. Therefore, the elimination of the ZOD is higly desired. The proposed new techniques to suppress the ZOD are the backbone of this thesis. We investigated ZOD sources in two different CGH systems and suggested different methods to remove the ZOD in each system. Two types of spatial light modulator (SLM) were employed for different type of CGHs, including a phase-only SLM and a binary amplitude-only SLM. All the proposed methods were examined with either simulation and experimental tests. For amplitude-only experiments, the ZOD suppression reached a factor of 3. Image quality and diffraction efficiency were also investigated for the proposed methods. / text

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.

<p>Intense developments in optical metamaterials have led to a renaissance in several optics fields. Metamaterials, artificially structured media, provide several additional degrees of freedom that cannot be accessed with conventional materials. For example, metamaterials offer a convenient and precise way to explore a wide range of refractive indices, including negative values. </p><p>In this dissertation, I introduce the idea of metamaterial based diffractive optics. Merging diffractive optics with metamaterials has several benefits, including access to almost continuous phase profiles and a wide range of available controlled anisotropy. I demonstrate this concept with several examples. I begin with an example of metamaterial based blazed diffraction grating using gradient index metamaterials for <em>f</em>É = 10.6 <em>f</em>Êm. A series of non-resonant metamaterial elements were designed and fabricated to mimic a saw-tooth refractive index profile with a linear index variation of . The linear gradient profile is repeated periodically to form the equivalent of a blazed grating, with the gradient occurring across a spatial distance of 61 <em>f</em>Êm. The index gradient is confirmed by comparing the measured magnitudes of the -1, 0 and +1 diffracted orders to those obtained from full wave simulations. </p><p>In addition to a metamaterial grating, a metamaterial based computer-generated phase hologram was designed by implementing the Gerchberg-Saxton (GS) iterative algorithm to form a 2D phase panel. A three layer metamaterial hologram was fabricated, with the size of 750 <em>f</em>Êm ~ 750 <em>f</em>Êm. Each pixel is comprised of metamaterial elements. This simple demonstration shows the potential for practical applications of metamaterial based diffractive optics.</p><p>The demand for compact and integrated optoelectronic systems increases the urgency for optical components that can simultaneously perform various functions. This dissertation also presents an optical element capable of multiplexing two diffraction patterns for two orthogonal linear polarizations, based on the use of non-resonant metamaterial cross elements. The metamaterial cross elements provide unique building blocks for engineering arbitrary birefringence. As a proof-of-concept demonstration, I present the design and experimental characterization of a polarization multiplexed blazed diffraction grating and a polarization multiplexed computer-generated hologram, for the telecommunication wavelength of <em>f</em>É = 1.55 <em>f</em>Êm. A quantitative study of the polarization multiplexed grating reveals that this approach yields a very large polarization contrast ratio. The results show that metamaterials can form the basis for a versatile and compact platform useful in the design of multi-functional photonic devices. </p><p>The examples I have mentioned only provide a glimpse of the opportunities for metamaterials. I envision more compact optical devices, with greater functionality, being realized with metamaterials.</p> / Dissertation

A method of holographic cross-connection is proposed for an Optical Ising machine system. The designed optical Ising machine based on multi-core fiber laser is introduced, including the theory of computation, history of optical computing, the concept of Ising model, the significance of optical Ising machine, the method to achieve Ising machine optically. The cross-connection part is based on computer-generated holograms (CGH), which is produced by Gerchburg-Saxton algorithm. The coupling coefficient between two channels as well as the phase change are controlled by CGHs. The design of holograms is discussed. The instrument used to display holograms is phase-only liquid crystal spatial light modulator (SLM) from HOLOEYE company. The optical system needed in this project, such as collimation lens and relay lens, is designed using Zemax. The system is first evaluated in Zemax simulation, and then constructed experimentally. The results show that we can control amplitude and phase of the reinjection beam at Multi-core fiber. Further experiment should be done to conclude that the control of the cross coupling between channels is achieved by displaying different holograms.

A tunable snapshot imaging spectrometer has been demonstrated. A liquid crystal spatial light modulator (LC SLM) has been integrated into a computed tomographic imaging spectrometer (CTIS) to achieve tunability. The LC SLM allows for rapid, programmable, and non-mechanical alteration of its phase profile by the application of appropriate voltages to its transparent electrodes.The goal of this dissertation is twofold: (1) to integrate a liquid crystal spatial light modulator into a CTIS instrument and characterize its performance as a tunable CTIS disperser, and (2) to implement tunability by analyzing different CTIS configurations.The theoretical model of CTIS operation, calibration, reconstruction, and disperser design are covered in detail. The cross talk of the LC SLM forces the use of a feedback design algorithm rather than designing the desired phase profile a priori in the computer. The modifications to the current polychromatic linear inversion technique for use with the LC SLM in feedback are presented. The result of the modifications is the successful integration of a reprogrammable (i.e. tunable) disperser for the CTIS instrument.The implementation of tunability is explored by analyzing the spectral resolution of a reconstructed point source for different disperser configurations. A method for experimentally determining the CTIS spectral resolution is presented.

In Optogenetics, cells, e.g. neurons or cardiac cells, are genetically altered to produce for example the lightsensitive protein Channelrhodopsin-2. Illuminating these cells induces action potentials or contractions and therefore allows to control electrical activity. Thus, light-induced cell stimulation can be used to gain insight to various biological processes. Many optogenetics studies, however, use only full field illumination and thus gain no local information about their specimen. But using modern spatial light modulators (SLM) in conjunction with computer-generated holograms (CGH), cells may be stimulated locally, thus enabling the research of the foundations of cell networks and cell communications. In our contribution, we present a digital holographic system for the patterned, spatially resolved stimulation of cell networks. We employ a fast ferroelectric liquid crystal on silicon SLM to display CGH at up to 1.7 kHz. With an effective working distance of 33 mm, we achieve a focus of 10 µm at a positioning accuracy of the individual foci of about 8 µm. We utilized our setup for the optogenetic stimulation of clusters of cardiac cells derived from induced pluripotent stem cells and were able to observe contractions correlated to both temporal frequency and spatial power distribution of the light incident on the cell clusters.