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

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

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

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)

Performance Analysis Of A High-Resolution Wide-Angle Foveated Optical System

Optical foveated imaging using liquid crystal spatial light modulators has received considerable attention in the recent years as a potential approach to reducing size and complexity in wide-angle lenses for high-resolution foveated imaging. In this paper we propose a very compact design for an F/2.8 visible monochromatic foveated optical system covering a total field-of-view of 80 degrees and capable of achieving a resolution in excess of 100 MPixels. The diffraction efficiency and image quality of the foveated optical system are estimated. The foveated optical system is compared to equivalent conventional wide-angle lenses in terms of size, complexity and image quality. Fabrication and assembly tolerances as well as limitations of the current transmissive LC SLM technology are taken into consideration. © 2010 Copyright SPIE - The International Society for Optical Engineering

Lens Design And System Optimization For Foveated Imaging

Foveated imaging addresses the need for compact wide-angle imagers capable of high-resolution and compressed data transmission. The principle behind foveated imaging is to cover a wide field-of-view (FOV) with a relatively simple and compact low-resolution lens, and use a liquid crystal spatial light modulator (SLM) to correct wavefront aberrations at any selected field point. The SLM correction provides a high-resolution fovea that can be actively moved anywhere within the FOV. While most research has focused so far mainly on SLM performance, the general trend being to increase SLM resolution and modulation depth, the actual lens design and system optimization aspects were often neglected. In this paper, we propose a wide-angle lens design intended for foveated imaging applications, and discuss typical tradeoffs. Taking this design as an example, we present a method to estimate the smallest SLM resolution required to correct the wavefront error effectively, showing that with the appropriate design, this resolution can be reduced up to 10 times compared to current designs. Increasing the SLM resolution beyond this point and increasing the modulation depth above one wavelength is not necessary, and will actually reduce the performance of the imaging system. We also demonstrate the importance of fabrication tolerances, and we propose a method to calibrate the SLM in order to cancel out all additional wavefront aberrations introduced by fabrication and assembly errors. © 2008 Copyright SPIE - The International Society for Optical Engineering

Wide Field-Of-View Imaging System Using A Liquid Crystal Spatial Light Modulator

This paper presents the optical design and experimental demonstration of a compact, foveated, wide field-of-view (FOV) imaging system using two lenses and a liquid crystal spatial light modulator (SLM). The FOV of this simple doublet system is dramatically improved by the SLM, which can be programmed to correct all the geometrical aberrations at any particular field angle. The SLM creates a variation in the image quality across the entire FOV, with a diffraction-limited performance at the field angle of interest (similar to the foveated human vision). The region of interest can be changed dynamically, such that any area within the FOV of the system can be highly resolved within milliseconds. The wide FOV, compactness, and absence of moving parts make this system a good candidate for tracking and surveillance applications. We designed an f/7.7 system, with a 60° full FOV, and a 27 mm effective focal length. Only two lenses and a beam splitter cube were used along with a reflective SLM. The theoretical wavefront aberration coefficients were used to program the SLM, which was placed in the pupil plane of the system. A prototype was built and the system was experimentally demonstrated using monochromatic light and a CCD camera