Tolerance analysis method for Shack-Hartmann sensors using a variable phase surface

Even after good calibration, the measurement accuracy of a Shack-Hartmann sensor can be affected by the fabrication and alignment tolerances of the wavefront sensing optical system. The shifts of the Shack-Hartmann spots caused by misalignments correspond to ray intercept errors on the detector that typically have to be converted into a meaningful input wavefront measurement error. This conversion cannot be directly obtained from a conventional tolerance analysis using optical design software, because of the intrinsic wavefront sampling by the lenslet array. The tolerancing method proposed in this paper solves the problem of converting conventional merit function degradation into input wavefront measurement error without employing a separate wavefront reconstruction algorithm. Using the proposed method, this investigation shows the effect of fabrication and misalignment errors on the accuracy of a calibrated Shack-Hartmann sensor, as a function of input wavefront vergence

Analysis and design of wide-angle foveated optical systems based on transmissive liquid crystal spatial light modulators

Optical foveated imaging using liquid crystal (LC) spatial light modulators (SLMs) has received considerable attention in recent years as a potential approach to reducing size and complexity in fast wideangle lenses. We cover a theoretical study quantifying the diffraction efficiency and image quality of foveated optical systems (FOSs) based on transmissive LC SLMs. A practical design example of a fast wideangle FOS based on the current transmissive LC SLM technology is proposed

Stability and collisions of moving semi-gap solitons in Bragg cross-gratings

We report results of a systematic study of one-dimensional four-wave moving solitons in a recently proposed model of the Bragg cross-grating in planar optical waveguides with the Kerr nonlinearity; the same model applies to a fiber Bragg grating (BG) carrying two polarizations of light. We concentrate on the case when the system's spectrum contains no true bandgap, but only semi-gaps (which are gaps only with respect to one branch of the dispersion relation), that nevertheless support soliton families. Solely zero-velocity solitons were previously studied in this system, while current experiments cannot generate solitons with the velocity smaller than half the maximum group velocity. We find the semi-gaps for the moving solitons in an analytical form, and demonstrated that they are completely filled with (numerically found) solitons. Stability of the moving solitons is identified in direct simulations. The stability region strongly depends on the frustration parameter, which controls the difference of the present system from the usual model for the single BG. A completely new situation is possible, when the velocity interval for stable solitons is limited not only from above, but also from below. Collisions between stable solitons may be both elastic and strongly inelastic. Close to their instability border, the solitons collide elastically only if their velocities c1 and c2 are small; however, collisions between more robust solitons are elastic in a strip around c1=-c2.Comment: 16 pages, 7 figures, Physics Letters A, in pres

Tolerance Analysis Of Optical Systems Containing Sampling Devices

Numerous optical systems, such as telescopes, adaptive optics systems, and aberrometers, are equipped with wavefront sensors, which often use sampling devices measuring the slope of the wavefront at discrete points across the pupil (e.g. Shack-Hartmann sensors). The accuracy of the sampled output signal is always affected by the fabrication and alignment tolerances of the wavefront sensing optical system. Typically, it is a requirement to express the measurement error in terms of input wavefront, so the optical ray intercept error has to be converted into wavefront measurement error. This conversion cannot be obtained directly from a conventional tolerance analysis because of the wavefront breaking by the sampling device. The tolerancing method proposed in this paper solves the problem of converting conventional merit function degradation into input wavefront measurement error. The proposed method consists of two parts. First, a Monte Carlo tolerance analysis based on a specific merit function is performed, and a 90% border system is selected. Then, an optimization is applied to the 90% border system, by varying a dummy phase surface introduced at the entrance pupil of the system. A concrete example is presented

Fundamental And Specific Steps In Shack-Hartmann Wavefront Sensor Design

Shack-Hartmann sensors are widely used to measure wavefront aberrations. We present the fundamental and specifie engineering steps in the design of Shack-Hartmann wavefront sensors. Typical performance requirements such as sensor dynamic range, sensitivity and accuracy are defined and discussed. We investigate the trade-offs between these performance metrics and the factors affecting the trade-offs. A first order approach for selecting the optimal parameters of the sensor central piece, the lenslet array, is presented. We also propose a quick tolerance analysis method that can predict the wavefront measurement error due to misalignments, using only the ray-tracing software

Using Molded Chalcogenide Glass Technology To Reduce Cost In A Compact Wide-Angle Thermal Imaging Lens

This paper presents the design, analysis, and fabrication of a telecentric 171.3 thermal imaging lens. The 14.8 mm wideangle lens provides a 62° diagonal field-of-view, and was designed to operate over the 8-14 urn infrared spectral band. Focus can be manually adjusted from 0.5 m to infinity, maintaining constant image quality over the entire range. A compact air-spaced doublet design limits the overall length to 34 mm and the maximum diameter to 28 mm. Lens materials were chosen to minimize chromatic aberrations, reduce cost, and fit within the molded chalcogenide glass manufacturing capabilities. Combining a molded aspheric chalcogenide lens with a polished spherical Germanium lens eliminated the need for a diffractive surface to correct chromatic aberrations, and reduced the fabrication cost. Vignetting was purposely introduced at the extreme fields to compensate for the effects of aberrations on the relative illumination variation across the field-of-view. Athermalization of the lens was achieved mechanically over the entire operating temperature range (- 40 to + 80°C)

Analysis And Design Of Wide-angle Foveated Optical Systems

The development of compact imaging systems capable of transmitting high-resolution images in real-time while covering a wide field-of-view (FOV) is critical in a variety of military and civilian applications: surveillance, threat detection, target acquisition, tracking, remote operation of unmanned vehicles, etc. Recently, optical foveated imaging using liquid crystal (LC) spatial light modulators (SLM) has received considerable attention as a potential approach to reducing size and complexity in fast wide-angle lenses. The fundamental concept behind optical foveated imaging is reducing the number of elements in a fast wide-angle lens by placing a phase SLM at the pupil stop to dynamically compensate aberrations left uncorrected by the optical design. In the recent years, considerable research and development has been conducted in the field of optical foveated imaging based on the LC SLM technology, and several foveated optical systems (FOS) prototypes have been built. However, most research has been focused so far on the experimental demonstration of the basic concept using off the shelf components, without much concern for the practicality or the optical performance of the systems. Published results quantify only the aberration correction capabilities of the FOS, often claiming diffraction limited performance at the region of interest (ROI). However, these results have continually overlooked diffraction effects on the zero-order efficiency and the image quality. The research work presented in this dissertation covers the methods and results of a detailed theoretical research study on the diffraction analysis, image quality, design, and optimization of fast wide-angle FOSs based on the current transmissive LC SLM technology. The amplitude and phase diffraction effects caused by the pixelated aperture of the SLM are explained and quantified, revealing fundamental limitations imposed by the current transmissive LC SLM technology. As a part of this study, five different fast wide-angle lens designs that can be used to build practical FOSs were developed, revealing additional challenges specific to the optical design of fast wide-angle systems, such as controlling the relative illumination, distortion, and distribution of aberrations across a wide FOV. One of the lens design examples was chosen as a study case to demonstrate the design, analysis, and optimization of a practical wide-angle FOS based on the current state-of-the-art transmissive LC SLM technology. The effects of fabrication and assembly tolerances on the image quality of fast wide-angle FOSs were also investigated, revealing the sensitivity of these fast well-corrected optical systems to manufacturing errors. The theoretical study presented in this dissertation sets fundamental analysis, design, and optimization guidelines for future developments in fast wide-angle FOSs based on transmissive SLM devices

Wavefront Sensor For Eye Aberrations Measurements

Ocular wavefront sensing is vital to improving our understanding of the human eye and to developing advanced vision correction methods, such as adaptive optics, customized contact lenses, and customized laser refractive surgery. It is also a necessary technique for high-resolution imaging of the retina. The most commonly used wavefront sensing method is based on the Shack-Hartmann wavefront sensor. Since Junzhong Liang\u27s first application of Shack-Hartmann wavefront sensing for the human eye in 1994, the method has quickly gained acceptance and popularity in the ophthalmic industry. Several commercial Shack-Hartmann eye aberrometers are currently available. While the existing aberrometers offer reasonable measurement accuracy and reproducibility, they do have a limited dynamic range. Although rare, highly aberrated eyes do exists (corneal transplant, keratoconus, post-lasik) that cannot be measured with the existing devices. Clinicians as well as optical engineers agree that there is room for improvement in the performance of these devices Although the optical aberrations of normal eyes have been studied by the Shack-Hartmann technique, little is known about the optical imperfections of abnormal eyes. Furthermore, it is not obvious that current Shack-Hartmann aberrometers are robust enough to successfully measure clinically abnormal eyes of poor optical quality Larry Thibos, School of Optometry, Indiana University. The ultimate goal for ophthalmic aberrometers and the main objective of this work is to increase the dynamic range of the wavefront sensor without sacrificing its sensitivity or accuracy. In this dissertation, we attempt to review and integrate knowledge and techniques from previous studies as well as to propose our own analytical approach to optimizing the optical design of the sensor in order to achieve the desired dynamic range. We present the underlying theory that governs the relationship between the performance metrics of the sensor: dynamic range, sensitivity, spatial resolution, and accuracy. We study the design constraints and trade-offs and present our system optimization method in detail. To validate the conceptual approach, a complex simulation model was developed. The comprehensive model was able to predict the performance of the sensor as a function of system design parameters, for a wide variety of ocular wavefronts. This simulation model did confirm the results obtained with our analytical approach. The simulator itself can now be used as a standalone tool for other Shack-Hartmann sensor designs. Finally, we were able to validate our theoretical work by designing and building an experimental prototype. We present some of the more practical design aspects, such as illumination choices and tolerance analysis methods. The prototype validated the conceptual approach used in the design and was able to demonstrate a vast increase in dynamic range while maintaining accurate and repeatable measurements

Projection based Head Mounted Display with Eye-Tracking Capabilities

Methods, systems, apparatus and devices for the lens design of an HMPD with eye-tracking capabilities. The integration uses a low-level optical configuration in order to achieve a compact, comfortable, easy-to-use system. The optical system is further designed and optimized for sharing of the optical path between the HMD and the Eye-Tracker with minimal performance loss for both tasks