Residual Rms Error Research Articles

Varifocal-Piston Micromirror With Quasi-Simply Supported Piecewise Linear Flexure

Micromirrors with variable focal length are critical components of various optical systems. However, due to the limitations of microfabrication and actuation mechanisms, it is very difficult to control accurately the surface shape of a varifocal mirror. In this study, a novel surface-micromachined varifocal piston micromirror is presented. By simulating quasi-simply-supported boundary conditions, an accurate focusing of the mirror was achieved. The mirror is controlled by a parallel-plate electrostatic actuator. When the micromirror is actuated, as the driving voltage increases, the micromirror moves and deforms in two stages. In the first stage, four beams that support the mirror bend, which produces the micromirror vertical translation. When the translation reaches its limit, the micromirror enters the second stage, during which it bends to a concave shape and thus can focus light. A prototype based on the proposed concept was fabricated using a commercially available surface micromachining process. An analytical formulation, finite element model, and experimental measurements were adopted to study the electromechanical and optical performances of the micromirror. The focus length could be adjusted from 79.8 mm to 2.03 mm with a residual rms error less than 15 nm by changing the driving voltage. When the deformation reached its maximum, the first 21 Zernike aberration coefficients were all less than 3 nm. The proposed concept is also applicable to circular mirrors.

Closed-loop optical stabilization and digital image registration in adaptive optics scanning light ophthalmoscopy.

Eye motion is a major impediment to the efficient acquisition of high resolution retinal images with the adaptive optics (AO) scanning light ophthalmoscope (AOSLO). Here we demonstrate a solution to this problem by implementing both optical stabilization and digital image registration in an AOSLO. We replaced the slow scanning mirror with a two-axis tip/tilt mirror for the dual functions of slow scanning and optical stabilization. Closed-loop optical stabilization reduced the amplitude of eye-movement related-image motion by a factor of 10-15. The residual RMS error after optical stabilization alone was on the order of the size of foveal cones: ~1.66-2.56 μm or ~0.34-0.53 arcmin with typical fixational eye motion for normal observers. The full implementation, with real-time digital image registration, corrected the residual eye motion after optical stabilization with an accuracy of ~0.20-0.25 μm or ~0.04-0.05 arcmin RMS, which to our knowledge is more accurate than any method previously reported.

Identification of climatic state with limited proxy data

Abstract. We investigate the identifiability of the climate by limited proxy data. We test a data assimilation approach through perfect model pseudoproxy experiments, using a simple likelihood-based weighting based on the particle filtering process. Our experimental set-up enables us to create a massive 10 000-member ensemble at modest computational cost, thus enabling us to generate statistically robust results. We find that the method works well when data are sparse and imprecise, but in this case the reconstruction has a rather low accuracy as indicated by residual RMS errors. Conversely, when data are relatively plentiful and accurate, the estimate tracks the target closely, at least when considering the hemispheric mean. However, in this case, our prior ensemble size of 10 000 appears to be inadequate to correctly represent the true posterior, and the regional performance is poor. Using correlations to assess performance gives a more encouraging picture, with significant correlations ranging from about 0.3 when data are sparse to values over 0.7 when data are plentiful, but the residual RMS errors are substantial in all cases. Our results imply that caution is required in interpreting climate reconstructions, especially when considering the regional scale, as skill on this basis is markedly lower than on the large scale of hemispheric mean temperature.

Roughness measurement of metals using a modified binary speckle image and adaptive optics

This paper proposes an integrated roughness measurement system that is based on adaptive optics (AO) and binary analysis of speckle pattern images. The aim of this study was to demonstrate the necessity for AO compensation in regions containing both heat and fluid flow turbulences. A speckle image was obtained by projecting a laser beam onto the specimen surface, and the laser pattern image reflected from the surface was binarized to experimentally correlate the intensity with the surface roughness. In the absence of the AO correction scheme, induced turbulences can severely increase the residual rms error from 0.14 to 1.4 μm. After a real-time closed-loop AO correction, we can reduce the wavefront root mean square (rms) error to 0.12 μm, which not only compensates for the aberration error from induced disturbances but also improves the overall performance of the optical system. In addition, an AO system having different gains was investigated, and a threshold gain value was found to be able to steadily compensate for the wavefront errors in less than 2 s. Measurement results of five steel samples having roughness ranging from 0.2 to 3.125 μm (0.3 λ and 5 λ, where λ is the diode laser wavelength) demonstrate an excellent correlation between the intensity distribution of binary images and average roughness with a correlation coefficient of 0.9982. Furthermore, the proposed AO-assisted system is in good agreement with the stylus method and less than 9.73% error values can be consistently obtained.

The Performance of Shoreline Detection Models Applied to Video Imagery

Digital images of the intertidal region were used to map shorelines and the intertidal bathymetry along four geo-morphically and hydrodynamically distinct coastlines in the United States, United Kingdom, The Netherlands, and Australia. Mapping methods, each of which was originally designed to perform well at only one of the four sites, were applied to all four sites, and the results were compared to direct topographic surveys. It was determined that the rms errors of image-derived versus directly surveyed elevations depended on the prevailing hydrodynamic conditions as well as differences in each of the four different mapping methods. Before these differences were accounted for, rms errors ranged from 0.3 to 0.7 m. An empirical correction model that computed local estimates of setup, swash, and surf beat amplitudes reduced errors by about 50%, with residual rms errors ranging between 0.1 and 0.4 m. The model required tuning only one parameter that determined how each method was affected by swash at infragravity and incident wave frequencies. In environments where all methods successfully identify shorelines, the methods can be used somewhat interchangeably. The diversity of methods is advantageous in situations where one or more methods are likely to fail (e.g., lack of color imagery, high degree of alongshore variability). This remote sensing methodology can be applied to the shoreline and intertidal mapping problem across diverse nearshore environments.

Wavefront correction with a 37-actuator ferrofluid deformable mirror

This paper discusses an innovative low-cost deformable mirror made of a magnetic liquid (ferrofluid) whose surface is actuated by an hexagonal array of small current carrying coils. Predicted and experimental performances of a 37-actuator ferrofluid deformable mirror are presented along with wavefront correction examples. We show the validity of the model used to compute the actuators currents to obtain a desired wavefront shape. We demonstrate that the ferrofluid deformable mirror can correct a 11 microm low order aberrated wavefront to a residual RMS error of 0.05 microm corresponding to a Strehl ratio of 0.82.

Use of a microelectromechanical mirror for adaptive optics in the human eye

Ophthalmic instrumentation equipped with adaptive optics offers the possibility of rapid and automated correction of the eye's optics for improving vision and for improving images of the retina. One factor that limits the widespread implementation of adaptive optics is the cost of the wave-front corrector, such as a deformable mirror. In addition, the large apertures of these elements require high pupil magnification, and hence the systems tend to be physically large. We present what are believed to be the first closed-loop results when a compact, low-cost, surface micromachined, microelectromechanical mirror is used in a vision adaptive-optics system. The correction performance of the mirror is shown to be comparable to that of a Xinetics mirror for a 4.6-mm pupil size. Furthermore, for a pupil diameter of 6.0-mm, the residual rms error is reduced from 0.36 to 0.12 microm and individual photoreceptors are resolved at a pupil eccentricity of 1 degrees from the fovea.

Linear scaling of vowel-formant ensembles (VFEs) in consonantal contexts

There are familiar terms such as “contour” and “trajectory” to refer to a vowel formant frequency as a function defined on the time axis, but there is no readily understood term for the analogous idea of how a formant behaves on the “vowel axis”. For this we introduce the concept of a vowel-formant ensemble (VFE) as the set of values realized for a given formant (e.g., F 2) in going from vowel to vowel among a speaker's vowel phonemes for a fixed time frame in a fixed CVC context. The VFE affords a simple description of our development: we observe that D.J. Broad and F. Clermont's [J. Acoust. Soc. Am. 81 (1987) 155] formant-contour model is a linear function of its vowel target and that as a consequence all its VFEs for a given speaker and formant number are linearly scaled copies of one another. Are VFEs in actual speech also linearly scaled? To show how this question can be addressed, we use F 1 and F 2 data on one male speaker's productions of 7 Australian English vowels in 7 CVd contexts, with each CVd repeated 5 times. Our hypothesized scaling relation gives a remarkably good fit to these data, with a residual rms error of only about 14 Hz for either formant after discounting random variations among repetitions. The linear scaling implies a type of normalization for context which shrinks the intra-vowel scatter in the F 1F 2 plane. VFE scaling is also a new tool which should be useful for showing how contextual effects vary over the duration of the syllable's vocalic nucleus.

High-quality correction of wavefront distortions using low-power phase conjugation in azo dye containing LC polymer

Dynamics of light wavefront correction using optical phase conjugation (OPC) in the film of azo dye containing liquid-crystal polymer has been investigated experimentally. The OPC reflectivity more than 35% was attained at ∼1 mW power of pump and signal CW beams at λ=532 nm. We studied the dynamics of compensation of wavefront distortions at different operation conditions. The OPC response time∼1 s was reached at the polymer temperature of 69 ° C. High-quality correction of light wavefront distortions was obtained: the residual RMS error of compensation decreased by a factor of ∼10 2 at the end of OPC transient process. Restoration of spatially modulated light beam on its passage through the phase plate with strong aberrations has been demonstrated.

Super-global distortion correction for a rotational C-arm x-ray image intensifier.

Image intensifier (II) distortion changes as a function of C-arm rotation angle because of changes in the orientation of the II with the earth's or other stray magnetic fields. For cone-beam computed tomography (CT), distortion correction for all angles is essential. The new super-global distortion correction consists of a model to continuously correct II distortion not only at each location in the image but for every rotational angle of the C arm. Calibration bead images were acquired with a standard C arm in 9 in. II mode. The super-global (SG) model is obtained from the single-plane global correction of the selected calibration images with given sampling angle interval. The fifth-order single-plane global corrections yielded a residual rms error of 0.20 pixels, while the SG model yielded a rms error of 0.21 pixels, a negligibly small difference. We evaluated the accuracy dependence of the SG model on various factors, such as the single-plane global fitting order, SG order, and angular sampling interval. We found that a good SG model can be obtained using a sixth-order SG polynomial fit based on the fifth-order single-plane global correction, and that a 10 degrees sampling interval was sufficient. Thus, the SG model saves processing resources and storage space. The residual errors from the mechanical errors of the x-ray system were also investigated, and found comparable with the SG residual error. Additionally, a single-plane global correction was done in the cylindrical coordinate system, and physical information about pincushion distortion and S distortion were observed and analyzed; however, this method is not recommended due to a lack of calculational efficiency. In conclusion, the SG model provides an accurate, fast, and simple correction for rotational C-arm images, which may be used for cone-beam CT.

Application of EOF's to multispectral imagery: data compression and noise detection for AVIRIS

Investigates the first stage of a two stage approach to data compression for multispectral imagery. The first stage is to compress the data spectrally using empirical orthogonal functions (EOFs). In the second stage, each EOF image is further compressed using standard techniques, such as transform encoding. The characteristics of EOFs make them ideal for spectral compression. The EOFs form the orthogonal basis in the data space which provides the most economical data representation. Furthermore, and perhaps of more interest, EOFs are effective noise filters. In the authors experiments with the 224 channel AVIRIS data, lossy compression ratios of order 50:1 are attained by the EOF representation under the condition that the residual rms error be smaller than the independently measured instrument noise. >

Performance of an automated rotating-detector ellipsometer

A computer-controlled rotating-detector ellipsometer (RODE) has been constructed using a windowless planar-diffused Si photodiode, a stepping motor, an operational amplifier, and a personal computer (PC) equipped with an A/D-D/A converter. The detector is mounted to the output shaft of the stepping motor at an optimum angle of incidence of ∼59° and is rotated through 360° about the incident beam as an axis. The detector output signal voltage is measured and stored in the PC at every 2° increment of the RODE angle θ. Fourier analysis of the recorded data provides a handedness-blind determination of the state of polarization of the incident light. A beam from a HeNe laser (λ=632.8 nm) is transmitted through the polarizing optics of an ellipsometer to provide the polarization states needed for calibration and testing. The calibration parameters mL and θr are determined by rotating the detector about a linearly polarized beam of light of zero reference azimuth. The RODE is subsequently tested and found to correctly measure the first two normalized Stokes parameters of a number of states with a residual rms error of ∼0.002. This limit on precision is dictated mainly by the 12-bit A/D converter. A small angular misalignment of the rotation axis of the detector with respect to the light-beam axis introduces odd harmonics in the detector signal; hence, its effect is readily isolated by appropriate data reduction. Thin-film coatings on the detector surface that significantly improve the performance of the RODE are proposed.

A Method for Estimation of Atmospheric Water Vapor Profiles by Microwave Radiometry

Simultaneous measurements of microwave emission from the earth, in the oxygen band near 60 GHz, and the water vapor line near 183 GHz are conducted to determine the atmospheric temperature as a function of the pressure and the water vapor burden, and a combination of these two profiles yields a profile of water vapor burden versus pressure. Numerical simulations are developed by using temperature and water vapor profiles from subtropical and midlatitude radiosonde stations, and by assuming surface reflectivities typical of either land or ocean. Over a land surface, the residual rms errors in the estimated water vapor burden profile between 300 and 1000 mb are determined to range from 23 to 43% of the a priori standard deviation of water vapor burden for the corresponding climate. The relative humidity profile is also estimated and found to contain rms errors ranging from 4 to 17% of saturation. Over a seawater surface, using three additional channels of 18.5, 22.2, and 31.7 GHz, the corresponding results are found to be 3-46% of the a priori standard deviation for water vapor burden and 4-15% rms error for relative humidity.