The human eye is a complex optical system with multiple elements. It is aspheric, nonsymmetric, and time dependent; yet, overall it has incredible performance. There have been various instruments developed over the years to measure and then to guide treatment to correct for ocular aberrations. As the development of these instruments (and treatments) has progressed, we have sought to correct more difficult cases, which may be more aberrated, time-dependent, or difficult in some other way. To this end, we have developed a new dynamic aberrometer that expands the boundaries of measurement capability with the aim of measuring and treating more difficult cases. This aberrometer has been designed that incorporates high-resolution Shack–Hartmann wavefront sensing, full gradient (spot) corneal topography, dynamic acquisition, and a subjective digital refractometer. This instrument is designed to measure extremely high aberrations and to provide information for treatment in multiple modalities. A small clinical study was conducted with subjects ranging from 23 to 64 years old to evaluate the effectiveness of the dynamic analysis at selecting a refraction. Examples are presented for measurements with keratoconus, irregular corneas, and tear-film irregularity. In the clinical study, young subjects showed an overall +0.27 D reduction in instrument induced myopia using dynamic measurement compared to a snapshot. The instrument has a large dynamic range for measuring subjects with keratoconus and other aberrated corneal conditions. The new instrument is effective at providing information needed for treatment in multiple modalities. The subjective digital refractometer corrects the fixation target for the objectively measured low-order aberrations (defocus and astigmatism). This provides immediate subjective feedback on the objective refraction and, with the ability to manually adjust the refraction parameters, the ability to compare objective and subjective refractions in the same setting.
Wavefront metrics such as root mean squared error provide excellent descriptions of optical quality but the connection to visual performance is not directly interpretable from the wavefront alone. Converting to visual acuity (VA) would provide a more accessible assessment of the effect of ocular wavefront. In this study, multiple measurements of wavefront and pupil diameter were acquired at 1 cd/m2 using the iDesign 1.3 (Johnson and Johnson Surgical Vision) in 552 eyes of 293 subjects. Uncorrected (UC) and best corrected (BC) VA were measured at 4m for each eye at 100 cd/m2 . VA was estimated using a neural contrast sensitivity function (NCSF) weighted modulation transfer function (MTF). To estimate BCVA, sphere and astigmatism terms were nulled. For each subject, classification was performed using random forest considering estimated VA, age, measured pupil diameter, manifest refraction spherical equivalent, manifest refraction cylinder and gender. Across all measurements, predicted differed from measured UCVA by -0.11 and BCVA by +1.6 (-10logMAR). The NCSF-based model predicts population mean VA to within approximately 2-lines but cannot predict an individual’s VA well, supporting the notion that other factors need to be considered to obtain more accurate estimates of VA. Classification with the random forest approach improved the accuracy of estimates of an individual subject’s VA; approximately 95% of the estimates match the measured VA.
Tinsley, under JWST funding, has led the team that has developed a novel and highly versatile piece of ground support equipment for optical surface testing of JWST beryllium mirror segments during optical fabrication. The infrared Scanning Shack Hartmann System (SSHS) offers the advantage of being able to characterize mid-to-high spatial frequency structure on a mirror from early stages of fabrication when slopes may be high and surface irregular, eliminating the need for an extra polishing step before metrology. Working at 9.3μm, the system will accept and measure a wide dynamic range of surface characteristics, including roll-off near the edge of the segment. Knowledge of these surface features at the early grinding stage is imperative if characteristics such as mirror edge roll-off are to be minimized. WaveFront Sciences, producer of commercial COAS and Columbus Shack Hartmann systems, has provided systems engineering and component support for the SSHS system.
The SSHS system is based around a special Long Wave Infrared (LWIR) wavefront sensor developed by WaveFront Sciences that is scanned over the mirror surface, making sub-aperture measurements. The smaller, high-resolution measurements are then stitched together to provide high-resolution measurement of the entire mirror surface, even though the surface is in a rough ground state.
The system leverages technology from smaller visible instrumentation produced by Wavefront Sciences, especially those for surface sub-aperture measurements of semiconductor wafers. This paper will describe the implementation of the first infrared scanning Shack Hartmann system at Tinsley to address optical fabrication optimization of the JWST Primary Mirror Segments.
The lens is one of the most commonly used optical elements. Yet it is sometimes difficult to make accurate effective focal length and pupil position measurements, especially for long focal length lenses. Many measurement methods rely on a mechanical measurement to determine the back focal length, or may require careful operator discrimination in determining the best focus position. Aberrations may confuse an automatic focal length measurement system. However, an accurate determination of the optical properties of a lens is often critical for building an accurate system model. We have developed a method for measurement of the focal length, pupil plane and collimation positions of positive lenses using a Shack-Hartmann wavefront sensor. The SHWFS uses a micro-optic lens array to separate the incoming wavefront into a pattern of focal spots. The position of these focal spots is related to the local wavefront slope. Wavefront reconstruction allows the complete incident wavefront to be retrieved. A Zernike decomposition reconstructor is used to separate the effects of lens focal power from other aberrations. The lens under test is illuminated by a point source on a computer-controlled stage. The transmitted wavefront was recorded by the SHWFS while the source was translated over a few mm range. By analyzing the Zernike coefficient associated with defocus, we were able to extract the focal length, pupil plane and collimation positions using a least squares fitting procedure. This procedure was tested for a variety of lenses of varying focal lengths, from 10 to 1000 mm focal length, and showed excellent repeatability and accuracy. These measurements were compared to knife-edge, manufacturer’s specification, and ray-tracing analysis for verification testing.
We have adapted a Shack-Hartmann wavefront sensor (SHWFS) to the measurement of highly aberrated large optics. The experiment uses a concave mirror operating at the radius point with a small lens to re-collimate the light onto the wavefront sensor. It is used to test large (300 mm) fused silica wafers in double pass transmission. The optic under test is placed in the intermediate path near the large return mirror. The aberrations of the large mirror, beam splitter and other optics are subtracted by recording a reference set of focal spot on the SHWFS without the wafer. The wavefront error for some of these wafers is nearly 100 waves, yet we are able to make accurate measurements with the wavefront sensor by selecting a sensor with the appropriate combination of focal length and lenslet diameter. The special sensor that we developed uses a megapixel camera with an arrangement of 100 X 100 lenslets. This sensor could achieve several hundred waves of dynamic range with better than λ/20 accuracy. Additional wafer thickness measurements that were made at NIST with the XCALIBIR interferometer corroborate the SHWFS results.
Human vision correction optics must be produced in quantity to be economical. At the same time every human eye is unique and requires a custom corrective solution. For this reason the vision industries need fast, versatile and accurate methodologies for characterizing optics for production and research. Current methods for measuring these optics generally yield a cubic spline taken from less than 10 points across the surface of the lens. As corrective optics have grown in complexity this has become inadequate. The Shack-Hartmann wavefront sensor is a device that measures phase and irradiance of light in a single snapshot using geometric properties of light. Advantages of the Shack-Hartmann sensor include small size, ruggedness, accuracy, and vibration insensitivity. This paper discusses a methodology for designing instruments based on Shack-Hartmann sensors. The method is then applied to the development of an instrument for accurate measurement of transmissive optics such as gradient bifocal spectacle lenses, progressive addition bifocal lenses, intrarocular devices, contact lenses, and human corneal tissue. In addition, this instrument may be configured to provide hundreds of points across the surface of the lens giving improved spatial resolution. Methods are explored for extending the dynamic range and accuracy to meet the expanding needs of the ophthalmic and optometric industries. Data is presented demonstrating the accuracy and repeatability of this technique for the target optics.
The design of a wavefront sensor may be determined by the lenslet array and camera selection. There are numerous different applications for these sensors, requiring widely differing dynamic range and accuracy. Performance metrics are needed to evaluate candidate designs and to compare results. We have developed a standard methodology for measuring the repeatability, accuracy and dynamic range of different wavefront sensor designs, and have experimentally applied these metrics to a number of different sensors.
We present a high-speed silicon wafer metrology tool capable of resolving surface features in the nanometer height range. This tool uses a high performance Shack-Hartman sensor to analyze the wavefront of a beam of light reflected from a silicon wafer surface. By translating the wafer to analyze small portions of the wafer in each camera frame and then continuously piecing the frames together, we can retain sub-millimeter spatial resolution while rapidly analyzing large apertures. This tool is particularly effective for resolving features near the wafer edge. We will describe the measures required to obtain this level of resolution. We also compare data taken with this device to that taken with the National Institute of Standards and Technology X-ray optics Calibration Interferometer (XCALIBIR). Finally, we show measurements of a variety of typical and atypical 200 mm diameter wafer samples.
We have measured the wavefront aberrations of fused silica and silicon microlenses using a Shack-Hartmann wavefront sensor system. The Shack-Hartmann sensor uses a combination of a microlens array and a CCD camera to measure wavefront local tilts with respect to a reference wavefront. Data reduction software then reconstructs the wavefront and expresses it in various forms such as Seidel or Zernike. We measured a series of our custom microlens arrays by placing a fiber source at a distance of one focal length behind the array to create a series of collimated beams from the individual lenslets. We then observed the quality of the collimated beams from single lenslets by using different aperture converters (for different sized lenslets) to expand the individual beams so that they filled a significant portion of the CCD area. For these microlens arrays, the P-V OPD was found to be less than λ/4 and the RMS wavefront error less than λ/20.
Scanning mirrors for micro-display systems typically require operation at frequencies over 15 kHz. These mirrors undergo large dynamic stresses and inertia related deformations. We report here on the measurement of these dynamic deformations using a commercially available Shack-Hartmann wavefront sensor with data reduction software. The measured deformations using the Shack-Hartmann wavefront sensor are shown to agree with measurements obtained using a stroboscopic interferometer. Advantages of the Shack- Hartmann wavefront sensor are discussed.
We are investigating the use of a Shack-Hartmann wavefront sensor for measuring optical component quality during manufacture and testing. In a variety of fields, an optical component is designed to pass an optical signal with minimal distortion. Quality control during the manufacturing and production process is a significant concern. Changes in beam parameters, such as RMS wavefront deviation, or the beam quality parameter M2, have been considered as indications of optical component quality. These characteristics can often be quickly determined using relatively simple algorithms and system layouts. A laboratory system has been prepared to investigate the use of a wavefront sensor to measure the quality of an optical component. The instrument provides a simultaneous measure of changes in M2 and induced RMS wavefront error. The results of the investigation are presented.
The most critical element in a ocular Shack-Hartmann wavefront sensor is the micro-optic lenslet array. This array largely determines the accuracy of the wavefront measurement and the dynamic range of the measurements. This paper discusses the details of how the density of the lenslet array affects the accuracy of the wavefront measurement. We briefly discuss wavefront reconstruction, which is the mathematical process that takes the output from the lenslet array and reconstructs the input wavefront. We compare the two primary methods of reconstruction, the zonal fit and the modal fit. We also show how a denser array can be designed to have a better dynamic range.
Laser beam measurement instruments have long been available for visible laser beams, but there is a growing need for such instruments in the near IR. This is especially true for the 1 - 1.7 micrometer region that is used for communication lasers. While a few cameras have been developed for this region, there are currently no instruments for measuring laser beam phase that operate in this regime. We have begun the development of an infrared wavefront sensor based on the Shack-Hartmann principal using an InGaAs IR camera. With this method, the laser beam is dissected into a number of focal spots, which are projected onto a detector. The focal spot position is related to the local wavefront slope. Through appropriate analysis, the laser beam intensity and phase distribution can be obtained.
The flight environment of next-generation theater missile defense interceptors involves hypersonic speeds that place severe aero-thermodynamic loads on missile components including the windows used for optical seekers. These heating effects can lead to significant boresight error and aberration. Ground-based tests are required to characterize these effects. We have developed methods to measure aberrations in seeker windows using a Shack-Hartmann wavefront sensor. Light from a laser or other source with a well known wavefront is passed through the window and falls on the sensor. The sensor uses an array of micro-lenses to generate a grid of focal spots on a CCD detector. The positions of the focal spots provide a measure of the wavefront slope over each micro-lens. The wavefront is reconstructed by integrating the slopes, and analyzed to characterize aberrations. During flight, optical seekers look upstream through a window at 'look angles' angles near 0 degrees relative to the free stream flow. A 0 degree angle corresponds to large angles approaching 90 degrees when measured relative to the normal of the window, and is difficult to simulate using conventional techniques to illuminate the wavefront sensor during wind tunnel tests. For this reason, we developed a technique using laser- induced optical breakdown that allows arbitrary look angles down to 0 degrees.
Measurement is an integral part of optics manufacture, where grinding and polishing steps are linked iteratively with the testing steps. While numerous test methods have been developed, many of these are prone to vibration effects that limit their application to in-situ monitoring, or have other limitations. We have applied Shack-Hartmann wavefront sensors to the problems of optics measurement. We have developed an instrument that allows testing in common configurations, and also provides new ways to test optics. The current device is extremely sensitive. We have demonstrated this device for testing various optical elements including lenses, mirrors and laser rods.
We have developed a two-dimensional Shack-Hartman wavefront sensor that uses binary optic lenslet arrays to directly measure the wavefront slope (phase gradient) and amplitude of the laser beam. This sensor uses an array of lenslets that dissects the beam into a number of samples. The focal spot location of each of these lenslets (measured by a CCD camera) is related to the incoming wavefront slope over the lenslet. By integrating these measurements over the laser aperture, the wavefront or phase distribution can be determined. Since the power focused by each lenslet is also easily determined, this allows a complete measurement of the intensity and phase distribution of the laser beam. Furthermore, all the information is obtained in a single measurement. Knowing the complete scalar field of the beam allows the detailed prediction of the actual beam's characteristics along its propagation path. In particular, the space-beamwidth product, M2, can be obtained in a single measurement. The intensity and phase information can be used in concert with information about other elements in the optical train to predict the beam size, shape, phase and other characteristics anywhere in the optical train. We present preliminary measurements of an Ar+ laser beam and associated M2 calculations.
Optical diagnostics are extremely useful in fluid mechanics because they generally have high inherent bandwidth, and are nonintrusive. However, since optical probe measurements inherently integrate all information along the optical path, it is often difficult to isolate out-of-plane components in 3D flow events. It is also hard to make independent measurements of internal flow structure. Using an arrangement of 1D wavefront sensor, we have developed a system that uses tomographic reconstruction to make 2D measurements in arbitrary flow. These measurements provide complete information in a plane normal to the flow. We have applied this system to the subsonic free jet because of the wide range of flow scales available. These measurements rely on the development of a series of 1D wavefront sensors that are used to measure line-integral density variations in the flow of interest. These sensors have been constructed using linear CCD cameras and binary optics lenslet arrays. In designing these arrays, we have considered the coherent coupling between adjacent lenses and have made comparisons between theory and experimental noise measurements. This paper will present examples of the wavefront sensor development, line-integral measurements as a function of various experimental parameters, and sample tomographic reconstructions.
KEYWORDS: Diffraction, Systems modeling, Adaptive optics, Control systems, Performance modeling, Mirrors, Control systems design, Sensors, Optics manufacturing, Algorithm development
The development of modeling algorithms for adaptive optics systems is important for evaluating both performance and design parameters prior to system construction. Two of the most critical subsystems to be modeled are the binary optic design and the adaptive control system. Since these two are intimately related, it is beneficial to model them simultaneously. Optic modeling techniques have some significant limitations. Diffraction effects directly limit the utility of geometrical ray-tracing models, and transform techniques such as the fast Fourier transform can be both cumbersome and memory intensive. We have developed a hybrid system incorporating elements of both ray-tracing and Fourier transform techniques. In this paper we present an analytical model of wavefront propagation through a binary optic lens system developed and implemented at Sandia National Laboratories. This model is unique in that it solves the transfer function for each portion of a diffractive optic analytically. The overall performance is obtained by a linear superposition of each result. The model has been successfully used in the design of a wide range of binary optics, including an adaptive optic for a beam combining system consisting of an array of rectangular mirrors, each controllable in tip/tilt and piston. Wavefront sensing and the control models for a beam combining system have been integrated and used to predict overall systems performance. Applicability of the model for design purposes is demonstrated with several lens designs through a comparison of model predictions with actual adaptive optics results.
The performance of an adaptive optical system is strongly dependent upon correctly measuring the wavefront of the arriving light. The most common wavefront measurement techniques used to date are the shearing interferometer and the Shack-Hartmann sensor. Shack-Hartmann sensors rely on the use of lenslet arrays to sample the aperture appropriately. These have traditionally been constructed using MLM or step and repeat technology, and more recently with binary optics technology. Diffractive optics fabrication methodology can be used to remove some of the limitations of the previous technologies and can allow for low-cost production of sophisticated elements. We have investigated several different specialized wavefront sensor configurations using both Shack-Hartmann and shearing interferometer principles. We have taken advantage of the arbitrary nature of these elements to match pupil shapes of detector and telescope aperture and to introduce magnification between the lenslet array and the detector. We have fabricated elements that facilitate matching the sampling to the current atmospheric conditions. The sensors were designed using a far-field diffraction model and a photolithography layout program. They were fabricated using photolithography and RIE etching. Several different designs are presented with some experimental results from a small-scale adaptive optics brass-board.
Scaling laser systems to large sizes for power beaming and other applications can sometimes be simplified by combining a number of smaller lasers. However, to fully utilize this scaling, coherent beam combination is necessary. This requires measuring and controlling each beam's pointing and phase relative to adjacent beams using an adaptive optical system. We have built a sub-scale brass-board to evaluate various methods for beam-combining. It includes a segmented adaptive optic and several different specialized wavefront sensors that are fabricated using diffractive optics methods. We have evaluated a number of different phasing algorithms, including hierarchical and matrix methods, and have demonstrated phasing of several elements. The system is currently extended to a large number of segments to evaluate various scaling methodologies.
Monolithic integration of a rare-earth-ion-based active waveguide on the same wafer as its diode pump laser would permit compact packaging of the technology demonstrated in fiber lasers and amplifiers. This new monolithic technology would offer the potential for developing compact infrared and visible (up- conversion) lasers, amplifiers, and other photonic integrated circuit components. One approach that we are investigating for such monolithic integration uses a high concentration of one or more rare-earth ions incorporated into polysiloxane spin-on glasses that are solvent-cast onto III-V semiconductor wafers. This `fiber on chip' technology substitutes a relatively high- ion-concentration, short-length metal-ion spin-on glass (MISOG) waveguide for the low-ion-concentration, long-length fiber. Progress to date on developing MISOG waveguide materials and technology is discussed.
Wavefront sensors have been used to make measurements in fluid-dynamics and for closed loop control of adaptive optics. In most common Shack-Hartmann wavefront sensors, the light is broken up into series of rectangular or hexagonal apertures that divide the light into a series of focal spots. The position of these focal spots is used to determine the wavefront slopes over each subaperture. Using binary optics technology, we have developed a hierarchical or fractal wavefront sensor that divides the subapertures up on a more optimal fashion. We have demonstrated this concept for up to four tiers and developed the wavefront reconstruction methods for both segmented adaptive optics and continuous wavefront measurement.
Geosynchronous satellites use solar arrays as their primary source of electrical power. During earth eclipse, which occurs 90 times each year, the satellites are powered by batteries, but the heavy charge-discharge cycle decreases their life expectancy. By beaming laser power to satellites during the eclipses, satellite life expectancy can be significantly increased. In this paper, we investigate the basic system parameters and trade-offs of using reactor pumped laser technology to beam power from the Nevada Test Site. A first order argument is used to develop a consistent set of requirements for such a system.
Optical measurement techniques are extremely useful in fluid mechanics because of their non- invasive nature. However, it is often difficult to separate measurement effects due to pressure, temperature and density in real flows. Using a variation of a Shack-Hartmann wavefront sensor, we have made wavefront measurements that have extremely large dynamic range coupled with excellent sensitivity at high temporal and spatial resolution. These wavefront variations can be directly related to density perturbations in the fluid. We have examined several classes of flow including volumetrically heated gas, grid turbulence and droplet evaporation.
One method for scaling lasers to higher power is to build several separate amplifier chains, and then coherently combine the individual beams together. To combine the beams the pathlengths must be matched to an integer number of waves, and the tip and tilt of each beam must be the same. Since optical tolerances are fractional micrometers, a sophisticated control system must be employed to actively measure tip/tilt and piston errors, and apply real time corrections. We have developed a test bed that allows us to develop the required control algorithms for two to four beams and then scale to a larger number.
Many side-pumped lasers exhibit significant index gradients across the gain region aperture. For pulsed lasers where these gradients are time dependent, extraction with good beam quality requires the use of an adaptive optic. Since these inhomogeneities are systematic, wavefront correction can be performed with a model deformable mirror. We have designed a resonator which uses a cylindrically deformable mirror to correct for wavefront aberrations in a pulsed nuclear-reactor-driven laser. The mirror is capable of correcting up to ten waves of cylindrical focus error while maintaining tip/tilt alignment of the resonator. It is based around the flat plate bending using magnetostrictive actuators. A cylindrical intracavity beam expander is used to image the DM into the laser gain region. The beam expander can be adjusted to vary the resonator magnification in one axis, or to control the stability of the resonator. The mirror is controlled closed loop using a four channel wavefront sensor and a digital control system.
The wavefront error across a laser aperture is often the limiting factor in laser resonator design and performance. For long-pulse, sidepumped lasers, such as some nuclear-reactor-pumped or flashlamp-pumped lasers, significant transverse index gradients can develop and couple to the laser resonator modes. To design a laser resonator for efficient power
extraction, a spatially and temporally resolved determination of the index variation is required. High-speed photography using a fastframing camera with a modification of the Hartmann technique is applied to measure the index field and the resulting wavefront error in the gain region of a pulsed,
nuclear-reactor-pumped laser. With moderate initial gas pressures, the index fields and the wavefront errors are found to have roughly parabolic shapes except near the side walls. These results are in reasonable agreement with the predictions of a gasdynamic model, which describes the gas motion induced by the spatial nonuniformity of the pumping.
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