In the imaging system, a blurred defocus image is a common problem. This is because different objects in the scene need different focus for imaging clearly. However, we can only have one focus distance in one picture. Therefore, the images of the other objects in different focus distance would be blurred by the faulty focuses. We apply wave front coding to solve the above defocus problem. Wave front coding is a technique that adds a phase mask in front of the lens, changing the image performance, and solving the problem of defocus. In this thesis, we used a new phase screen, computed accordingly its optical transfer function and then simulated the resulting images. We compared with other phase screens provided by other researchers for different defocus situations. From our results, our pupil and optical transfer function are slightly superior.

The image quality will degrade if the misfocusing problem occurs in the imaging system. This paper is aimed to design and analyze a phase mask for mutifocusing problem. Depth of field is the range to get a clear image. As the lens can only gather the light in a fixed range. Image will be more blurred when it is more from this range. In 1995 Dowski and Cathey proposed the wave-front coding to increase the system's depth of field so that the image will less susceptible to blur due to the mutifocusing problem. A treatment with a mask before the lens can extend the depth of field. In this paper, we extend to multi-levels phase mask. The simulation results show that multi-level phase mask has a better performance than the two-level phase mask.

The search for life on other worlds is an exciting scientific endeavor that could change the way we perceive our place in the universe. Thousands of extrasolar planets have been discovered using indirect detection techniques. One of the most promising methods for discovering new exoplanets and searching for life is direct imaging with a coronagraph. Exoplanet coronagraphy of Earth-like planets is a challenging task, but we have developed many of the tools necessary to make it feasible. The Phase-Induced Amplitude Apodization (PIAA) Coronagraph is one of the highest-performing architectures for direct exoplanet imaging. With a complex phase-shifting focal plane mask, the PIAA Complex Mask Coronagraph (PIAACMC) can approach the theoretical performance limit for any direct detection technique. The architecture design is flexible enough to be applied to any arbitrary aperture shape, including segmented and obscured apertures. This is an important feature for compatibility with next-generation ground and space-based telescopes. PIAA and PIAACMC focal plane masks have been demonstrated in monochromatic light. An important next step for high-performance coronagraphy is the development of broadband phase-shifting focal plane masks. In this dissertation, we present an algorithm for designing the PIAA and PIAACMC focal plane masks to operate in broadband. We also demonstrate manufacturing of the focal plane masks, and show laboratory results. We use simulations to show the potential performance of the coronagraph system, and the use of wavefront control to correct for mask manufacturing errors. Given the laboratory results and simulations, we show new areas of exoplanet science that can potentially be explored using coronagraph technology. The main conclusion of this dissertation is that we now have the tools required to design and manufacture PIAA and PIAACMC achromatic focal plane masks. These tools can be applied to current and future telescope systems to enable new discoveries in exoplanet science.

For several years, we have been developing vortex phase masks based on sub-wavelength gratings, known as Annular Groove Phase Masks. Etched onto diamond substrates, these AGPMs are currently designed to be used in the thermal infrared (ranging from 3 to 13 pm). Our AGPMs were first installed on VLT/NACO and VLT/VISIR in 2012, followed by LBT/LMIRCam in 2013 and Keck/NIRC2 in 2015. In this paper, we review the development, commissioning, on-sky performance, and early scientific results of these new coronagraphic modes and report on the lessons learned. We conclude with perspectives for future developments and applications.

In this study, an investigation was undertaken to research the use of holographic phase masks (HPMs) in photo-thermo-refractive (PTR) glass as mode converters for linearly polarized (LP) fiber modes. A Spatial Light Modulator (SLM) was used to generate higher-order transverse fiber modes LPm,n. Under proper incidence condition on the holographic device, LPm,n modes are diffracted and simultaneously converted into higher order or lower order LP modes. The process was analyzed by imaging the far field on a CCD camera. It is demonstrated that using this novel method of converting transverse fiber modes several combinations of LP modes can be converted to each other with mode conversion efficiencies up to 70%. Mode purities were found to be around 85% for up conversion and around 90% for down conversion, respectively. It is noticed that this approach has several promising applications such as mode multiplexing, beam cleaning and power scaling of higher-order mode fiber lasers and amplifiers by combining mode conversion and beam combining.

In many applications such as beam shaping, mode conversion, and phase encoding it is necessary to alter the spatial phase profile of a beam via a phase mask. Conventional techniques to accomplish this either involve surface relief profiling in thin films such as PMMA or refractive index modulation in bulk photorefractive crystals such as lithium niobate. These materials have been used extensively for the past several decades and perform admirably in low power conditions. However, in high power systems these materials will be destroyed, requiring a new means of producing phase masks. In this dissertation a method for producing robust phase masks in the bulk of photo-thermo-refractive glass is developed and successfully demonstrated. Three main applications of phase masks were studied in detail. The first is mode conversion, where binary phase masks convert a Gaussian beam to higher order modes. The second is beam shaping, where phase masks are used as focusing elements and for optical vortex generation. Near-theoretical conversion efficiency was achieved for all elements in these cases. The third application is aberration analysis and correction. Here the degradation of volume Bragg gratings recorded in an aberrated holographic system was modeled, with the simulations indicating that correcting elements are generally necessary for high-quality production of gratings. Corrective phase masks are designed which can selectively correct one or multiple aberrations of varying magnitudes are shown. A new type of optical element is also developed in which a phase mask is encoded into a transmitting Bragg grating. This technique combines the local phase modulation of a phase mask with the multiplexing ability of transmitting Bragg gratings, allowing for multiple phase masks to be recorded in a single element. These masks may be used at any wavelength iii satisfying the Bragg condition, increasing the useful wavelength regime of a single element by orders of magnitude.

The traditional approach to imaging system design places the sole burden of image formation on optical components. In contrast, a computational imaging system relies on a combination of optics and post-processing to produce the final image and/or output measurement. Therefore, the joint-optimization (JO) of the optical and the post-processing degrees of freedom plays a critical role in the design of computational imaging systems. The JO framework also allows us to incorporate task-specific performance measures to optimize an imaging system for a specific task. In this dissertation, we consider the design of computational imaging systems within a JO framework for two separate tasks: object reconstruction and iris-recognition. The goal of these design studies is to optimize the imaging system to overcome the performance degradations introduced by under-sampled image measurements. Within the JO framework, we engineer the optical point spread function (PSF) of the imager, representing the optical degrees of freedom, in conjunction with the post-processing algorithm parameters to maximize the task performance. For the object reconstruction task, the optimized imaging system achieves a 50% improvement in resolution and nearly 20% lower reconstruction root-mean-square-error (RMSE ) as compared to the un-optimized imaging system. For the iris-recognition task, the optimized imaging system achieves a 33% improvement in false rejection ratio (FRR) for a fixed alarm ratio (FAR) relative to the conventional imaging system. The effect of the performance measures like resolution, RMSE, FRR, and FAR on the optimal design highlights the crucial role of task-specific design metrics in the JO framework. We introduce a fundamental measure of task-specific performance known as task-specific information (TSI), an information-theoretic measure that quantifies the information content of an image measurement relevant to a specific task. A variety of source-models are derived to illustrate the application of a TSI-based analysis to conventional and compressive imaging (CI) systems for various tasks such as target detection and classification. A TSI-based design and optimization framework is also developed and applied to the design of CI systems for the task of target detection, it yields a six-fold performance improvement over the conventional imaging system at low signal-to-noise ratios.

In optical imaging system, misfocus occurs because of a nonaccuate focal length. In recent years, the improvement for misfocus problem has caught much attention in researches. This thesis is aimed to explore the misfocus improvement and analysis. Lens plays an important role in optical image system. It can focus light at one point. The distance between the focal point and the lens is called focal length. Focal length is determined by the object distance and the image distance. As light is focused farther out of the focal point, the image will blur. It is called misfocus. The general method to improve misfocus image is done by post-processing. In 1995, wave-front coding was first proposed by Dowski and Cathey. They placed the phase mask in front of the lens, and then emphasized on the processing. In recent years, more and more researches work on this field. In this thesis, a one ring phase mask is designed by modulating the phase difference in the ring to make the improvement better. Research before wave-front coding in order to achieve a closed optical transfer function for different degrees of misfocus, but we hope the phase mask can provide immediate improvement. This idea can be applied to real-time video monitoring.

On March 2015 an L'-band vortex coronagraph based on an Annular Groove Phase Mask made up of a diamond sub-wavelength grating was installed on NIRC2 as a demonstration project. This vortex coronagraph operates in the L' band not only in order to take advantage from the favorable star/planet contrast ratio when observing beyond the K band, but also to exploit the fact that the Keck II Adaptive Optics (AO) system delivers nearly extreme adaptive optics image quality (Strehl ratios values near 90%) at 3.7 mu m. We describe the hardware installation of the vortex phase mask during a routine NIRC2 service mission. The success of the project depends on extensive software development which has allowed the achievement of exquisite real-time pointing control as well as further contrast improvements by using speckle nulling to mitigate the effect of static speckles. First light of the new coronagraphic mode was on June 2015 with already very good initial results. Subsequent commissioning nights were interlaced with science nights by members of the VORTEX team with their respective scientific programs. The new capability and excellent results so far have motivated the VORTEX team and the Keck Science Steering Committee (KSSC) to offer the new mode in shared risk mode for 2016B.

This thesis describes the problem of fiber gratings, focusing primarily on the use of Bragg's grids in the sensor. It describes the types of fiber mesh production, especially the method of writing with a phase mask. The next part deals with the possibilities of using apodization in fiber optic systems. It deals with the various functions that can be used to describe apodization. The following part describes the moire principle, especially the method of overlapping two phase masks with a different period.